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

Percentage Accurate: 85.0% → 98.3%

Time: 10.4s

Alternatives: 14

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 85.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 89.1%

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

   1. associate-/l* 98.5%

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

3. Simplified 98.5%

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

4. Final simplification 98.5%

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

Alternative 2: 76.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5.1 \cdot 10^{+160}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq -8.6 \cdot 10^{+143}:\\ \;\;\;\;y \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{elif}\;t \leq -8.2 \cdot 10^{+44} \lor \neg \left(t \leq 1500\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -5.1e+160)
   (+ x y)
   (if (<= t -8.6e+143)
     (* y (- 1.0 (/ z t)))
     (if (or (<= t -8.2e+44) (not (<= t 1500.0)))
       (+ x y)
       (+ x (* z (/ y a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -5.1e+160) {
		tmp = x + y;
	} else if (t <= -8.6e+143) {
		tmp = y * (1.0 - (z / t));
	} else if ((t <= -8.2e+44) || !(t <= 1500.0)) {
		tmp = x + y;
	} else {
		tmp = x + (z * (y / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-5.1d+160)) then
        tmp = x + y
    else if (t <= (-8.6d+143)) then
        tmp = y * (1.0d0 - (z / t))
    else if ((t <= (-8.2d+44)) .or. (.not. (t <= 1500.0d0))) then
        tmp = x + y
    else
        tmp = x + (z * (y / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -5.1e+160) {
		tmp = x + y;
	} else if (t <= -8.6e+143) {
		tmp = y * (1.0 - (z / t));
	} else if ((t <= -8.2e+44) || !(t <= 1500.0)) {
		tmp = x + y;
	} else {
		tmp = x + (z * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -5.1e+160:
		tmp = x + y
	elif t <= -8.6e+143:
		tmp = y * (1.0 - (z / t))
	elif (t <= -8.2e+44) or not (t <= 1500.0):
		tmp = x + y
	else:
		tmp = x + (z * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -5.1e+160)
		tmp = Float64(x + y);
	elseif (t <= -8.6e+143)
		tmp = Float64(y * Float64(1.0 - Float64(z / t)));
	elseif ((t <= -8.2e+44) || !(t <= 1500.0))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(z * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -5.1e+160)
		tmp = x + y;
	elseif (t <= -8.6e+143)
		tmp = y * (1.0 - (z / t));
	elseif ((t <= -8.2e+44) || ~((t <= 1500.0)))
		tmp = x + y;
	else
		tmp = x + (z * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -5.1e+160], N[(x + y), $MachinePrecision], If[LessEqual[t, -8.6e+143], N[(y * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t, -8.2e+44], N[Not[LessEqual[t, 1500.0]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -5.1000000000000001e160 or -8.60000000000000003e143 < t < -8.1999999999999993e44 or 1500 < t

   1. Initial program 81.8%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in t around inf 78.1%

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

      1. +-commutative 78.1%

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

   6. Simplified 78.1%

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

   if -5.1000000000000001e160 < t < -8.60000000000000003e143

   1. Initial program 85.0%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in a around 0 85.0%

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

      1. mul-1-neg 85.0%

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

      2. unsub-neg 85.0%

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

      3. associate-/l* 99.7%

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

   6. Simplified 99.7%

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

   7. Taylor expanded in y around inf 100.0%

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

   if -8.1999999999999993e44 < t < 1500

   1. Initial program 95.3%

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

      1. associate-/l* 97.3%

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

   3. Simplified 97.3%

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

   4. Taylor expanded in z around inf 89.3%

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

      1. associate-*l/ 92.9%

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

      2. *-commutative 92.9%

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

   6. Simplified 92.9%

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

   7. Taylor expanded in a around inf 80.5%

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

4. Final simplification 79.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.1 \cdot 10^{+160}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq -8.6 \cdot 10^{+143}:\\ \;\;\;\;y \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{elif}\;t \leq -8.2 \cdot 10^{+44} \lor \neg \left(t \leq 1500\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \end{array} \]

