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

Percentage Accurate: 85.2% → 98.4%

Time: 8.1s

Alternatives: 11

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: 85.2% 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: 98.4% 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 86.3%

   \[x + \frac{y \cdot \left(z - t\right)}{a - t} \]
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. Final simplification 98.4%

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

Alternative 2: 76.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.05 \cdot 10^{+14}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 9.8 \cdot 10^{-98}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 5.6 \cdot 10^{+41}:\\ \;\;\;\;x - \frac{y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.05e+14)
   (+ x y)
   (if (<= t 9.8e-98)
     (+ x (/ y (/ a z)))
     (if (<= t 5.6e+41) (- x (/ y (/ t z))) (+ x y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.05e+14) {
		tmp = x + y;
	} else if (t <= 9.8e-98) {
		tmp = x + (y / (a / z));
	} else if (t <= 5.6e+41) {
		tmp = x - (y / (t / z));
	} 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) :: tmp
    if (t <= (-1.05d+14)) then
        tmp = x + y
    else if (t <= 9.8d-98) then
        tmp = x + (y / (a / z))
    else if (t <= 5.6d+41) then
        tmp = x - (y / (t / z))
    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 tmp;
	if (t <= -1.05e+14) {
		tmp = x + y;
	} else if (t <= 9.8e-98) {
		tmp = x + (y / (a / z));
	} else if (t <= 5.6e+41) {
		tmp = x - (y / (t / z));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.05e+14:
		tmp = x + y
	elif t <= 9.8e-98:
		tmp = x + (y / (a / z))
	elif t <= 5.6e+41:
		tmp = x - (y / (t / z))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.05e+14)
		tmp = Float64(x + y);
	elseif (t <= 9.8e-98)
		tmp = Float64(x + Float64(y / Float64(a / z)));
	elseif (t <= 5.6e+41)
		tmp = Float64(x - Float64(y / Float64(t / z)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.05e+14)
		tmp = x + y;
	elseif (t <= 9.8e-98)
		tmp = x + (y / (a / z));
	elseif (t <= 5.6e+41)
		tmp = x - (y / (t / z));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.05e+14], N[(x + y), $MachinePrecision], If[LessEqual[t, 9.8e-98], N[(x + N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.6e+41], N[(x - N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.05e14 or 5.5999999999999999e41 < t

