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

Percentage Accurate: 85.6% → 99.7%

Time: 9.2s

Alternatives: 16

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 85.6% 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: 99.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot \left(z - t\right)}{z - a}\\ \mathbf{if}\;t_1 \leq -\infty \lor \neg \left(t_1 \leq 2 \cdot 10^{+305}\right):\\ \;\;\;\;x + \frac{z - t}{\frac{z - a}{y}}\\ \mathbf{else}:\\ \;\;\;\;t_1 + x\\ \end{array} \end{array} \]

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 2e+305)))
     (+ 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 <= 2e+305)) {
		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 <= 2e+305)) {
		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 <= 2e+305):
		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 <= 2e+305))
		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 <= 2e+305)))
		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, 2e+305]], $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 1.9999999999999999e305 < (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a))

   1. Initial program 31.7%

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

      1. associate-*l/ 99.8%

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

   3. Simplified 99.8%

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

      1. *-commutative 99.8%

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

      2. clear-num 99.7%

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

      3. un-div-inv 99.9%

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

   5. Applied egg-rr 99.9%

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

   if -inf.0 < (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a)) < 1.9999999999999999e305

   1. Initial program 99.9%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z - t\right)}{z - a} \leq -\infty \lor \neg \left(\frac{y \cdot \left(z - t\right)}{z - a} \leq 2 \cdot 10^{+305}\right):\\ \;\;\;\;x + \frac{z - t}{\frac{z - a}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot \left(z - t\right)}{z - a} + x\\ \end{array} \]

Alternative 2: 99.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot \left(z - t\right)}{z - a}\\ \mathbf{if}\;t_1 \leq -\infty \lor \neg \left(t_1 \leq 2 \cdot 10^{+305}\right):\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{z - a}\\ \mathbf{else}:\\ \;\;\;\;t_1 + x\\ \end{array} \end{array} \]

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 2e+305)))
     (+ x (* (- z t) (/ y (- z a))))
     (+ 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 <= 2e+305)) {
		tmp = x + ((z - t) * (y / (z - a)));
	} 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 <= 2e+305)) {
		tmp = x + ((z - t) * (y / (z - a)));
	} 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 <= 2e+305):
		tmp = x + ((z - t) * (y / (z - a)))
	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 <= 2e+305))
		tmp = Float64(x + Float64(Float64(z - t) * Float64(y / Float64(z - a))));
	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 <= 2e+305)))
		tmp = x + ((z - t) * (y / (z - a)));
	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, 2e+305]], $MachinePrecision]], N[(x + N[(N[(z - t), $MachinePrecision] * N[(y / N[(z - a), $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 1.9999999999999999e305 < (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a))

   1. Initial program 31.7%

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

      1. associate-*l/ 99.8%

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

   3. Simplified 99.8%

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

   if -inf.0 < (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a)) < 1.9999999999999999e305

   1. Initial program 99.9%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z - t\right)}{z - a} \leq -\infty \lor \neg \left(\frac{y \cdot \left(z - t\right)}{z - a} \leq 2 \cdot 10^{+305}\right):\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{z - a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot \left(z - t\right)}{z - a} + x\\ \end{array} \]

Alternative 3: 62.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y}{a}\\ \mathbf{if}\;z \leq -1.45 \cdot 10^{+24}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq -1.25 \cdot 10^{-192}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{-215}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.05 \cdot 10^{-282}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1 \cdot 10^{-302}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{+65}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ y a))))
   (if (<= z -1.45e+24)
     (+ y x)
     (if (<= z -1.25e-192)
       x
       (if (<= z -5.5e-215)
         t_1
         (if (<= z -2.05e-282)
           x
           (if (<= z -1e-302) t_1 (if (<= z 3.3e+65) x (+ y x)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (y / a);
	double tmp;
	if (z <= -1.45e+24) {
		tmp = y + x;
	} else if (z <= -1.25e-192) {
		tmp = x;
	} else if (z <= -5.5e-215) {
		tmp = t_1;
	} else if (z <= -2.05e-282) {
		tmp = x;
	} else if (z <= -1e-302) {
		tmp = t_1;
	} else if (z <= 3.3e+65) {
		tmp = x;
	} 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 = t * (y / a)
    if (z <= (-1.45d+24)) then
        tmp = y + x
    else if (z <= (-1.25d-192)) then
        tmp = x
    else if (z <= (-5.5d-215)) then
        tmp = t_1
    else if (z <= (-2.05d-282)) then
        tmp = x
    else if (z <= (-1d-302)) then
        tmp = t_1
    else if (z <= 3.3d+65) then
        tmp = x
    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 = t * (y / a);
	double tmp;
	if (z <= -1.45e+24) {
		tmp = y + x;
	} else if (z <= -1.25e-192) {
		tmp = x;
	} else if (z <= -5.5e-215) {
		tmp = t_1;
	} else if (z <= -2.05e-282) {
		tmp = x;
	} else if (z <= -1e-302) {
		tmp = t_1;
	} else if (z <= 3.3e+65) {
		tmp = x;
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * (y / a)
	tmp = 0
	if z <= -1.45e+24:
		tmp = y + x
	elif z <= -1.25e-192:
		tmp = x
	elif z <= -5.5e-215:
		tmp = t_1
	elif z <= -2.05e-282:
		tmp = x
	elif z <= -1e-302:
		tmp = t_1
	elif z <= 3.3e+65:
		tmp = x
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(y / a))
	tmp = 0.0
	if (z <= -1.45e+24)
		tmp = Float64(y + x);
	elseif (z <= -1.25e-192)
		tmp = x;
	elseif (z <= -5.5e-215)
		tmp = t_1;
	elseif (z <= -2.05e-282)
		tmp = x;
	elseif (z <= -1e-302)
		tmp = t_1;
	elseif (z <= 3.3e+65)
		tmp = x;
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * (y / a);
	tmp = 0.0;
	if (z <= -1.45e+24)
		tmp = y + x;
	elseif (z <= -1.25e-192)
		tmp = x;
	elseif (z <= -5.5e-215)
		tmp = t_1;
	elseif (z <= -2.05e-282)
		tmp = x;
	elseif (z <= -1e-302)
		tmp = t_1;
	elseif (z <= 3.3e+65)
		tmp = x;
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.45e+24], N[(y + x), $MachinePrecision], If[LessEqual[z, -1.25e-192], x, If[LessEqual[z, -5.5e-215], t$95$1, If[LessEqual[z, -2.05e-282], x, If[LessEqual[z, -1e-302], t$95$1, If[LessEqual[z, 3.3e+65], x, N[(y + x), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.4499999999999999e24 or 3.30000000000000023e65 < z

