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

Percentage Accurate: 92.5% → 97.8%

Time: 10.0s

Alternatives: 15

Speedup: 1.0×

• 25.3% 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: 92.5% 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, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.5 \cdot 10^{+79}:\\ \;\;\;\;x + y \cdot \frac{z - x}{t}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{t}, z - x, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.5e+79) (+ x (* y (/ (- z x) t))) (fma (/ y t) (- z x) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.5e+79) {
		tmp = x + (y * ((z - x) / t));
	} else {
		tmp = fma((y / t), (z - x), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.5e+79)
		tmp = Float64(x + Float64(y * Float64(Float64(z - x) / t)));
	else
		tmp = fma(Float64(y / t), Float64(z - x), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.5e+79], N[(x + N[(y * N[(N[(z - x), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y / t), $MachinePrecision] * N[(z - x), $MachinePrecision] + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.49999999999999987e79

   1. Initial program 86.0%

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

      1. associate-/l* 97.3%

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

   3. Simplified 97.3%

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

      1. frac-2neg 97.3%

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

      2. distribute-frac-neg 97.3%

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

      3. remove-double-neg 97.3%

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

      4. distribute-frac-neg 97.3%

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

      5. frac-2neg 97.3%

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

      6. associate-/l* 86.0%

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

      7. unsub-neg 86.0%

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

      8. associate-/l* 97.3%

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

      9. frac-2neg 97.3%

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

      10. distribute-frac-neg 97.3%

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

      11. remove-double-neg 97.3%

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

      12. div-inv 97.3%

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

      13. distribute-neg-frac 97.3%

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

      14. clear-num 97.4%

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

      15. frac-2neg 97.4%

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

      16. neg-sub0 97.4%

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

      17. sub-neg 97.4%

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

      18. +-commutative 97.4%

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

      19. associate--r+ 97.4%

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

      20. neg-sub0 97.4%

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

      21. remove-double-neg 97.4%

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

      22. remove-double-neg 97.4%

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

   5. Applied egg-rr 97.4%

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

   if -1.49999999999999987e79 < y

   1. Initial program 93.7%

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

      1. +-commutative 93.7%

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

      2. associate-*l/ 98.6%

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

      3. fma-def 98.6%

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

   3. Simplified 98.6%

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

4. Final simplification 98.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.5 \cdot 10^{+79}:\\ \;\;\;\;x + y \cdot \frac{z - x}{t}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{t}, z - x, x\right)\\ \end{array} \]

Alternative 2: 83.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.52 \cdot 10^{-86} \lor \neg \left(z \leq 1.6 \cdot 10^{+27}\right):\\ \;\;\;\;x + \frac{z}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{x}{-t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.52e-86) (not (<= z 1.6e+27)))
   (+ x (/ z (/ t y)))
   (+ x (* y (/ x (- t))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.52e-86) || !(z <= 1.6e+27)) {
		tmp = x + (z / (t / y));
	} else {
		tmp = x + (y * (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 ((z <= (-1.52d-86)) .or. (.not. (z <= 1.6d+27))) then
        tmp = x + (z / (t / y))
    else
        tmp = x + (y * (x / -t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.52e-86) || !(z <= 1.6e+27)) {
		tmp = x + (z / (t / y));
	} else {
		tmp = x + (y * (x / -t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.52e-86) or not (z <= 1.6e+27):
		tmp = x + (z / (t / y))
	else:
		tmp = x + (y * (x / -t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.52e-86) || !(z <= 1.6e+27))
		tmp = Float64(x + Float64(z / Float64(t / y)));
	else
		tmp = Float64(x + Float64(y * Float64(x / Float64(-t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.52e-86) || ~((z <= 1.6e+27)))
		tmp = x + (z / (t / y));
	else
		tmp = x + (y * (x / -t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.52e-86], N[Not[LessEqual[z, 1.6e+27]], $MachinePrecision]], N[(x + N[(z / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(x / (-t)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.52e-86 or 1.60000000000000008e27 < z