   1. Initial program 77.6%

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

      1. associate-*l/ 95.2%

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

   3. Simplified 95.2%

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

   4. Taylor expanded in t around inf 83.7%

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

   if -1.05e14 < t < 9.80000000000000028e-98

   1. Initial program 92.1%

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

      1. associate-*l/ 98.2%

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

   3. Simplified 98.2%

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

   4. Taylor expanded in t around 0 74.5%

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

      1. associate-/l* 80.5%

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

   6. Simplified 80.5%

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

   if 9.80000000000000028e-98 < t < 5.5999999999999999e41

   1. Initial program 97.0%

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

      1. associate-*l/ 94.4%

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

   3. Simplified 94.4%

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

   4. Taylor expanded in z around inf 81.8%

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

      1. associate-/l* 84.7%

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

   6. Simplified 84.7%

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

   7. Taylor expanded in a around 0 73.0%

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

      1. +-commutative 73.0%

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

      2. mul-1-neg 73.0%

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

      3. unsub-neg 73.0%

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

      4. associate-/l* 73.1%

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

   9. Simplified 73.1%

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

4. Final simplification 81.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.05 \cdot 10^{+14}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 9.8 \cdot 10^{-98}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 5.6 \cdot 10^{+41}:\\ \;\;\;\;x - \frac{y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 3: 77.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -42000000000000:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 5.3 \cdot 10^{-98}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{+41}:\\ \;\;\;\;x - \frac{y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -42000000000000.0)
   (+ x y)
   (if (<= t 5.3e-98)
     (+ x (* (- z t) (/ y a)))
     (if (<= t 5.5e+41) (- x (/ y (/ t z))) (+ x y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -42000000000000.0) {
		tmp = x + y;
	} else if (t <= 5.3e-98) {
		tmp = x + ((z - t) * (y / a));
	} else if (t <= 5.5e+41) {
		tmp = x - (y / (t / z));
	} 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) :: tmp
    if (t <= (-42000000000000.0d0)) then
        tmp = x + y
    else if (t <= 5.3d-98) then
        tmp = x + ((z - t) * (y / a))
    else if (t <= 5.5d+41) then
        tmp = x - (y / (t / z))
    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 tmp;
	if (t <= -42000000000000.0) {
		tmp = x + y;
	} else if (t <= 5.3e-98) {
		tmp = x + ((z - t) * (y / a));
	} else if (t <= 5.5e+41) {
		tmp = x - (y / (t / z));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -42000000000000.0:
		tmp = x + y
	elif t <= 5.3e-98:
		tmp = x + ((z - t) * (y / a))
	elif t <= 5.5e+41:
		tmp = x - (y / (t / z))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -42000000000000.0)
		tmp = Float64(x + y);
	elseif (t <= 5.3e-98)
		tmp = Float64(x + Float64(Float64(z - t) * Float64(y / a)));
	elseif (t <= 5.5e+41)
		tmp = Float64(x - Float64(y / Float64(t / z)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -42000000000000.0)
		tmp = x + y;
	elseif (t <= 5.3e-98)
		tmp = x + ((z - t) * (y / a));
	elseif (t <= 5.5e+41)
		tmp = x - (y / (t / z));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -42000000000000.0], N[(x + y), $MachinePrecision], If[LessEqual[t, 5.3e-98], N[(x + N[(N[(z - t), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.5e+41], N[(x - N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.2e13 or 5.5000000000000003e41 < t

   1. Initial program 77.6%

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

      1. associate-*l/ 95.2%

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

   3. Simplified 95.2%

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

   4. Taylor expanded in t around inf 83.7%

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

   if -4.2e13 < t < 5.30000000000000031e-98

   1. Initial program 92.1%

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

      1. associate-*l/ 98.2%

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

   3. Simplified 98.2%

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

   4. Taylor expanded in a around inf 81.8%

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

   if 5.30000000000000031e-98 < t < 5.5000000000000003e41

   1. Initial program 97.0%

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

      1. associate-*l/ 94.4%

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

   3. Simplified 94.4%

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

   4. Taylor expanded in z around inf 81.8%

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

      1. associate-/l* 84.7%

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

   6. Simplified 84.7%

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

   7. Taylor expanded in a around 0 73.0%

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

      1. +-commutative 73.0%

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

      2. mul-1-neg 73.0%

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

      3. unsub-neg 73.0%

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

      4. associate-/l* 73.1%

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

   9. Simplified 73.1%

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

4. Final simplification 81.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -42000000000000:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 5.3 \cdot 10^{-98}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{+41}:\\ \;\;\;\;x - \frac{y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 4: 87.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5.8 \cdot 10^{+19} \lor \neg \left(t \leq 4.9 \cdot 10^{+28}\right):\\ \;\;\;\;x + \frac{y}{\frac{t - a}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a - t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -5.8e+19) (not (<= t 4.9e+28)))
   (+ x (/ y (/ (- t a) t)))
   (+ x (/ y (/ (- a t) z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -5.8e+19) || !(t <= 4.9e+28)) {
		tmp = x + (y / ((t - a) / t));
	} else {
		tmp = x + (y / ((a - t) / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-5.8d+19)) .or. (.not. (t <= 4.9d+28))) then
        tmp = x + (y / ((t - a) / t))
    else
        tmp = x + (y / ((a - t) / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -5.8e+19) || !(t <= 4.9e+28)) {
		tmp = x + (y / ((t - a) / t));
	} else {
		tmp = x + (y / ((a - t) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -5.8e+19) or not (t <= 4.9e+28):
		tmp = x + (y / ((t - a) / t))
	else:
		tmp = x + (y / ((a - t) / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -5.8e+19) || !(t <= 4.9e+28))
		tmp = Float64(x + Float64(y / Float64(Float64(t - a) / t)));
	else
		tmp = Float64(x + Float64(y / Float64(Float64(a - t) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -5.8e+19) || ~((t <= 4.9e+28)))
		tmp = x + (y / ((t - a) / t));
	else
		tmp = x + (y / ((a - t) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -5.8e+19], N[Not[LessEqual[t, 4.9e+28]], $MachinePrecision]], N[(x + N[(y / N[(N[(t - a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(N[(a - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -5.8e19 or 4.8999999999999996e28 < t

