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

Percentage Accurate: 86.1% → 98.2%

Time: 8.9s

Alternatives: 12

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 86.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 1.4 \cdot 10^{+119}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z 1.4e+119)
   (+ x (* y (/ (- z t) (- a t))))
   (+ x (* (- z t) (/ y (- a t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= 1.4e+119) {
		tmp = x + (y * ((z - t) / (a - t)));
	} else {
		tmp = x + ((z - t) * (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 (z <= 1.4d+119) then
        tmp = x + (y * ((z - t) / (a - t)))
    else
        tmp = x + ((z - t) * (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 (z <= 1.4e+119) {
		tmp = x + (y * ((z - t) / (a - t)));
	} else {
		tmp = x + ((z - t) * (y / (a - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= 1.4e+119:
		tmp = x + (y * ((z - t) / (a - t)))
	else:
		tmp = x + ((z - t) * (y / (a - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= 1.4e+119)
		tmp = Float64(x + Float64(y * Float64(Float64(z - t) / Float64(a - t))));
	else
		tmp = Float64(x + Float64(Float64(z - t) * Float64(y / Float64(a - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= 1.4e+119)
		tmp = x + (y * ((z - t) / (a - t)));
	else
		tmp = x + ((z - t) * (y / (a - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, 1.4e+119], N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(z - t), $MachinePrecision] * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 1.40000000000000007e119

   1. Initial program 87.8%

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

      1. associate-/l* 99.5%

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

   3. Simplified 99.5%

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

   if 1.40000000000000007e119 < z

   1. Initial program 74.0%

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

      1. *-commutative 74.0%

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

      2. associate-/l* 99.9%

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

   4. Applied egg-rr 99.9%

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

4. Final simplification 99.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 1.4 \cdot 10^{+119}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 79.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + t \cdot \frac{y}{t - a}\\ \mathbf{if}\;t \leq -3.8 \cdot 10^{+75}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -20500:\\ \;\;\;\;x - y \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq -2.9 \cdot 10^{-50} \lor \neg \left(t \leq 1.8 \cdot 10^{-119}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* t (/ y (- t a))))))
   (if (<= t -3.8e+75)
     t_1
     (if (<= t -20500.0)
       (- x (* y (/ z t)))
       (if (or (<= t -2.9e-50) (not (<= t 1.8e-119)))
         t_1
         (+ x (* z (/ y a))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (t * (y / (t - a)));
	double tmp;
	if (t <= -3.8e+75) {
		tmp = t_1;
	} else if (t <= -20500.0) {
		tmp = x - (y * (z / t));
	} else if ((t <= -2.9e-50) || !(t <= 1.8e-119)) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = x + (t * (y / (t - a)))
    if (t <= (-3.8d+75)) then
        tmp = t_1
    else if (t <= (-20500.0d0)) then
        tmp = x - (y * (z / t))
    else if ((t <= (-2.9d-50)) .or. (.not. (t <= 1.8d-119))) then
        tmp = t_1
    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 t_1 = x + (t * (y / (t - a)));
	double tmp;
	if (t <= -3.8e+75) {
		tmp = t_1;
	} else if (t <= -20500.0) {
		tmp = x - (y * (z / t));
	} else if ((t <= -2.9e-50) || !(t <= 1.8e-119)) {
		tmp = t_1;
	} else {
		tmp = x + (z * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (t * (y / (t - a)))
	tmp = 0
	if t <= -3.8e+75:
		tmp = t_1
	elif t <= -20500.0:
		tmp = x - (y * (z / t))
	elif (t <= -2.9e-50) or not (t <= 1.8e-119):
		tmp = t_1
	else:
		tmp = x + (z * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(t * Float64(y / Float64(t - a))))
	tmp = 0.0
	if (t <= -3.8e+75)
		tmp = t_1;
	elseif (t <= -20500.0)
		tmp = Float64(x - Float64(y * Float64(z / t)));
	elseif ((t <= -2.9e-50) || !(t <= 1.8e-119))
		tmp = t_1;
	else
		tmp = Float64(x + Float64(z * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (t * (y / (t - a)));
	tmp = 0.0;
	if (t <= -3.8e+75)
		tmp = t_1;
	elseif (t <= -20500.0)
		tmp = x - (y * (z / t));
	elseif ((t <= -2.9e-50) || ~((t <= 1.8e-119)))
		tmp = t_1;
	else
		tmp = x + (z * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(t * N[(y / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.8e+75], t$95$1, If[LessEqual[t, -20500.0], N[(x - N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t, -2.9e-50], N[Not[LessEqual[t, 1.8e-119]], $MachinePrecision]], t$95$1, N[(x + N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.8000000000000002e75 or -20500 < t < -2.90000000000000008e-50 or 1.8e-119 < t

