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

Percentage Accurate: 85.6% → 96.2%

Time: 8.9s

Alternatives: 10

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 85.6% 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: 96.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 87.5%

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

   1. *-commutative 87.5%

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

   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. Final simplification 98.1%

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

Alternative 2: 78.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - y \cdot \frac{z}{t - a}\\ \mathbf{if}\;t \leq -1.52 \cdot 10^{+240}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq -6 \cdot 10^{+40}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -9.5 \cdot 10^{-9}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 3.8 \cdot 10^{-123}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{+94}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* y (/ z (- t a))))))
   (if (<= t -1.52e+240)
     (+ x y)
     (if (<= t -6e+40)
       t_1
       (if (<= t -9.5e-9)
         (+ x y)
         (if (<= t 3.8e-123)
           (+ x (* z (/ y a)))
           (if (<= t 2.6e+94) t_1 (+ x y))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (y * (z / (t - a)));
	double tmp;
	if (t <= -1.52e+240) {
		tmp = x + y;
	} else if (t <= -6e+40) {
		tmp = t_1;
	} else if (t <= -9.5e-9) {
		tmp = x + y;
	} else if (t <= 3.8e-123) {
		tmp = x + (z * (y / a));
	} else if (t <= 2.6e+94) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = x - (y * (z / (t - a)))
    if (t <= (-1.52d+240)) then
        tmp = x + y
    else if (t <= (-6d+40)) then
        tmp = t_1
    else if (t <= (-9.5d-9)) then
        tmp = x + y
    else if (t <= 3.8d-123) then
        tmp = x + (z * (y / a))
    else if (t <= 2.6d+94) then
        tmp = t_1
    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 t_1 = x - (y * (z / (t - a)));
	double tmp;
	if (t <= -1.52e+240) {
		tmp = x + y;
	} else if (t <= -6e+40) {
		tmp = t_1;
	} else if (t <= -9.5e-9) {
		tmp = x + y;
	} else if (t <= 3.8e-123) {
		tmp = x + (z * (y / a));
	} else if (t <= 2.6e+94) {
		tmp = t_1;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (y * (z / (t - a)))
	tmp = 0
	if t <= -1.52e+240:
		tmp = x + y
	elif t <= -6e+40:
		tmp = t_1
	elif t <= -9.5e-9:
		tmp = x + y
	elif t <= 3.8e-123:
		tmp = x + (z * (y / a))
	elif t <= 2.6e+94:
		tmp = t_1
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(y * Float64(z / Float64(t - a))))
	tmp = 0.0
	if (t <= -1.52e+240)
		tmp = Float64(x + y);
	elseif (t <= -6e+40)
		tmp = t_1;
	elseif (t <= -9.5e-9)
		tmp = Float64(x + y);
	elseif (t <= 3.8e-123)
		tmp = Float64(x + Float64(z * Float64(y / a)));
	elseif (t <= 2.6e+94)
		tmp = t_1;
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (y * (z / (t - a)));
	tmp = 0.0;
	if (t <= -1.52e+240)
		tmp = x + y;
	elseif (t <= -6e+40)
		tmp = t_1;
	elseif (t <= -9.5e-9)
		tmp = x + y;
	elseif (t <= 3.8e-123)
		tmp = x + (z * (y / a));
	elseif (t <= 2.6e+94)
		tmp = t_1;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(y * N[(z / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.52e+240], N[(x + y), $MachinePrecision], If[LessEqual[t, -6e+40], t$95$1, If[LessEqual[t, -9.5e-9], N[(x + y), $MachinePrecision], If[LessEqual[t, 3.8e-123], N[(x + N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.6e+94], t$95$1, N[(x + y), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.5200000000000001e240 or -6.0000000000000004e40 < t < -9.5000000000000007e-9 or 2.5999999999999999e94 < t

   1. Initial program 70.7%

      \[x + \frac{y \cdot \left(z - t\right)}{a - t} \]
   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 t around inf 85.9%

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

      1. +-commutative 85.9%

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

   7. Simplified 85.9%

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

   if -1.5200000000000001e240 < t < -6.0000000000000004e40 or 3.79999999999999996e-123 < t < 2.5999999999999999e94