Alternative 3: 63.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z}{a - t}\\ \mathbf{if}\;z \leq -3.2 \cdot 10^{+146}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{-134}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 1.82 \cdot 10^{-53}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+239}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ z (- a t)))))
   (if (<= z -3.2e+146)
     t_1
     (if (<= z 6.5e-134)
       (+ x y)
       (if (<= z 1.82e-53) x (if (<= z 1.4e+239) (+ x y) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (z / (a - t));
	double tmp;
	if (z <= -3.2e+146) {
		tmp = t_1;
	} else if (z <= 6.5e-134) {
		tmp = x + y;
	} else if (z <= 1.82e-53) {
		tmp = x;
	} else if (z <= 1.4e+239) {
		tmp = x + y;
	} 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 = y * (z / (a - t))
    if (z <= (-3.2d+146)) then
        tmp = t_1
    else if (z <= 6.5d-134) then
        tmp = x + y
    else if (z <= 1.82d-53) then
        tmp = x
    else if (z <= 1.4d+239) then
        tmp = x + y
    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 = y * (z / (a - t));
	double tmp;
	if (z <= -3.2e+146) {
		tmp = t_1;
	} else if (z <= 6.5e-134) {
		tmp = x + y;
	} else if (z <= 1.82e-53) {
		tmp = x;
	} else if (z <= 1.4e+239) {
		tmp = x + y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * (z / (a - t))
	tmp = 0
	if z <= -3.2e+146:
		tmp = t_1
	elif z <= 6.5e-134:
		tmp = x + y
	elif z <= 1.82e-53:
		tmp = x
	elif z <= 1.4e+239:
		tmp = x + y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(z / Float64(a - t)))
	tmp = 0.0
	if (z <= -3.2e+146)
		tmp = t_1;
	elseif (z <= 6.5e-134)
		tmp = Float64(x + y);
	elseif (z <= 1.82e-53)
		tmp = x;
	elseif (z <= 1.4e+239)
		tmp = Float64(x + y);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * (z / (a - t));
	tmp = 0.0;
	if (z <= -3.2e+146)
		tmp = t_1;
	elseif (z <= 6.5e-134)
		tmp = x + y;
	elseif (z <= 1.82e-53)
		tmp = x;
	elseif (z <= 1.4e+239)
		tmp = x + y;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.2e+146], t$95$1, If[LessEqual[z, 6.5e-134], N[(x + y), $MachinePrecision], If[LessEqual[z, 1.82e-53], x, If[LessEqual[z, 1.4e+239], N[(x + y), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.2e146 or 1.40000000000000001e239 < z

   1. Initial program 78.3%

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

      1. associate-/l* 94.3%

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

   3. Simplified 94.3%

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

      1. clear-num 94.2%

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

      2. associate-/r/ 94.4%

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

      3. clear-num 94.4%

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

   5. Applied egg-rr 94.4%

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

   6. Taylor expanded in y around inf 81.8%

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

      1. div-sub 81.8%

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

   8. Simplified 81.8%

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

   9. Taylor expanded in z around inf 79.8%

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

   if -3.2e146 < z < 6.4999999999999998e-134 or 1.8199999999999999e-53 < z < 1.40000000000000001e239

   1. Initial program 91.5%

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

      1. associate-/l* 99.5%

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

   3. Simplified 99.5%

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

   4. Taylor expanded in t around inf 71.2%

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

      1. +-commutative 71.2%

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

   6. Simplified 71.2%

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

   if 6.4999999999999998e-134 < z < 1.8199999999999999e-53

   1. Initial program 94.8%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around inf 78.2%

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

4. Final simplification 73.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{+146}:\\ \;\;\;\;y \cdot \frac{z}{a - t}\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{-134}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 1.82 \cdot 10^{-53}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+239}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{a - t}\\ \end{array} \]

