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

Percentage Accurate: 98.0% → 98.8%

Time: 8.6s

Alternatives: 13

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 98.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - z}{a - z}\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;x + \frac{y \cdot t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot t\_1\\ \end{array} \end{array} \]

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 52.7%

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

   3. Taylor expanded in t around inf 99.7%

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

      1. mul-1-neg 99.7%

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

      2. associate-/l* 99.7%

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

   5. Simplified 99.7%

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

   6. Taylor expanded in x around 0 99.7%

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

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

   1. Initial program 98.7%

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

4. Final simplification 98.8%

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

Alternative 2: 81.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{-17} \lor \neg \left(z \leq 4 \cdot 10^{-29}\right):\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1e-17) (not (<= z 4e-29)))
   (+ x (* y (/ z (- z a))))
   (+ x (* t (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1e-17) || !(z <= 4e-29)) {
		tmp = x + (y * (z / (z - a)));
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-1d-17)) .or. (.not. (z <= 4d-29))) then
        tmp = x + (y * (z / (z - a)))
    else
        tmp = x + (t * (y / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1e-17) || !(z <= 4e-29)) {
		tmp = x + (y * (z / (z - a)));
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1e-17) or not (z <= 4e-29):
		tmp = x + (y * (z / (z - a)))
	else:
		tmp = x + (t * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1e-17) || !(z <= 4e-29))
		tmp = Float64(x + Float64(y * Float64(z / Float64(z - a))));
	else
		tmp = Float64(x + Float64(t * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1e-17) || ~((z <= 4e-29)))
		tmp = x + (y * (z / (z - a)));
	else
		tmp = x + (t * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1e-17], N[Not[LessEqual[z, 4e-29]], $MachinePrecision]], N[(x + N[(y * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.00000000000000007e-17 or 3.99999999999999977e-29 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in t around 0 64.5%

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

      1. associate-/l* 86.9%

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

   5. Simplified 86.9%

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

   if -1.00000000000000007e-17 < z < 3.99999999999999977e-29

   1. Initial program 94.0%

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

   3. Taylor expanded in z around 0 75.3%

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

      1. associate-/l* 81.8%

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

   5. Simplified 81.8%

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

4. Final simplification 84.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{-17} \lor \neg \left(z \leq 4 \cdot 10^{-29}\right):\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 81.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.6 \cdot 10^{+44} \lor \neg \left(z \leq 2.6 \cdot 10^{-9}\right):\\ \;\;\;\;x + y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -5.6e+44) (not (<= z 2.6e-9)))
   (+ x (* y (- 1.0 (/ t z))))
   (+ x (* t (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -5.6e+44) || !(z <= 2.6e-9)) {
		tmp = x + (y * (1.0 - (t / z)));
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-5.6d+44)) .or. (.not. (z <= 2.6d-9))) then
        tmp = x + (y * (1.0d0 - (t / z)))
    else
        tmp = x + (t * (y / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -5.6e+44) || !(z <= 2.6e-9)) {
		tmp = x + (y * (1.0 - (t / z)));
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -5.6e+44) or not (z <= 2.6e-9):
		tmp = x + (y * (1.0 - (t / z)))
	else:
		tmp = x + (t * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -5.6e+44) || !(z <= 2.6e-9))
		tmp = Float64(x + Float64(y * Float64(1.0 - Float64(t / z))));
	else
		tmp = Float64(x + Float64(t * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -5.6e+44) || ~((z <= 2.6e-9)))
		tmp = x + (y * (1.0 - (t / z)));
	else
		tmp = x + (t * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -5.6e+44], N[Not[LessEqual[z, 2.6e-9]], $MachinePrecision]], N[(x + N[(y * N[(1.0 - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.6000000000000002e44 or 2.6000000000000001e-9 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in a around 0 62.6%

