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

Percentage Accurate: 98.1% → 98.1%

Time: 9.0s

Alternatives: 10

Speedup: 1.0×

Specification

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]

Initial Program: 98.1% 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]

Alternative 1: 98.1% 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 98.4%

   \[x + y \cdot \frac{z - t}{a - t} \]
2. Add Preprocessing
3. Add Preprocessing

Alternative 2: 87.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.3 \cdot 10^{+45} \lor \neg \left(t \leq 2.55 \cdot 10^{+39}\right):\\ \;\;\;\;x + y \cdot \frac{t - z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -3.3e+45) (not (<= t 2.55e+39)))
   (+ x (* y (/ (- t z) t)))
   (+ x (* y (/ z (- a t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -3.3e+45) || !(t <= 2.55e+39)) {
		tmp = x + (y * ((t - z) / t));
	} else {
		tmp = x + (y * (z / (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 <= (-3.3d+45)) .or. (.not. (t <= 2.55d+39))) then
        tmp = x + (y * ((t - z) / t))
    else
        tmp = x + (y * (z / (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 <= -3.3e+45) || !(t <= 2.55e+39)) {
		tmp = x + (y * ((t - z) / t));
	} else {
		tmp = x + (y * (z / (a - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -3.3e+45) or not (t <= 2.55e+39):
		tmp = x + (y * ((t - z) / t))
	else:
		tmp = x + (y * (z / (a - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -3.3e+45) || !(t <= 2.55e+39))
		tmp = Float64(x + Float64(y * Float64(Float64(t - z) / t)));
	else
		tmp = Float64(x + Float64(y * Float64(z / Float64(a - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -3.3e+45) || ~((t <= 2.55e+39)))
		tmp = x + (y * ((t - z) / t));
	else
		tmp = x + (y * (z / (a - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -3.3e+45], N[Not[LessEqual[t, 2.55e+39]], $MachinePrecision]], N[(x + N[(y * N[(N[(t - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.3000000000000001e45 or 2.5499999999999999e39 < t

   1. Initial program 99.9%

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

   3. Taylor expanded in a around 0 69.9%

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

      1. mul-1-neg 69.9%

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

      2. associate-/l* 88.8%

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

      3. distribute-rgt-neg-in 88.8%

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

      4. distribute-frac-neg 88.8%

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

      5. neg-sub0 88.8%

         \[\leadsto x + y \cdot \frac{\color{blue}{0 - \left(z - t\right)}}{t} \]

      6. sub-neg 88.8%

         \[\leadsto x + y \cdot \frac{0 - \color{blue}{\left(z + \left(-t\right)\right)}}{t} \]

      7. +-commutative 88.8%

         \[\leadsto x + y \cdot \frac{0 - \color{blue}{\left(\left(-t\right) + z\right)}}{t} \]

      8. associate--r+ 88.8%

         \[\leadsto x + y \cdot \frac{\color{blue}{\left(0 - \left(-t\right)\right) - z}}{t} \]