   1. Initial program 71.9%

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

      1. associate-*l/ 95.9%

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

   3. Simplified 95.9%

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

   4. Taylor expanded in z around inf 73.6%

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

      1. +-commutative 73.6%

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

   6. Simplified 73.6%

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

   if -1.4499999999999999e24 < z < -1.25e-192 or -5.50000000000000004e-215 < z < -2.04999999999999989e-282 or -9.9999999999999996e-303 < z < 3.30000000000000023e65

   1. Initial program 94.7%

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

      1. associate-*l/ 94.2%

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

   3. Simplified 94.2%

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

   4. Taylor expanded in x around inf 60.4%

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

   if -1.25e-192 < z < -5.50000000000000004e-215 or -2.04999999999999989e-282 < z < -9.9999999999999996e-303

   1. Initial program 94.1%

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

      1. associate-*l/ 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in t around inf 94.1%

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

      1. mul-1-neg 94.1%

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

      2. associate-*r/ 99.7%

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

      3. distribute-lft-neg-out 99.7%

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

      4. *-commutative 99.7%

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

   6. Simplified 99.7%

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

   7. Taylor expanded in x around 0 94.1%

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

      1. mul-1-neg 94.1%

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

      2. associate-*l/ 88.3%

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

      3. distribute-lft-neg-in 88.3%

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

      4. cancel-sign-sub-inv 88.3%

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

   9. Simplified 88.3%

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

   10. Taylor expanded in x around 0 88.0%

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

       1. mul-1-neg 88.0%

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

       2. associate-*l/ 82.2%

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

       3. distribute-rgt-neg-in 82.2%

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

   12. Simplified 82.2%

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

   13. Taylor expanded in z around 0 76.5%

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

       1. associate-*r/ 82.1%

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

   15. Simplified 82.1%

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

4. Final simplification 66.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{+24}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq -1.25 \cdot 10^{-192}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{-215}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq -2.05 \cdot 10^{-282}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1 \cdot 10^{-302}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{+65}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 4: 62.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{+24}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq -1.25 \cdot 10^{-192}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.55 \cdot 10^{-214}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq -3 \cdot 10^{-280}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -2.9 \cdot 10^{-303}:\\ \;\;\;\;\frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{+65}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.25e+24)
   (+ y x)
   (if (<= z -1.25e-192)
     x
     (if (<= z -1.55e-214)
       (* t (/ y a))
       (if (<= z -3e-280)
         x
         (if (<= z -2.9e-303) (/ (* y t) a) (if (<= z 2.4e+65) x (+ y x))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.25e+24) {
		tmp = y + x;
	} else if (z <= -1.25e-192) {
		tmp = x;
	} else if (z <= -1.55e-214) {
		tmp = t * (y / a);
	} else if (z <= -3e-280) {
		tmp = x;
	} else if (z <= -2.9e-303) {
		tmp = (y * t) / a;
	} else if (z <= 2.4e+65) {
		tmp = x;
	} 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+24)) then
        tmp = y + x
    else if (z <= (-1.25d-192)) then
        tmp = x
    else if (z <= (-1.55d-214)) then
        tmp = t * (y / a)
    else if (z <= (-3d-280)) then
        tmp = x
    else if (z <= (-2.9d-303)) then
        tmp = (y * t) / a
    else if (z <= 2.4d+65) then
        tmp = x
    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+24) {
		tmp = y + x;
	} else if (z <= -1.25e-192) {
		tmp = x;
	} else if (z <= -1.55e-214) {
		tmp = t * (y / a);
	} else if (z <= -3e-280) {
		tmp = x;
	} else if (z <= -2.9e-303) {
		tmp = (y * t) / a;
	} else if (z <= 2.4e+65) {
		tmp = x;
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.25e+24:
		tmp = y + x
	elif z <= -1.25e-192:
		tmp = x
	elif z <= -1.55e-214:
		tmp = t * (y / a)
	elif z <= -3e-280:
		tmp = x
	elif z <= -2.9e-303:
		tmp = (y * t) / a
	elif z <= 2.4e+65:
		tmp = x
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.25e+24)
		tmp = Float64(y + x);
	elseif (z <= -1.25e-192)
		tmp = x;
	elseif (z <= -1.55e-214)
		tmp = Float64(t * Float64(y / a));
	elseif (z <= -3e-280)
		tmp = x;
	elseif (z <= -2.9e-303)
		tmp = Float64(Float64(y * t) / a);
	elseif (z <= 2.4e+65)
		tmp = x;
	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+24)
		tmp = y + x;
	elseif (z <= -1.25e-192)
		tmp = x;
	elseif (z <= -1.55e-214)
		tmp = t * (y / a);
	elseif (z <= -3e-280)
		tmp = x;
	elseif (z <= -2.9e-303)
		tmp = (y * t) / a;
	elseif (z <= 2.4e+65)
		tmp = x;
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.25e+24], N[(y + x), $MachinePrecision], If[LessEqual[z, -1.25e-192], x, If[LessEqual[z, -1.55e-214], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -3e-280], x, If[LessEqual[z, -2.9e-303], N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[z, 2.4e+65], x, N[(y + x), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.25000000000000011e24 or 2.4000000000000002e65 < z