   1. Initial program 94.6%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 84.1%

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

      1. associate-/l* 89.3%

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

   7. Simplified 89.3%

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

   if -9.5000000000000007e-9 < t < 3.79999999999999996e-123

   1. Initial program 94.9%

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

      1. *-commutative 94.9%

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

      2. associate-/l* 99.3%

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

   4. Applied egg-rr 99.3%

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

   5. Taylor expanded in t around 0 89.8%

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

      1. *-commutative 89.8%

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

      2. associate-/l* 94.2%

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

   7. Simplified 94.2%

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

4. Final simplification 90.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.52 \cdot 10^{+240}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq -6 \cdot 10^{+40}:\\ \;\;\;\;x - y \cdot \frac{z}{t - a}\\ \mathbf{elif}\;t \leq -9.5 \cdot 10^{-9}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 3.8 \cdot 10^{-123}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{+94}:\\ \;\;\;\;x - y \cdot \frac{z}{t - a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 76.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.6 \cdot 10^{+122}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq -2.2 \cdot 10^{+38}:\\ \;\;\;\;x - y \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq -1.5 \cdot 10^{-7} \lor \neg \left(t \leq 1.95 \cdot 10^{+67}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -4.6e+122)
   (+ x y)
   (if (<= t -2.2e+38)
     (- x (* y (/ z t)))
     (if (or (<= t -1.5e-7) (not (<= t 1.95e+67)))
       (+ x y)
       (+ x (* z (/ y a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -4.6e+122) {
		tmp = x + y;
	} else if (t <= -2.2e+38) {
		tmp = x - (y * (z / t));
	} else if ((t <= -1.5e-7) || !(t <= 1.95e+67)) {
		tmp = x + y;
	} else {
		tmp = x + (z * (y / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-4.6d+122)) then
        tmp = x + y
    else if (t <= (-2.2d+38)) then
        tmp = x - (y * (z / t))
    else if ((t <= (-1.5d-7)) .or. (.not. (t <= 1.95d+67))) then
        tmp = x + y
    else
        tmp = x + (z * (y / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -4.6e+122) {
		tmp = x + y;
	} else if (t <= -2.2e+38) {
		tmp = x - (y * (z / t));
	} else if ((t <= -1.5e-7) || !(t <= 1.95e+67)) {
		tmp = x + y;
	} else {
		tmp = x + (z * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -4.6e+122:
		tmp = x + y
	elif t <= -2.2e+38:
		tmp = x - (y * (z / t))
	elif (t <= -1.5e-7) or not (t <= 1.95e+67):
		tmp = x + y
	else:
		tmp = x + (z * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -4.6e+122)
		tmp = Float64(x + y);
	elseif (t <= -2.2e+38)
		tmp = Float64(x - Float64(y * Float64(z / t)));
	elseif ((t <= -1.5e-7) || !(t <= 1.95e+67))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(z * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -4.6e+122)
		tmp = x + y;
	elseif (t <= -2.2e+38)
		tmp = x - (y * (z / t));
	elseif ((t <= -1.5e-7) || ~((t <= 1.95e+67)))
		tmp = x + y;
	else
		tmp = x + (z * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -4.6e+122], N[(x + y), $MachinePrecision], If[LessEqual[t, -2.2e+38], N[(x - N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t, -1.5e-7], N[Not[LessEqual[t, 1.95e+67]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.6000000000000001e122 or -2.20000000000000006e38 < t < -1.4999999999999999e-7 or 1.95000000000000003e67 < t

   1. Initial program 76.0%

      \[x + \frac{y \cdot \left(z - t\right)}{a - t} \]
   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 84.8%

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

      1. +-commutative 84.8%

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

   7. Simplified 84.8%

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

   if -4.6000000000000001e122 < t < -2.20000000000000006e38

   1. Initial program 93.9%

      \[x + \frac{y \cdot \left(z - t\right)}{a - t} \]
   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 74.9%