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

      1. associate-/l* 87.2%

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

      2. div-sub 87.2%

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

      3. *-inverses 87.2%

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

   5. Simplified 87.2%

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

   if -5.6000000000000002e44 < z < 2.6000000000000001e-9

   1. Initial program 94.5%

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

   3. Taylor expanded in z around 0 73.9%

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

      1. associate-/l* 79.8%

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

   5. Simplified 79.8%

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

4. Final simplification 83.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.6 \cdot 10^{+44} \lor \neg \left(z \leq 2.6 \cdot 10^{-9}\right):\\ \;\;\;\;x + y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 87.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{-15}:\\ \;\;\;\;x + \frac{y}{1 - \frac{a}{z}}\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{+14}:\\ \;\;\;\;x + t \cdot \frac{y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -7.2e-15)
   (+ x (/ y (- 1.0 (/ a z))))
   (if (<= z 1.55e+14) (+ x (* t (/ y (- a z)))) (+ x (* y (/ z (- z a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -7.2e-15) {
		tmp = x + (y / (1.0 - (a / z)));
	} else if (z <= 1.55e+14) {
		tmp = x + (t * (y / (a - z)));
	} else {
		tmp = x + (y * (z / (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 <= (-7.2d-15)) then
        tmp = x + (y / (1.0d0 - (a / z)))
    else if (z <= 1.55d+14) then
        tmp = x + (t * (y / (a - z)))
    else
        tmp = x + (y * (z / (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 <= -7.2e-15) {
		tmp = x + (y / (1.0 - (a / z)));
	} else if (z <= 1.55e+14) {
		tmp = x + (t * (y / (a - z)));
	} else {
		tmp = x + (y * (z / (z - a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -7.2e-15:
		tmp = x + (y / (1.0 - (a / z)))
	elif z <= 1.55e+14:
		tmp = x + (t * (y / (a - z)))
	else:
		tmp = x + (y * (z / (z - a)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -7.2e-15)
		tmp = Float64(x + Float64(y / Float64(1.0 - Float64(a / z))));
	elseif (z <= 1.55e+14)
		tmp = Float64(x + Float64(t * Float64(y / Float64(a - z))));
	else
		tmp = Float64(x + Float64(y * Float64(z / Float64(z - a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -7.2e-15)
		tmp = x + (y / (1.0 - (a / z)));
	elseif (z <= 1.55e+14)
		tmp = x + (t * (y / (a - z)));
	else
		tmp = x + (y * (z / (z - a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -7.2e-15], N[(x + N[(y / N[(1.0 - N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.55e+14], N[(x + N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.2000000000000002e-15

   1. Initial program 99.8%

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

      1. clear-num 99.9%

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

      2. un-div-inv 99.9%

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

   4. Applied egg-rr 99.9%

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

   5. Taylor expanded in t around 0 85.7%

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

      1. div-sub 85.7%

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

      2. *-inverses 85.7%

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

   7. Simplified 85.7%

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

   if -7.2000000000000002e-15 < z < 1.55e14

   1. Initial program 94.4%

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

   3. Taylor expanded in t around inf 87.9%

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

      1. mul-1-neg 87.9%

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

      2. associate-/l* 93.4%

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

   5. Simplified 93.4%

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

   if 1.55e14 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in t around 0 66.0%

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

      1. associate-/l* 90.4%

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

   5. Simplified 90.4%

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

4. Final simplification 90.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{-15}:\\ \;\;\;\;x + \frac{y}{1 - \frac{a}{z}}\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{+14}:\\ \;\;\;\;x + t \cdot \frac{y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 86.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{-16}:\\ \;\;\;\;x + \frac{y}{1 - \frac{a}{z}}\\ \mathbf{elif}\;z \leq 55000000000000:\\ \;\;\;\;x + \frac{y \cdot t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.15e-16)
   (+ x (/ y (- 1.0 (/ a z))))
   (if (<= z 55000000000000.0)
     (+ x (/ (* y t) (- a z)))
     (+ x (* y (/ z (- z a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.15e-16) {
		tmp = x + (y / (1.0 - (a / z)));
	} else if (z <= 55000000000000.0) {
		tmp = x + ((y * t) / (a - z));
	} else {
		tmp = x + (y * (z / (z - a)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-1.15d-16)) then
        tmp = x + (y / (1.0d0 - (a / z)))
    else if (z <= 55000000000000.0d0) then
        tmp = x + ((y * t) / (a - z))
    else
        tmp = x + (y * (z / (z - a)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.15e-16) {
		tmp = x + (y / (1.0 - (a / z)));
	} else if (z <= 55000000000000.0) {
		tmp = x + ((y * t) / (a - z));
	} else {
		tmp = x + (y * (z / (z - a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.15e-16:
		tmp = x + (y / (1.0 - (a / z)))
	elif z <= 55000000000000.0:
		tmp = x + ((y * t) / (a - z))
	else:
		tmp = x + (y * (z / (z - a)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.15e-16)
		tmp = Float64(x + Float64(y / Float64(1.0 - Float64(a / z))));
	elseif (z <= 55000000000000.0)
		tmp = Float64(x + Float64(Float64(y * t) / Float64(a - z)));
	else
		tmp = Float64(x + Float64(y * Float64(z / Float64(z - a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.15e-16)
		tmp = x + (y / (1.0 - (a / z)));
	elseif (z <= 55000000000000.0)
		tmp = x + ((y * t) / (a - z));
	else
		tmp = x + (y * (z / (z - a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.15e-16], N[(x + N[(y / N[(1.0 - N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 55000000000000.0], N[(x + N[(N[(y * t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.15e-16