   1. Initial program 77.9%

      \[x + \frac{y \cdot \left(z - t\right)}{a - t} \]
   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 0 88.0%

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

      1. associate-*r/ 88.0%

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

      2. neg-mul-1 88.0%

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

      3. neg-sub0 88.0%

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

      4. associate--r- 88.0%

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

      5. neg-sub0 88.0%

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

   6. Simplified 88.0%

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

   7. Taylor expanded in y around 0 69.6%

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

      1. associate-/l* 88.0%

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

   9. Simplified 88.0%

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

   if -5.8e19 < t < 4.8999999999999996e28

   1. Initial program 93.2%

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

      1. associate-*l/ 97.3%

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

   3. Simplified 97.3%

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

   4. Taylor expanded in z around inf 86.8%

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

      1. associate-/l* 91.4%

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

   6. Simplified 91.4%

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

4. Final simplification 89.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.8 \cdot 10^{+19} \lor \neg \left(t \leq 4.9 \cdot 10^{+28}\right):\\ \;\;\;\;x + \frac{y}{\frac{t - a}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a - t}{z}}\\ \end{array} \]

Alternative 5: 87.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -8.6 \cdot 10^{+21} \lor \neg \left(t \leq 1.55 \cdot 10^{+32}\right):\\ \;\;\;\;x - \frac{y}{\frac{t}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a - t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -8.6e+21) (not (<= t 1.55e+32)))
   (- x (/ y (/ t (- z t))))
   (+ x (/ y (/ (- a t) z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -8.6e+21) || !(t <= 1.55e+32)) {
		tmp = x - (y / (t / (z - t)));
	} else {
		tmp = x + (y / ((a - t) / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-8.6d+21)) .or. (.not. (t <= 1.55d+32))) then
        tmp = x - (y / (t / (z - t)))
    else
        tmp = x + (y / ((a - t) / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -8.6e+21) || !(t <= 1.55e+32)) {
		tmp = x - (y / (t / (z - t)));
	} else {
		tmp = x + (y / ((a - t) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -8.6e+21) or not (t <= 1.55e+32):
		tmp = x - (y / (t / (z - t)))
	else:
		tmp = x + (y / ((a - t) / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -8.6e+21) || !(t <= 1.55e+32))
		tmp = Float64(x - Float64(y / Float64(t / Float64(z - t))));
	else
		tmp = Float64(x + Float64(y / Float64(Float64(a - t) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -8.6e+21) || ~((t <= 1.55e+32)))
		tmp = x - (y / (t / (z - t)));
	else
		tmp = x + (y / ((a - t) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -8.6e+21], N[Not[LessEqual[t, 1.55e+32]], $MachinePrecision]], N[(x - N[(y / N[(t / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(N[(a - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -8.6e21 or 1.54999999999999997e32 < t

   1. Initial program 77.6%

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

      1. associate-*l/ 95.2%

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

   3. Simplified 95.2%

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

   4. Taylor expanded in a around 0 73.3%

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

      1. +-commutative 73.3%

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

      2. mul-1-neg 73.3%

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

      3. unsub-neg 73.3%

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

      4. *-commutative 73.3%

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

      5. associate-/l* 93.2%

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

   6. Simplified 93.2%

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

   if -8.6e21 < t < 1.54999999999999997e32

   1. Initial program 93.2%

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

      1. associate-*l/ 97.4%

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

   3. Simplified 97.4%

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

   4. Taylor expanded in z around inf 85.8%

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

      1. associate-/l* 90.4%

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

   6. Simplified 90.4%

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

4. Final simplification 91.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.6 \cdot 10^{+21} \lor \neg \left(t \leq 1.55 \cdot 10^{+32}\right):\\ \;\;\;\;x - \frac{y}{\frac{t}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a - t}{z}}\\ \end{array} \]

