Optimisation.CirclePacking:place from circle-packing-0.1.0.4, D

Percentage Accurate: 93.1% → 97.8%

Time: 8.4s

Alternatives: 10

Speedup: 1.0×

• 25.0% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 93.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 95.1%

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

3. Taylor expanded in z around 0 90.8%

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

   1. +-commutative 90.8%

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

   2. *-commutative 90.8%

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

   3. associate-*r/ 90.8%

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

   4. mul-1-neg 90.8%

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

   5. associate-/l* 92.4%

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

   6. distribute-lft-neg-in 92.4%

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

   7. distribute-rgt-in 97.6%

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

   8. sub-neg 97.6%

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

5. Simplified 97.6%

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

Alternative 2: 86.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.9 \cdot 10^{+51} \lor \neg \left(x \leq 12000000000000\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{t} \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -1.9e+51) (not (<= x 12000000000000.0)))
   (* x (- 1.0 (/ y t)))
   (+ x (* (/ y t) z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.9e+51) || !(x <= 12000000000000.0)) {
		tmp = x * (1.0 - (y / t));
	} else {
		tmp = x + ((y / t) * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-1.9d+51)) .or. (.not. (x <= 12000000000000.0d0))) then
        tmp = x * (1.0d0 - (y / t))
    else
        tmp = x + ((y / t) * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.9e+51) || !(x <= 12000000000000.0)) {
		tmp = x * (1.0 - (y / t));
	} else {
		tmp = x + ((y / t) * z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -1.9e+51) or not (x <= 12000000000000.0):
		tmp = x * (1.0 - (y / t))
	else:
		tmp = x + ((y / t) * z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -1.9e+51) || !(x <= 12000000000000.0))
		tmp = Float64(x * Float64(1.0 - Float64(y / t)));
	else
		tmp = Float64(x + Float64(Float64(y / t) * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -1.9e+51) || ~((x <= 12000000000000.0)))
		tmp = x * (1.0 - (y / t));
	else
		tmp = x + ((y / t) * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -1.9e+51], N[Not[LessEqual[x, 12000000000000.0]], $MachinePrecision]], N[(x * N[(1.0 - N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y / t), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.8999999999999999e51 or 1.2e13 < x

   1. Initial program 93.2%

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

   3. Taylor expanded in x around inf 90.4%

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

      1. mul-1-neg 90.4%

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

      2. unsub-neg 90.4%

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

   5. Simplified 90.4%

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

   if -1.8999999999999999e51 < x < 1.2e13

   1. Initial program 96.6%

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

   3. Taylor expanded in z around 0 93.8%

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

      1. +-commutative 93.8%

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

      2. *-commutative 93.8%

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

      3. associate-*r/ 93.0%

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

      4. mul-1-neg 93.0%

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

      5. associate-/l* 90.9%

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

      6. distribute-lft-neg-in 90.9%

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

      7. distribute-rgt-in 95.8%

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

      8. sub-neg 95.8%

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

   5. Simplified 95.8%

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

   6. Taylor expanded in z around inf 87.0%

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

4. Final simplification 88.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.9 \cdot 10^{+51} \lor \neg \left(x \leq 12000000000000\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{t} \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 84.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.05 \cdot 10^{+51} \lor \neg \left(x \leq 15500000000000\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -2.05e+51) (not (<= x 15500000000000.0)))
   (* x (- 1.0 (/ y t)))
   (+ x (* y (/ z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -2.05e+51) || !(x <= 15500000000000.0)) {
		tmp = x * (1.0 - (y / t));
	} else {
		tmp = x + (y * (z / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-2.05d+51)) .or. (.not. (x <= 15500000000000.0d0))) then
        tmp = x * (1.0d0 - (y / t))
    else
        tmp = x + (y * (z / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -2.05e+51) || !(x <= 15500000000000.0)) {
		tmp = x * (1.0 - (y / t));
	} else {
		tmp = x + (y * (z / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -2.05e+51) or not (x <= 15500000000000.0):
		tmp = x * (1.0 - (y / t))
	else:
		tmp = x + (y * (z / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -2.05e+51) || !(x <= 15500000000000.0))
		tmp = Float64(x * Float64(1.0 - Float64(y / t)));
	else
		tmp = Float64(x + Float64(y * Float64(z / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -2.05e+51) || ~((x <= 15500000000000.0)))
		tmp = x * (1.0 - (y / t));
	else
		tmp = x + (y * (z / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -2.05e+51], N[Not[LessEqual[x, 15500000000000.0]], $MachinePrecision]], N[(x * N[(1.0 - N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.05000000000000005e51 or 1.55e13 < x

