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

Percentage Accurate: 98.2% → 98.2%

Time: 8.4s

Alternatives: 12

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 98.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.1%

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

Alternative 2: 75.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.3 \cdot 10^{+117}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{-89}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq 2.65 \cdot 10^{+134}:\\ \;\;\;\;x - y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -3.3e+117)
   (+ x y)
   (if (<= t 3.4e-89)
     (+ x (* z (/ y a)))
     (if (<= t 2.65e+134) (- x (* y (/ z t))) (+ x y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -3.3e+117) {
		tmp = x + y;
	} else if (t <= 3.4e-89) {
		tmp = x + (z * (y / a));
	} else if (t <= 2.65e+134) {
		tmp = x - (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 <= (-3.3d+117)) then
        tmp = x + y
    else if (t <= 3.4d-89) then
        tmp = x + (z * (y / a))
    else if (t <= 2.65d+134) then
        tmp = x - (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 <= -3.3e+117) {
		tmp = x + y;
	} else if (t <= 3.4e-89) {
		tmp = x + (z * (y / a));
	} else if (t <= 2.65e+134) {
		tmp = x - (y * (z / t));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -3.3e+117:
		tmp = x + y
	elif t <= 3.4e-89:
		tmp = x + (z * (y / a))
	elif t <= 2.65e+134:
		tmp = x - (y * (z / t))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -3.3e+117)
		tmp = Float64(x + y);
	elseif (t <= 3.4e-89)
		tmp = Float64(x + Float64(z * Float64(y / a)));
	elseif (t <= 2.65e+134)
		tmp = Float64(x - Float64(y * Float64(z / 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 <= -3.3e+117)
		tmp = x + y;
	elseif (t <= 3.4e-89)
		tmp = x + (z * (y / a));
	elseif (t <= 2.65e+134)
		tmp = x - (y * (z / t));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -3.3e+117], N[(x + y), $MachinePrecision], If[LessEqual[t, 3.4e-89], N[(x + N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.65e+134], N[(x - N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.2999999999999998e117 or 2.6500000000000001e134 < t

   1. Initial program 99.9%

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

   3. Taylor expanded in t around inf 81.8%

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

      1. +-commutative 81.8%

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

   5. Simplified 81.8%

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

   if -3.2999999999999998e117 < t < 3.4e-89

   1. Initial program 96.6%

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

   3. Taylor expanded in z around inf 87.8%

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

      1. div-inv 87.8%

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

      2. *-commutative 87.8%

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

      3. associate-*l* 90.5%

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

      4. div-inv 90.6%

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

   5. Applied egg-rr 90.6%

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

   6. Taylor expanded in a around inf 77.4%

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

   if 3.4e-89 < t < 2.6500000000000001e134

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 90.2%

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

   4. Taylor expanded in a around 0 81.0%

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

      1. mul-1-neg 81.0%

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

      2. unsub-neg 81.0%

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

      3. associate-/l* 83.5%

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

   6. Simplified 83.5%

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

4. Final simplification 79.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.3 \cdot 10^{+117}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{-89}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq 2.65 \cdot 10^{+134}:\\ \;\;\;\;x - y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 86.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.55 \cdot 10^{+126} \lor \neg \left(t \leq 4.1 \cdot 10^{+135}\right):\\ \;\;\;\;x + y \cdot \frac{t}{t - a}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.55e+126) (not (<= t 4.1e+135)))
   (+ x (* y (/ t (- t a))))
   (+ x (* z (/ y (- a t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.55e+126) || !(t <= 4.1e+135)) {
		tmp = x + (y * (t / (t - a)));
	} else {
		tmp = x + (z * (y / (a - t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-1.55d+126)) .or. (.not. (t <= 4.1d+135))) then
        tmp = x + (y * (t / (t - a)))
    else
        tmp = x + (z * (y / (a - t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.55e+126) || !(t <= 4.1e+135)) {
		tmp = x + (y * (t / (t - a)));
	} else {
		tmp = x + (z * (y / (a - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -1.55e+126) or not (t <= 4.1e+135):
		tmp = x + (y * (t / (t - a)))
	else:
		tmp = x + (z * (y / (a - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1.55e+126) || !(t <= 4.1e+135))
		tmp = Float64(x + Float64(y * Float64(t / Float64(t - a))));
	else
		tmp = Float64(x + Float64(z * Float64(y / Float64(a - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -1.55e+126) || ~((t <= 4.1e+135)))
		tmp = x + (y * (t / (t - a)));
	else
		tmp = x + (z * (y / (a - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -1.55e+126], N[Not[LessEqual[t, 4.1e+135]], $MachinePrecision]], N[(x + N[(y * N[(t / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.55e126 or 4.1e135 < t