Alternative 4: 59.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{+190}:\\ \;\;\;\;\frac{z}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 1.06 \cdot 10^{-132}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-64}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{+242}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{-z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.3e+190)
   (/ z (/ a y))
   (if (<= z 1.06e-132)
     (+ x y)
     (if (<= z 3.8e-64) x (if (<= z 1.65e+242) (+ x y) (* y (/ (- z) t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.3e+190) {
		tmp = z / (a / y);
	} else if (z <= 1.06e-132) {
		tmp = x + y;
	} else if (z <= 3.8e-64) {
		tmp = x;
	} else if (z <= 1.65e+242) {
		tmp = x + y;
	} else {
		tmp = y * (-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 (z <= (-1.3d+190)) then
        tmp = z / (a / y)
    else if (z <= 1.06d-132) then
        tmp = x + y
    else if (z <= 3.8d-64) then
        tmp = x
    else if (z <= 1.65d+242) then
        tmp = x + y
    else
        tmp = y * (-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 (z <= -1.3e+190) {
		tmp = z / (a / y);
	} else if (z <= 1.06e-132) {
		tmp = x + y;
	} else if (z <= 3.8e-64) {
		tmp = x;
	} else if (z <= 1.65e+242) {
		tmp = x + y;
	} else {
		tmp = y * (-z / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.3e+190:
		tmp = z / (a / y)
	elif z <= 1.06e-132:
		tmp = x + y
	elif z <= 3.8e-64:
		tmp = x
	elif z <= 1.65e+242:
		tmp = x + y
	else:
		tmp = y * (-z / t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.3e+190)
		tmp = Float64(z / Float64(a / y));
	elseif (z <= 1.06e-132)
		tmp = Float64(x + y);
	elseif (z <= 3.8e-64)
		tmp = x;
	elseif (z <= 1.65e+242)
		tmp = Float64(x + y);
	else
		tmp = Float64(y * Float64(Float64(-z) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.3e+190)
		tmp = z / (a / y);
	elseif (z <= 1.06e-132)
		tmp = x + y;
	elseif (z <= 3.8e-64)
		tmp = x;
	elseif (z <= 1.65e+242)
		tmp = x + y;
	else
		tmp = y * (-z / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.3e+190], N[(z / N[(a / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.06e-132], N[(x + y), $MachinePrecision], If[LessEqual[z, 3.8e-64], x, If[LessEqual[z, 1.65e+242], N[(x + y), $MachinePrecision], N[(y * N[((-z) / t), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.30000000000000005e190

   1. Initial program 81.2%

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

      1. associate-/l* 90.2%

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

   3. Simplified 90.2%

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

      1. clear-num 90.2%

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

      2. associate-/r/ 90.3%

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

      3. clear-num 90.2%

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

   5. Applied egg-rr 90.2%

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

   6. Taylor expanded in y around inf 74.7%

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

      1. div-sub 74.7%

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

   8. Simplified 74.7%

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

   9. Taylor expanded in a around inf 58.3%

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

   10. Taylor expanded in z around inf 46.1%

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

       1. *-commutative 46.1%

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

       2. associate-/l* 61.9%

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

   12. Simplified 61.9%

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

   if -1.30000000000000005e190 < z < 1.05999999999999997e-132 or 3.8000000000000002e-64 < z < 1.65000000000000011e242

   1. Initial program 90.8%

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

      1. associate-/l* 99.5%

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

   3. Simplified 99.5%

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

   4. Taylor expanded in t around inf 70.6%

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

      1. +-commutative 70.6%

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

   6. Simplified 70.6%

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

   if 1.05999999999999997e-132 < z < 3.8000000000000002e-64

   1. Initial program 94.8%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around inf 78.2%

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

   if 1.65000000000000011e242 < z

   1. Initial program 76.7%

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

      1. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in z around inf 76.7%

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

      1. associate-*l/ 99.7%

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

      2. *-commutative 99.7%

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

   6. Simplified 99.7%

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

   7. Taylor expanded in a around 0 45.5%

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

      1. mul-1-neg 45.5%

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

      2. unsub-neg 45.5%

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

      3. associate-/l* 57.2%

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

   9. Simplified 57.2%

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

   10. Taylor expanded in x around 0 45.5%

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

       1. associate-*r/ 57.2%

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

       2. neg-mul-1 57.2%

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

       3. distribute-rgt-neg-out 57.2%

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

       4. distribute-neg-frac 57.2%

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

   12. Simplified 57.2%

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

4. Final simplification 69.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{+190}:\\ \;\;\;\;\frac{z}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 1.06 \cdot 10^{-132}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-64}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{+242}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{-z}{t}\\ \end{array} \]

