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

Percentage Accurate: 85.2% → 98.1%

Time: 11.3s

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: 85.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x + \frac{y \cdot \left(z - t\right)}{a - t} \leq -1 \cdot 10^{-8}:\\ \;\;\;\;x - \frac{y}{a - t} \cdot \left(t - z\right)\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{t - z}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (+ x (/ (* y (- z t)) (- a t))) -1e-8)
   (- x (* (/ y (- a t)) (- t z)))
   (- x (* y (/ (- t z) (- a t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x + ((y * (z - t)) / (a - t))) <= -1e-8) {
		tmp = x - ((y / (a - t)) * (t - z));
	} else {
		tmp = x - (y * ((t - z) / (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 ((x + ((y * (z - t)) / (a - t))) <= (-1d-8)) then
        tmp = x - ((y / (a - t)) * (t - z))
    else
        tmp = x - (y * ((t - z) / (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 ((x + ((y * (z - t)) / (a - t))) <= -1e-8) {
		tmp = x - ((y / (a - t)) * (t - z));
	} else {
		tmp = x - (y * ((t - z) / (a - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (x + ((y * (z - t)) / (a - t))) <= -1e-8:
		tmp = x - ((y / (a - t)) * (t - z))
	else:
		tmp = x - (y * ((t - z) / (a - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(x + Float64(Float64(y * Float64(z - t)) / Float64(a - t))) <= -1e-8)
		tmp = Float64(x - Float64(Float64(y / Float64(a - t)) * Float64(t - z)));
	else
		tmp = Float64(x - Float64(y * Float64(Float64(t - z) / Float64(a - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x + ((y * (z - t)) / (a - t))) <= -1e-8)
		tmp = x - ((y / (a - t)) * (t - z));
	else
		tmp = x - (y * ((t - z) / (a - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(x + N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], -1e-8], N[(x - N[(N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(y * N[(N[(t - z), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t))) < -1e-8

   1. Initial program 80.3%

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

      1. *-commutative 80.3%

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

      2. associate-/l* 100.0%

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

   4. Applied egg-rr 100.0%

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

   if -1e-8 < (+.f64 x (/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t)))