   1. Initial program 71.9%

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

      1. associate-*l/ 95.9%

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

   3. Simplified 95.9%

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

   4. Taylor expanded in z around inf 73.6%

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

      1. +-commutative 73.6%

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

   6. Simplified 73.6%

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

   if -1.25000000000000011e24 < z < -1.25e-192 or -1.55000000000000002e-214 < z < -2.99999999999999987e-280 or -2.90000000000000014e-303 < z < 2.4000000000000002e65

   1. Initial program 94.7%

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

      1. associate-*l/ 94.2%

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

   3. Simplified 94.2%

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

   4. Taylor expanded in x around inf 60.4%

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

   if -1.25e-192 < z < -1.55000000000000002e-214

   1. Initial program 89.5%

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

      1. associate-*l/ 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in t around inf 89.5%

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

      1. mul-1-neg 89.5%

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

      2. associate-*r/ 99.7%

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

      3. distribute-lft-neg-out 99.7%

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

      4. *-commutative 99.7%

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

   6. Simplified 99.7%

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

   7. Taylor expanded in x around 0 89.5%

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

      1. mul-1-neg 89.5%

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

      2. associate-*l/ 99.7%

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

      3. distribute-lft-neg-in 99.7%

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

      4. cancel-sign-sub-inv 99.7%

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

   9. Simplified 99.7%

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

   10. Taylor expanded in x around 0 89.5%

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

       1. mul-1-neg 89.5%

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

       2. associate-*l/ 99.7%

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

       3. distribute-rgt-neg-in 99.7%

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

   12. Simplified 99.7%

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

   13. Taylor expanded in z around 0 69.0%

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

       1. associate-*r/ 79.2%

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

   15. Simplified 79.2%

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

   if -2.99999999999999987e-280 < z < -2.90000000000000014e-303

   1. Initial program 100.0%

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

      1. associate-*l/ 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in t around inf 100.0%

      \[\leadsto x + \color{blue}{-1 \cdot \frac{t \cdot y}{z - a}} \]
   5. 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/ 99.8%