      9. neg-sub0 88.8%

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

      10. remove-double-neg 88.8%

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

   5. Simplified 88.8%

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

   if -3.3000000000000001e45 < t < 2.5499999999999999e39

   1. Initial program 97.5%

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

   3. Taylor expanded in z around inf 86.1%

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

      1. associate-/l* 86.7%

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

   5. Simplified 86.7%

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

4. Final simplification 87.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.3 \cdot 10^{+45} \lor \neg \left(t \leq 2.55 \cdot 10^{+39}\right):\\ \;\;\;\;x + y \cdot \frac{t - z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 83.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6 \cdot 10^{+140} \lor \neg \left(t \leq 4.3 \cdot 10^{+49}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -6e+140) (not (<= t 4.3e+49)))
   (+ x y)
   (+ x (* y (/ z (- a t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -6e+140) || !(t <= 4.3e+49)) {
		tmp = x + y;
	} else {
		tmp = x + (y * (z / (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 <= (-6d+140)) .or. (.not. (t <= 4.3d+49))) then
        tmp = x + y
    else
        tmp = x + (y * (z / (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 <= -6e+140) || !(t <= 4.3e+49)) {
		tmp = x + y;
	} else {
		tmp = x + (y * (z / (a - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -6e+140) or not (t <= 4.3e+49):
		tmp = x + y
	else:
		tmp = x + (y * (z / (a - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -6e+140) || !(t <= 4.3e+49))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(y * Float64(z / Float64(a - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -6e+140) || ~((t <= 4.3e+49)))
		tmp = x + y;
	else
		tmp = x + (y * (z / (a - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -6e+140], N[Not[LessEqual[t, 4.3e+49]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -5.99999999999999993e140 or 4.2999999999999999e49 < t

   1. Initial program 99.9%

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

   3. Taylor expanded in t around inf 80.5%

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

      1. +-commutative 80.5%

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

   5. Simplified 80.5%

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

   if -5.99999999999999993e140 < t < 4.2999999999999999e49

   1. Initial program 97.7%

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

   3. Taylor expanded in z around inf 84.8%

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

      1. associate-/l* 85.9%

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

   5. Simplified 85.9%

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

4. Final simplification 84.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6 \cdot 10^{+140} \lor \neg \left(t \leq 4.3 \cdot 10^{+49}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 86.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.1 \cdot 10^{+45}:\\ \;\;\;\;x - y \cdot \left(\frac{z}{t} + -1\right)\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{-57}:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{1 - \frac{a}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -2.1e+45)
   (- x (* y (+ (/ z t) -1.0)))
   (if (<= t 1.4e-57) (+ x (* z (/ y (- a t)))) (+ x (/ y (- 1.0 (/ a t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.1e+45) {
		tmp = x - (y * ((z / t) + -1.0));
	} else if (t <= 1.4e-57) {
		tmp = x + (z * (y / (a - t)));
	} else {
		tmp = x + (y / (1.0 - (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 <= (-2.1d+45)) then
        tmp = x - (y * ((z / t) + (-1.0d0)))
    else if (t <= 1.4d-57) then
        tmp = x + (z * (y / (a - t)))
    else
        tmp = x + (y / (1.0d0 - (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 <= -2.1e+45) {
		tmp = x - (y * ((z / t) + -1.0));
	} else if (t <= 1.4e-57) {
		tmp = x + (z * (y / (a - t)));
	} else {
		tmp = x + (y / (1.0 - (a / t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -2.1e+45:
		tmp = x - (y * ((z / t) + -1.0))
	elif t <= 1.4e-57:
		tmp = x + (z * (y / (a - t)))
	else:
		tmp = x + (y / (1.0 - (a / t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -2.1e+45)
		tmp = Float64(x - Float64(y * Float64(Float64(z / t) + -1.0)));
	elseif (t <= 1.4e-57)
		tmp = Float64(x + Float64(z * Float64(y / Float64(a - t))));
	else
		tmp = Float64(x + Float64(y / Float64(1.0 - Float64(a / t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -2.1e+45)
		tmp = x - (y * ((z / t) + -1.0));
	elseif (t <= 1.4e-57)
		tmp = x + (z * (y / (a - t)));
	else
		tmp = x + (y / (1.0 - (a / t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -2.1e+45], N[(x - N[(y * N[(N[(z / t), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.4e-57], N[(x + N[(z * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(1.0 - N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.09999999999999995e45