   1. Initial program 87.1%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{y \cdot \left(z - t\right)}{a - t} \leq -1 \cdot 10^{-8}:\\ \;\;\;\;x - \frac{y}{a - t} \cdot \left(t - z\right)\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{t - z}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 76.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + z \cdot \frac{y}{a}\\ t_2 := x - y \cdot \frac{z}{t}\\ \mathbf{if}\;t \leq -6.5 \cdot 10^{+186}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq -2.4 \cdot 10^{+42}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -8.5 \cdot 10^{-15}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -9.8 \cdot 10^{-68}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -7.5 \cdot 10^{-83} \lor \neg \left(t \leq 0.85\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* z (/ y a)))) (t_2 (- x (* y (/ z t)))))
   (if (<= t -6.5e+186)
     (+ x y)
     (if (<= t -2.4e+42)
       t_2
       (if (<= t -8.5e-15)
         t_1
         (if (<= t -9.8e-68)
           t_2
           (if (or (<= t -7.5e-83) (not (<= t 0.85))) (+ x y) t_1)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (z * (y / a));
	double t_2 = x - (y * (z / t));
	double tmp;
	if (t <= -6.5e+186) {
		tmp = x + y;
	} else if (t <= -2.4e+42) {
		tmp = t_2;
	} else if (t <= -8.5e-15) {
		tmp = t_1;
	} else if (t <= -9.8e-68) {
		tmp = t_2;
	} else if ((t <= -7.5e-83) || !(t <= 0.85)) {
		tmp = x + y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + (z * (y / a))
    t_2 = x - (y * (z / t))
    if (t <= (-6.5d+186)) then
        tmp = x + y
    else if (t <= (-2.4d+42)) then
        tmp = t_2
    else if (t <= (-8.5d-15)) then
        tmp = t_1
    else if (t <= (-9.8d-68)) then
        tmp = t_2
    else if ((t <= (-7.5d-83)) .or. (.not. (t <= 0.85d0))) then
        tmp = x + y
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (z * (y / a));
	double t_2 = x - (y * (z / t));
	double tmp;
	if (t <= -6.5e+186) {
		tmp = x + y;
	} else if (t <= -2.4e+42) {
		tmp = t_2;
	} else if (t <= -8.5e-15) {
		tmp = t_1;
	} else if (t <= -9.8e-68) {
		tmp = t_2;
	} else if ((t <= -7.5e-83) || !(t <= 0.85)) {
		tmp = x + y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (z * (y / a))
	t_2 = x - (y * (z / t))
	tmp = 0
	if t <= -6.5e+186:
		tmp = x + y
	elif t <= -2.4e+42:
		tmp = t_2
	elif t <= -8.5e-15:
		tmp = t_1
	elif t <= -9.8e-68:
		tmp = t_2
	elif (t <= -7.5e-83) or not (t <= 0.85):
		tmp = x + y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(z * Float64(y / a)))
	t_2 = Float64(x - Float64(y * Float64(z / t)))
	tmp = 0.0
	if (t <= -6.5e+186)
		tmp = Float64(x + y);
	elseif (t <= -2.4e+42)
		tmp = t_2;
	elseif (t <= -8.5e-15)
		tmp = t_1;
	elseif (t <= -9.8e-68)
		tmp = t_2;
	elseif ((t <= -7.5e-83) || !(t <= 0.85))
		tmp = Float64(x + y);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (z * (y / a));
	t_2 = x - (y * (z / t));
	tmp = 0.0;
	if (t <= -6.5e+186)
		tmp = x + y;
	elseif (t <= -2.4e+42)
		tmp = t_2;
	elseif (t <= -8.5e-15)
		tmp = t_1;
	elseif (t <= -9.8e-68)
		tmp = t_2;
	elseif ((t <= -7.5e-83) || ~((t <= 0.85)))
		tmp = x + y;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x - N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -6.5e+186], N[(x + y), $MachinePrecision], If[LessEqual[t, -2.4e+42], t$95$2, If[LessEqual[t, -8.5e-15], t$95$1, If[LessEqual[t, -9.8e-68], t$95$2, If[Or[LessEqual[t, -7.5e-83], N[Not[LessEqual[t, 0.85]], $MachinePrecision]], N[(x + y), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -6.4999999999999997e186 or -9.79999999999999954e-68 < t < -7.4999999999999997e-83 or 0.849999999999999978 < t

   1. Initial program 66.1%

      \[x + \frac{y \cdot \left(z - t\right)}{a - t} \]
   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 79.4%

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

      1. +-commutative 79.4%

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

   7. Simplified 79.4%

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

   if -6.4999999999999997e186 < t < -2.3999999999999999e42 or -8.50000000000000007e-15 < t < -9.79999999999999954e-68

   1. Initial program 91.5%

      \[x + \frac{y \cdot \left(z - t\right)}{a - t} \]
   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 81.0%

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

   6. Taylor expanded in a around 0 76.9%

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

      1. mul-1-neg 76.9%

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

      2. unsub-neg 76.9%

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

      3. associate-*r/ 79.9%

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

   8. Simplified 79.9%

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

   if -2.3999999999999999e42 < t < -8.50000000000000007e-15 or -7.4999999999999997e-83 < t < 0.849999999999999978