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

      3. distribute-lft-neg-out 99.8%

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

      4. *-commutative 99.8%

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

   6. Simplified 99.8%

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

   7. Taylor expanded in x around 0 100.0%

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

      1. mul-1-neg 100.0%

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

      2. associate-*l/ 73.7%

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

      3. distribute-lft-neg-in 73.7%

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

      4. cancel-sign-sub-inv 73.7%

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

   9. Simplified 73.7%

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

   10. Taylor expanded in x around 0 86.0%

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

       1. mul-1-neg 86.0%

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

       2. associate-*l/ 59.8%

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

       3. distribute-rgt-neg-in 59.8%

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

   12. Simplified 59.8%

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

   13. Taylor expanded in z around 0 86.0%

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

4. Final simplification 66.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{+24}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq -1.25 \cdot 10^{-192}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.55 \cdot 10^{-214}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq -3 \cdot 10^{-280}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -2.9 \cdot 10^{-303}:\\ \;\;\;\;\frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{+65}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 5: 80.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{y}{\frac{a}{z - t}}\\ \mathbf{if}\;a \leq -6.2 \cdot 10^{-97}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{-175}:\\ \;\;\;\;x + \frac{y}{\frac{z}{z - t}}\\ \mathbf{elif}\;a \leq 2.5 \cdot 10^{+77}:\\ \;\;\;\;x - \frac{y \cdot t}{z - a}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (/ y (/ a (- z t))))))
   (if (<= a -6.2e-97)
     t_1
     (if (<= a 1.6e-175)
       (+ x (/ y (/ z (- z t))))
       (if (<= a 2.5e+77) (- x (/ (* y t) (- z a))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (y / (a / (z - t)));
	double tmp;
	if (a <= -6.2e-97) {
		tmp = t_1;
	} else if (a <= 1.6e-175) {
		tmp = x + (y / (z / (z - t)));
	} else if (a <= 2.5e+77) {
		tmp = x - ((y * t) / (z - 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 - (y / (a / (z - t)))
    if (a <= (-6.2d-97)) then
        tmp = t_1
    else if (a <= 1.6d-175) then
        tmp = x + (y / (z / (z - t)))
    else if (a <= 2.5d+77) then
        tmp = x - ((y * t) / (z - 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 - (y / (a / (z - t)));
	double tmp;
	if (a <= -6.2e-97) {
		tmp = t_1;
	} else if (a <= 1.6e-175) {
		tmp = x + (y / (z / (z - t)));
	} else if (a <= 2.5e+77) {
		tmp = x - ((y * t) / (z - a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (y / (a / (z - t)))
	tmp = 0
	if a <= -6.2e-97:
		tmp = t_1
	elif a <= 1.6e-175:
		tmp = x + (y / (z / (z - t)))
	elif a <= 2.5e+77:
		tmp = x - ((y * t) / (z - a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(y / Float64(a / Float64(z - t))))
	tmp = 0.0
	if (a <= -6.2e-97)
		tmp = t_1;
	elseif (a <= 1.6e-175)
		tmp = Float64(x + Float64(y / Float64(z / Float64(z - t))));
	elseif (a <= 2.5e+77)
		tmp = Float64(x - Float64(Float64(y * t) / Float64(z - a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (y / (a / (z - t)));
	tmp = 0.0;
	if (a <= -6.2e-97)
		tmp = t_1;
	elseif (a <= 1.6e-175)
		tmp = x + (y / (z / (z - t)));
	elseif (a <= 2.5e+77)
		tmp = x - ((y * t) / (z - a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(y / N[(a / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -6.2e-97], t$95$1, If[LessEqual[a, 1.6e-175], N[(x + N[(y / N[(z / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.5e+77], N[(x - N[(N[(y * t), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -6.20000000000000004e-97 or 2.50000000000000002e77 < a

   1. Initial program 82.7%

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

      1. associate-*l/ 97.9%

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

   3. Simplified 97.9%

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

      1. *-commutative 97.9%

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

      2. clear-num 97.9%

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

      3. un-div-inv 97.9%

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

   5. Applied egg-rr 97.9%

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

   6. Taylor expanded in a around inf 79.5%

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

      1. mul-1-neg 79.5%

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

      2. unsub-neg 79.5%

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

      3. associate-/l* 89.4%

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

   8. Simplified 89.4%

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

   if -6.20000000000000004e-97 < a < 1.6e-175

   1. Initial program 86.3%

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

      1. associate-*l/ 91.7%

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

   3. Simplified 91.7%

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

   4. Taylor expanded in a around 0 77.7%

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

      1. +-commutative 77.7%

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

      2. associate-/l* 87.2%

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

   6. Simplified 87.2%

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

   if 1.6e-175 < a < 2.50000000000000002e77

   1. Initial program 97.8%

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

      1. associate-*l/ 91.7%

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

   3. Simplified 91.7%

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

   4. Taylor expanded in t around inf 89.7%

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

      1. associate-*r/ 89.7%

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

      2. mul-1-neg 89.7%

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

      3. distribute-lft-neg-out 89.7%

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

      4. *-commutative 89.7%

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

   6. Simplified 89.7%

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

4. Final simplification 88.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6.2 \cdot 10^{-97}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z - t}}\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{-175}:\\ \;\;\;\;x + \frac{y}{\frac{z}{z - t}}\\ \mathbf{elif}\;a \leq 2.5 \cdot 10^{+77}:\\ \;\;\;\;x - \frac{y \cdot t}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z - t}}\\ \end{array} \]

Alternative 6: 75.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.95 \cdot 10^{-94} \lor \neg \left(a \leq 4.4 \cdot 10^{-53}\right):\\ \;\;\;\;x - \frac{y}{\frac{-a}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -1.95e-94) (not (<= a 4.4e-53)))
   (- x (/ y (/ (- a) t)))
   (+ x (/ (* y (- z t)) z))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.95e-94) || !(a <= 4.4e-53)) {
		tmp = x - (y / (-a / t));
	} else {
		tmp = x + ((y * (z - 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 ((a <= (-1.95d-94)) .or. (.not. (a <= 4.4d-53))) then
        tmp = x - (y / (-a / t))
    else
        tmp = x + ((y * (z - 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 ((a <= -1.95e-94) || !(a <= 4.4e-53)) {
		tmp = x - (y / (-a / t));
	} else {
		tmp = x + ((y * (z - t)) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -1.95e-94) or not (a <= 4.4e-53):
		tmp = x - (y / (-a / t))
	else:
		tmp = x + ((y * (z - t)) / z)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -1.95e-94) || !(a <= 4.4e-53))
		tmp = Float64(x - Float64(y / Float64(Float64(-a) / t)));
	else
		tmp = Float64(x + Float64(Float64(y * Float64(z - t)) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -1.95e-94) || ~((a <= 4.4e-53)))
		tmp = x - (y / (-a / t));
	else
		tmp = x + ((y * (z - t)) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -1.95e-94], N[Not[LessEqual[a, 4.4e-53]], $MachinePrecision]], N[(x - N[(y / N[((-a) / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.9500000000000001e-94 or 4.40000000000000037e-53 < a