   1. Initial program 99.9%

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

   3. Taylor expanded in a around 0 71.1%

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

      1. mul-1-neg 71.1%

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

      2. unsub-neg 71.1%

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

      3. associate-/l* 90.1%

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

      4. div-sub 90.2%

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

      5. sub-neg 90.2%

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

      6. *-inverses 90.2%

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

      7. metadata-eval 90.2%

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

   5. Simplified 90.2%

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

   if -2.09999999999999995e45 < t < 1.4e-57

   1. Initial program 97.0%

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

      1. clear-num 96.2%

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

      2. un-div-inv 96.3%

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

   4. Applied egg-rr 96.3%

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

      1. associate-/r/ 96.9%

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

   6. Applied egg-rr 96.9%

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

   7. Taylor expanded in z around inf 89.7%

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

   if 1.4e-57 < t

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 72.9%

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

      1. +-commutative 72.9%

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

      2. associate-*r/ 72.9%

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

      3. mul-1-neg 72.9%

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

      4. distribute-lft-neg-out 72.9%

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

      5. *-commutative 72.9%

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

      6. *-lft-identity 72.9%

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

      7. times-frac 87.9%

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

      8. /-rgt-identity 87.9%

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

      9. distribute-neg-frac 87.9%

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

      10. distribute-neg-frac2 87.9%

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

      11. neg-sub0 87.9%

          \[\leadsto y \cdot \frac{t}{\color{blue}{0 - \left(a - t\right)}} + x \]

      12. sub-neg 87.9%

          \[\leadsto y \cdot \frac{t}{0 - \color{blue}{\left(a + \left(-t\right)\right)}} + x \]

      13. +-commutative 87.9%

          \[\leadsto y \cdot \frac{t}{0 - \color{blue}{\left(\left(-t\right) + a\right)}} + x \]

      14. associate--r+ 87.9%

          \[\leadsto y \cdot \frac{t}{\color{blue}{\left(0 - \left(-t\right)\right) - a}} + x \]

      15. neg-sub0 87.9%

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

      16. remove-double-neg 87.9%

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

   5. Simplified 87.9%

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

      1. clear-num 87.9%

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

      2. un-div-inv 87.9%

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

      3. div-sub 87.9%

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

      4. *-inverses 87.9%

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

   7. Applied egg-rr 87.9%

      \[\leadsto \color{blue}{\frac{y}{1 - \frac{a}{t}}} + x \]
3. Recombined 3 regimes into one program.

4. Final simplification 89.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.1 \cdot 10^{+45}:\\ \;\;\;\;x - y \cdot \left(\frac{z}{t} + -1\right)\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{-57}:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{1 - \frac{a}{t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 86.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -8.8 \cdot 10^{+45}:\\ \;\;\;\;x + y \cdot \frac{t - z}{t}\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{-57}:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{1 - \frac{a}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -8.8e+45)
   (+ x (* y (/ (- t z) t)))
   (if (<= t 1.3e-57) (+ x (* z (/ y (- a t)))) (+ x (/ y (- 1.0 (/ a t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -8.8e+45) {
		tmp = x + (y * ((t - z) / t));
	} else if (t <= 1.3e-57) {
		tmp = x + (z * (y / (a - t)));
	} else {
		tmp = x + (y / (1.0 - (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 <= (-8.8d+45)) then
        tmp = x + (y * ((t - z) / t))
    else if (t <= 1.3d-57) then
        tmp = x + (z * (y / (a - t)))
    else
        tmp = x + (y / (1.0d0 - (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 <= -8.8e+45) {
		tmp = x + (y * ((t - z) / t));
	} else if (t <= 1.3e-57) {
		tmp = x + (z * (y / (a - t)));
	} else {
		tmp = x + (y / (1.0 - (a / t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -8.8e+45:
		tmp = x + (y * ((t - z) / t))
	elif t <= 1.3e-57:
		tmp = x + (z * (y / (a - t)))
	else:
		tmp = x + (y / (1.0 - (a / t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -8.8e+45)
		tmp = Float64(x + Float64(y * Float64(Float64(t - z) / t)));
	elseif (t <= 1.3e-57)
		tmp = Float64(x + Float64(z * Float64(y / Float64(a - t))));
	else
		tmp = Float64(x + Float64(y / Float64(1.0 - Float64(a / t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -8.8e+45)
		tmp = x + (y * ((t - z) / t));
	elseif (t <= 1.3e-57)
		tmp = x + (z * (y / (a - t)));
	else
		tmp = x + (y / (1.0 - (a / t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -8.8e+45], N[(x + N[(y * N[(N[(t - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.3e-57], N[(x + N[(z * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(1.0 - N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -8.8000000000000001e45