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 57.8%

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

      1. +-commutative 57.8%

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

      2. associate-*r/ 57.8%

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

      3. mul-1-neg 57.8%

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

      4. distribute-lft-neg-out 57.8%

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

      5. *-commutative 57.8%

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

      6. *-lft-identity 57.8%

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

      7. times-frac 87.1%

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

      8. /-rgt-identity 87.1%

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

      9. distribute-neg-frac 87.1%

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

      10. distribute-neg-frac2 87.1%

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

      11. neg-sub0 87.1%

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

      12. sub-neg 87.1%

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

      13. +-commutative 87.1%

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

      14. associate--r+ 87.1%

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

      15. neg-sub0 87.1%

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

      16. remove-double-neg 87.1%

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

   5. Simplified 87.1%

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

   if -1.55e126 < t < 4.1e135

   1. Initial program 97.4%

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

   3. Taylor expanded in z around inf 87.8%

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

      1. div-inv 87.8%

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

      2. *-commutative 87.8%

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

      3. associate-*l* 90.9%

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

      4. div-inv 90.9%

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

   5. Applied egg-rr 90.9%

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

4. Final simplification 89.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.55 \cdot 10^{+126} \lor \neg \left(t \leq 4.1 \cdot 10^{+135}\right):\\ \;\;\;\;x + y \cdot \frac{t}{t - a}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 84.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.8 \cdot 10^{+193} \lor \neg \left(t \leq 3.05 \cdot 10^{+134}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -3.8e+193) (not (<= t 3.05e+134)))
   (+ x y)
   (+ x (* z (/ y (- a t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -3.8e+193) || !(t <= 3.05e+134)) {
		tmp = x + y;
	} else {
		tmp = x + (z * (y / (a - t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-3.8d+193)) .or. (.not. (t <= 3.05d+134))) then
        tmp = x + y
    else
        tmp = x + (z * (y / (a - t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -3.8e+193) || !(t <= 3.05e+134)) {
		tmp = x + y;
	} else {
		tmp = x + (z * (y / (a - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -3.8e+193) or not (t <= 3.05e+134):
		tmp = x + y
	else:
		tmp = x + (z * (y / (a - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -3.8e+193) || !(t <= 3.05e+134))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(z * Float64(y / Float64(a - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -3.8e+193) || ~((t <= 3.05e+134)))
		tmp = x + y;
	else
		tmp = x + (z * (y / (a - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -3.8e+193], N[Not[LessEqual[t, 3.05e+134]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(z * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.79999999999999972e193 or 3.04999999999999989e134 < t