   1. Initial program 85.0%

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

      1. associate-*l/ 97.6%

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

   3. Simplified 97.6%

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

      1. *-commutative 97.6%

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

      2. clear-num 97.6%

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

      3. un-div-inv 98.1%

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

   5. Applied egg-rr 98.1%

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

   6. Taylor expanded in a around inf 80.4%

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

      1. mul-1-neg 80.4%

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

      2. unsub-neg 80.4%

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

      3. associate-/l* 89.0%

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

   8. Simplified 89.0%

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

   9. Taylor expanded in z around 0 79.5%

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

       1. associate-*r/ 79.5%

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

       2. neg-mul-1 79.5%

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

   11. Simplified 79.5%

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

   if -1.9500000000000001e-94 < a < 4.40000000000000037e-53

   1. Initial program 88.6%

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

      1. associate-*l/ 90.8%

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

   3. Simplified 90.8%

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

   4. Taylor expanded in a around 0 75.8%

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

4. Final simplification 78.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.95 \cdot 10^{-94} \lor \neg \left(a \leq 4.4 \cdot 10^{-53}\right):\\ \;\;\;\;x - \frac{y}{\frac{-a}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{z}\\ \end{array} \]

Alternative 7: 78.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -6 \cdot 10^{-92} \lor \neg \left(a \leq 2.4 \cdot 10^{-51}\right):\\ \;\;\;\;x - \frac{y}{\frac{-a}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z - t}{\frac{z}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -6e-92) (not (<= a 2.4e-51)))
   (- x (/ y (/ (- a) t)))
   (+ x (/ (- z t) (/ z y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -6e-92) || !(a <= 2.4e-51)) {
		tmp = x - (y / (-a / t));
	} else {
		tmp = x + ((z - t) / (z / 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 ((a <= (-6d-92)) .or. (.not. (a <= 2.4d-51))) then
        tmp = x - (y / (-a / t))
    else
        tmp = x + ((z - t) / (z / 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 ((a <= -6e-92) || !(a <= 2.4e-51)) {
		tmp = x - (y / (-a / t));
	} else {
		tmp = x + ((z - t) / (z / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -6e-92) or not (a <= 2.4e-51):
		tmp = x - (y / (-a / t))
	else:
		tmp = x + ((z - t) / (z / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -6e-92) || !(a <= 2.4e-51))
		tmp = Float64(x - Float64(y / Float64(Float64(-a) / t)));
	else
		tmp = Float64(x + Float64(Float64(z - t) / Float64(z / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -6e-92) || ~((a <= 2.4e-51)))
		tmp = x - (y / (-a / t));
	else
		tmp = x + ((z - t) / (z / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -6e-92], N[Not[LessEqual[a, 2.4e-51]], $MachinePrecision]], N[(x - N[(y / N[((-a) / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(z - t), $MachinePrecision] / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -6.00000000000000027e-92 or 2.4e-51 < a

   1. Initial program 85.0%

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

      1. associate-*l/ 97.6%

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

   3. Simplified 97.6%

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

      1. *-commutative 97.6%

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

      2. clear-num 97.6%

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

      3. un-div-inv 98.1%

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

   5. Applied egg-rr 98.1%

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

   6. Taylor expanded in a around inf 80.4%

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

      1. mul-1-neg 80.4%

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

      2. unsub-neg 80.4%

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

      3. associate-/l* 89.0%

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

   8. Simplified 89.0%

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

   9. Taylor expanded in z around 0 79.5%

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

       1. associate-*r/ 79.5%

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

       2. neg-mul-1 79.5%

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

   11. Simplified 79.5%

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

   if -6.00000000000000027e-92 < a < 2.4e-51

   1. Initial program 88.6%

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

      1. associate-*l/ 90.8%

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

   3. Simplified 90.8%

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

      1. *-commutative 90.8%

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

      2. clear-num 90.7%

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

      3. un-div-inv 91.8%

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

   5. Applied egg-rr 91.8%

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

   6. Taylor expanded in z around inf 82.0%

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

4. Final simplification 80.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6 \cdot 10^{-92} \lor \neg \left(a \leq 2.4 \cdot 10^{-51}\right):\\ \;\;\;\;x - \frac{y}{\frac{-a}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z - t}{\frac{z}{y}}\\ \end{array} \]