   1. Initial program 93.2%

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

   3. Taylor expanded in x around inf 90.4%

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

      1. mul-1-neg 90.4%

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

      2. unsub-neg 90.4%

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

   5. Simplified 90.4%

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

   if -2.05000000000000005e51 < x < 1.55e13

   1. Initial program 96.6%

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

   3. Taylor expanded in z around inf 86.5%

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

      1. associate-/l* 86.3%

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

   5. Simplified 86.3%

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

4. Final simplification 88.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.05 \cdot 10^{+51} \lor \neg \left(x \leq 15500000000000\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 76.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1250 \lor \neg \left(x \leq 1.25 \cdot 10^{-135}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - x}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -1250.0) (not (<= x 1.25e-135)))
   (* x (- 1.0 (/ y t)))
   (* y (/ (- z x) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1250.0) || !(x <= 1.25e-135)) {
		tmp = x * (1.0 - (y / t));
	} else {
		tmp = y * ((z - x) / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-1250.0d0)) .or. (.not. (x <= 1.25d-135))) then
        tmp = x * (1.0d0 - (y / t))
    else
        tmp = y * ((z - x) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1250.0) || !(x <= 1.25e-135)) {
		tmp = x * (1.0 - (y / t));
	} else {
		tmp = y * ((z - x) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -1250.0) or not (x <= 1.25e-135):
		tmp = x * (1.0 - (y / t))
	else:
		tmp = y * ((z - x) / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -1250.0) || !(x <= 1.25e-135))
		tmp = Float64(x * Float64(1.0 - Float64(y / t)));
	else
		tmp = Float64(y * Float64(Float64(z - x) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -1250.0) || ~((x <= 1.25e-135)))
		tmp = x * (1.0 - (y / t));
	else
		tmp = y * ((z - x) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -1250.0], N[Not[LessEqual[x, 1.25e-135]], $MachinePrecision]], N[(x * N[(1.0 - N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(N[(z - x), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1250 or 1.25000000000000005e-135 < x

   1. Initial program 94.3%

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

   3. Taylor expanded in x around inf 82.6%

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

      1. mul-1-neg 82.6%

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

      2. unsub-neg 82.6%

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

   5. Simplified 82.6%

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

   if -1250 < x < 1.25000000000000005e-135

   1. Initial program 96.3%

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

   3. Taylor expanded in y around -inf 72.4%

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

      1. associate-/l* 74.1%

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

      2. *-commutative 74.1%

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

   5. Applied egg-rr 74.1%

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

4. Final simplification 79.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1250 \lor \neg \left(x \leq 1.25 \cdot 10^{-135}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - x}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 73.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5000000000 \lor \neg \left(t \leq 2.95 \cdot 10^{+181}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t} \cdot \left(z - x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -5000000000.0) (not (<= t 2.95e+181)))
   (* x (- 1.0 (/ y t)))
   (* (/ y t) (- z x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -5000000000.0) || !(t <= 2.95e+181)) {
		tmp = x * (1.0 - (y / t));
	} else {
		tmp = (y / t) * (z - x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((t <= (-5000000000.0d0)) .or. (.not. (t <= 2.95d+181))) then
        tmp = x * (1.0d0 - (y / t))
    else
        tmp = (y / t) * (z - x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -5000000000.0) || !(t <= 2.95e+181)) {
		tmp = x * (1.0 - (y / t));
	} else {
		tmp = (y / t) * (z - x);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -5000000000.0) or not (t <= 2.95e+181):
		tmp = x * (1.0 - (y / t))
	else:
		tmp = (y / t) * (z - x)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -5000000000.0) || !(t <= 2.95e+181))
		tmp = Float64(x * Float64(1.0 - Float64(y / t)));
	else
		tmp = Float64(Float64(y / t) * Float64(z - x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -5000000000.0) || ~((t <= 2.95e+181)))
		tmp = x * (1.0 - (y / t));
	else
		tmp = (y / t) * (z - x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -5000000000.0], N[Not[LessEqual[t, 2.95e+181]], $MachinePrecision]], N[(x * N[(1.0 - N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y / t), $MachinePrecision] * N[(z - x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -5e9 or 2.9499999999999999e181 < t