   1. Initial program 99.9%

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

   3. Taylor expanded in t around inf 89.5%

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

      1. +-commutative 89.5%

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

   5. Simplified 89.5%

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

   if -3.79999999999999972e193 < t < 3.04999999999999989e134

   1. Initial program 97.5%

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

   3. Taylor expanded in z around inf 85.7%

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

      1. div-inv 85.7%

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

      2. *-commutative 85.7%

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

      3. associate-*l* 88.2%

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

      4. div-inv 88.2%

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

   5. Applied egg-rr 88.2%

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

4. Final simplification 88.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.8 \cdot 10^{+193} \lor \neg \left(t \leq 3.05 \cdot 10^{+134}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 87.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -9 \cdot 10^{+123}:\\ \;\;\;\;x + y \cdot \frac{t}{t - a}\\ \mathbf{elif}\;t \leq 2.95 \cdot 10^{+38}:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \left(\frac{z}{t} + -1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -9e+123)
   (+ x (* y (/ t (- t a))))
   (if (<= t 2.95e+38)
     (+ x (* z (/ y (- a t))))
     (- x (* y (+ (/ z t) -1.0))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -9e+123) {
		tmp = x + (y * (t / (t - a)));
	} else if (t <= 2.95e+38) {
		tmp = x + (z * (y / (a - t)));
	} else {
		tmp = x - (y * ((z / t) + -1.0));
	}
	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 <= (-9d+123)) then
        tmp = x + (y * (t / (t - a)))
    else if (t <= 2.95d+38) then
        tmp = x + (z * (y / (a - t)))
    else
        tmp = x - (y * ((z / t) + (-1.0d0)))
    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 <= -9e+123) {
		tmp = x + (y * (t / (t - a)));
	} else if (t <= 2.95e+38) {
		tmp = x + (z * (y / (a - t)));
	} else {
		tmp = x - (y * ((z / t) + -1.0));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -9e+123:
		tmp = x + (y * (t / (t - a)))
	elif t <= 2.95e+38:
		tmp = x + (z * (y / (a - t)))
	else:
		tmp = x - (y * ((z / t) + -1.0))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -9e+123)
		tmp = Float64(x + Float64(y * Float64(t / Float64(t - a))));
	elseif (t <= 2.95e+38)
		tmp = Float64(x + Float64(z * Float64(y / Float64(a - t))));
	else
		tmp = Float64(x - Float64(y * Float64(Float64(z / t) + -1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -9e+123)
		tmp = x + (y * (t / (t - a)));
	elseif (t <= 2.95e+38)
		tmp = x + (z * (y / (a - t)));
	else
		tmp = x - (y * ((z / t) + -1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -9e+123], N[(x + N[(y * N[(t / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.95e+38], N[(x + N[(z * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(y * N[(N[(z / t), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -8.99999999999999965e123