   1. Initial program 80.0%

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

      1. associate-/l* 99.3%

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

   3. Simplified 99.3%

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

   5. Taylor expanded in z around 0 68.1%

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

      1. associate-*r/ 68.1%

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

      2. mul-1-neg 68.1%

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

      3. distribute-lft-neg-out 68.1%

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

      4. *-commutative 68.1%

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

      5. associate-/l* 85.6%

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

      6. distribute-neg-frac 85.6%

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

      7. distribute-neg-frac2 85.6%

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

      8. neg-sub0 85.6%

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

      9. associate--r- 85.6%

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

      10. neg-sub0 85.6%

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

   7. Simplified 85.6%

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

   8. Taylor expanded in y around 0 68.1%

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

      1. associate-/l* 83.3%

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

   10. Simplified 83.3%

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

   if -3.8000000000000002e75 < t < -20500

   1. Initial program 99.9%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 94.4%

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

      1. associate-/l* 94.4%

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

   7. Simplified 94.4%

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

   8. Taylor expanded in a around 0 83.4%

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

      1. mul-1-neg 83.4%

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

      2. unsub-neg 83.4%

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

      3. associate-/l* 83.5%

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

   10. Simplified 83.5%

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

   if -2.90000000000000008e-50 < t < 1.8e-119

   1. Initial program 93.5%

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

      1. *-commutative 93.5%

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

      2. associate-/l* 97.8%

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

   4. Applied egg-rr 97.8%

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

   5. Taylor expanded in t around 0 81.7%

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

      1. *-commutative 81.7%

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

      2. associate-*r/ 88.0%

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

   7. Simplified 88.0%

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

4. Final simplification 84.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.8 \cdot 10^{+75}:\\ \;\;\;\;x + t \cdot \frac{y}{t - a}\\ \mathbf{elif}\;t \leq -20500:\\ \;\;\;\;x - y \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq -2.9 \cdot 10^{-50} \lor \neg \left(t \leq 1.8 \cdot 10^{-119}\right):\\ \;\;\;\;x + t \cdot \frac{y}{t - a}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 76.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -9 \cdot 10^{+76}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq -5.2 \cdot 10^{-51}:\\ \;\;\;\;x - y \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq 2.12 \cdot 10^{-47}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -9e+76)
   (+ x y)
   (if (<= t -5.2e-51)
     (- x (* y (/ z t)))
     (if (<= t 2.12e-47) (+ x (* z (/ y a))) (+ x y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -9e+76) {
		tmp = x + y;
	} else if (t <= -5.2e-51) {
		tmp = x - (y * (z / t));
	} else if (t <= 2.12e-47) {
		tmp = x + (z * (y / a));
	} 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 <= (-9d+76)) then
        tmp = x + y
    else if (t <= (-5.2d-51)) then
        tmp = x - (y * (z / t))
    else if (t <= 2.12d-47) then
        tmp = x + (z * (y / a))
    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 <= -9e+76) {
		tmp = x + y;
	} else if (t <= -5.2e-51) {
		tmp = x - (y * (z / t));
	} else if (t <= 2.12e-47) {
		tmp = x + (z * (y / a));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -9e+76:
		tmp = x + y
	elif t <= -5.2e-51:
		tmp = x - (y * (z / t))
	elif t <= 2.12e-47:
		tmp = x + (z * (y / a))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -9e+76)
		tmp = Float64(x + y);
	elseif (t <= -5.2e-51)
		tmp = Float64(x - Float64(y * Float64(z / t)));
	elseif (t <= 2.12e-47)
		tmp = Float64(x + Float64(z * Float64(y / a)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -9e+76)
		tmp = x + y;
	elseif (t <= -5.2e-51)
		tmp = x - (y * (z / t));
	elseif (t <= 2.12e-47)
		tmp = x + (z * (y / a));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -9e+76], N[(x + y), $MachinePrecision], If[LessEqual[t, -5.2e-51], N[(x - N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.12e-47], N[(x + N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -8.9999999999999995e76 or 2.12e-47 < t