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

      1. associate-/l* 80.8%

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

   7. Simplified 80.8%

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

   8. Taylor expanded in a around 0 74.4%

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

      1. mul-1-neg 74.4%

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

      2. unsub-neg 74.4%

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

      3. associate-/l* 80.4%

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

   10. Simplified 80.4%

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

   if -1.4999999999999999e-7 < t < 1.95000000000000003e67

   1. Initial program 95.3%

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

      1. *-commutative 95.3%

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

      2. associate-/l* 98.2%

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

   4. Applied egg-rr 98.2%

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

   5. Taylor expanded in t around 0 85.3%

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

      1. *-commutative 85.3%

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

      2. associate-/l* 89.2%

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

   7. Simplified 89.2%

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

4. Final simplification 86.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.6 \cdot 10^{+122}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq -2.2 \cdot 10^{+38}:\\ \;\;\;\;x - y \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq -1.5 \cdot 10^{-7} \lor \neg \left(t \leq 1.95 \cdot 10^{+67}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 63.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6.9 \cdot 10^{-19}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 2 \cdot 10^{-257}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 3 \cdot 10^{-213}:\\ \;\;\;\;z \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq 4.4 \cdot 10^{-82}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -6.9e-19)
   (+ x y)
   (if (<= t 2e-257)
     x
     (if (<= t 3e-213) (* z (/ y a)) (if (<= t 4.4e-82) x (+ x y))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -6.9e-19) {
		tmp = x + y;
	} else if (t <= 2e-257) {
		tmp = x;
	} else if (t <= 3e-213) {
		tmp = z * (y / a);
	} else if (t <= 4.4e-82) {
		tmp = x;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-6.9d-19)) then
        tmp = x + y
    else if (t <= 2d-257) then
        tmp = x
    else if (t <= 3d-213) then
        tmp = z * (y / a)
    else if (t <= 4.4d-82) then
        tmp = x
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -6.9e-19) {
		tmp = x + y;
	} else if (t <= 2e-257) {
		tmp = x;
	} else if (t <= 3e-213) {
		tmp = z * (y / a);
	} else if (t <= 4.4e-82) {
		tmp = x;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -6.9e-19:
		tmp = x + y
	elif t <= 2e-257:
		tmp = x
	elif t <= 3e-213:
		tmp = z * (y / a)
	elif t <= 4.4e-82:
		tmp = x
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -6.9e-19)
		tmp = Float64(x + y);
	elseif (t <= 2e-257)
		tmp = x;
	elseif (t <= 3e-213)
		tmp = Float64(z * Float64(y / a));
	elseif (t <= 4.4e-82)
		tmp = x;
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -6.9e-19)
		tmp = x + y;
	elseif (t <= 2e-257)
		tmp = x;
	elseif (t <= 3e-213)
		tmp = z * (y / a);
	elseif (t <= 4.4e-82)
		tmp = x;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -6.9e-19], N[(x + y), $MachinePrecision], If[LessEqual[t, 2e-257], x, If[LessEqual[t, 3e-213], N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.4e-82], x, N[(x + y), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -6.8999999999999999e-19 or 4.39999999999999971e-82 < t

   1. Initial program 82.2%

      \[x + \frac{y \cdot \left(z - t\right)}{a - t} \]
   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 76.7%

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

      1. +-commutative 76.7%

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

   7. Simplified 76.7%

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

   if -6.8999999999999999e-19 < t < 2e-257 or 2.99999999999999986e-213 < t < 4.39999999999999971e-82