   1. Initial program 89.8%

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

      1. associate-/l* 93.3%

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

   3. Simplified 93.3%

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

      1. associate-/r/ 99.3%

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

   5. Applied egg-rr 99.3%

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

   6. Taylor expanded in z around inf 85.9%

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

      1. associate-*r/ 86.0%

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

      2. *-commutative 86.0%

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

      3. associate-/r/ 90.9%

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

   8. Simplified 90.9%

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

   if -1.52e-86 < z < 1.60000000000000008e27

   1. Initial program 94.5%

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

   2. Taylor expanded in z around 0 85.3%

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

      1. mul-1-neg 85.3%

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

      2. *-commutative 85.3%

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

      3. distribute-rgt-neg-out 85.3%

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

   4. Simplified 85.3%

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

      1. div-inv 85.3%

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

      2. associate-*l* 88.3%

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

      3. *-commutative 88.3%

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

      4. div-inv 88.3%

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

      5. frac-2neg 88.3%

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

      6. remove-double-neg 88.3%

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

   6. Applied egg-rr 88.3%

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

4. Final simplification 89.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.52 \cdot 10^{-86} \lor \neg \left(z \leq 1.6 \cdot 10^{+27}\right):\\ \;\;\;\;x + \frac{z}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{x}{-t}\\ \end{array} \]

Alternative 3: 82.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{-86} \lor \neg \left(z \leq 3.6 \cdot 10^{+28}\right):\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.55e-86) (not (<= z 3.6e+28)))
   (+ x (* y (/ z t)))
   (* x (- 1.0 (/ y t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.55e-86) || !(z <= 3.6e+28)) {
		tmp = x + (y * (z / t));
	} else {
		tmp = x * (1.0 - (y / 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 ((z <= (-1.55d-86)) .or. (.not. (z <= 3.6d+28))) then
        tmp = x + (y * (z / t))
    else
        tmp = x * (1.0d0 - (y / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.55e-86) || !(z <= 3.6e+28)) {
		tmp = x + (y * (z / t));
	} else {
		tmp = x * (1.0 - (y / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.55e-86) or not (z <= 3.6e+28):
		tmp = x + (y * (z / t))
	else:
		tmp = x * (1.0 - (y / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.55e-86) || !(z <= 3.6e+28))
		tmp = Float64(x + Float64(y * Float64(z / t)));
	else
		tmp = Float64(x * Float64(1.0 - Float64(y / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.55e-86) || ~((z <= 3.6e+28)))
		tmp = x + (y * (z / t));
	else
		tmp = x * (1.0 - (y / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.55e-86], N[Not[LessEqual[z, 3.6e+28]], $MachinePrecision]], N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.54999999999999994e-86 or 3.5999999999999999e28 < z

   1. Initial program 89.8%

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

      1. associate-/l* 93.3%

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

   3. Simplified 93.3%

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

   4. Taylor expanded in z around inf 85.9%

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

      1. *-commutative 85.9%

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

      2. associate-*l/ 86.0%

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

      3. *-commutative 86.0%

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

   6. Simplified 86.0%

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

   if -1.54999999999999994e-86 < z < 3.5999999999999999e28

   1. Initial program 94.5%

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

      1. associate-/l* 97.9%

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

   3. Simplified 97.9%

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

   4. Taylor expanded in x around inf 86.1%

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

      1. associate-*r/ 86.1%

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

      2. associate-*l/ 86.1%

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

      3. distribute-rgt-in 86.1%

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

      4. *-lft-identity 86.1%

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

      5. associate-*l/ 86.1%

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

      6. associate-*r/ 86.1%

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

      7. mul-1-neg 86.1%

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

      8. distribute-lft-neg-in 86.1%

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

      9. distribute-rgt-neg-out 86.1%

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

      10. distribute-rgt-neg-out 86.1%

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

      11. associate-*l/ 85.3%

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

      12. *-commutative 85.3%

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

      13. unsub-neg 85.3%

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

      14. *-commutative 85.3%

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

      15. associate-*l/ 86.1%

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

      16. *-commutative 86.1%

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

   6. Simplified 86.1%

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

   7. Taylor expanded in x around 0 86.1%

      \[\leadsto \color{blue}{x \cdot \left(1 - \frac{y}{t}\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 86.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{-86} \lor \neg \left(z \leq 3.6 \cdot 10^{+28}\right):\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \end{array} \]

Alternative 4: 83.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{-83} \lor \neg \left(z \leq 5.8 \cdot 10^{+29}\right):\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -2.4e-83) (not (<= z 5.8e+29)))
   (+ x (/ y (/ t z)))
   (* x (- 1.0 (/ y t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2.4e-83) || !(z <= 5.8e+29)) {
		tmp = x + (y / (t / z));
	} else {
		tmp = x * (1.0 - (y / 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 ((z <= (-2.4d-83)) .or. (.not. (z <= 5.8d+29))) then
        tmp = x + (y / (t / z))
    else
        tmp = x * (1.0d0 - (y / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2.4e-83) || !(z <= 5.8e+29)) {
		tmp = x + (y / (t / z));
	} else {
		tmp = x * (1.0 - (y / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -2.4e-83) or not (z <= 5.8e+29):
		tmp = x + (y / (t / z))
	else:
		tmp = x * (1.0 - (y / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -2.4e-83) || !(z <= 5.8e+29))
		tmp = Float64(x + Float64(y / Float64(t / z)));
	else
		tmp = Float64(x * Float64(1.0 - Float64(y / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -2.4e-83) || ~((z <= 5.8e+29)))
		tmp = x + (y / (t / z));
	else
		tmp = x * (1.0 - (y / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -2.4e-83], N[Not[LessEqual[z, 5.8e+29]], $MachinePrecision]], N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.4000000000000001e-83 or 5.7999999999999999e29 < z