   1. Initial program 99.9%

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

   3. Taylor expanded in a around 0 71.1%

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

      1. mul-1-neg 71.1%

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

      2. associate-/l* 90.1%

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

      3. distribute-rgt-neg-in 90.1%

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

      4. distribute-frac-neg 90.1%

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

      5. neg-sub0 90.1%

         \[\leadsto x + y \cdot \frac{\color{blue}{0 - \left(z - t\right)}}{t} \]

      6. sub-neg 90.1%

         \[\leadsto x + y \cdot \frac{0 - \color{blue}{\left(z + \left(-t\right)\right)}}{t} \]

      7. +-commutative 90.1%

         \[\leadsto x + y \cdot \frac{0 - \color{blue}{\left(\left(-t\right) + z\right)}}{t} \]

      8. associate--r+ 90.1%

         \[\leadsto x + y \cdot \frac{\color{blue}{\left(0 - \left(-t\right)\right) - z}}{t} \]

      9. neg-sub0 90.1%

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

      10. remove-double-neg 90.1%

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

   5. Simplified 90.1%

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

   if -8.8000000000000001e45 < t < 1.29999999999999993e-57

   1. Initial program 97.0%

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

      1. clear-num 96.2%

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

      2. un-div-inv 96.3%

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

   4. Applied egg-rr 96.3%

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

      1. associate-/r/ 96.9%

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

   6. Applied egg-rr 96.9%

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

   7. Taylor expanded in z around inf 89.7%

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

   if 1.29999999999999993e-57 < t

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 72.9%

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

      1. +-commutative 72.9%

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

      2. associate-*r/ 72.9%

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

      3. mul-1-neg 72.9%

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

      4. distribute-lft-neg-out 72.9%

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

      5. *-commutative 72.9%

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

      6. *-lft-identity 72.9%

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

      7. times-frac 87.9%

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

      8. /-rgt-identity 87.9%

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

      9. distribute-neg-frac 87.9%

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

      10. distribute-neg-frac2 87.9%

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

      11. neg-sub0 87.9%

          \[\leadsto y \cdot \frac{t}{\color{blue}{0 - \left(a - t\right)}} + x \]

      12. sub-neg 87.9%

          \[\leadsto y \cdot \frac{t}{0 - \color{blue}{\left(a + \left(-t\right)\right)}} + x \]

      13. +-commutative 87.9%

          \[\leadsto y \cdot \frac{t}{0 - \color{blue}{\left(\left(-t\right) + a\right)}} + x \]

      14. associate--r+ 87.9%

          \[\leadsto y \cdot \frac{t}{\color{blue}{\left(0 - \left(-t\right)\right) - a}} + x \]

      15. neg-sub0 87.9%

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

      16. remove-double-neg 87.9%

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

   5. Simplified 87.9%

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

      1. clear-num 87.9%

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

      2. un-div-inv 87.9%

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

      3. div-sub 87.9%

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

      4. *-inverses 87.9%

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

   7. Applied egg-rr 87.9%

      \[\leadsto \color{blue}{\frac{y}{1 - \frac{a}{t}}} + x \]
3. Recombined 3 regimes into one program.