   1. Initial program 96.2%

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

      1. associate-/l* 95.1%

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

   3. Simplified 95.1%

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

   5. Taylor expanded in x around inf 65.2%

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

   if 2e-257 < t < 2.99999999999999986e-213

   1. Initial program 83.7%

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

      1. associate-/l* 83.1%

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

   3. Simplified 83.1%

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

   5. Taylor expanded in t around 0 83.7%

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

      1. +-commutative 83.7%

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

      2. associate-/l* 83.1%

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

   7. Simplified 83.1%

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

   8. Taylor expanded in z around inf 99.5%

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

      1. +-commutative 99.5%

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

   10. Simplified 99.5%

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

   11. Taylor expanded in y around inf 99.5%

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

4. Final simplification 72.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.9 \cdot 10^{-19}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 2 \cdot 10^{-257}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 3 \cdot 10^{-213}:\\ \;\;\;\;z \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq 4.4 \cdot 10^{-82}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 87.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{+22} \lor \neg \left(z \leq 1.1 \cdot 10^{-35}\right):\\ \;\;\;\;x - y \cdot \frac{z}{t - a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{t - a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.5e+22) (not (<= z 1.1e-35)))
   (- x (* y (/ z (- t a))))
   (+ x (* y (/ t (- t a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.5e+22) || !(z <= 1.1e-35)) {
		tmp = x - (y * (z / (t - a)));
	} 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 <= (-1.5d+22)) .or. (.not. (z <= 1.1d-35))) then
        tmp = x - (y * (z / (t - a)))
    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 <= -1.5e+22) || !(z <= 1.1e-35)) {
		tmp = x - (y * (z / (t - a)));
	} else {
		tmp = x + (y * (t / (t - a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.5e+22) or not (z <= 1.1e-35):
		tmp = x - (y * (z / (t - a)))
	else:
		tmp = x + (y * (t / (t - a)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.5e+22) || !(z <= 1.1e-35))
		tmp = Float64(x - Float64(y * Float64(z / Float64(t - a))));
	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 <= -1.5e+22) || ~((z <= 1.1e-35)))
		tmp = x - (y * (z / (t - a)));
	else
		tmp = x + (y * (t / (t - a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.5e+22], N[Not[LessEqual[z, 1.1e-35]], $MachinePrecision]], N[(x - N[(y * N[(z / N[(t - a), $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 < -1.5e22 or 1.09999999999999997e-35 < z

   1. Initial program 87.3%

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

      1. associate-/l* 96.8%

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

   3. Simplified 96.8%

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

   5. Taylor expanded in z around inf 83.5%

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

      1. associate-/l* 88.0%

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

   7. Simplified 88.0%

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

   if -1.5e22 < z < 1.09999999999999997e-35

   1. Initial program 87.7%

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

      1. associate-/l* 98.6%

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

   3. Simplified 98.6%

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

   5. Taylor expanded in z around 0 83.4%

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

      1. mul-1-neg 83.4%

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

      2. unsub-neg 83.4%

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

      3. *-commutative 83.4%

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

      4. associate-/l* 94.4%

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

   7. Simplified 94.4%

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

4. Final simplification 91.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{+22} \lor \neg \left(z \leq 1.1 \cdot 10^{-35}\right):\\ \;\;\;\;x - y \cdot \frac{z}{t - a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{t - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 87.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6 \cdot 10^{-7} \lor \neg \left(t \leq 8.6 \cdot 10^{+79}\right):\\ \;\;\;\;x - y \cdot \left(\frac{z}{t} + -1\right)\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{z}{t - a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -6e-7) (not (<= t 8.6e+79)))
   (- x (* y (+ (/ z t) -1.0)))
   (- x (* y (/ z (- t a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -6e-7) || !(t <= 8.6e+79)) {
		tmp = x - (y * ((z / t) + -1.0));
	} else {
		tmp = x - (y * (z / (t - a)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-6d-7)) .or. (.not. (t <= 8.6d+79))) then
        tmp = x - (y * ((z / t) + (-1.0d0)))
    else
        tmp = x - (y * (z / (t - a)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -6e-7) || !(t <= 8.6e+79)) {
		tmp = x - (y * ((z / t) + -1.0));
	} else {
		tmp = x - (y * (z / (t - a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -6e-7) or not (t <= 8.6e+79):
		tmp = x - (y * ((z / t) + -1.0))
	else:
		tmp = x - (y * (z / (t - a)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -6e-7) || !(t <= 8.6e+79))
		tmp = Float64(x - Float64(y * Float64(Float64(z / t) + -1.0)));
	else
		tmp = Float64(x - Float64(y * Float64(z / Float64(t - a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -6e-7) || ~((t <= 8.6e+79)))
		tmp = x - (y * ((z / t) + -1.0));
	else
		tmp = x - (y * (z / (t - a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -6e-7], N[Not[LessEqual[t, 8.6e+79]], $MachinePrecision]], N[(x - N[(y * N[(N[(z / t), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(y * N[(z / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -5.9999999999999997e-7 or 8.6000000000000006e79 < t

   1. Initial program 77.7%

      \[x + \frac{y \cdot \left(z - t\right)}{a - t} \]
   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 a around 0 67.9%