Alternative 5: 59.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z}{a}\\ \mathbf{if}\;z \leq -5.2 \cdot 10^{+190}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{-133}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 6.4 \cdot 10^{-61}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.45 \cdot 10^{+246}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ z a))))
   (if (<= z -5.2e+190)
     t_1
     (if (<= z 3.9e-133)
       (+ x y)
       (if (<= z 6.4e-61) x (if (<= z 3.45e+246) (+ x y) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (z / a);
	double tmp;
	if (z <= -5.2e+190) {
		tmp = t_1;
	} else if (z <= 3.9e-133) {
		tmp = x + y;
	} else if (z <= 6.4e-61) {
		tmp = x;
	} else if (z <= 3.45e+246) {
		tmp = x + y;
	} 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 = y * (z / a)
    if (z <= (-5.2d+190)) then
        tmp = t_1
    else if (z <= 3.9d-133) then
        tmp = x + y
    else if (z <= 6.4d-61) then
        tmp = x
    else if (z <= 3.45d+246) then
        tmp = x + y
    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 = y * (z / a);
	double tmp;
	if (z <= -5.2e+190) {
		tmp = t_1;
	} else if (z <= 3.9e-133) {
		tmp = x + y;
	} else if (z <= 6.4e-61) {
		tmp = x;
	} else if (z <= 3.45e+246) {
		tmp = x + y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * (z / a)
	tmp = 0
	if z <= -5.2e+190:
		tmp = t_1
	elif z <= 3.9e-133:
		tmp = x + y
	elif z <= 6.4e-61:
		tmp = x
	elif z <= 3.45e+246:
		tmp = x + y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(z / a))
	tmp = 0.0
	if (z <= -5.2e+190)
		tmp = t_1;
	elseif (z <= 3.9e-133)
		tmp = Float64(x + y);
	elseif (z <= 6.4e-61)
		tmp = x;
	elseif (z <= 3.45e+246)
		tmp = Float64(x + y);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * (z / a);
	tmp = 0.0;
	if (z <= -5.2e+190)
		tmp = t_1;
	elseif (z <= 3.9e-133)
		tmp = x + y;
	elseif (z <= 6.4e-61)
		tmp = x;
	elseif (z <= 3.45e+246)
		tmp = x + y;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.2e+190], t$95$1, If[LessEqual[z, 3.9e-133], N[(x + y), $MachinePrecision], If[LessEqual[z, 6.4e-61], x, If[LessEqual[z, 3.45e+246], N[(x + y), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.20000000000000022e190 or 3.45e246 < z

   1. Initial program 79.2%

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

      1. associate-/l* 93.5%

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

   3. Simplified 93.5%

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

      1. clear-num 93.4%

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

      2. associate-/r/ 93.5%

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

      3. clear-num 93.5%

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

   5. Applied egg-rr 93.5%

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

   6. Taylor expanded in y around inf 83.2%

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

      1. div-sub 83.2%

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

   8. Simplified 83.2%

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

   9. Taylor expanded in t around 0 56.9%

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

   if -5.20000000000000022e190 < z < 3.90000000000000029e-133 or 6.4000000000000003e-61 < z < 3.45e246

   1. Initial program 90.8%

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

      1. associate-/l* 99.5%

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

   3. Simplified 99.5%

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

   4. Taylor expanded in t around inf 70.3%

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

      1. +-commutative 70.3%

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

   6. Simplified 70.3%

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

   if 3.90000000000000029e-133 < z < 6.4000000000000003e-61

   1. Initial program 94.8%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around inf 78.2%

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

4. Final simplification 68.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{+190}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{-133}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 6.4 \cdot 10^{-61}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.45 \cdot 10^{+246}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \end{array} \]