Alternative 8: 79.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.02 \cdot 10^{-94} \lor \neg \left(a \leq 5 \cdot 10^{-57}\right):\\ \;\;\;\;x - \frac{y}{\frac{-a}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{z}{z - t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -1.02e-94) (not (<= a 5e-57)))
   (- x (/ y (/ (- a) t)))
   (+ x (/ y (/ z (- z t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.02e-94) || !(a <= 5e-57)) {
		tmp = x - (y / (-a / t));
	} else {
		tmp = x + (y / (z / (z - t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-1.02d-94)) .or. (.not. (a <= 5d-57))) then
        tmp = x - (y / (-a / t))
    else
        tmp = x + (y / (z / (z - t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.02e-94) || !(a <= 5e-57)) {
		tmp = x - (y / (-a / t));
	} else {
		tmp = x + (y / (z / (z - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -1.02e-94) or not (a <= 5e-57):
		tmp = x - (y / (-a / t))
	else:
		tmp = x + (y / (z / (z - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -1.02e-94) || !(a <= 5e-57))
		tmp = Float64(x - Float64(y / Float64(Float64(-a) / t)));
	else
		tmp = Float64(x + Float64(y / Float64(z / Float64(z - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -1.02e-94) || ~((a <= 5e-57)))
		tmp = x - (y / (-a / t));
	else
		tmp = x + (y / (z / (z - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -1.02e-94], N[Not[LessEqual[a, 5e-57]], $MachinePrecision]], N[(x - N[(y / N[((-a) / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(z / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.02e-94 or 5.0000000000000002e-57 < a

   1. Initial program 85.0%

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

      1. associate-*l/ 97.6%

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

   3. Simplified 97.6%

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

      1. *-commutative 97.6%

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

      2. clear-num 97.6%

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

      3. un-div-inv 98.1%

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

   5. Applied egg-rr 98.1%

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

   6. Taylor expanded in a around inf 80.4%

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

      1. mul-1-neg 80.4%

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

      2. unsub-neg 80.4%

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

      3. associate-/l* 89.0%

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

   8. Simplified 89.0%

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

   9. Taylor expanded in z around 0 79.5%

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

       1. associate-*r/ 79.5%

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

       2. neg-mul-1 79.5%

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

   11. Simplified 79.5%

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

   if -1.02e-94 < a < 5.0000000000000002e-57

   1. Initial program 88.6%

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

      1. associate-*l/ 90.8%

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

   3. Simplified 90.8%

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

   4. Taylor expanded in a around 0 75.8%

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

      1. +-commutative 75.8%

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

      2. associate-/l* 84.0%

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

   6. Simplified 84.0%

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

4. Final simplification 81.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.02 \cdot 10^{-94} \lor \neg \left(a \leq 5 \cdot 10^{-57}\right):\\ \;\;\;\;x - \frac{y}{\frac{-a}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{z}{z - t}}\\ \end{array} \]

Alternative 9: 87.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{+147} \lor \neg \left(z \leq 7 \cdot 10^{+67}\right):\\ \;\;\;\;x + \frac{y}{\frac{z}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{t}{z - a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.4e+147) (not (<= z 7e+67)))
   (+ x (/ y (/ z (- z t))))
   (- x (* y (/ t (- z a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.4e+147) || !(z <= 7e+67)) {
		tmp = x + (y / (z / (z - t)));
	} else {
		tmp = x - (y * (t / (z - a)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-1.4d+147)) .or. (.not. (z <= 7d+67))) then
        tmp = x + (y / (z / (z - t)))
    else
        tmp = x - (y * (t / (z - a)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.4e+147) || !(z <= 7e+67)) {
		tmp = x + (y / (z / (z - t)));
	} else {
		tmp = x - (y * (t / (z - a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.4e+147) or not (z <= 7e+67):
		tmp = x + (y / (z / (z - t)))
	else:
		tmp = x - (y * (t / (z - a)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.4e+147) || !(z <= 7e+67))
		tmp = Float64(x + Float64(y / Float64(z / Float64(z - t))));
	else
		tmp = Float64(x - Float64(y * Float64(t / Float64(z - a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.4e+147) || ~((z <= 7e+67)))
		tmp = x + (y / (z / (z - t)));
	else
		tmp = x - (y * (t / (z - a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.4e+147], N[Not[LessEqual[z, 7e+67]], $MachinePrecision]], N[(x + N[(y / N[(z / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(y * N[(t / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.4e147 or 7e67 < z

   1. Initial program 67.8%

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

      1. associate-*l/ 94.5%

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

   3. Simplified 94.5%

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

   4. Taylor expanded in a around 0 59.5%

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

      1. +-commutative 59.5%

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

      2. associate-/l* 89.0%

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

   6. Simplified 89.0%

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

   if -1.4e147 < z < 7e67

   1. Initial program 93.3%

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

      1. associate-*l/ 95.4%

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

   3. Simplified 95.4%

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

   4. Taylor expanded in t around inf 84.2%

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

      1. mul-1-neg 84.2%

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

      2. associate-*r/ 86.8%

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

      3. distribute-lft-neg-out 86.8%

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

      4. *-commutative 86.8%

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

   6. Simplified 86.8%

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

   7. Taylor expanded in x around 0 84.2%

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

      1. mul-1-neg 84.2%

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

      2. associate-*l/ 87.2%

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

      3. distribute-lft-neg-in 87.2%

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

      4. cancel-sign-sub-inv 87.2%

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

   9. Simplified 87.2%

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

4. Final simplification 87.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{+147} \lor \neg \left(z \leq 7 \cdot 10^{+67}\right):\\ \;\;\;\;x + \frac{y}{\frac{z}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{t}{z - a}\\ \end{array} \]