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

      1. mul-1-neg 67.9%

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

      2. unsub-neg 67.9%

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

      3. associate-/l* 87.7%

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

      4. div-sub 87.7%

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

      5. sub-neg 87.7%

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

      6. *-inverses 87.7%

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

      7. metadata-eval 87.7%

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

   7. Simplified 87.7%

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

   if -5.9999999999999997e-7 < t < 8.6000000000000006e79

   1. Initial program 95.4%

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

      1. associate-/l* 95.9%

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

   3. Simplified 95.9%

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

   5. Taylor expanded in z around inf 91.4%

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

      1. associate-/l* 92.6%

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

   7. Simplified 92.6%

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

4. Final simplification 90.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6 \cdot 10^{-7} \lor \neg \left(t \leq 8.6 \cdot 10^{+79}\right):\\ \;\;\;\;x - y \cdot \left(\frac{z}{t} + -1\right)\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{z}{t - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 76.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.8 \cdot 10^{-12} \lor \neg \left(t \leq 1.9 \cdot 10^{+67}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -4.8e-12) (not (<= t 1.9e+67))) (+ x y) (+ x (* z (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -4.8e-12) || !(t <= 1.9e+67)) {
		tmp = x + y;
	} else {
		tmp = x + (z * (y / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-4.8d-12)) .or. (.not. (t <= 1.9d+67))) then
        tmp = x + y
    else
        tmp = x + (z * (y / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -4.8e-12) || !(t <= 1.9e+67)) {
		tmp = x + y;
	} else {
		tmp = x + (z * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -4.8e-12) or not (t <= 1.9e+67):
		tmp = x + y
	else:
		tmp = x + (z * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -4.8e-12) || !(t <= 1.9e+67))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(z * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -4.8e-12) || ~((t <= 1.9e+67)))
		tmp = x + y;
	else
		tmp = x + (z * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -4.8e-12], N[Not[LessEqual[t, 1.9e+67]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -4.79999999999999974e-12 or 1.9000000000000001e67 < t

   1. Initial program 78.3%

      \[x + \frac{y \cdot \left(z - t\right)}{a - t} \]
   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 80.2%

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

      1. +-commutative 80.2%

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

   7. Simplified 80.2%

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

   if -4.79999999999999974e-12 < t < 1.9000000000000001e67

   1. Initial program 95.3%

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

      1. *-commutative 95.3%

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

      2. associate-/l* 98.2%

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

   4. Applied egg-rr 98.2%

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

   5. Taylor expanded in t around 0 85.3%

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

      1. *-commutative 85.3%

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

      2. associate-/l* 89.2%

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

   7. Simplified 89.2%

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

4. Final simplification 85.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.8 \cdot 10^{-12} \lor \neg \left(t \leq 1.9 \cdot 10^{+67}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 63.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5.3 \cdot 10^{-19} \lor \neg \left(t \leq 4 \cdot 10^{-82}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -5.3e-19) (not (<= t 4e-82))) (+ x y) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -5.3e-19) || !(t <= 4e-82)) {
		tmp = x + y;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-5.3d-19)) .or. (.not. (t <= 4d-82))) then
        tmp = x + y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -5.3e-19) || !(t <= 4e-82)) {
		tmp = x + y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -5.3e-19) or not (t <= 4e-82):
		tmp = x + y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -5.3e-19) || !(t <= 4e-82))
		tmp = Float64(x + y);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -5.3e-19) || ~((t <= 4e-82)))
		tmp = x + y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -5.3e-19], N[Not[LessEqual[t, 4e-82]], $MachinePrecision]], N[(x + y), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if t < -5.29999999999999972e-19 or 4e-82 < t

   1. Initial program 82.2%

      \[x + \frac{y \cdot \left(z - t\right)}{a - t} \]
   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 76.7%

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

      1. +-commutative 76.7%

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

   7. Simplified 76.7%

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

   if -5.29999999999999972e-19 < t < 4e-82

   1. Initial program 95.5%

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

      1. associate-/l* 94.4%

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

   3. Simplified 94.4%

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

   5. Taylor expanded in x around inf 61.6%

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

4. Final simplification 70.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.3 \cdot 10^{-19} \lor \neg \left(t \leq 4 \cdot 10^{-82}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 98.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 87.5%

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

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

Alternative 10: 50.7% 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 87.5%

   \[x + \frac{y \cdot \left(z - t\right)}{a - t} \]
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 x around inf 56.7%

   \[\leadsto \color{blue}{x} \]
6. 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 2024105 
(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))))