4. Final simplification 89.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.8 \cdot 10^{+45}:\\ \;\;\;\;x + y \cdot \frac{t - z}{t}\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{-57}:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{1 - \frac{a}{t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 86.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.7 \cdot 10^{+45}:\\ \;\;\;\;x + y \cdot \frac{t - z}{t}\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{-57}:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{t - a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -2.7e+45)
   (+ x (* y (/ (- t z) t)))
   (if (<= t 1.4e-57) (+ x (* z (/ y (- a t)))) (+ x (* y (/ t (- t a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.7e+45) {
		tmp = x + (y * ((t - z) / t));
	} else if (t <= 1.4e-57) {
		tmp = x + (z * (y / (a - t)));
	} else {
		tmp = x + (y * (t / (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 (t <= (-2.7d+45)) then
        tmp = x + (y * ((t - z) / t))
    else if (t <= 1.4d-57) then
        tmp = x + (z * (y / (a - t)))
    else
        tmp = x + (y * (t / (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 (t <= -2.7e+45) {
		tmp = x + (y * ((t - z) / t));
	} else if (t <= 1.4e-57) {
		tmp = x + (z * (y / (a - t)));
	} else {
		tmp = x + (y * (t / (t - a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -2.7e+45:
		tmp = x + (y * ((t - z) / t))
	elif t <= 1.4e-57:
		tmp = x + (z * (y / (a - t)))
	else:
		tmp = x + (y * (t / (t - a)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -2.7e+45)
		tmp = Float64(x + Float64(y * Float64(Float64(t - z) / t)));
	elseif (t <= 1.4e-57)
		tmp = Float64(x + Float64(z * Float64(y / Float64(a - t))));
	else
		tmp = Float64(x + Float64(y * Float64(t / Float64(t - a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -2.7e+45)
		tmp = x + (y * ((t - z) / t));
	elseif (t <= 1.4e-57)
		tmp = x + (z * (y / (a - t)));
	else
		tmp = x + (y * (t / (t - a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -2.7e+45], N[(x + N[(y * N[(N[(t - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.4e-57], N[(x + N[(z * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(t / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.69999999999999984e45

   1. Initial program 99.9%

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

   3. Taylor expanded in a around 0 71.1%

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

      1. mul-1-neg 71.1%

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

      2. associate-/l* 90.1%

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

      3. distribute-rgt-neg-in 90.1%

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

      4. distribute-frac-neg 90.1%

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

      5. neg-sub0 90.1%

         \[\leadsto x + y \cdot \frac{\color{blue}{0 - \left(z - t\right)}}{t} \]

      6. sub-neg 90.1%

         \[\leadsto x + y \cdot \frac{0 - \color{blue}{\left(z + \left(-t\right)\right)}}{t} \]

      7. +-commutative 90.1%

         \[\leadsto x + y \cdot \frac{0 - \color{blue}{\left(\left(-t\right) + z\right)}}{t} \]

      8. associate--r+ 90.1%

         \[\leadsto x + y \cdot \frac{\color{blue}{\left(0 - \left(-t\right)\right) - z}}{t} \]

      9. neg-sub0 90.1%

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

      10. remove-double-neg 90.1%

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

   5. Simplified 90.1%

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

   if -2.69999999999999984e45 < t < 1.4e-57

   1. Initial program 97.0%

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

      1. clear-num 96.2%

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

      2. un-div-inv 96.3%

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

   4. Applied egg-rr 96.3%

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

      1. associate-/r/ 96.9%

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

   6. Applied egg-rr 96.9%

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

   7. Taylor expanded in z around inf 89.7%

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

   if 1.4e-57 < t

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 72.9%

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

      1. +-commutative 72.9%

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

      2. associate-*r/ 72.9%

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

      3. mul-1-neg 72.9%

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

      4. distribute-lft-neg-out 72.9%

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

      5. *-commutative 72.9%

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

      6. *-lft-identity 72.9%

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

      7. times-frac 87.9%

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

      8. /-rgt-identity 87.9%

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

      9. distribute-neg-frac 87.9%

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

      10. distribute-neg-frac2 87.9%

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

      11. neg-sub0 87.9%

          \[\leadsto y \cdot \frac{t}{\color{blue}{0 - \left(a - t\right)}} + x \]

      12. sub-neg 87.9%

          \[\leadsto y \cdot \frac{t}{0 - \color{blue}{\left(a + \left(-t\right)\right)}} + x \]

      13. +-commutative 87.9%

          \[\leadsto y \cdot \frac{t}{0 - \color{blue}{\left(\left(-t\right) + a\right)}} + x \]

      14. associate--r+ 87.9%

          \[\leadsto y \cdot \frac{t}{\color{blue}{\left(0 - \left(-t\right)\right) - a}} + x \]