Alternative 10: 81.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -6 \cdot 10^{-92} \lor \neg \left(a \leq 1.15 \cdot 10^{-33}\right):\\ \;\;\;\;x - \frac{y}{\frac{a}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{z}{z - t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -6e-92) (not (<= a 1.15e-33)))
   (- x (/ y (/ a (- z t))))
   (+ x (/ y (/ z (- z t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -6e-92) || !(a <= 1.15e-33)) {
		tmp = x - (y / (a / (z - t)));
	} else {
		tmp = x + (y / (z / (z - t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-6d-92)) .or. (.not. (a <= 1.15d-33))) then
        tmp = x - (y / (a / (z - t)))
    else
        tmp = x + (y / (z / (z - t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -6e-92) || !(a <= 1.15e-33)) {
		tmp = x - (y / (a / (z - t)));
	} else {
		tmp = x + (y / (z / (z - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -6e-92) or not (a <= 1.15e-33):
		tmp = x - (y / (a / (z - t)))
	else:
		tmp = x + (y / (z / (z - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -6e-92) || !(a <= 1.15e-33))
		tmp = Float64(x - Float64(y / Float64(a / Float64(z - t))));
	else
		tmp = Float64(x + Float64(y / Float64(z / Float64(z - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -6e-92) || ~((a <= 1.15e-33)))
		tmp = x - (y / (a / (z - t)));
	else
		tmp = x + (y / (z / (z - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -6e-92], N[Not[LessEqual[a, 1.15e-33]], $MachinePrecision]], N[(x - N[(y / N[(a / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(z / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -6.00000000000000027e-92 or 1.14999999999999993e-33 < a

   1. Initial program 84.8%

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

      1. associate-*l/ 97.5%

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

   3. Simplified 97.5%

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

      1. *-commutative 97.5%

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

      2. clear-num 97.5%

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

      3. un-div-inv 98.1%

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

   5. Applied egg-rr 98.1%

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

   6. Taylor expanded in a around inf 80.8%

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

      1. mul-1-neg 80.8%

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

      2. unsub-neg 80.8%

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

      3. associate-/l* 89.5%

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

   8. Simplified 89.5%

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

   if -6.00000000000000027e-92 < a < 1.14999999999999993e-33

   1. Initial program 88.9%

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

      1. associate-*l/ 91.0%

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

   3. Simplified 91.0%

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

   4. Taylor expanded in a around 0 75.4%

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

      1. +-commutative 75.4%

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

      2. associate-/l* 83.5%

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

   6. Simplified 83.5%

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

4. Final simplification 87.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6 \cdot 10^{-92} \lor \neg \left(a \leq 1.15 \cdot 10^{-33}\right):\\ \;\;\;\;x - \frac{y}{\frac{a}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{z}{z - t}}\\ \end{array} \]

Alternative 11: 76.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.18 \cdot 10^{+85} \lor \neg \left(z \leq 2.1 \cdot 10^{+71}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{-a}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.18e+85) (not (<= z 2.1e+71)))
   (+ y x)
   (- x (/ y (/ (- a) t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.18e+85) || !(z <= 2.1e+71)) {
		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 <= (-1.18d+85)) .or. (.not. (z <= 2.1d+71))) 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 <= -1.18e+85) || !(z <= 2.1e+71)) {
		tmp = y + x;
	} else {
		tmp = x - (y / (-a / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.18e+85) or not (z <= 2.1e+71):
		tmp = y + x
	else:
		tmp = x - (y / (-a / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.18e+85) || !(z <= 2.1e+71))
		tmp = Float64(y + x);
	else
		tmp = Float64(x - Float64(y / Float64(Float64(-a) / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.18e+85) || ~((z <= 2.1e+71)))
		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, -1.18e+85], N[Not[LessEqual[z, 2.1e+71]], $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 < -1.17999999999999997e85 or 2.09999999999999989e71 < z

   1. Initial program 69.4%

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

      1. associate-*l/ 95.3%

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

   3. Simplified 95.3%

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

   4. Taylor expanded in z around inf 76.8%

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

      1. +-commutative 76.8%

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

   6. Simplified 76.8%

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

   if -1.17999999999999997e85 < z < 2.09999999999999989e71

   1. Initial program 94.4%

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

      1. associate-*l/ 95.0%

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

   3. Simplified 95.0%

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

      1. *-commutative 95.0%

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

      2. clear-num 95.0%

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

      3. un-div-inv 96.1%

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

   5. Applied egg-rr 96.1%

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

   6. Taylor expanded in a around inf 78.2%

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

      1. mul-1-neg 78.2%

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

      2. unsub-neg 78.2%

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

      3. associate-/l* 81.7%

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

   8. Simplified 81.7%

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

   9. Taylor expanded in z around 0 76.6%

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

       1. associate-*r/ 76.6%

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

       2. neg-mul-1 76.6%

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

   11. Simplified 76.6%

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

4. Final simplification 76.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.18 \cdot 10^{+85} \lor \neg \left(z \leq 2.1 \cdot 10^{+71}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{-a}{t}}\\ \end{array} \]