   1. Initial program 99.8%

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

      1. clear-num 99.9%

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

      2. un-div-inv 99.9%

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

   4. Applied egg-rr 99.9%

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

   5. Taylor expanded in t around 0 85.7%

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

      1. div-sub 85.7%

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

      2. *-inverses 85.7%

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

   7. Simplified 85.7%

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

   if -1.15e-16 < z < 5.5e13

   1. Initial program 94.4%

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

   3. Taylor expanded in t around inf 87.9%

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

      1. mul-1-neg 87.9%

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

      2. associate-/l* 93.4%

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

   5. Simplified 93.4%

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

   6. Taylor expanded in x around 0 87.9%

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

   if 5.5e13 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in t around 0 66.0%

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

      1. associate-/l* 90.4%

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

   5. Simplified 90.4%

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

4. Final simplification 87.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{-16}:\\ \;\;\;\;x + \frac{y}{1 - \frac{a}{z}}\\ \mathbf{elif}\;z \leq 55000000000000:\\ \;\;\;\;x + \frac{y \cdot t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 81.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.7 \cdot 10^{-15}:\\ \;\;\;\;x + \frac{y}{1 - \frac{a}{z}}\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{-23}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -5.7e-15)
   (+ x (/ y (- 1.0 (/ a z))))
   (if (<= z 1.35e-23) (+ x (* t (/ y a))) (+ x (* y (/ z (- z a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -5.7e-15) {
		tmp = x + (y / (1.0 - (a / z)));
	} else if (z <= 1.35e-23) {
		tmp = x + (t * (y / a));
	} else {
		tmp = x + (y * (z / (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 <= (-5.7d-15)) then
        tmp = x + (y / (1.0d0 - (a / z)))
    else if (z <= 1.35d-23) then
        tmp = x + (t * (y / a))
    else
        tmp = x + (y * (z / (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 <= -5.7e-15) {
		tmp = x + (y / (1.0 - (a / z)));
	} else if (z <= 1.35e-23) {
		tmp = x + (t * (y / a));
	} else {
		tmp = x + (y * (z / (z - a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -5.7e-15:
		tmp = x + (y / (1.0 - (a / z)))
	elif z <= 1.35e-23:
		tmp = x + (t * (y / a))
	else:
		tmp = x + (y * (z / (z - a)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -5.7e-15)
		tmp = Float64(x + Float64(y / Float64(1.0 - Float64(a / z))));
	elseif (z <= 1.35e-23)
		tmp = Float64(x + Float64(t * Float64(y / a)));
	else
		tmp = Float64(x + Float64(y * Float64(z / Float64(z - a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -5.7e-15)
		tmp = x + (y / (1.0 - (a / z)));
	elseif (z <= 1.35e-23)
		tmp = x + (t * (y / a));
	else
		tmp = x + (y * (z / (z - a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -5.7e-15], N[(x + N[(y / N[(1.0 - N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.35e-23], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.7000000000000003e-15

   1. Initial program 99.8%

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

      1. clear-num 99.9%

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

      2. un-div-inv 99.9%

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

   4. Applied egg-rr 99.9%

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

   5. Taylor expanded in t around 0 85.7%

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

      1. div-sub 85.7%

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

      2. *-inverses 85.7%

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

   7. Simplified 85.7%

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

   if -5.7000000000000003e-15 < z < 1.34999999999999992e-23

   1. Initial program 94.0%

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

   3. Taylor expanded in z around 0 75.3%

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

      1. associate-/l* 81.8%

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

   5. Simplified 81.8%

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

   if 1.34999999999999992e-23 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in t around 0 67.4%