   1. Initial program 74.8%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in t around inf 84.1%

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

   if -8.9999999999999995e76 < t < -5.2e-51

   1. Initial program 99.9%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 86.9%

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

      1. associate-/l* 86.9%

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

   7. Simplified 86.9%

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

   8. Taylor expanded in a around 0 71.5%

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

      1. mul-1-neg 71.5%

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

      2. unsub-neg 71.5%

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

      3. associate-/l* 71.6%

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

   10. Simplified 71.6%

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

   if -5.2e-51 < t < 2.12e-47

   1. Initial program 94.6%

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

      1. *-commutative 94.6%

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

      2. associate-/l* 98.1%

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

   4. Applied egg-rr 98.1%

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

   5. Taylor expanded in t around 0 77.5%

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

      1. *-commutative 77.5%

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

      2. associate-*r/ 82.7%

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

   7. Simplified 82.7%

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

4. Final simplification 82.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9 \cdot 10^{+76}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq -5.2 \cdot 10^{-51}:\\ \;\;\;\;x - y \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq 2.12 \cdot 10^{-47}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 85.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{+46} \lor \neg \left(z \leq 8.6 \cdot 10^{+48}\right):\\ \;\;\;\;x + y \cdot \frac{z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{t - a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -5.2e+46) (not (<= z 8.6e+48)))
   (+ x (* y (/ z (- a t))))
   (+ x (* t (/ y (- t a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -5.2e+46) || !(z <= 8.6e+48)) {
		tmp = x + (y * (z / (a - t)));
	} else {
		tmp = x + (t * (y / (t - a)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-5.2d+46)) .or. (.not. (z <= 8.6d+48))) then
        tmp = x + (y * (z / (a - t)))
    else
        tmp = x + (t * (y / (t - a)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -5.2e+46) || !(z <= 8.6e+48)) {
		tmp = x + (y * (z / (a - t)));
	} else {
		tmp = x + (t * (y / (t - a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -5.2e+46) or not (z <= 8.6e+48):
		tmp = x + (y * (z / (a - t)))
	else:
		tmp = x + (t * (y / (t - a)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -5.2e+46) || !(z <= 8.6e+48))
		tmp = Float64(x + Float64(y * Float64(z / Float64(a - t))));
	else
		tmp = Float64(x + Float64(t * Float64(y / Float64(t - a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -5.2e+46) || ~((z <= 8.6e+48)))
		tmp = x + (y * (z / (a - t)));
	else
		tmp = x + (t * (y / (t - a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -5.2e+46], N[Not[LessEqual[z, 8.6e+48]], $MachinePrecision]], N[(x + N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(t * N[(y / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.20000000000000027e46 or 8.59999999999999957e48 < z