Alternative 12: 75.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.6 \cdot 10^{+84} \lor \neg \left(z \leq 2.35 \cdot 10^{+67}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -8.6e+84) (not (<= z 2.35e+67))) (+ y x) (+ x (/ (* y t) a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -8.6e+84) || !(z <= 2.35e+67)) {
		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 <= (-8.6d+84)) .or. (.not. (z <= 2.35d+67))) 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 <= -8.6e+84) || !(z <= 2.35e+67)) {
		tmp = y + x;
	} else {
		tmp = x + ((y * t) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -8.6e+84) or not (z <= 2.35e+67):
		tmp = y + x
	else:
		tmp = x + ((y * t) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -8.6e+84) || !(z <= 2.35e+67))
		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 <= -8.6e+84) || ~((z <= 2.35e+67)))
		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, -8.6e+84], N[Not[LessEqual[z, 2.35e+67]], $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 < -8.5999999999999992e84 or 2.35000000000000009e67 < z

   1. Initial program 69.4%

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

      1. associate-*l/ 95.3%

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

   3. Simplified 95.3%

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

   4. Taylor expanded in z around inf 76.8%

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

      1. +-commutative 76.8%

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

   6. Simplified 76.8%

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

   if -8.5999999999999992e84 < z < 2.35000000000000009e67

   1. Initial program 94.4%

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

      1. associate-*l/ 95.0%

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

   3. Simplified 95.0%

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

   4. Taylor expanded in z around 0 72.4%

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

4. Final simplification 73.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.6 \cdot 10^{+84} \lor \neg \left(z \leq 2.35 \cdot 10^{+67}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \end{array} \]

Alternative 13: 76.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{+86}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{+65}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -3.4e+86) (+ y x) (if (<= z 2.4e+65) (+ x (* y (/ t a))) (+ y x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.4e+86) {
		tmp = y + x;
	} else if (z <= 2.4e+65) {
		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 <= (-3.4d+86)) then
        tmp = y + x
    else if (z <= 2.4d+65) 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 <= -3.4e+86) {
		tmp = y + x;
	} else if (z <= 2.4e+65) {
		tmp = x + (y * (t / a));
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -3.4e+86:
		tmp = y + x
	elif z <= 2.4e+65:
		tmp = x + (y * (t / a))
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -3.4e+86)
		tmp = Float64(y + x);
	elseif (z <= 2.4e+65)
		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 <= -3.4e+86)
		tmp = y + x;
	elseif (z <= 2.4e+65)
		tmp = x + (y * (t / a));
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -3.4e+86], N[(y + x), $MachinePrecision], If[LessEqual[z, 2.4e+65], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -3.3999999999999998e86 or 2.4000000000000002e65 < z

   1. Initial program 69.4%

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

      1. associate-*l/ 95.3%

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

   3. Simplified 95.3%

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

   4. Taylor expanded in z around inf 76.8%

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

      1. +-commutative 76.8%

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

   6. Simplified 76.8%

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

   if -3.3999999999999998e86 < z < 2.4000000000000002e65

   1. Initial program 94.4%

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

      1. associate-*l/ 95.0%

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

   3. Simplified 95.0%

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

   4. Taylor expanded in z around 0 72.4%

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

      1. +-commutative 72.4%

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

      2. associate-/l* 75.7%

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

      3. associate-/r/ 76.1%

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

   6. Simplified 76.1%

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

4. Final simplification 76.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{+86}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{+65}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 14: 96.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 86.3%

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

   1. associate-*l/ 95.1%

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

3. Simplified 95.1%

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

4. Final simplification 95.1%

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

Alternative 15: 63.4% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{+24} \lor \neg \left(z \leq 2.4 \cdot 10^{+65}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -3.2e+24) (not (<= z 2.4e+65))) (+ y x) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -3.2e+24) || !(z <= 2.4e+65)) {
		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 <= (-3.2d+24)) .or. (.not. (z <= 2.4d+65))) 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 <= -3.2e+24) || !(z <= 2.4e+65)) {
		tmp = y + x;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -3.2e+24) or not (z <= 2.4e+65):
		tmp = y + x
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -3.2e+24) || !(z <= 2.4e+65))
		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 <= -3.2e+24) || ~((z <= 2.4e+65)))
		tmp = y + x;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -3.2e+24], N[Not[LessEqual[z, 2.4e+65]], $MachinePrecision]], N[(y + x), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -3.1999999999999997e24 or 2.4000000000000002e65 < z

   1. Initial program 71.9%

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

      1. associate-*l/ 95.9%

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

   3. Simplified 95.9%

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

   4. Taylor expanded in z around inf 73.6%

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

      1. +-commutative 73.6%

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

   6. Simplified 73.6%

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

   if -3.1999999999999997e24 < z < 2.4000000000000002e65

   1. Initial program 94.6%

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

      1. associate-*l/ 94.7%

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

   3. Simplified 94.7%

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

   4. Taylor expanded in x around inf 55.3%

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

4. Final simplification 62.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{+24} \lor \neg \left(z \leq 2.4 \cdot 10^{+65}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 16: 50.9% accurate, 11.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 86.3%

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

   1. associate-*l/ 95.1%

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

3. Simplified 95.1%

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

4. Taylor expanded in x around inf 52.6%

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

5. Final simplification 52.6%

   \[\leadsto x \]

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 2023293 
(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))))