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 59.2%

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

      1. +-commutative 59.2%

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

      2. associate-*r/ 59.2%

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

      3. mul-1-neg 59.2%

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

      4. distribute-lft-neg-out 59.2%

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

      5. *-commutative 59.2%

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

      6. *-lft-identity 59.2%

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

      7. times-frac 88.0%

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

      8. /-rgt-identity 88.0%

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

      9. distribute-neg-frac 88.0%

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

      10. distribute-neg-frac2 88.0%

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

      11. neg-sub0 88.0%

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

      12. sub-neg 88.0%

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

      13. +-commutative 88.0%

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

      14. associate--r+ 88.0%

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

      15. neg-sub0 88.0%

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

      16. remove-double-neg 88.0%

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

   5. Simplified 88.0%

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

   if -8.99999999999999965e123 < t < 2.94999999999999991e38

   1. Initial program 97.2%

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

   3. Taylor expanded in z around inf 88.6%

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

      1. div-inv 88.6%

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

      2. *-commutative 88.6%

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

      3. associate-*l* 91.3%

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

      4. div-inv 91.4%

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

   5. Applied egg-rr 91.4%

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

   if 2.94999999999999991e38 < t

   1. Initial program 99.9%

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

   3. Taylor expanded in a around 0 68.8%

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

      1. mul-1-neg 68.8%

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

      2. unsub-neg 68.8%

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

      3. associate-/l* 96.3%

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

      4. div-sub 96.3%

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

      5. sub-neg 96.3%

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

      6. *-inverses 96.3%

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

      7. metadata-eval 96.3%

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

   5. Simplified 96.3%

      \[\leadsto \color{blue}{x - y \cdot \left(\frac{z}{t} + -1\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 92.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9 \cdot 10^{+123}:\\ \;\;\;\;x + y \cdot \frac{t}{t - a}\\ \mathbf{elif}\;t \leq 2.95 \cdot 10^{+38}:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \left(\frac{z}{t} + -1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 76.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.45 \cdot 10^{+117} \lor \neg \left(t \leq 1.3 \cdot 10^{+38}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -2.45e+117) (not (<= t 1.3e+38))) (+ x y) (+ x (* z (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -2.45e+117) || !(t <= 1.3e+38)) {
		tmp = x + y;
	} else {
		tmp = x + (z * (y / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-2.45d+117)) .or. (.not. (t <= 1.3d+38))) then
        tmp = x + y
    else
        tmp = x + (z * (y / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -2.45e+117) || !(t <= 1.3e+38)) {
		tmp = x + y;
	} else {
		tmp = x + (z * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -2.45e+117) or not (t <= 1.3e+38):
		tmp = x + y
	else:
		tmp = x + (z * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -2.45e+117) || !(t <= 1.3e+38))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(z * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -2.45e+117) || ~((t <= 1.3e+38)))
		tmp = x + y;
	else
		tmp = x + (z * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -2.45e+117], N[Not[LessEqual[t, 1.3e+38]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.45e117 or 1.3e38 < t

   1. Initial program 99.9%

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

   3. Taylor expanded in t around inf 79.0%

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

      1. +-commutative 79.0%

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

   5. Simplified 79.0%

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

   if -2.45e117 < t < 1.3e38

   1. Initial program 97.1%

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

   3. Taylor expanded in z around inf 89.1%

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

      1. div-inv 89.1%

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

      2. *-commutative 89.1%

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

      3. associate-*l* 91.3%

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

      4. div-inv 91.3%

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

   5. Applied egg-rr 91.3%

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

   6. Taylor expanded in a around inf 74.8%

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

4. Final simplification 76.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.45 \cdot 10^{+117} \lor \neg \left(t \leq 1.3 \cdot 10^{+38}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 62.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.22 \cdot 10^{+55} \lor \neg \left(y \leq 1.85 \cdot 10^{+136}\right):\\ \;\;\;\;y \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -1.22e+55) (not (<= y 1.85e+136)))
   (* y (- 1.0 (/ z t)))
   (+ x y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -1.22e+55) || !(y <= 1.85e+136)) {
		tmp = y * (1.0 - (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 ((y <= (-1.22d+55)) .or. (.not. (y <= 1.85d+136))) then
        tmp = y * (1.0d0 - (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 ((y <= -1.22e+55) || !(y <= 1.85e+136)) {
		tmp = y * (1.0 - (z / t));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -1.22e+55) or not (y <= 1.85e+136):
		tmp = y * (1.0 - (z / t))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -1.22e+55) || !(y <= 1.85e+136))
		tmp = Float64(y * Float64(1.0 - Float64(z / t)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -1.22e+55) || ~((y <= 1.85e+136)))
		tmp = y * (1.0 - (z / t));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -1.22e+55], N[Not[LessEqual[y, 1.85e+136]], $MachinePrecision]], N[(y * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.22e55 or 1.85000000000000005e136 < y