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

      1. associate-/l* 88.4%

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

   5. Simplified 88.4%

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

Alternative 7: 74.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{+153} \lor \neg \left(z \leq 3.2 \cdot 10^{-9}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.9e+153) (not (<= z 3.2e-9))) (+ x y) (+ x (* t (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.9e+153) || !(z <= 3.2e-9)) {
		tmp = x + y;
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-1.9d+153)) .or. (.not. (z <= 3.2d-9))) then
        tmp = x + y
    else
        tmp = x + (t * (y / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.9e+153) || !(z <= 3.2e-9)) {
		tmp = x + y;
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.9e+153) or not (z <= 3.2e-9):
		tmp = x + y
	else:
		tmp = x + (t * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.9e+153) || !(z <= 3.2e-9))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(t * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.9e+153) || ~((z <= 3.2e-9)))
		tmp = x + y;
	else
		tmp = x + (t * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.9e+153], N[Not[LessEqual[z, 3.2e-9]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.89999999999999983e153 or 3.20000000000000012e-9 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 81.9%

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

   if -1.89999999999999983e153 < z < 3.20000000000000012e-9

   1. Initial program 95.2%

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

   3. Taylor expanded in z around 0 71.9%

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

      1. associate-/l* 77.7%

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

   5. Simplified 77.7%

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

4. Final simplification 79.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{+153} \lor \neg \left(z \leq 3.2 \cdot 10^{-9}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 60.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.6 \cdot 10^{+224} \lor \neg \left(t \leq 8.6 \cdot 10^{+195}\right):\\ \;\;\;\;t \cdot \frac{y}{-z}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -3.6e+224) (not (<= t 8.6e+195))) (* t (/ y (- z))) (+ x y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -3.6e+224) || !(t <= 8.6e+195)) {
		tmp = t * (y / -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 <= (-3.6d+224)) .or. (.not. (t <= 8.6d+195))) then
        tmp = t * (y / -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 <= -3.6e+224) || !(t <= 8.6e+195)) {
		tmp = t * (y / -z);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -3.6e+224) or not (t <= 8.6e+195):
		tmp = t * (y / -z)
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -3.6e+224) || !(t <= 8.6e+195))
		tmp = Float64(t * Float64(y / Float64(-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 <= -3.6e+224) || ~((t <= 8.6e+195)))
		tmp = t * (y / -z);
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -3.6e+224], N[Not[LessEqual[t, 8.6e+195]], $MachinePrecision]], N[(t * N[(y / (-z)), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.6e224 or 8.59999999999999962e195 < t

   1. Initial program 89.0%

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

   3. Taylor expanded in t around inf 84.9%

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

      1. mul-1-neg 84.9%

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

      2. associate-/l* 97.5%

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

   5. Simplified 97.5%

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

   6. Taylor expanded in z around inf 53.6%

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

      1. mul-1-neg 53.6%

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

      2. sub-neg 53.6%

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

      3. *-commutative 53.6%

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

   8. Simplified 53.6%

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

   9. Taylor expanded in x around 0 49.3%

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

       1. mul-1-neg 49.3%

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

       2. associate-*l/ 43.0%

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

       3. *-commutative 43.0%

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

       4. distribute-rgt-neg-in 43.0%

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

       5. distribute-neg-frac 43.0%

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

   11. Simplified 43.0%

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

   12. Taylor expanded in y around 0 49.3%

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

       1. associate-*r/ 49.3%

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

       2. *-commutative 49.3%

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

       3. associate-*r* 49.3%

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

       4. rem-cube-cbrt 49.3%

          \[\leadsto \frac{t \cdot \left(y \cdot \color{blue}{{\left(\sqrt[3]{-1}\right)}^{3}}\right)}{z} \]

       5. associate-/l* 49.2%

          \[\leadsto \color{blue}{t \cdot \frac{y \cdot {\left(\sqrt[3]{-1}\right)}^{3}}{z}} \]