   1. Initial program 89.8%

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

      1. associate-/l* 93.3%

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

   3. Simplified 93.3%

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

   4. Taylor expanded in z around inf 85.9%

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

      1. associate-/l* 87.1%

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

   6. Simplified 87.1%

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

   if -2.4000000000000001e-83 < z < 5.7999999999999999e29

   1. Initial program 94.5%

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

      1. associate-/l* 97.9%

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

   3. Simplified 97.9%

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

   4. Taylor expanded in x around inf 86.1%

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

      1. associate-*r/ 86.1%

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

      2. associate-*l/ 86.1%

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

      3. distribute-rgt-in 86.1%

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

      4. *-lft-identity 86.1%

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

      5. associate-*l/ 86.1%

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

      6. associate-*r/ 86.1%

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

      7. mul-1-neg 86.1%

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

      8. distribute-lft-neg-in 86.1%

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

      9. distribute-rgt-neg-out 86.1%

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

      10. distribute-rgt-neg-out 86.1%

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

      11. associate-*l/ 85.3%

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

      12. *-commutative 85.3%

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

      13. unsub-neg 85.3%

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

      14. *-commutative 85.3%

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

      15. associate-*l/ 86.1%

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

      16. *-commutative 86.1%

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

   6. Simplified 86.1%

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

   7. Taylor expanded in x around 0 86.1%

      \[\leadsto \color{blue}{x \cdot \left(1 - \frac{y}{t}\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 86.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{-83} \lor \neg \left(z \leq 5.8 \cdot 10^{+29}\right):\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \end{array} \]

Alternative 5: 85.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.26 \cdot 10^{-83} \lor \neg \left(z \leq 5.1 \cdot 10^{+28}\right):\\ \;\;\;\;x + \frac{z}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.26e-83) (not (<= z 5.1e+28)))
   (+ x (/ z (/ t y)))
   (* x (- 1.0 (/ y t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.26e-83) || !(z <= 5.1e+28)) {
		tmp = x + (z / (t / y));
	} else {
		tmp = x * (1.0 - (y / 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 ((z <= (-1.26d-83)) .or. (.not. (z <= 5.1d+28))) then
        tmp = x + (z / (t / y))
    else
        tmp = x * (1.0d0 - (y / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.26e-83) || !(z <= 5.1e+28)) {
		tmp = x + (z / (t / y));
	} else {
		tmp = x * (1.0 - (y / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.26e-83) or not (z <= 5.1e+28):
		tmp = x + (z / (t / y))
	else:
		tmp = x * (1.0 - (y / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.26e-83) || !(z <= 5.1e+28))
		tmp = Float64(x + Float64(z / Float64(t / y)));
	else
		tmp = Float64(x * Float64(1.0 - Float64(y / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.26e-83) || ~((z <= 5.1e+28)))
		tmp = x + (z / (t / y));
	else
		tmp = x * (1.0 - (y / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.26e-83], N[Not[LessEqual[z, 5.1e+28]], $MachinePrecision]], N[(x + N[(z / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.2600000000000001e-83 or 5.1000000000000004e28 < z