   1. Initial program 94.5%

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

      1. *-commutative 94.5%

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

      2. associate-/l* 99.2%

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

   4. Applied egg-rr 99.2%

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

   5. Taylor expanded in t around 0 79.4%

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

      1. *-commutative 79.4%

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

      2. associate-/l* 83.5%

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

   7. Simplified 83.5%

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

4. Final simplification 81.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.5 \cdot 10^{+186}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq -2.4 \cdot 10^{+42}:\\ \;\;\;\;x - y \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq -8.5 \cdot 10^{-15}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq -9.8 \cdot 10^{-68}:\\ \;\;\;\;x - y \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq -7.5 \cdot 10^{-83} \lor \neg \left(t \leq 0.85\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 75.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6.5 \cdot 10^{+186}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq -2.2 \cdot 10^{+20}:\\ \;\;\;\;x - y \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq -0.055:\\ \;\;\;\;\frac{y \cdot t}{t - a}\\ \mathbf{elif}\;t \leq -3.8 \cdot 10^{-21} \lor \neg \left(t \leq -7.5 \cdot 10^{-83}\right) \land t \leq 2150:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -6.5e+186)
   (+ x y)
   (if (<= t -2.2e+20)
     (- x (* y (/ z t)))
     (if (<= t -0.055)
       (/ (* y t) (- t a))
       (if (or (<= t -3.8e-21) (and (not (<= t -7.5e-83)) (<= t 2150.0)))
         (+ x (* z (/ y a)))
         (+ x y))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -6.5e+186) {
		tmp = x + y;
	} else if (t <= -2.2e+20) {
		tmp = x - (y * (z / t));
	} else if (t <= -0.055) {
		tmp = (y * t) / (t - a);
	} else if ((t <= -3.8e-21) || (!(t <= -7.5e-83) && (t <= 2150.0))) {
		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 <= (-6.5d+186)) then
        tmp = x + y
    else if (t <= (-2.2d+20)) then
        tmp = x - (y * (z / t))
    else if (t <= (-0.055d0)) then
        tmp = (y * t) / (t - a)
    else if ((t <= (-3.8d-21)) .or. (.not. (t <= (-7.5d-83))) .and. (t <= 2150.0d0)) 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 <= -6.5e+186) {
		tmp = x + y;
	} else if (t <= -2.2e+20) {
		tmp = x - (y * (z / t));
	} else if (t <= -0.055) {
		tmp = (y * t) / (t - a);
	} else if ((t <= -3.8e-21) || (!(t <= -7.5e-83) && (t <= 2150.0))) {
		tmp = x + (z * (y / a));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -6.5e+186:
		tmp = x + y
	elif t <= -2.2e+20:
		tmp = x - (y * (z / t))
	elif t <= -0.055:
		tmp = (y * t) / (t - a)
	elif (t <= -3.8e-21) or (not (t <= -7.5e-83) and (t <= 2150.0)):
		tmp = x + (z * (y / a))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -6.5e+186)
		tmp = Float64(x + y);
	elseif (t <= -2.2e+20)
		tmp = Float64(x - Float64(y * Float64(z / t)));
	elseif (t <= -0.055)
		tmp = Float64(Float64(y * t) / Float64(t - a));
	elseif ((t <= -3.8e-21) || (!(t <= -7.5e-83) && (t <= 2150.0)))
		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 <= -6.5e+186)
		tmp = x + y;
	elseif (t <= -2.2e+20)
		tmp = x - (y * (z / t));
	elseif (t <= -0.055)
		tmp = (y * t) / (t - a);
	elseif ((t <= -3.8e-21) || (~((t <= -7.5e-83)) && (t <= 2150.0)))
		tmp = x + (z * (y / a));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -6.5e+186], N[(x + y), $MachinePrecision], If[LessEqual[t, -2.2e+20], N[(x - N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -0.055], N[(N[(y * t), $MachinePrecision] / N[(t - a), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t, -3.8e-21], And[N[Not[LessEqual[t, -7.5e-83]], $MachinePrecision], LessEqual[t, 2150.0]]], N[(x + N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -6.4999999999999997e186 or -3.7999999999999998e-21 < t < -7.4999999999999997e-83 or 2150 < t

   1. Initial program 68.7%

      \[x + \frac{y \cdot \left(z - t\right)}{a - t} \]
   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 t around inf 77.9%

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

      1. +-commutative 77.9%

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

   7. Simplified 77.9%

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

   if -6.4999999999999997e186 < t < -2.2e20

   1. Initial program 89.8%

      \[x + \frac{y \cdot \left(z - t\right)}{a - t} \]
   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 z around inf 83.6%

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

   6. Taylor expanded in a around 0 80.3%

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

      1. mul-1-neg 80.3%

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

      2. unsub-neg 80.3%

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

      3. associate-*r/ 83.9%

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

   8. Simplified 83.9%

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

   if -2.2e20 < t < -0.0550000000000000003

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

      2. associate-/l* 99.6%

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

   4. Applied egg-rr 99.6%

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

   5. Taylor expanded in z around 0 76.4%

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

      1. mul-1-neg 76.4%

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

      2. unsub-neg 76.4%

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

      3. associate-/l* 76.0%

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

   7. Simplified 76.0%

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

   8. Taylor expanded in x around 0 76.4%

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

      1. associate-*r/ 76.4%

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

      2. *-commutative 76.4%

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

      3. neg-mul-1 76.4%

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

      4. distribute-rgt-neg-in 76.4%

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

   10. Simplified 76.4%

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

   if -0.0550000000000000003 < t < -3.7999999999999998e-21 or -7.4999999999999997e-83 < t < 2150