       6. rem-cube-cbrt 49.2%

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

       7. *-commutative 49.2%

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

       8. mul-1-neg 49.2%

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

   14. Simplified 49.2%

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

   if -3.6e224 < t < 8.59999999999999962e195

   1. Initial program 98.6%

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

   3. Taylor expanded in z around inf 66.1%

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

4. Final simplification 63.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.6 \cdot 10^{+224} \lor \neg \left(t \leq 8.6 \cdot 10^{+195}\right):\\ \;\;\;\;t \cdot \frac{y}{-z}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 60.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6.9 \cdot 10^{+221} \lor \neg \left(t \leq 4.1 \cdot 10^{+192}\right):\\ \;\;\;\;\frac{y}{\frac{z}{-t}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -6.9e+221) (not (<= t 4.1e+192))) (/ y (/ z (- t))) (+ x y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -6.9e+221) || !(t <= 4.1e+192)) {
		tmp = y / (z / -t);
	} 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 <= (-6.9d+221)) .or. (.not. (t <= 4.1d+192))) then
        tmp = y / (z / -t)
    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 <= -6.9e+221) || !(t <= 4.1e+192)) {
		tmp = y / (z / -t);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -6.9e+221) or not (t <= 4.1e+192):
		tmp = y / (z / -t)
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -6.9e+221) || !(t <= 4.1e+192))
		tmp = Float64(y / Float64(z / Float64(-t)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -6.9e+221) || ~((t <= 4.1e+192)))
		tmp = y / (z / -t);
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -6.9e+221], N[Not[LessEqual[t, 4.1e+192]], $MachinePrecision]], N[(y / N[(z / (-t)), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -6.9e221 or 4.10000000000000003e192 < t

   1. Initial program 89.0%

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

   3. Taylor expanded in t around inf 84.9%

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

      1. mul-1-neg 84.9%

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

      2. associate-/l* 97.5%

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

   5. Simplified 97.5%

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

   6. Taylor expanded in z around inf 53.6%

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

      1. mul-1-neg 53.6%

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

      2. sub-neg 53.6%

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

      3. *-commutative 53.6%

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

   8. Simplified 53.6%

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

   9. Taylor expanded in x around 0 49.3%

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

       1. mul-1-neg 49.3%

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

       2. associate-*l/ 43.0%

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

       3. *-commutative 43.0%

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

       4. distribute-rgt-neg-in 43.0%

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

       5. distribute-neg-frac 43.0%

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

   11. Simplified 43.0%

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

       1. distribute-frac-neg 43.0%

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

       2. distribute-rgt-neg-out 43.0%

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

       3. add-sqr-sqrt 26.5%

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

       4. sqrt-unprod 22.4%

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

       5. sqr-neg 22.4%

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

       6. sqrt-unprod 2.8%

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

       7. add-sqr-sqrt 8.2%

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

       8. clear-num 8.2%

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

       9. un-div-inv 8.2%

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

       10. add-sqr-sqrt 2.8%

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

       11. sqrt-unprod 22.4%

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

       12. sqr-neg 22.4%

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

       13. sqrt-unprod 26.5%

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

       14. add-sqr-sqrt 44.2%

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

   13. Applied egg-rr 44.2%

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

   if -6.9e221 < t < 4.10000000000000003e192

   1. Initial program 98.6%

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

   3. Taylor expanded in z around inf 66.1%

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

4. Final simplification 62.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.9 \cdot 10^{+221} \lor \neg \left(t \leq 4.1 \cdot 10^{+192}\right):\\ \;\;\;\;\frac{y}{\frac{z}{-t}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 60.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2 \cdot 10^{+223}:\\ \;\;\;\;t \cdot \frac{y}{-z}\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{+197}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot t}{-z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -2e+223)
   (* t (/ y (- z)))
   (if (<= t 1.4e+197) (+ x y) (/ (* y t) (- z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2e+223) {
		tmp = t * (y / -z);
	} else if (t <= 1.4e+197) {
		tmp = x + y;
	} else {
		tmp = (y * t) / -z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-2d+223)) then
        tmp = t * (y / -z)
    else if (t <= 1.4d+197) then
        tmp = x + y
    else
        tmp = (y * t) / -z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2e+223) {
		tmp = t * (y / -z);
	} else if (t <= 1.4e+197) {
		tmp = x + y;
	} else {
		tmp = (y * t) / -z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -2e+223:
		tmp = t * (y / -z)
	elif t <= 1.4e+197:
		tmp = x + y
	else:
		tmp = (y * t) / -z
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -2e+223)
		tmp = Float64(t * Float64(y / Float64(-z)));
	elseif (t <= 1.4e+197)
		tmp = Float64(x + y);
	else
		tmp = Float64(Float64(y * t) / Float64(-z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -2e+223)
		tmp = t * (y / -z);
	elseif (t <= 1.4e+197)
		tmp = x + y;
	else
		tmp = (y * t) / -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -2e+223], N[(t * N[(y / (-z)), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.4e+197], N[(x + y), $MachinePrecision], N[(N[(y * t), $MachinePrecision] / (-z)), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.00000000000000009e223