   1. Initial program 90.8%

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

   3. Taylor expanded in x around inf 81.4%

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

      1. mul-1-neg 81.4%

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

      2. unsub-neg 81.4%

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

   5. Simplified 81.4%

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

   if -5e9 < t < 2.9499999999999999e181

   1. Initial program 97.6%

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

   3. Taylor expanded in y around -inf 77.3%

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

   4. Taylor expanded in z around 0 71.2%

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

      1. +-commutative 91.5%

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

      2. *-commutative 91.5%

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

      3. associate-*r/ 90.2%

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

      4. mul-1-neg 90.2%

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

      5. associate-/l* 88.8%

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

      6. distribute-lft-neg-in 88.8%

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

      7. distribute-rgt-in 96.9%

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

      8. sub-neg 96.9%

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

   6. Simplified 76.6%

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

4. Final simplification 78.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5000000000 \lor \neg \left(t \leq 2.95 \cdot 10^{+181}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t} \cdot \left(z - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 74.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.3 \cdot 10^{-87} \lor \neg \left(x \leq 2.5 \cdot 10^{-136}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -1.3e-87) (not (<= x 2.5e-136)))
   (* x (- 1.0 (/ y t)))
   (* y (/ z t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.3e-87) || !(x <= 2.5e-136)) {
		tmp = x * (1.0 - (y / t));
	} else {
		tmp = y * (z / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-1.3d-87)) .or. (.not. (x <= 2.5d-136))) then
        tmp = x * (1.0d0 - (y / t))
    else
        tmp = y * (z / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.3e-87) || !(x <= 2.5e-136)) {
		tmp = x * (1.0 - (y / t));
	} else {
		tmp = y * (z / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -1.3e-87) or not (x <= 2.5e-136):
		tmp = x * (1.0 - (y / t))
	else:
		tmp = y * (z / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -1.3e-87) || !(x <= 2.5e-136))
		tmp = Float64(x * Float64(1.0 - Float64(y / t)));
	else
		tmp = Float64(y * Float64(z / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -1.3e-87) || ~((x <= 2.5e-136)))
		tmp = x * (1.0 - (y / t));
	else
		tmp = y * (z / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -1.3e-87], N[Not[LessEqual[x, 2.5e-136]], $MachinePrecision]], N[(x * N[(1.0 - N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.30000000000000001e-87 or 2.5000000000000001e-136 < x

   1. Initial program 94.0%

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

   3. Taylor expanded in x around inf 78.6%

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

      1. mul-1-neg 78.6%

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

      2. unsub-neg 78.6%

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

   5. Simplified 78.6%

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

   if -1.30000000000000001e-87 < x < 2.5000000000000001e-136

   1. Initial program 97.5%

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

   3. Taylor expanded in y around -inf 78.5%

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

   4. Taylor expanded in z around inf 70.8%

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

      1. associate-/l* 90.6%

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

   6. Simplified 71.6%

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

4. Final simplification 76.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.3 \cdot 10^{-87} \lor \neg \left(x \leq 2.5 \cdot 10^{-136}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 84.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6.5 \cdot 10^{-17}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq 1.75 \cdot 10^{-106}:\\ \;\;\;\;\frac{y \cdot \left(z - x\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{t} \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -6.5e-17)
   (+ x (* y (/ z t)))
   (if (<= t 1.75e-106) (/ (* y (- z x)) t) (+ x (* (/ y t) z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -6.5e-17) {
		tmp = x + (y * (z / t));
	} else if (t <= 1.75e-106) {
		tmp = (y * (z - x)) / t;
	} else {
		tmp = x + ((y / t) * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= (-6.5d-17)) then
        tmp = x + (y * (z / t))
    else if (t <= 1.75d-106) then
        tmp = (y * (z - x)) / t
    else
        tmp = x + ((y / t) * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -6.5e-17) {
		tmp = x + (y * (z / t));
	} else if (t <= 1.75e-106) {
		tmp = (y * (z - x)) / t;
	} else {
		tmp = x + ((y / t) * z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -6.5e-17:
		tmp = x + (y * (z / t))
	elif t <= 1.75e-106:
		tmp = (y * (z - x)) / t
	else:
		tmp = x + ((y / t) * z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -6.5e-17)
		tmp = Float64(x + Float64(y * Float64(z / t)));
	elseif (t <= 1.75e-106)
		tmp = Float64(Float64(y * Float64(z - x)) / t);
	else
		tmp = Float64(x + Float64(Float64(y / t) * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -6.5e-17)
		tmp = x + (y * (z / t));
	elseif (t <= 1.75e-106)
		tmp = (y * (z - x)) / t;
	else
		tmp = x + ((y / t) * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -6.5e-17], N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.75e-106], N[(N[(y * N[(z - x), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], N[(x + N[(N[(y / t), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -6.4999999999999996e-17