Alternative 6: 60.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{+186}:\\ \;\;\;\;\frac{z}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{-131}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{-62}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 9.4 \cdot 10^{+250}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -3.4e+186)
   (/ z (/ a y))
   (if (<= z 2.4e-131)
     (+ x y)
     (if (<= z 4.6e-62) x (if (<= z 9.4e+250) (+ x y) (* y (/ z a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.4e+186) {
		tmp = z / (a / y);
	} else if (z <= 2.4e-131) {
		tmp = x + y;
	} else if (z <= 4.6e-62) {
		tmp = x;
	} else if (z <= 9.4e+250) {
		tmp = x + y;
	} else {
		tmp = y * (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 <= (-3.4d+186)) then
        tmp = z / (a / y)
    else if (z <= 2.4d-131) then
        tmp = x + y
    else if (z <= 4.6d-62) then
        tmp = x
    else if (z <= 9.4d+250) then
        tmp = x + y
    else
        tmp = y * (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 <= -3.4e+186) {
		tmp = z / (a / y);
	} else if (z <= 2.4e-131) {
		tmp = x + y;
	} else if (z <= 4.6e-62) {
		tmp = x;
	} else if (z <= 9.4e+250) {
		tmp = x + y;
	} else {
		tmp = y * (z / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -3.4e+186:
		tmp = z / (a / y)
	elif z <= 2.4e-131:
		tmp = x + y
	elif z <= 4.6e-62:
		tmp = x
	elif z <= 9.4e+250:
		tmp = x + y
	else:
		tmp = y * (z / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -3.4e+186)
		tmp = Float64(z / Float64(a / y));
	elseif (z <= 2.4e-131)
		tmp = Float64(x + y);
	elseif (z <= 4.6e-62)
		tmp = x;
	elseif (z <= 9.4e+250)
		tmp = Float64(x + y);
	else
		tmp = Float64(y * Float64(z / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -3.4e+186)
		tmp = z / (a / y);
	elseif (z <= 2.4e-131)
		tmp = x + y;
	elseif (z <= 4.6e-62)
		tmp = x;
	elseif (z <= 9.4e+250)
		tmp = x + y;
	else
		tmp = y * (z / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -3.4e+186], N[(z / N[(a / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.4e-131], N[(x + y), $MachinePrecision], If[LessEqual[z, 4.6e-62], x, If[LessEqual[z, 9.4e+250], N[(x + y), $MachinePrecision], N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.40000000000000005e186

   1. Initial program 81.2%

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

      1. associate-/l* 90.2%

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

   3. Simplified 90.2%

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

      1. clear-num 90.2%

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

      2. associate-/r/ 90.3%

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

      3. clear-num 90.2%

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

   5. Applied egg-rr 90.2%

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

   6. Taylor expanded in y around inf 74.7%

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

      1. div-sub 74.7%

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

   8. Simplified 74.7%

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

   9. Taylor expanded in a around inf 58.3%

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

   10. Taylor expanded in z around inf 46.1%

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

       1. *-commutative 46.1%

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

       2. associate-/l* 61.9%

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

   12. Simplified 61.9%

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

   if -3.40000000000000005e186 < z < 2.4e-131 or 4.60000000000000001e-62 < z < 9.3999999999999999e250

   1. Initial program 90.8%

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

      1. associate-/l* 99.5%

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

   3. Simplified 99.5%

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

   4. Taylor expanded in t around inf 70.3%

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

      1. +-commutative 70.3%

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

   6. Simplified 70.3%

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

   if 2.4e-131 < z < 4.60000000000000001e-62

   1. Initial program 94.8%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around inf 78.2%

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

   if 9.3999999999999999e250 < z

   1. Initial program 75.1%

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

      1. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

      1. clear-num 99.7%

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

      2. associate-/r/ 100.0%

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

      3. clear-num 100.0%

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

   5. Applied egg-rr 100.0%

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

   6. Taylor expanded in y around inf 100.0%

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

      1. div-sub 100.0%

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

   8. Simplified 100.0%

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

   9. Taylor expanded in t around 0 54.1%

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

4. Final simplification 68.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{+186}:\\ \;\;\;\;\frac{z}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{-131}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{-62}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 9.4 \cdot 10^{+250}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \end{array} \]