      15. neg-sub0 87.9%

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

      16. remove-double-neg 87.9%

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

   5. Simplified 87.9%

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

4. Final simplification 89.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.7 \cdot 10^{+45}:\\ \;\;\;\;x + y \cdot \frac{t - z}{t}\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{-57}:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{t - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 76.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4 \cdot 10^{+45} \lor \neg \left(t \leq 6.8 \cdot 10^{+38}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -4e+45) (not (<= t 6.8e+38))) (+ x y) (+ x (* y (/ z a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -4e+45) || !(t <= 6.8e+38)) {
		tmp = x + y;
	} else {
		tmp = x + (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 ((t <= (-4d+45)) .or. (.not. (t <= 6.8d+38))) then
        tmp = x + y
    else
        tmp = x + (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 ((t <= -4e+45) || !(t <= 6.8e+38)) {
		tmp = x + y;
	} else {
		tmp = x + (y * (z / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -4e+45) or not (t <= 6.8e+38):
		tmp = x + y
	else:
		tmp = x + (y * (z / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -4e+45) || !(t <= 6.8e+38))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(y * Float64(z / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -4e+45) || ~((t <= 6.8e+38)))
		tmp = x + y;
	else
		tmp = x + (y * (z / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -4e+45], N[Not[LessEqual[t, 6.8e+38]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.9999999999999997e45 or 6.79999999999999992e38 < t

   1. Initial program 99.9%

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

   3. Taylor expanded in t around inf 78.9%

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

      1. +-commutative 78.9%

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

   5. Simplified 78.9%

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

   if -3.9999999999999997e45 < t < 6.79999999999999992e38

   1. Initial program 97.5%

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

   3. Taylor expanded in t around 0 70.9%

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

      1. +-commutative 70.9%

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

      2. associate-/l* 72.7%

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

   5. Simplified 72.7%

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

4. Final simplification 75.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4 \cdot 10^{+45} \lor \neg \left(t \leq 6.8 \cdot 10^{+38}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 77.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.5 \cdot 10^{+44} \lor \neg \left(t \leq 1.65 \cdot 10^{+39}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -4.5e+44) (not (<= t 1.65e+39))) (+ x y) (+ x (* z (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -4.5e+44) || !(t <= 1.65e+39)) {
		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 <= (-4.5d+44)) .or. (.not. (t <= 1.65d+39))) 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 <= -4.5e+44) || !(t <= 1.65e+39)) {
		tmp = x + y;
	} else {
		tmp = x + (z * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -4.5e+44) or not (t <= 1.65e+39):
		tmp = x + y
	else:
		tmp = x + (z * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -4.5e+44) || !(t <= 1.65e+39))
		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 <= -4.5e+44) || ~((t <= 1.65e+39)))
		tmp = x + y;
	else
		tmp = x + (z * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -4.5e+44], N[Not[LessEqual[t, 1.65e+39]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -4.5e44 or 1.6500000000000001e39 < t