   1. Initial program 94.3%

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

      1. *-commutative 94.3%

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

      2. associate-/l* 99.2%

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

   4. Applied egg-rr 99.2%

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

   5. Taylor expanded in t around 0 80.1%

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

      1. *-commutative 80.1%

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

      2. associate-/l* 84.3%

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

   7. Simplified 84.3%

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

4. Final simplification 81.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.5 \cdot 10^{+186}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq -2.2 \cdot 10^{+20}:\\ \;\;\;\;x - y \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq -0.055:\\ \;\;\;\;\frac{y \cdot t}{t - a}\\ \mathbf{elif}\;t \leq -3.8 \cdot 10^{-21} \lor \neg \left(t \leq -7.5 \cdot 10^{-83}\right) \land t \leq 2150:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 84.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.2 \cdot 10^{+187} \lor \neg \left(t \leq 2.4 \cdot 10^{+129}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -4.2e+187) (not (<= t 2.4e+129)))
   (+ x y)
   (+ x (* y (/ z (- a t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -4.2e+187) || !(t <= 2.4e+129)) {
		tmp = x + y;
	} else {
		tmp = x + (y * (z / (a - t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-4.2d+187)) .or. (.not. (t <= 2.4d+129))) then
        tmp = x + y
    else
        tmp = x + (y * (z / (a - t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -4.2e+187) || !(t <= 2.4e+129)) {
		tmp = x + y;
	} else {
		tmp = x + (y * (z / (a - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -4.2e+187) or not (t <= 2.4e+129):
		tmp = x + y
	else:
		tmp = x + (y * (z / (a - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -4.2e+187) || !(t <= 2.4e+129))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(y * Float64(z / Float64(a - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -4.2e+187) || ~((t <= 2.4e+129)))
		tmp = x + y;
	else
		tmp = x + (y * (z / (a - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -4.2e+187], N[Not[LessEqual[t, 2.4e+129]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -4.2e187 or 2.3999999999999999e129 < t

   1. Initial program 58.0%

      \[x + \frac{y \cdot \left(z - t\right)}{a - t} \]
   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 83.6%

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

      1. +-commutative 83.6%

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

   7. Simplified 83.6%

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

   if -4.2e187 < t < 2.3999999999999999e129

   1. Initial program 94.0%

      \[x + \frac{y \cdot \left(z - t\right)}{a - t} \]
   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 86.2%

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

      1. associate-/l* 87.5%

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

   7. Simplified 87.5%

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

4. Final simplification 86.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.2 \cdot 10^{+187} \lor \neg \left(t \leq 2.4 \cdot 10^{+129}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 84.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.5 \cdot 10^{+187} \lor \neg \left(t \leq 1.4 \cdot 10^{+129}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -2.5e+187) (not (<= t 1.4e+129)))
   (+ x y)
   (+ x (* z (/ y (- a t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -2.5e+187) || !(t <= 1.4e+129)) {
		tmp = x + y;
	} else {
		tmp = x + (z * (y / (a - t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-2.5d+187)) .or. (.not. (t <= 1.4d+129))) then
        tmp = x + y
    else
        tmp = x + (z * (y / (a - t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -2.5e+187) || !(t <= 1.4e+129)) {
		tmp = x + y;
	} else {
		tmp = x + (z * (y / (a - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -2.5e+187) or not (t <= 1.4e+129):
		tmp = x + y
	else:
		tmp = x + (z * (y / (a - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -2.5e+187) || !(t <= 1.4e+129))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(z * Float64(y / Float64(a - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -2.5e+187) || ~((t <= 1.4e+129)))
		tmp = x + y;
	else
		tmp = x + (z * (y / (a - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -2.5e+187], N[Not[LessEqual[t, 1.4e+129]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(z * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.5000000000000001e187 or 1.39999999999999987e129 < t

   1. Initial program 58.0%

      \[x + \frac{y \cdot \left(z - t\right)}{a - t} \]
   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 83.6%

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

      1. +-commutative 83.6%

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

   7. Simplified 83.6%

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

   if -2.5000000000000001e187 < t < 1.39999999999999987e129

   1. Initial program 94.0%

      \[x + \frac{y \cdot \left(z - t\right)}{a - t} \]
   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 86.2%