Alternative 6: 84.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.2 \cdot 10^{+23}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 6.1 \cdot 10^{+41}:\\ \;\;\;\;x + \frac{y}{\frac{a - t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -3.2e+23)
   (+ x y)
   (if (<= t 6.1e+41) (+ x (/ y (/ (- a t) z))) (+ x y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -3.2e+23) {
		tmp = x + y;
	} else if (t <= 6.1e+41) {
		tmp = x + (y / ((a - t) / z));
	} 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) :: tmp
    if (t <= (-3.2d+23)) then
        tmp = x + y
    else if (t <= 6.1d+41) then
        tmp = x + (y / ((a - t) / z))
    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 tmp;
	if (t <= -3.2e+23) {
		tmp = x + y;
	} else if (t <= 6.1e+41) {
		tmp = x + (y / ((a - t) / z));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -3.2e+23:
		tmp = x + y
	elif t <= 6.1e+41:
		tmp = x + (y / ((a - t) / z))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -3.2e+23)
		tmp = Float64(x + y);
	elseif (t <= 6.1e+41)
		tmp = Float64(x + Float64(y / Float64(Float64(a - t) / z)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -3.2e+23)
		tmp = x + y;
	elseif (t <= 6.1e+41)
		tmp = x + (y / ((a - t) / z));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -3.2e+23], N[(x + y), $MachinePrecision], If[LessEqual[t, 6.1e+41], N[(x + N[(y / N[(N[(a - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < -3.2e23 or 6.09999999999999998e41 < t

   1. Initial program 77.2%

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

      1. associate-*l/ 95.1%

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

   3. Simplified 95.1%

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

   4. Taylor expanded in t around inf 84.3%

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

   if -3.2e23 < t < 6.09999999999999998e41

   1. Initial program 93.3%

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

      1. associate-*l/ 97.4%

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

   3. Simplified 97.4%

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

   4. Taylor expanded in z around inf 86.0%

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

      1. associate-/l* 90.6%

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

   6. Simplified 90.6%

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

4. Final simplification 87.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.2 \cdot 10^{+23}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 6.1 \cdot 10^{+41}:\\ \;\;\;\;x + \frac{y}{\frac{a - t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 7: 76.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -900000000000 \lor \neg \left(t \leq 2 \cdot 10^{-11}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -900000000000.0) (not (<= t 2e-11)))
   (+ x y)
   (+ x (* y (/ z a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -900000000000.0) || !(t <= 2e-11)) {
		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 <= (-900000000000.0d0)) .or. (.not. (t <= 2d-11))) 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 <= -900000000000.0) || !(t <= 2e-11)) {
		tmp = x + y;
	} else {
		tmp = x + (y * (z / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -900000000000.0) or not (t <= 2e-11):
		tmp = x + y
	else:
		tmp = x + (y * (z / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -900000000000.0) || !(t <= 2e-11))
		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 <= -900000000000.0) || ~((t <= 2e-11)))
		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, -900000000000.0], N[Not[LessEqual[t, 2e-11]], $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 < -9e11 or 1.99999999999999988e-11 < t

   1. Initial program 80.3%

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

      1. associate-*l/ 95.8%

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

   3. Simplified 95.8%

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

   4. Taylor expanded in t around inf 80.4%

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

   if -9e11 < t < 1.99999999999999988e-11

   1. Initial program 92.4%

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

      1. associate-*l/ 97.0%

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

   3. Simplified 97.0%

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

      1. *-commutative 97.0%

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

      2. clear-num 97.0%

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

      3. un-div-inv 97.3%

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

   5. Applied egg-rr 97.3%

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

   6. Taylor expanded in t around 0 71.5%

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

      1. associate-*r/ 77.0%

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

   8. Simplified 77.0%

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

4. Final simplification 78.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -900000000000 \lor \neg \left(t \leq 2 \cdot 10^{-11}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \end{array} \]