   1. Initial program 99.9%

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

   3. Taylor expanded in t around inf 78.9%

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

      1. +-commutative 78.9%

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

   5. Simplified 78.9%

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

   if -4.5e44 < t < 1.6500000000000001e39

   1. Initial program 97.5%

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

      1. clear-num 96.9%

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

      2. un-div-inv 96.9%

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

   4. Applied egg-rr 96.9%

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

      1. associate-/r/ 96.8%

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

   6. Applied egg-rr 96.8%

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

   7. Taylor expanded in z around inf 86.6%

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

   8. Taylor expanded in a around inf 71.4%

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

4. Final simplification 74.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.5 \cdot 10^{+44} \lor \neg \left(t \leq 1.65 \cdot 10^{+39}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 64.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.3 \cdot 10^{+44} \lor \neg \left(t \leq 1.4 \cdot 10^{-92}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -3.3e+44) (not (<= t 1.4e-92))) (+ x y) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -3.3e+44) || !(t <= 1.4e-92)) {
		tmp = x + y;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-3.3d+44)) .or. (.not. (t <= 1.4d-92))) then
        tmp = x + y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -3.3e+44) || !(t <= 1.4e-92)) {
		tmp = x + y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -3.3e+44) or not (t <= 1.4e-92):
		tmp = x + y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -3.3e+44) || !(t <= 1.4e-92))
		tmp = Float64(x + y);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -3.3e+44) || ~((t <= 1.4e-92)))
		tmp = x + y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -3.3e+44], N[Not[LessEqual[t, 1.4e-92]], $MachinePrecision]], N[(x + y), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if t < -3.30000000000000013e44 or 1.4e-92 < t

   1. Initial program 99.9%

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

   3. Taylor expanded in t around inf 72.0%

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

      1. +-commutative 72.0%

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

   5. Simplified 72.0%

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

   if -3.30000000000000013e44 < t < 1.4e-92

   1. Initial program 96.8%

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

   3. Taylor expanded in x around inf 49.3%

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

4. Final simplification 61.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.3 \cdot 10^{+44} \lor \neg \left(t \leq 1.4 \cdot 10^{-92}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 51.5% 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 98.4%

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

3. Taylor expanded in x around inf 48.7%

   \[\leadsto \color{blue}{x} \]
4. Add Preprocessing

Developer Target 1: 99.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;y < -8.508084860551241 \cdot 10^{-17}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y < 2.894426862792089 \cdot 10^{-49}:\\ \;\;\;\;x + \left(y \cdot \left(z - t\right)\right) \cdot \frac{1}{a - t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* y (/ (- z t) (- a t))))))
   (if (< y -8.508084860551241e-17)
     t_1
     (if (< y 2.894426862792089e-49)
       (+ x (* (* y (- z t)) (/ 1.0 (- a t))))
       t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * ((z - t) / (a - t)));
	double tmp;
	if (y < -8.508084860551241e-17) {
		tmp = t_1;
	} else if (y < 2.894426862792089e-49) {
		tmp = x + ((y * (z - t)) * (1.0 / (a - t)));
	} 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 * ((z - t) / (a - t)))
    if (y < (-8.508084860551241d-17)) then
        tmp = t_1
    else if (y < 2.894426862792089d-49) then
        tmp = x + ((y * (z - t)) * (1.0d0 / (a - t)))
    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 * ((z - t) / (a - t)));
	double tmp;
	if (y < -8.508084860551241e-17) {
		tmp = t_1;
	} else if (y < 2.894426862792089e-49) {
		tmp = x + ((y * (z - t)) * (1.0 / (a - t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y * ((z - t) / (a - t)))
	tmp = 0
	if y < -8.508084860551241e-17:
		tmp = t_1
	elif y < 2.894426862792089e-49:
		tmp = x + ((y * (z - t)) * (1.0 / (a - t)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y * Float64(Float64(z - t) / Float64(a - t))))
	tmp = 0.0
	if (y < -8.508084860551241e-17)
		tmp = t_1;
	elseif (y < 2.894426862792089e-49)
		tmp = Float64(x + Float64(Float64(y * Float64(z - t)) * Float64(1.0 / Float64(a - t))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y * ((z - t) / (a - t)));
	tmp = 0.0;
	if (y < -8.508084860551241e-17)
		tmp = t_1;
	elseif (y < 2.894426862792089e-49)
		tmp = x + ((y * (z - t)) * (1.0 / (a - t)));
	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[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[y, -8.508084860551241e-17], t$95$1, If[Less[y, 2.894426862792089e-49], N[(x + N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] * N[(1.0 / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Reproduce

herbie shell --seed 2024135 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisLine from plot-0.2.3.4, B"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< y -8508084860551241/100000000000000000000000000000000) (+ x (* y (/ (- z t) (- a t)))) (if (< y 2894426862792089/10000000000000000000000000000000000000000000000000000000000000000) (+ x (* (* y (- z t)) (/ 1 (- a t)))) (+ x (* y (/ (- z t) (- a t)))))))

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