   1. Initial program 83.6%

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

      1. associate-/l* 94.9%

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

   3. Simplified 94.9%

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

   5. Taylor expanded in z around inf 80.7%

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

      1. associate-/l* 84.8%

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

   7. Simplified 84.8%

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

   if -5.20000000000000027e46 < z < 8.59999999999999957e48

   1. Initial program 88.1%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around 0 80.7%

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

      1. associate-*r/ 80.7%

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

      2. mul-1-neg 80.7%

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

      3. distribute-lft-neg-out 80.7%

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

      4. *-commutative 80.7%

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

      5. associate-/l* 92.6%

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

      6. distribute-neg-frac 92.6%

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

      7. distribute-neg-frac2 92.6%

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

      8. neg-sub0 92.6%

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

      9. associate--r- 92.6%

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

      10. neg-sub0 92.6%

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

   7. Simplified 92.6%

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

   8. Taylor expanded in y around 0 80.7%

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

      1. associate-/l* 88.8%

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

   10. Simplified 88.8%

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

4. Final simplification 87.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{+46} \lor \neg \left(z \leq 8.6 \cdot 10^{+48}\right):\\ \;\;\;\;x + y \cdot \frac{z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{t - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 86.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{+46} \lor \neg \left(z \leq 7 \cdot 10^{+47}\right):\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{t - a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -5.2e+46) (not (<= z 7e+47)))
   (+ x (* z (/ y (- a t))))
   (+ x (* t (/ y (- t a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -5.2e+46) || !(z <= 7e+47)) {
		tmp = x + (z * (y / (a - t)));
	} else {
		tmp = x + (t * (y / (t - a)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-5.2d+46)) .or. (.not. (z <= 7d+47))) then
        tmp = x + (z * (y / (a - t)))
    else
        tmp = x + (t * (y / (t - a)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -5.2e+46) || !(z <= 7e+47)) {
		tmp = x + (z * (y / (a - t)));
	} else {
		tmp = x + (t * (y / (t - a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -5.2e+46) or not (z <= 7e+47):
		tmp = x + (z * (y / (a - t)))
	else:
		tmp = x + (t * (y / (t - a)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -5.2e+46) || !(z <= 7e+47))
		tmp = Float64(x + Float64(z * Float64(y / Float64(a - t))));
	else
		tmp = Float64(x + Float64(t * Float64(y / Float64(t - a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -5.2e+46) || ~((z <= 7e+47)))
		tmp = x + (z * (y / (a - t)));
	else
		tmp = x + (t * (y / (t - a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -5.2e+46], N[Not[LessEqual[z, 7e+47]], $MachinePrecision]], N[(x + N[(z * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(t * N[(y / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.20000000000000027e46 or 7.00000000000000031e47 < z