Alternative 7: 72.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + z \cdot \frac{y}{a}\\ \mathbf{if}\;x \leq -4.5 \cdot 10^{-63}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{-95}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;x \leq 1.35 \cdot 10^{+96}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* z (/ y a)))))
   (if (<= x -4.5e-63)
     t_1
     (if (<= x 2.3e-95)
       (* y (/ (- z t) (- a t)))
       (if (<= x 1.35e+96) t_1 (+ x y))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (z * (y / a));
	double tmp;
	if (x <= -4.5e-63) {
		tmp = t_1;
	} else if (x <= 2.3e-95) {
		tmp = y * ((z - t) / (a - t));
	} else if (x <= 1.35e+96) {
		tmp = t_1;
	} else {
		tmp = x + 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) :: t_1
    real(8) :: tmp
    t_1 = x + (z * (y / a))
    if (x <= (-4.5d-63)) then
        tmp = t_1
    else if (x <= 2.3d-95) then
        tmp = y * ((z - t) / (a - t))
    else if (x <= 1.35d+96) then
        tmp = t_1
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (z * (y / a));
	double tmp;
	if (x <= -4.5e-63) {
		tmp = t_1;
	} else if (x <= 2.3e-95) {
		tmp = y * ((z - t) / (a - t));
	} else if (x <= 1.35e+96) {
		tmp = t_1;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (z * (y / a))
	tmp = 0
	if x <= -4.5e-63:
		tmp = t_1
	elif x <= 2.3e-95:
		tmp = y * ((z - t) / (a - t))
	elif x <= 1.35e+96:
		tmp = t_1
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(z * Float64(y / a)))
	tmp = 0.0
	if (x <= -4.5e-63)
		tmp = t_1;
	elseif (x <= 2.3e-95)
		tmp = Float64(y * Float64(Float64(z - t) / Float64(a - t)));
	elseif (x <= 1.35e+96)
		tmp = t_1;
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (z * (y / a));
	tmp = 0.0;
	if (x <= -4.5e-63)
		tmp = t_1;
	elseif (x <= 2.3e-95)
		tmp = y * ((z - t) / (a - t));
	elseif (x <= 1.35e+96)
		tmp = t_1;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -4.5e-63], t$95$1, If[LessEqual[x, 2.3e-95], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.35e+96], t$95$1, N[(x + y), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.5e-63 or 2.29999999999999999e-95 < x < 1.35000000000000011e96

   1. Initial program 91.6%

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

      1. associate-/l* 98.2%

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

   3. Simplified 98.2%

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

   4. Taylor expanded in z around inf 86.1%

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

      1. associate-*l/ 89.0%

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

      2. *-commutative 89.0%

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

   6. Simplified 89.0%

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

   7. Taylor expanded in a around inf 79.5%

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

   if -4.5e-63 < x < 2.29999999999999999e-95

   1. Initial program 88.0%

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

      1. associate-/l* 99.1%

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

   3. Simplified 99.1%

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

      1. clear-num 98.9%

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

      2. associate-/r/ 98.7%

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

      3. clear-num 98.7%

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

   5. Applied egg-rr 98.7%

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

   6. Taylor expanded in y around inf 81.1%

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

      1. div-sub 81.1%

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

   8. Simplified 81.1%

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

   if 1.35000000000000011e96 < x

   1. Initial program 85.2%

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

      1. associate-/l* 98.1%

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

   3. Simplified 98.1%

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

   4. Taylor expanded in t around inf 81.9%

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

      1. +-commutative 81.9%

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

   6. Simplified 81.9%

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

4. Final simplification 80.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.5 \cdot 10^{-63}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{-95}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;x \leq 1.35 \cdot 10^{+96}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 8: 81.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.7 \cdot 10^{-210} \lor \neg \left(x \leq 3.5 \cdot 10^{-95}\right):\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= x -3.7e-210) (not (<= x 3.5e-95)))
   (+ x (* z (/ y (- a t))))
   (* y (/ (- z t) (- a t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -3.7e-210) || !(x <= 3.5e-95)) {
		tmp = x + (z * (y / (a - t)));
	} else {
		tmp = y * ((z - t) / (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 ((x <= (-3.7d-210)) .or. (.not. (x <= 3.5d-95))) then
        tmp = x + (z * (y / (a - t)))
    else
        tmp = y * ((z - t) / (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 ((x <= -3.7e-210) || !(x <= 3.5e-95)) {
		tmp = x + (z * (y / (a - t)));
	} else {
		tmp = y * ((z - t) / (a - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (x <= -3.7e-210) or not (x <= 3.5e-95):
		tmp = x + (z * (y / (a - t)))
	else:
		tmp = y * ((z - t) / (a - t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((x <= -3.7e-210) || !(x <= 3.5e-95))
		tmp = Float64(x + Float64(z * Float64(y / Float64(a - t))));
	else
		tmp = Float64(y * Float64(Float64(z - t) / Float64(a - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x <= -3.7e-210) || ~((x <= 3.5e-95)))
		tmp = x + (z * (y / (a - t)));
	else
		tmp = y * ((z - t) / (a - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[x, -3.7e-210], N[Not[LessEqual[x, 3.5e-95]], $MachinePrecision]], N[(x + N[(z * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.7000000000000003e-210 or 3.4999999999999997e-95 < x