   1. Initial program 91.3%

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

   3. Taylor expanded in z around inf 86.3%

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

      1. associate-/l* 88.4%

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

   5. Simplified 88.4%

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

   if -6.4999999999999996e-17 < t < 1.75e-106

   1. Initial program 99.8%

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

   3. Taylor expanded in y around -inf 88.0%

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

   if 1.75e-106 < t

   1. Initial program 92.8%

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

   3. Taylor expanded in z around 0 91.5%

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

      1. +-commutative 91.5%

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

      2. *-commutative 91.5%

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

      3. associate-*r/ 93.8%

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

      4. mul-1-neg 93.8%

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

      5. associate-/l* 97.3%

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

      6. distribute-lft-neg-in 97.3%

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

      7. distribute-rgt-in 98.6%

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

      8. sub-neg 98.6%

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

   5. Simplified 98.6%

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

   6. Taylor expanded in z around inf 90.5%

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

Alternative 8: 54.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.32 \cdot 10^{-73} \lor \neg \left(y \leq 2.1 \cdot 10^{+28}\right):\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.32e-73) (not (<= y 2.1e+28))) (* y (/ z t)) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.32e-73) || !(y <= 2.1e+28)) {
		tmp = y * (z / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-1.32d-73)) .or. (.not. (y <= 2.1d+28))) then
        tmp = y * (z / t)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.32e-73) || !(y <= 2.1e+28)) {
		tmp = y * (z / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -1.32e-73) or not (y <= 2.1e+28):
		tmp = y * (z / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1.32e-73) || !(y <= 2.1e+28))
		tmp = Float64(y * Float64(z / t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -1.32e-73) || ~((y <= 2.1e+28)))
		tmp = y * (z / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -1.32e-73], N[Not[LessEqual[y, 2.1e+28]], $MachinePrecision]], N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -1.31999999999999998e-73 or 2.09999999999999989e28 < y

   1. Initial program 91.1%

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

   3. Taylor expanded in y around -inf 75.1%

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

   4. Taylor expanded in z around inf 49.8%

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

      1. associate-/l* 71.0%

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

   6. Simplified 52.9%

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

   if -1.31999999999999998e-73 < y < 2.09999999999999989e28

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 65.1%

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

4. Final simplification 58.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.32 \cdot 10^{-73} \lor \neg \left(y \leq 2.1 \cdot 10^{+28}\right):\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 53.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -920000000:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 2.95 \cdot 10^{+181}:\\ \;\;\;\;\frac{y}{t} \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -920000000.0) x (if (<= t 2.95e+181) (* (/ y t) z) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -920000000.0) {
		tmp = x;
	} else if (t <= 2.95e+181) {
		tmp = (y / t) * z;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= (-920000000.0d0)) then
        tmp = x
    else if (t <= 2.95d+181) then
        tmp = (y / t) * z
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -920000000.0) {
		tmp = x;
	} else if (t <= 2.95e+181) {
		tmp = (y / t) * z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -920000000.0:
		tmp = x
	elif t <= 2.95e+181:
		tmp = (y / t) * z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -920000000.0)
		tmp = x;
	elseif (t <= 2.95e+181)
		tmp = Float64(Float64(y / t) * z);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -920000000.0)
		tmp = x;
	elseif (t <= 2.95e+181)
		tmp = (y / t) * z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -920000000.0], x, If[LessEqual[t, 2.95e+181], N[(N[(y / t), $MachinePrecision] * z), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if t < -9.2e8 or 2.9499999999999999e181 < t

   1. Initial program 90.8%

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

   3. Taylor expanded in y around 0 73.4%

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

   if -9.2e8 < t < 2.9499999999999999e181

   1. Initial program 97.6%

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

   3. Taylor expanded in y around -inf 77.3%

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

   4. Taylor expanded in z around 0 71.2%

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

      1. +-commutative 91.5%

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

      2. *-commutative 91.5%

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

      3. associate-*r/ 90.2%

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

      4. mul-1-neg 90.2%

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

      5. associate-/l* 88.8%

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

      6. distribute-lft-neg-in 88.8%

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

      7. distribute-rgt-in 96.9%

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

      8. sub-neg 96.9%

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

   6. Simplified 76.6%

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

   7. Taylor expanded in z around inf 52.0%

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

Alternative 10: 38.5% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 95.1%

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

3. Taylor expanded in y around 0 40.6%

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

Developer Target 1: 90.8% accurate, 0.6× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024191 
(FPCore (x y z t)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, D"
  :precision binary64

  :alt
  (! :herbie-platform default (- x (+ (* x (/ y t)) (* (- z) (/ y t)))))

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