   1. Initial program 83.6%

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

      1. *-commutative 83.6%

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

      2. associate-/l* 99.9%

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

   4. Applied egg-rr 99.9%

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

   5. Taylor expanded in z around inf 80.7%

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

      1. associate-*l/ 89.8%

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

      2. *-commutative 89.8%

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

   7. Simplified 89.8%

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

   if -5.20000000000000027e46 < z < 7.00000000000000031e47

   1. Initial program 88.1%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around 0 80.7%

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

      1. associate-*r/ 80.7%

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

      2. mul-1-neg 80.7%

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

      3. distribute-lft-neg-out 80.7%

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

      4. *-commutative 80.7%

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

      5. associate-/l* 92.6%

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

      6. distribute-neg-frac 92.6%

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

      7. distribute-neg-frac2 92.6%

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

      8. neg-sub0 92.6%

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

      9. associate--r- 92.6%

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

      10. neg-sub0 92.6%

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

   7. Simplified 92.6%

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

   8. Taylor expanded in y around 0 80.7%

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

      1. associate-/l* 88.8%

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

   10. Simplified 88.8%

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

4. Final simplification 89.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{+46} \lor \neg \left(z \leq 7 \cdot 10^{+47}\right):\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{t - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 87.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{+46} \lor \neg \left(z \leq 6.7 \cdot 10^{+47}\right):\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{t - a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -6.5e+46) (not (<= z 6.7e+47)))
   (+ x (* z (/ y (- a t))))
   (+ x (* y (/ t (- t a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -6.5e+46) || !(z <= 6.7e+47)) {
		tmp = x + (z * (y / (a - t)));
	} else {
		tmp = x + (y * (t / (t - a)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-6.5d+46)) .or. (.not. (z <= 6.7d+47))) then
        tmp = x + (z * (y / (a - t)))
    else
        tmp = x + (y * (t / (t - a)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -6.5e+46) || !(z <= 6.7e+47)) {
		tmp = x + (z * (y / (a - t)));
	} else {
		tmp = x + (y * (t / (t - a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -6.5e+46) or not (z <= 6.7e+47):
		tmp = x + (z * (y / (a - t)))
	else:
		tmp = x + (y * (t / (t - a)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -6.5e+46) || !(z <= 6.7e+47))
		tmp = Float64(x + Float64(z * Float64(y / Float64(a - t))));
	else
		tmp = Float64(x + Float64(y * Float64(t / Float64(t - a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -6.5e+46) || ~((z <= 6.7e+47)))
		tmp = x + (z * (y / (a - t)));
	else
		tmp = x + (y * (t / (t - a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -6.5e+46], N[Not[LessEqual[z, 6.7e+47]], $MachinePrecision]], N[(x + N[(z * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(t / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -6.50000000000000008e46 or 6.69999999999999973e47 < z

   1. Initial program 83.6%

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

      1. *-commutative 83.6%

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

      2. associate-/l* 99.9%

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

   4. Applied egg-rr 99.9%

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

   5. Taylor expanded in z around inf 80.7%

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

      1. associate-*l/ 89.8%

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

      2. *-commutative 89.8%

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

   7. Simplified 89.8%

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

   if -6.50000000000000008e46 < z < 6.69999999999999973e47

   1. Initial program 88.1%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around 0 80.7%

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

      1. associate-*r/ 80.7%

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

      2. mul-1-neg 80.7%

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

      3. distribute-lft-neg-out 80.7%

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

      4. *-commutative 80.7%

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

      5. associate-/l* 92.6%

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

      6. distribute-neg-frac 92.6%

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

      7. distribute-neg-frac2 92.6%

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

      8. neg-sub0 92.6%

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

      9. associate--r- 92.6%

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

      10. neg-sub0 92.6%

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

   7. Simplified 92.6%

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

4. Final simplification 91.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{+46} \lor \neg \left(z \leq 6.7 \cdot 10^{+47}\right):\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{t - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 76.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.05 \cdot 10^{-49} \lor \neg \left(t \leq 2.7 \cdot 10^{-42}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.05e-49) (not (<= t 2.7e-42))) (+ x y) (+ x (* y (/ z a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.05e-49) || !(t <= 2.7e-42)) {
		tmp = x + y;
	} else {
		tmp = x + (y * (z / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-1.05d-49)) .or. (.not. (t <= 2.7d-42))) then
        tmp = x + y
    else
        tmp = x + (y * (z / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.05e-49) || !(t <= 2.7e-42)) {
		tmp = x + y;
	} else {
		tmp = x + (y * (z / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -1.05e-49) or not (t <= 2.7e-42):
		tmp = x + y
	else:
		tmp = x + (y * (z / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1.05e-49) || !(t <= 2.7e-42))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(y * Float64(z / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -1.05e-49) || ~((t <= 2.7e-42)))
		tmp = x + y;
	else
		tmp = x + (y * (z / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -1.05e-49], N[Not[LessEqual[t, 2.7e-42]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.0499999999999999e-49 or 2.69999999999999999e-42 < t