   1. Initial program 90.5%

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

      1. associate-/l* 98.4%

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

   3. Simplified 98.4%

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

   4. Taylor expanded in z around inf 85.1%

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

      1. associate-*l/ 88.4%

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

      2. *-commutative 88.4%

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

   6. Simplified 88.4%

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

   if -3.7000000000000003e-210 < x < 3.4999999999999997e-95

   1. Initial program 84.9%

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

      1. associate-/l* 98.8%

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

   3. Simplified 98.8%

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

      1. clear-num 98.5%

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

      2. associate-/r/ 98.3%

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

      3. clear-num 98.4%

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

   5. Applied egg-rr 98.4%

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

   6. Taylor expanded in y around inf 88.2%

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

      1. div-sub 88.2%

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

   8. Simplified 88.2%

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

4. Final simplification 88.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.7 \cdot 10^{-210} \lor \neg \left(x \leq 3.5 \cdot 10^{-95}\right):\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \end{array} \]

Alternative 9: 85.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.45 \cdot 10^{-26} \lor \neg \left(z \leq 2.2 \cdot 10^{-109}\right):\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{t}{\frac{a - t}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2.45e-26) (not (<= z 2.2e-109)))
   (+ x (* z (/ y (- a t))))
   (- x (/ t (/ (- a t) y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.45e-26) || !(z <= 2.2e-109)) {
		tmp = x + (z * (y / (a - t)));
	} else {
		tmp = x - (t / ((a - t) / 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 ((z <= (-2.45d-26)) .or. (.not. (z <= 2.2d-109))) then
        tmp = x + (z * (y / (a - t)))
    else
        tmp = x - (t / ((a - t) / 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 ((z <= -2.45e-26) || !(z <= 2.2e-109)) {
		tmp = x + (z * (y / (a - t)));
	} else {
		tmp = x - (t / ((a - t) / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -2.45e-26) or not (z <= 2.2e-109):
		tmp = x + (z * (y / (a - t)))
	else:
		tmp = x - (t / ((a - t) / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2.45e-26) || !(z <= 2.2e-109))
		tmp = Float64(x + Float64(z * Float64(y / Float64(a - t))));
	else
		tmp = Float64(x - Float64(t / Float64(Float64(a - t) / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -2.45e-26) || ~((z <= 2.2e-109)))
		tmp = x + (z * (y / (a - t)));
	else
		tmp = x - (t / ((a - t) / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -2.45e-26], N[Not[LessEqual[z, 2.2e-109]], $MachinePrecision]], N[(x + N[(z * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(t / N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.45e-26 or 2.1999999999999999e-109 < z

   1. Initial program 87.9%

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

      1. associate-/l* 97.6%

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

   3. Simplified 97.6%

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

   4. Taylor expanded in z around inf 84.0%

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

      1. associate-*l/ 89.7%

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

      2. *-commutative 89.7%

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

   6. Simplified 89.7%

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

   if -2.45e-26 < z < 2.1999999999999999e-109

   1. Initial program 90.9%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

      1. clear-num 99.8%

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

      2. associate-/r/ 99.9%

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

      3. clear-num 99.9%

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

   5. Applied egg-rr 99.9%

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

   6. Taylor expanded in z around 0 86.8%

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

      1. mul-1-neg 86.8%

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

      2. unsub-neg 86.8%

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

      3. associate-/l* 91.3%

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

   8. Simplified 91.3%

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

4. Final simplification 90.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.45 \cdot 10^{-26} \lor \neg \left(z \leq 2.2 \cdot 10^{-109}\right):\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{t}{\frac{a - t}{y}}\\ \end{array} \]

Alternative 10: 87.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7.2 \cdot 10^{+49} \lor \neg \left(t \leq 65200\right):\\ \;\;\;\;x - \frac{y}{\frac{t}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -7.2e+49) (not (<= t 65200.0)))
   (- x (/ y (/ t (- z t))))
   (+ x (* z (/ y (- a t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -7.2e+49) || !(t <= 65200.0)) {
		tmp = x - (y / (t / (z - t)));
	} else {
		tmp = x + (z * (y / (a - t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-7.2d+49)) .or. (.not. (t <= 65200.0d0))) then
        tmp = x - (y / (t / (z - t)))
    else
        tmp = x + (z * (y / (a - t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -7.2e+49) || !(t <= 65200.0)) {
		tmp = x - (y / (t / (z - t)));
	} else {
		tmp = x + (z * (y / (a - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -7.2e+49) or not (t <= 65200.0):
		tmp = x - (y / (t / (z - t)))
	else:
		tmp = x + (z * (y / (a - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -7.2e+49) || !(t <= 65200.0))
		tmp = Float64(x - Float64(y / Float64(t / Float64(z - t))));
	else
		tmp = Float64(x + Float64(z * Float64(y / Float64(a - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -7.2e+49) || ~((t <= 65200.0)))
		tmp = x - (y / (t / (z - t)));
	else
		tmp = x + (z * (y / (a - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -7.2e+49], N[Not[LessEqual[t, 65200.0]], $MachinePrecision]], N[(x - N[(y / N[(t / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -7.19999999999999993e49 or 65200 < t