Alternative 8: 77.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5000000000 \lor \neg \left(t \leq 9.8 \cdot 10^{-11}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -5000000000.0) (not (<= t 9.8e-11)))
   (+ x y)
   (+ x (/ y (/ a z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -5000000000.0) || !(t <= 9.8e-11)) {
		tmp = x + y;
	} else {
		tmp = x + (y / (a / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-5000000000.0d0)) .or. (.not. (t <= 9.8d-11))) then
        tmp = x + y
    else
        tmp = x + (y / (a / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -5000000000.0) || !(t <= 9.8e-11)) {
		tmp = x + y;
	} else {
		tmp = x + (y / (a / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -5000000000.0) or not (t <= 9.8e-11):
		tmp = x + y
	else:
		tmp = x + (y / (a / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -5000000000.0) || !(t <= 9.8e-11))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(y / Float64(a / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -5000000000.0) || ~((t <= 9.8e-11)))
		tmp = x + y;
	else
		tmp = x + (y / (a / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -5000000000.0], N[Not[LessEqual[t, 9.8e-11]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -5e9 or 9.7999999999999998e-11 < t

   1. Initial program 80.3%

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

      1. associate-*l/ 95.8%

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

   3. Simplified 95.8%

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

   4. Taylor expanded in t around inf 80.4%

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

   if -5e9 < t < 9.7999999999999998e-11

   1. Initial program 92.4%

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

      1. associate-*l/ 97.0%

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

   3. Simplified 97.0%

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

   4. Taylor expanded in t around 0 71.5%

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

      1. associate-/l* 77.5%

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

   6. Simplified 77.5%

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

4. Final simplification 79.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5000000000 \lor \neg \left(t \leq 9.8 \cdot 10^{-11}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \end{array} \]

Alternative 9: 95.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 86.3%

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

   1. associate-*l/ 96.4%

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

3. Simplified 96.4%

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

4. Final simplification 96.4%

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

Alternative 10: 63.2% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.6 \cdot 10^{-136}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{+41}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -2.6e-136) (+ x y) (if (<= t 5.2e+41) x (+ x y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.6e-136) {
		tmp = x + y;
	} else if (t <= 5.2e+41) {
		tmp = x;
	} 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) :: tmp
    if (t <= (-2.6d-136)) then
        tmp = x + y
    else if (t <= 5.2d+41) then
        tmp = x
    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 tmp;
	if (t <= -2.6e-136) {
		tmp = x + y;
	} else if (t <= 5.2e+41) {
		tmp = x;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -2.6e-136:
		tmp = x + y
	elif t <= 5.2e+41:
		tmp = x
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -2.6e-136)
		tmp = Float64(x + y);
	elseif (t <= 5.2e+41)
		tmp = x;
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -2.6e-136)
		tmp = x + y;
	elseif (t <= 5.2e+41)
		tmp = x;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -2.6e-136], N[(x + y), $MachinePrecision], If[LessEqual[t, 5.2e+41], x, N[(x + y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < -2.59999999999999997e-136 or 5.2000000000000001e41 < t

   1. Initial program 81.0%

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

      1. associate-*l/ 95.7%

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

   3. Simplified 95.7%

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

   4. Taylor expanded in t around inf 73.7%

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

   if -2.59999999999999997e-136 < t < 5.2000000000000001e41

   1. Initial program 93.7%

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

      1. associate-*l/ 97.4%

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

   3. Simplified 97.4%

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

   4. Taylor expanded in x around inf 60.3%

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

4. Final simplification 68.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.6 \cdot 10^{-136}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{+41}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 11: 50.4% accurate, 11.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 86.3%

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

   1. associate-*l/ 96.4%

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

3. Simplified 96.4%

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

4. Taylor expanded in x around inf 51.9%

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

5. Final simplification 51.9%

   \[\leadsto x \]

Developer target: 98.4% 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 2023200 
(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))))