   1. Initial program 88.0%

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

   3. Taylor expanded in t around inf 82.2%

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

      1. mul-1-neg 82.2%

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

      2. associate-/l* 99.8%

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

   5. Simplified 99.8%

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

   6. Taylor expanded in z around inf 50.5%

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

      1. mul-1-neg 50.5%

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

      2. sub-neg 50.5%

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

      3. *-commutative 50.5%

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

   8. Simplified 50.5%

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

   9. Taylor expanded in x around 0 50.5%

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

       1. mul-1-neg 50.5%

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

       2. associate-*l/ 45.2%

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

       3. *-commutative 45.2%

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

       4. distribute-rgt-neg-in 45.2%

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

       5. distribute-neg-frac 45.2%

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

   11. Simplified 45.2%

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

   12. Taylor expanded in y around 0 50.5%

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

       1. associate-*r/ 50.5%

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

       2. *-commutative 50.5%

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

       3. associate-*r* 50.5%

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

       4. rem-cube-cbrt 50.5%

          \[\leadsto \frac{t \cdot \left(y \cdot \color{blue}{{\left(\sqrt[3]{-1}\right)}^{3}}\right)}{z} \]

       5. associate-/l* 56.3%

          \[\leadsto \color{blue}{t \cdot \frac{y \cdot {\left(\sqrt[3]{-1}\right)}^{3}}{z}} \]

       6. rem-cube-cbrt 56.3%

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

       7. *-commutative 56.3%

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

       8. mul-1-neg 56.3%

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

   14. Simplified 56.3%

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

   if -2.00000000000000009e223 < t < 1.3999999999999999e197

   1. Initial program 98.6%

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

   3. Taylor expanded in z around inf 66.1%

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

   if 1.3999999999999999e197 < t

   1. Initial program 89.6%

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

   3. Taylor expanded in t around inf 86.5%

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

      1. mul-1-neg 86.5%

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

      2. associate-/l* 96.2%

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

   5. Simplified 96.2%

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

   6. Taylor expanded in z around inf 55.3%

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

      1. mul-1-neg 55.3%

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

      2. sub-neg 55.3%

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

      3. *-commutative 55.3%

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

   8. Simplified 55.3%

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

   9. Taylor expanded in x around 0 48.6%

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

       1. associate-*r/ 48.6%

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

       2. neg-mul-1 48.6%

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

       3. *-commutative 48.6%

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

       4. distribute-rgt-neg-in 48.6%

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

   11. Simplified 48.6%

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

4. Final simplification 63.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2 \cdot 10^{+223}:\\ \;\;\;\;t \cdot \frac{y}{-z}\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{+197}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot t}{-z}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 63.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{-17} \lor \neg \left(z \leq 2.2 \cdot 10^{-27}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2.2e-17) (not (<= z 2.2e-27))) (+ x y) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.2e-17) || !(z <= 2.2e-27)) {
		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 ((z <= (-2.2d-17)) .or. (.not. (z <= 2.2d-27))) 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 ((z <= -2.2e-17) || !(z <= 2.2e-27)) {
		tmp = x + y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -2.2e-17) or not (z <= 2.2e-27):
		tmp = x + y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2.2e-17) || !(z <= 2.2e-27))
		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 ((z <= -2.2e-17) || ~((z <= 2.2e-27)))
		tmp = x + y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -2.2e-17], N[Not[LessEqual[z, 2.2e-27]], $MachinePrecision]], N[(x + y), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -2.2e-17 or 2.19999999999999987e-27 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 75.2%

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

   if -2.2e-17 < z < 2.19999999999999987e-27

   1. Initial program 94.0%

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

   3. Taylor expanded in t around inf 88.6%

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

      1. mul-1-neg 88.6%

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

      2. associate-/l* 94.5%

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

   5. Simplified 94.5%

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

   6. Taylor expanded in x around inf 48.4%

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

4. Final simplification 61.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{-17} \lor \neg \left(z \leq 2.2 \cdot 10^{-27}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 98.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.9%

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

   1. clear-num 96.9%

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

   2. un-div-inv 97.5%

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

4. Applied egg-rr 97.5%

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

Alternative 13: 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 96.9%

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

3. Taylor expanded in t around inf 73.6%

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

   1. mul-1-neg 73.6%

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

   2. associate-/l* 76.7%

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

5. Simplified 76.7%

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

6. Taylor expanded in x around inf 47.5%

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

Developer target: 98.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024107 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisLine from plot-0.2.3.4, A"
  :precision binary64

  :alt
  (+ x (/ y (/ (- z a) (- z t))))

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