   1. Initial program 81.7%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in a around 0 73.6%

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

      1. mul-1-neg 73.6%

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

      2. unsub-neg 73.6%

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

      3. associate-/l* 87.9%

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

   6. Simplified 87.9%

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

   if -7.19999999999999993e49 < t < 65200

   1. Initial program 95.4%

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

      1. associate-/l* 97.3%

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

   3. Simplified 97.3%

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

   4. Taylor expanded in z around inf 89.4%

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

      1. associate-*l/ 93.0%

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

      2. *-commutative 93.0%

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

   6. Simplified 93.0%

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

4. Final simplification 90.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.2 \cdot 10^{+49} \lor \neg \left(t \leq 65200\right):\\ \;\;\;\;x - \frac{y}{\frac{t}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \end{array} \]

Alternative 11: 98.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 89.1%

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

   1. associate-/l* 98.5%

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

3. Simplified 98.5%

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

   1. clear-num 98.4%

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

   2. associate-/r/ 98.4%

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

   3. clear-num 98.4%

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

5. Applied egg-rr 98.4%

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

6. Final simplification 98.4%

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

Alternative 12: 52.1% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.95 \cdot 10^{-211}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 3.7 \cdot 10^{-96}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -2.95e-211) x (if (<= x 3.7e-96) y x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -2.95e-211) {
		tmp = x;
	} else if (x <= 3.7e-96) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (x <= (-2.95d-211)) then
        tmp = x
    else if (x <= 3.7d-96) then
        tmp = y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -2.95e-211) {
		tmp = x;
	} else if (x <= 3.7e-96) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -2.95e-211:
		tmp = x
	elif x <= 3.7e-96:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -2.95e-211)
		tmp = x;
	elseif (x <= 3.7e-96)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -2.95e-211)
		tmp = x;
	elseif (x <= 3.7e-96)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -2.95e-211], x, If[LessEqual[x, 3.7e-96], y, x]]

Derivation

1. Split input into 2 regimes

2. if x < -2.9500000000000001e-211 or 3.69999999999999986e-96 < x

   1. Initial program 90.5%

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

      1. associate-/l* 98.4%

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

   3. Simplified 98.4%

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

   4. Taylor expanded in x around inf 62.5%

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

   if -2.9500000000000001e-211 < x < 3.69999999999999986e-96

   1. Initial program 84.9%

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

      1. associate-/l* 98.8%

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

   3. Simplified 98.8%

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

      1. clear-num 98.5%

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

      2. associate-/r/ 98.3%

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

      3. clear-num 98.4%

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

   5. Applied egg-rr 98.4%

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

   6. Taylor expanded in y around inf 88.2%

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

      1. div-sub 88.2%

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

   8. Simplified 88.2%

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

   9. Taylor expanded in t around inf 34.2%

      \[\leadsto y \cdot \color{blue}{1} \]
3. Recombined 2 regimes into one program.

4. Final simplification 55.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.95 \cdot 10^{-211}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 3.7 \cdot 10^{-96}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 13: 59.3% accurate, 3.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 89.1%

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

   1. associate-/l* 98.5%

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

3. Simplified 98.5%

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

4. Taylor expanded in t around inf 58.9%

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

   1. +-commutative 58.9%

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

6. Simplified 58.9%

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

7. Final simplification 58.9%

   \[\leadsto x + y \]

Alternative 14: 49.6% accurate, 11.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 89.1%

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

   1. associate-/l* 98.5%

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

3. Simplified 98.5%

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

4. Taylor expanded in x around inf 49.7%

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

5. Final simplification 49.7%

   \[\leadsto x \]

Developer target: 98.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023308 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, B"
  :precision binary64

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

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