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

      1. div-inv 86.2%

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

      2. *-commutative 86.2%

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

      3. associate-*l* 88.6%

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

      4. *-commutative 88.6%

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

      5. associate-*l/ 88.7%

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

      6. *-un-lft-identity 88.7%

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

   7. Applied egg-rr 88.7%

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

4. Final simplification 87.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.5 \cdot 10^{+187} \lor \neg \left(t \leq 1.4 \cdot 10^{+129}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 86.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.5 \cdot 10^{+111} \lor \neg \left(t \leq 3.3 \cdot 10^{+123}\right):\\ \;\;\;\;x + \frac{y}{1 - \frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -2.5e+111) (not (<= t 3.3e+123)))
   (+ x (/ y (- 1.0 (/ a t))))
   (+ x (* z (/ y (- a t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -2.5e+111) || !(t <= 3.3e+123)) {
		tmp = x + (y / (1.0 - (a / t)));
	} else {
		tmp = x + (z * (y / (a - t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-2.5d+111)) .or. (.not. (t <= 3.3d+123))) then
        tmp = x + (y / (1.0d0 - (a / t)))
    else
        tmp = x + (z * (y / (a - t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -2.5e+111) || !(t <= 3.3e+123)) {
		tmp = x + (y / (1.0 - (a / t)));
	} else {
		tmp = x + (z * (y / (a - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -2.5e+111) or not (t <= 3.3e+123):
		tmp = x + (y / (1.0 - (a / t)))
	else:
		tmp = x + (z * (y / (a - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -2.5e+111) || !(t <= 3.3e+123))
		tmp = Float64(x + Float64(y / Float64(1.0 - Float64(a / t))));
	else
		tmp = Float64(x + Float64(z * Float64(y / Float64(a - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -2.5e+111) || ~((t <= 3.3e+123)))
		tmp = x + (y / (1.0 - (a / t)));
	else
		tmp = x + (z * (y / (a - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -2.5e+111], N[Not[LessEqual[t, 3.3e+123]], $MachinePrecision]], N[(x + N[(y / N[(1.0 - N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.4999999999999998e111 or 3.30000000000000003e123 < t

   1. Initial program 61.3%

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

      1. clear-num 99.9%

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

      2. un-div-inv 99.9%

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

   6. Applied egg-rr 99.9%

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

      1. div-sub 99.9%

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

   8. Applied egg-rr 99.9%

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

   9. Taylor expanded in z around 0 90.9%

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

       1. +-commutative 90.9%

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

       2. mul-1-neg 90.9%

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

       3. unsub-neg 90.9%

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

   11. Simplified 90.9%

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

   if -2.4999999999999998e111 < t < 3.30000000000000003e123

   1. Initial program 95.2%

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

      1. associate-/l* 96.6%

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

   3. Simplified 96.6%

      \[\leadsto \color{blue}{x + y \cdot \frac{z - t}{a - t}} \]
   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. div-inv 86.8%

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

      2. *-commutative 86.8%

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

      3. associate-*l* 89.4%

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

      4. *-commutative 89.4%

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

      5. associate-*l/ 89.5%

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

      6. *-un-lft-identity 89.5%

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

   7. Applied egg-rr 89.5%

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

4. Final simplification 89.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.5 \cdot 10^{+111} \lor \neg \left(t \leq 3.3 \cdot 10^{+123}\right):\\ \;\;\;\;x + \frac{y}{1 - \frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 87.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -0.0074 \lor \neg \left(t \leq 1.45 \cdot 10^{+76}\right):\\ \;\;\;\;x - y \cdot \left(\frac{z}{t} + -1\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -0.0074) (not (<= t 1.45e+76)))
   (- x (* y (+ (/ z t) -1.0)))
   (+ x (* z (/ y (- a t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -0.0074) || !(t <= 1.45e+76)) {
		tmp = x - (y * ((z / t) + -1.0));
	} else {
		tmp = x + (z * (y / (a - t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-0.0074d0)) .or. (.not. (t <= 1.45d+76))) then
        tmp = x - (y * ((z / t) + (-1.0d0)))
    else
        tmp = x + (z * (y / (a - t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -0.0074) || !(t <= 1.45e+76)) {
		tmp = x - (y * ((z / t) + -1.0));
	} else {
		tmp = x + (z * (y / (a - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -0.0074) or not (t <= 1.45e+76):
		tmp = x - (y * ((z / t) + -1.0))
	else:
		tmp = x + (z * (y / (a - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -0.0074) || !(t <= 1.45e+76))
		tmp = Float64(x - Float64(y * Float64(Float64(z / t) + -1.0)));
	else
		tmp = Float64(x + Float64(z * Float64(y / Float64(a - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -0.0074) || ~((t <= 1.45e+76)))
		tmp = x - (y * ((z / t) + -1.0));
	else
		tmp = x + (z * (y / (a - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -0.0074], N[Not[LessEqual[t, 1.45e+76]], $MachinePrecision]], N[(x - N[(y * N[(N[(z / t), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -0.0074000000000000003 or 1.4500000000000001e76 < t