   1. Initial program 98.0%

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

      1. clear-num 97.9%

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

      2. un-div-inv 98.0%

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

   4. Applied egg-rr 98.0%

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

   5. Taylor expanded in a around 0 41.2%

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

      1. mul-1-neg 41.2%

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

      2. unsub-neg 41.2%

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

      3. associate-/l* 60.5%

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

      4. div-sub 60.5%

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

      5. *-inverses 60.5%

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

   7. Simplified 60.5%

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

   8. Taylor expanded in x around 0 52.0%

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

      1. sub-neg 52.0%

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

      2. metadata-eval 52.0%

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

      3. neg-mul-1 52.0%

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

      4. distribute-rgt-neg-in 52.0%

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

      5. +-commutative 52.0%

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

      6. distribute-neg-in 52.0%

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

      7. metadata-eval 52.0%

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

      8. sub-neg 52.0%

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

   10. Simplified 52.0%

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

   if -1.22e55 < y < 1.85000000000000005e136

   1. Initial program 98.1%

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

   3. Taylor expanded in t around inf 69.4%

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

      1. +-commutative 69.4%

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

   5. Simplified 69.4%

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

4. Final simplification 62.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.22 \cdot 10^{+55} \lor \neg \left(y \leq 1.85 \cdot 10^{+136}\right):\\ \;\;\;\;y \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 59.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{+121} \lor \neg \left(z \leq 2.9 \cdot 10^{+227}\right):\\ \;\;\;\;y \cdot \frac{-z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.35e+121) (not (<= z 2.9e+227))) (* y (/ (- z) t)) (+ x y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.35e+121) || !(z <= 2.9e+227)) {
		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 ((z <= (-1.35d+121)) .or. (.not. (z <= 2.9d+227))) 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 ((z <= -1.35e+121) || !(z <= 2.9e+227)) {
		tmp = y * (-z / t);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.35e+121) or not (z <= 2.9e+227):
		tmp = y * (-z / t)
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.35e+121) || !(z <= 2.9e+227))
		tmp = Float64(y * Float64(Float64(-z) / t));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.35e+121) || ~((z <= 2.9e+227)))
		tmp = y * (-z / t);
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.35e+121], N[Not[LessEqual[z, 2.9e+227]], $MachinePrecision]], N[(y * N[((-z) / t), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.3500000000000001e121 or 2.8999999999999998e227 < z

   1. Initial program 96.4%

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

      1. clear-num 96.4%

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

      2. un-div-inv 96.5%

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

   4. Applied egg-rr 96.5%

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

   5. Taylor expanded in a around 0 56.9%

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

      1. mul-1-neg 56.9%

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

      2. unsub-neg 56.9%

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

      3. associate-/l* 62.0%

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

      4. div-sub 62.0%

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

      5. *-inverses 62.0%

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

   7. Simplified 62.0%

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

   8. Taylor expanded in z around inf 49.5%

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

      1. mul-1-neg 49.5%

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

      2. distribute-neg-frac2 49.5%

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

      3. associate-*r/ 49.4%

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

   10. Simplified 49.4%

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

   if -1.3500000000000001e121 < z < 2.8999999999999998e227

   1. Initial program 98.5%

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

   3. Taylor expanded in t around inf 63.0%

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

      1. +-commutative 63.0%

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

   5. Simplified 63.0%

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

4. Final simplification 60.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{+121} \lor \neg \left(z \leq 2.9 \cdot 10^{+227}\right):\\ \;\;\;\;y \cdot \frac{-z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 59.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{+121}:\\ \;\;\;\;\frac{y}{t} \cdot \left(-z\right)\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{+225}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{-z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.35e+121)
   (* (/ y t) (- z))
   (if (<= z 1.7e+225) (+ x y) (* y (/ (- z) t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.35e+121) {
		tmp = (y / t) * -z;
	} else if (z <= 1.7e+225) {
		tmp = x + y;
	} else {
		tmp = y * (-z / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-1.35d+121)) then
        tmp = (y / t) * -z
    else if (z <= 1.7d+225) then
        tmp = x + y
    else
        tmp = y * (-z / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.35e+121) {
		tmp = (y / t) * -z;
	} else if (z <= 1.7e+225) {
		tmp = x + y;
	} else {
		tmp = y * (-z / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.35e+121:
		tmp = (y / t) * -z
	elif z <= 1.7e+225:
		tmp = x + y
	else:
		tmp = y * (-z / t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.35e+121)
		tmp = Float64(Float64(y / t) * Float64(-z));
	elseif (z <= 1.7e+225)
		tmp = Float64(x + y);
	else
		tmp = Float64(y * Float64(Float64(-z) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.35e+121)
		tmp = (y / t) * -z;
	elseif (z <= 1.7e+225)
		tmp = x + y;
	else
		tmp = y * (-z / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.35e+121], N[(N[(y / t), $MachinePrecision] * (-z)), $MachinePrecision], If[LessEqual[z, 1.7e+225], N[(x + y), $MachinePrecision], N[(y * N[((-z) / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.3500000000000001e121