   1. Initial program 80.0%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in t around inf 77.8%

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

   if -1.0499999999999999e-49 < t < 2.69999999999999999e-42

   1. Initial program 94.6%

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

      1. associate-/l* 94.5%

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

   3. Simplified 94.5%

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

   5. Taylor expanded in t around 0 77.5%

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

      1. associate-/l* 79.1%

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

   7. Simplified 79.1%

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

4. Final simplification 78.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.05 \cdot 10^{-49} \lor \neg \left(t \leq 2.7 \cdot 10^{-42}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 76.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.5 \cdot 10^{+53} \lor \neg \left(t \leq 4.4 \cdot 10^{-54}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.5e+53) (not (<= t 4.4e-54))) (+ x y) (+ x (* z (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.5e+53) || !(t <= 4.4e-54)) {
		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 <= (-1.5d+53)) .or. (.not. (t <= 4.4d-54))) 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 <= -1.5e+53) || !(t <= 4.4e-54)) {
		tmp = x + y;
	} else {
		tmp = x + (z * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -1.5e+53) or not (t <= 4.4e-54):
		tmp = x + y
	else:
		tmp = x + (z * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1.5e+53) || !(t <= 4.4e-54))
		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 <= -1.5e+53) || ~((t <= 4.4e-54)))
		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, -1.5e+53], N[Not[LessEqual[t, 4.4e-54]], $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 < -1.49999999999999999e53 or 4.3999999999999999e-54 < t

   1. Initial program 75.4%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in t around inf 82.9%

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

   if -1.49999999999999999e53 < t < 4.3999999999999999e-54

   1. Initial program 95.7%

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

      1. *-commutative 95.7%

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

      2. associate-/l* 98.5%

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

   4. Applied egg-rr 98.5%

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

   5. Taylor expanded in t around 0 73.6%

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

      1. *-commutative 73.6%

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

      2. associate-*r/ 77.7%

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

   7. Simplified 77.7%

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

4. Final simplification 80.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.5 \cdot 10^{+53} \lor \neg \left(t \leq 4.4 \cdot 10^{-54}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 61.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -4.6 \cdot 10^{+220}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -4.6e+220) (+ x (* t (/ y a))) (+ x y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -4.6e+220) {
		tmp = x + (t * (y / a));
	} 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 <= (-4.6d+220)) then
        tmp = x + (t * (y / a))
    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 <= -4.6e+220) {
		tmp = x + (t * (y / a));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -4.6e+220:
		tmp = x + (t * (y / a))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -4.6e+220)
		tmp = Float64(x + Float64(t * Float64(y / a)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -4.6e+220)
		tmp = x + (t * (y / a));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -4.6e+220], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -4.59999999999999993e220

   1. Initial program 91.3%

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

      1. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in a around inf 91.3%

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

      1. associate-/l* 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in z around 0 78.1%

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

      1. mul-1-neg 78.1%

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

      2. unsub-neg 78.1%

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

      3. associate-/l* 78.1%

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

   10. Simplified 78.1%

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

       1. sub-neg 78.1%

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

       2. associate-*r/ 78.1%

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

       3. distribute-neg-frac2 78.1%

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

       4. add-sqr-sqrt 78.1%

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

       5. sqrt-unprod 73.4%

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

       6. sqr-neg 73.4%

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

       7. sqrt-unprod 0.0%

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

       8. add-sqr-sqrt 78.0%

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

       9. associate-*r/ 78.2%

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

   12. Applied egg-rr 78.2%

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

   if -4.59999999999999993e220 < a

   1. Initial program 85.6%

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

      1. associate-/l* 97.5%

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

   3. Simplified 97.5%

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

   5. Taylor expanded in t around inf 65.7%

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

4. Final simplification 66.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.6 \cdot 10^{+220}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 98.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 86.1%

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

   1. associate-/l* 97.7%

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

3. Simplified 97.7%

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

5. Final simplification 97.7%

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

Alternative 11: 60.1% accurate, 3.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 86.1%

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

   1. associate-/l* 97.7%

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

3. Simplified 97.7%

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

5. Taylor expanded in t around inf 64.9%

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

6. Final simplification 64.9%

   \[\leadsto x + y \]
7. Add Preprocessing

Alternative 12: 51.0% accurate, 11.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 86.1%

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

   1. associate-/l* 97.7%

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

3. Simplified 97.7%

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

5. Taylor expanded in t around 0 60.5%

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

6. Taylor expanded in x around inf 51.6%

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

7. Final simplification 51.6%

   \[\leadsto x \]
8. Add Preprocessing

Developer target: 98.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024077 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, B"
  :precision binary64

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

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