   1. Initial program 70.4%

      \[x + \frac{y \cdot \left(z - t\right)}{a - t} \]
   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 0 65.3%

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

      1. mul-1-neg 65.3%

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

      2. unsub-neg 65.3%

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

      3. associate-/l* 90.5%

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

      4. div-sub 90.5%

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

      5. sub-neg 90.5%

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

      6. *-inverses 90.5%

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

      7. metadata-eval 90.5%

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

   7. Simplified 90.5%

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

   if -0.0074000000000000003 < t < 1.4500000000000001e76

   1. Initial program 94.9%

      \[x + \frac{y \cdot \left(z - t\right)}{a - t} \]
   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 88.1%

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

      1. div-inv 88.1%

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

      2. *-commutative 88.1%

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

      3. associate-*l* 92.4%

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

      4. *-commutative 92.4%

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

      5. associate-*l/ 92.5%

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

      6. *-un-lft-identity 92.5%

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

   7. Applied egg-rr 92.5%

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

4. Final simplification 91.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -0.0074 \lor \neg \left(t \leq 1.45 \cdot 10^{+76}\right):\\ \;\;\;\;x - y \cdot \left(\frac{z}{t} + -1\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 85.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.2 \cdot 10^{+109}:\\ \;\;\;\;x + \frac{y}{1 - \frac{a}{t}}\\ \mathbf{elif}\;t \leq 3.1 \cdot 10^{+125}:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{t - a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -3.2e+109)
   (+ x (/ y (- 1.0 (/ a t))))
   (if (<= t 3.1e+125) (+ 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 (t <= -3.2e+109) {
		tmp = x + (y / (1.0 - (a / t)));
	} else if (t <= 3.1e+125) {
		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 (t <= (-3.2d+109)) then
        tmp = x + (y / (1.0d0 - (a / t)))
    else if (t <= 3.1d+125) 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 (t <= -3.2e+109) {
		tmp = x + (y / (1.0 - (a / t)));
	} else if (t <= 3.1e+125) {
		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 t <= -3.2e+109:
		tmp = x + (y / (1.0 - (a / t)))
	elif t <= 3.1e+125:
		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 (t <= -3.2e+109)
		tmp = Float64(x + Float64(y / Float64(1.0 - Float64(a / t))));
	elseif (t <= 3.1e+125)
		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 (t <= -3.2e+109)
		tmp = x + (y / (1.0 - (a / t)));
	elseif (t <= 3.1e+125)
		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[LessEqual[t, -3.2e+109], N[(x + N[(y / N[(1.0 - N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.1e+125], 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 3 regimes

2. if t < -3.2000000000000001e109

   1. Initial program 60.4%

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

      1. clear-num 100.0%

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

      2. un-div-inv 100.0%

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

   6. Applied egg-rr 100.0%

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

      1. div-sub 100.0%

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

   8. Applied egg-rr 100.0%

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

   9. Taylor expanded in z around 0 92.1%

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

       1. +-commutative 92.1%

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

       2. mul-1-neg 92.1%

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

       3. unsub-neg 92.1%

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

   11. Simplified 92.1%

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

   if -3.2000000000000001e109 < t < 3.1e125

   1. Initial program 95.2%

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

      1. associate-/l* 96.6%

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

   3. Simplified 96.6%

      \[\leadsto \color{blue}{x + y \cdot \frac{z - t}{a - t}} \]
   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. div-inv 86.8%