   1. Initial program 89.8%

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

      1. associate-/l* 93.3%

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

   3. Simplified 93.3%

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

      1. associate-/r/ 99.3%

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

   5. Applied egg-rr 99.3%

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

   6. Taylor expanded in z around inf 85.9%

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

      1. associate-*r/ 86.0%

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

      2. *-commutative 86.0%

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

      3. associate-/r/ 90.9%

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

   8. Simplified 90.9%

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

   if -1.2600000000000001e-83 < z < 5.1000000000000004e28

   1. Initial program 94.5%

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

      1. associate-/l* 97.9%

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

   3. Simplified 97.9%

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

   4. Taylor expanded in x around inf 86.1%

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

      1. associate-*r/ 86.1%

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

      2. associate-*l/ 86.1%

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

      3. distribute-rgt-in 86.1%

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

      4. *-lft-identity 86.1%

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

      5. associate-*l/ 86.1%

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

      6. associate-*r/ 86.1%

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

      7. mul-1-neg 86.1%

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

      8. distribute-lft-neg-in 86.1%

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

      9. distribute-rgt-neg-out 86.1%

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

      10. distribute-rgt-neg-out 86.1%

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

      11. associate-*l/ 85.3%

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

      12. *-commutative 85.3%

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

      13. unsub-neg 85.3%

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

      14. *-commutative 85.3%

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

      15. associate-*l/ 86.1%

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

      16. *-commutative 86.1%

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

   6. Simplified 86.1%

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

   7. Taylor expanded in x around 0 86.1%

      \[\leadsto \color{blue}{x \cdot \left(1 - \frac{y}{t}\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 88.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.26 \cdot 10^{-83} \lor \neg \left(z \leq 5.1 \cdot 10^{+28}\right):\\ \;\;\;\;x + \frac{z}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \end{array} \]

Alternative 6: 85.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{-85} \lor \neg \left(z \leq 1.3 \cdot 10^{+29}\right):\\ \;\;\;\;x + \frac{z}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot \frac{y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1e-85) (not (<= z 1.3e+29)))
   (+ x (/ z (/ t y)))
   (- x (* x (/ y t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1e-85) || !(z <= 1.3e+29)) {
		tmp = x + (z / (t / y));
	} else {
		tmp = x - (x * (y / 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 ((z <= (-1d-85)) .or. (.not. (z <= 1.3d+29))) then
        tmp = x + (z / (t / y))
    else
        tmp = x - (x * (y / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1e-85) || !(z <= 1.3e+29)) {
		tmp = x + (z / (t / y));
	} else {
		tmp = x - (x * (y / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1e-85) or not (z <= 1.3e+29):
		tmp = x + (z / (t / y))
	else:
		tmp = x - (x * (y / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1e-85) || !(z <= 1.3e+29))
		tmp = Float64(x + Float64(z / Float64(t / y)));
	else
		tmp = Float64(x - Float64(x * Float64(y / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1e-85) || ~((z <= 1.3e+29)))
		tmp = x + (z / (t / y));
	else
		tmp = x - (x * (y / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1e-85], N[Not[LessEqual[z, 1.3e+29]], $MachinePrecision]], N[(x + N[(z / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(x * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -9.9999999999999998e-86 or 1.3e29 < z

   1. Initial program 89.8%

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

      1. associate-/l* 93.3%

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

   3. Simplified 93.3%

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

      1. associate-/r/ 99.3%

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

   5. Applied egg-rr 99.3%

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

   6. Taylor expanded in z around inf 85.9%

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

      1. associate-*r/ 86.0%

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

      2. *-commutative 86.0%

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

      3. associate-/r/ 90.9%

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

   8. Simplified 90.9%

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

   if -9.9999999999999998e-86 < z < 1.3e29

   1. Initial program 94.5%

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

      1. associate-/l* 97.9%

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

   3. Simplified 97.9%

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

   4. Taylor expanded in x around inf 86.1%

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

      1. associate-*r/ 86.1%

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

      2. associate-*l/ 86.1%

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

      3. distribute-rgt-in 86.1%

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

      4. *-lft-identity 86.1%

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

      5. associate-*l/ 86.1%

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

      6. associate-*r/ 86.1%

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

      7. mul-1-neg 86.1%

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

      8. distribute-lft-neg-in 86.1%

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

      9. distribute-rgt-neg-out 86.1%

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

      10. distribute-rgt-neg-out 86.1%

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

      11. associate-*l/ 85.3%

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

      12. *-commutative 85.3%

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

      13. unsub-neg 85.3%

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

      14. *-commutative 85.3%

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

      15. associate-*l/ 86.1%

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

      16. *-commutative 86.1%

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

   6. Simplified 86.1%

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

4. Final simplification 88.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{-85} \lor \neg \left(z \leq 1.3 \cdot 10^{+29}\right):\\ \;\;\;\;x + \frac{z}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot \frac{y}{t}\\ \end{array} \]