   1. Initial program 94.7%

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

      1. clear-num 94.7%

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

      2. un-div-inv 94.8%

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

   4. Applied egg-rr 94.8%

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

   5. Taylor expanded in a around 0 49.0%

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

      1. mul-1-neg 49.0%

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

      2. unsub-neg 49.0%

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

      3. associate-/l* 56.8%

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

      4. div-sub 56.8%

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

      5. *-inverses 56.8%

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

   7. Simplified 56.8%

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

   8. Taylor expanded in z around inf 40.5%

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

      1. mul-1-neg 40.5%

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

      2. distribute-neg-frac 40.5%

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

      3. *-commutative 40.5%

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

      4. distribute-rgt-neg-in 40.5%

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

      5. associate-*r/ 40.5%

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

   10. Simplified 40.5%

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

   if -1.3500000000000001e121 < z < 1.70000000000000009e225

   1. Initial program 98.5%

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

   3. Taylor expanded in t around inf 63.0%

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

      1. +-commutative 63.0%

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

   5. Simplified 63.0%

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

   if 1.70000000000000009e225 < z

   1. Initial program 99.9%

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

      1. clear-num 99.8%

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

      2. un-div-inv 99.8%

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

   4. Applied egg-rr 99.8%

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

   5. Taylor expanded in a around 0 72.6%

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

      1. mul-1-neg 72.6%

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

      2. unsub-neg 72.6%

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

      3. associate-/l* 72.5%

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

      4. div-sub 72.5%

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

      5. *-inverses 72.5%

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

   7. Simplified 72.5%

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

   8. Taylor expanded in z around inf 67.4%

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

      1. mul-1-neg 67.4%

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

      2. distribute-neg-frac2 67.4%

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

      3. associate-*r/ 67.3%

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

   10. Simplified 67.3%

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

4. Final simplification 60.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{+121}:\\ \;\;\;\;\frac{y}{t} \cdot \left(-z\right)\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{+225}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{-z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 61.6% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -7.2 \cdot 10^{+95}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (if (<= a -7.2e+95) x (+ x y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -7.2e+95) {
		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 (a <= (-7.2d+95)) 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 (a <= -7.2e+95) {
		tmp = x;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -7.2e+95:
		tmp = x
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -7.2e+95)
		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 (a <= -7.2e+95)
		tmp = x;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -7.2e+95], x, N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -7.19999999999999955e95

   1. Initial program 97.7%

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

   3. Taylor expanded in x around inf 61.1%

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

   if -7.19999999999999955e95 < a

   1. Initial program 98.2%

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

   3. Taylor expanded in t around inf 55.2%

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

      1. +-commutative 55.2%

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

   5. Simplified 55.2%

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

4. Final simplification 56.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7.2 \cdot 10^{+95}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 50.2% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 1.7 \cdot 10^{+268}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (if (<= t 1.7e+268) x y))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= 1.7e+268) {
		tmp = x;
	} else {
		tmp = 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 <= 1.7d+268) then
        tmp = x
    else
        tmp = 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 <= 1.7e+268) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= 1.7e+268:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= 1.7e+268)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= 1.7e+268)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, 1.7e+268], x, y]

Derivation

1. Split input into 2 regimes

2. if t < 1.7000000000000001e268

   1. Initial program 98.0%

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

   3. Taylor expanded in x around inf 47.1%

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

   if 1.7000000000000001e268 < t

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 100.0%

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

      1. +-commutative 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in y around inf 100.0%

      \[\leadsto \color{blue}{y} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 12: 50.5% accurate, 11.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.1%

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

3. Taylor expanded in x around inf 46.1%

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

Developer Target 1: 99.3% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (y * ((z - t) / (a - t)))
    if (y < (-8.508084860551241d-17)) then
        tmp = t_1
    else if (y < 2.894426862792089d-49) then
        tmp = x + ((y * (z - t)) * (1.0d0 / (a - t)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

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

Python

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

Julia

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

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y * ((z - t) / (a - t)));
	tmp = 0.0;
	if (y < -8.508084860551241e-17)
		tmp = t_1;
	elseif (y < 2.894426862792089e-49)
		tmp = x + ((y * (z - t)) * (1.0 / (a - t)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[y, -8.508084860551241e-17], t$95$1, If[Less[y, 2.894426862792089e-49], N[(x + N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] * N[(1.0 / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Reproduce

herbie shell --seed 2024185 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisLine from plot-0.2.3.4, B"
  :precision binary64

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

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