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

      2. *-commutative 86.8%

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

      3. associate-*l* 89.4%

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

      4. *-commutative 89.4%

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

      5. associate-*l/ 89.5%

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

      6. *-un-lft-identity 89.5%

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

   7. Applied egg-rr 89.5%

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

   if 3.1e125 < t

   1. Initial program 62.0%

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

      1. *-commutative 62.0%

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

      2. associate-/l* 99.9%

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

   4. Applied egg-rr 99.9%

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

   5. Taylor expanded in z around 0 56.5%

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

      1. mul-1-neg 56.5%

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

      2. unsub-neg 56.5%

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

      3. associate-/l* 89.9%

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

   7. Simplified 89.9%

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

4. Final simplification 89.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.2 \cdot 10^{+109}:\\ \;\;\;\;x + \frac{y}{1 - \frac{a}{t}}\\ \mathbf{elif}\;t \leq 3.1 \cdot 10^{+125}:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{t - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 76.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -0.0033 \lor \neg \left(t \leq 1850\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -0.0033) (not (<= t 1850.0))) (+ x y) (+ x (* z (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -0.0033) || !(t <= 1850.0)) {
		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 <= (-0.0033d0)) .or. (.not. (t <= 1850.0d0))) 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 <= -0.0033) || !(t <= 1850.0)) {
		tmp = x + y;
	} else {
		tmp = x + (z * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -0.0033) or not (t <= 1850.0):
		tmp = x + y
	else:
		tmp = x + (z * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -0.0033) || !(t <= 1850.0))
		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 <= -0.0033) || ~((t <= 1850.0)))
		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, -0.0033], N[Not[LessEqual[t, 1850.0]], $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 < -0.0033 or 1850 < t

   1. Initial program 72.0%

      \[x + \frac{y \cdot \left(z - t\right)}{a - t} \]
   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 73.7%

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

      1. +-commutative 73.7%

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

   7. Simplified 73.7%

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

   if -0.0033 < t < 1850

   1. Initial program 94.7%

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

      1. *-commutative 94.7%

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

      2. associate-/l* 99.2%

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

   4. Applied egg-rr 99.2%

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

   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-/l* 81.4%

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

   7. Simplified 81.4%

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

4. Final simplification 78.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -0.0033 \lor \neg \left(t \leq 1850\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 62.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.45 \cdot 10^{-84} \lor \neg \left(t \leq 2.1 \cdot 10^{+112}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.45e-84) (not (<= t 2.1e+112))) (+ x y) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.45e-84) || !(t <= 2.1e+112)) {
		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 <= (-1.45d-84)) .or. (.not. (t <= 2.1d+112))) 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 <= -1.45e-84) || !(t <= 2.1e+112)) {
		tmp = x + y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -1.45e-84) or not (t <= 2.1e+112):
		tmp = x + y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1.45e-84) || !(t <= 2.1e+112))
		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 <= -1.45e-84) || ~((t <= 2.1e+112)))
		tmp = x + y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -1.45e-84], N[Not[LessEqual[t, 2.1e+112]], $MachinePrecision]], N[(x + y), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if t < -1.4500000000000001e-84 or 2.0999999999999999e112 < t

   1. Initial program 71.8%

      \[x + \frac{y \cdot \left(z - t\right)}{a - t} \]
   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 73.5%

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

      1. +-commutative 73.5%

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

   7. Simplified 73.5%

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

   if -1.4500000000000001e-84 < t < 2.0999999999999999e112

   1. Initial program 95.8%

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

      1. associate-/l* 95.6%

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

   3. Simplified 95.6%

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

   5. Taylor expanded in x around inf 52.1%

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

4. Final simplification 62.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.45 \cdot 10^{-84} \lor \neg \left(t \leq 2.1 \cdot 10^{+112}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 97.9% 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 84.6%

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

   1. associate-/l* 97.6%

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

3. Simplified 97.6%

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

5. Final simplification 97.6%

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

Alternative 12: 50.2% 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 84.6%

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

   1. associate-/l* 97.6%

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

3. Simplified 97.6%

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

5. Taylor expanded in x around inf 49.7%

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

6. Final simplification 49.7%

   \[\leadsto x \]
7. Add Preprocessing

Developer target: 98.0% 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 2024096 
(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))))