Alternative 7: 85.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.45 \cdot 10^{-83} \lor \neg \left(z \leq 3.7 \cdot 10^{+27}\right):\\ \;\;\;\;x + \frac{z}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x}{\frac{t}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -2.45e-83) (not (<= z 3.7e+27)))
   (+ x (/ z (/ t y)))
   (- x (/ x (/ t y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2.45e-83) || !(z <= 3.7e+27)) {
		tmp = x + (z / (t / y));
	} else {
		tmp = x - (x / (t / y));
	}
	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 ((z <= (-2.45d-83)) .or. (.not. (z <= 3.7d+27))) then
        tmp = x + (z / (t / y))
    else
        tmp = x - (x / (t / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2.45e-83) || !(z <= 3.7e+27)) {
		tmp = x + (z / (t / y));
	} else {
		tmp = x - (x / (t / y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -2.45e-83) or not (z <= 3.7e+27):
		tmp = x + (z / (t / y))
	else:
		tmp = x - (x / (t / y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -2.45e-83) || !(z <= 3.7e+27))
		tmp = Float64(x + Float64(z / Float64(t / y)));
	else
		tmp = Float64(x - Float64(x / Float64(t / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -2.45e-83) || ~((z <= 3.7e+27)))
		tmp = x + (z / (t / y));
	else
		tmp = x - (x / (t / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -2.45e-83], N[Not[LessEqual[z, 3.7e+27]], $MachinePrecision]], N[(x + N[(z / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(x / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.45e-83 or 3.70000000000000002e27 < z

   1. Initial program 89.8%

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

      1. associate-/l* 93.3%

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

   3. Simplified 93.3%

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

      1. associate-/r/ 99.3%

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

   5. Applied egg-rr 99.3%

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

   6. Taylor expanded in z around inf 85.9%

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

      1. associate-*r/ 86.0%

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

      2. *-commutative 86.0%

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

      3. associate-/r/ 90.9%

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

   8. Simplified 90.9%

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

   if -2.45e-83 < z < 3.70000000000000002e27

   1. Initial program 94.5%

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

      1. associate-/l* 97.9%

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

   3. Simplified 97.9%

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

   4. Taylor expanded in x around inf 86.1%

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

      1. associate-*r/ 86.1%

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

      2. associate-*l/ 86.1%

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

      3. distribute-rgt-in 86.1%

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

      4. *-lft-identity 86.1%

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

      5. associate-*l/ 86.1%

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

      6. associate-*r/ 86.1%

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

      7. mul-1-neg 86.1%

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

      8. distribute-lft-neg-in 86.1%

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

      9. distribute-rgt-neg-out 86.1%

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

      10. distribute-rgt-neg-out 86.1%

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

      11. associate-*l/ 85.3%

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

      12. *-commutative 85.3%

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

      13. unsub-neg 85.3%

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

      14. *-commutative 85.3%

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

      15. associate-*l/ 86.1%

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

      16. *-commutative 86.1%

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

   6. Simplified 86.1%

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

      1. clear-num 86.1%

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

      2. un-div-inv 86.1%

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

   8. Applied egg-rr 86.1%

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

4. Final simplification 88.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.45 \cdot 10^{-83} \lor \neg \left(z \leq 3.7 \cdot 10^{+27}\right):\\ \;\;\;\;x + \frac{z}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x}{\frac{t}{y}}\\ \end{array} \]

Alternative 8: 84.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.45 \cdot 10^{-83} \lor \neg \left(z \leq 1.66 \cdot 10^{+27}\right):\\ \;\;\;\;x + \frac{z}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{t}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -2.45e-83) (not (<= z 1.66e+27)))
   (+ x (/ z (/ t y)))
   (- x (/ y (/ t x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2.45e-83) || !(z <= 1.66e+27)) {
		tmp = x + (z / (t / y));
	} else {
		tmp = x - (y / (t / 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 ((z <= (-2.45d-83)) .or. (.not. (z <= 1.66d+27))) then
        tmp = x + (z / (t / y))
    else
        tmp = x - (y / (t / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2.45e-83) || !(z <= 1.66e+27)) {
		tmp = x + (z / (t / y));
	} else {
		tmp = x - (y / (t / x));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -2.45e-83) or not (z <= 1.66e+27):
		tmp = x + (z / (t / y))
	else:
		tmp = x - (y / (t / x))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -2.45e-83) || !(z <= 1.66e+27))
		tmp = Float64(x + Float64(z / Float64(t / y)));
	else
		tmp = Float64(x - Float64(y / Float64(t / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -2.45e-83) || ~((z <= 1.66e+27)))
		tmp = x + (z / (t / y));
	else
		tmp = x - (y / (t / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -2.45e-83], N[Not[LessEqual[z, 1.66e+27]], $MachinePrecision]], N[(x + N[(z / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(y / N[(t / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.45e-83 or 1.65999999999999986e27 < z

   1. Initial program 89.8%

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

      1. associate-/l* 93.3%

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

   3. Simplified 93.3%

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

      1. associate-/r/ 99.3%

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

   5. Applied egg-rr 99.3%

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

   6. Taylor expanded in z around inf 85.9%

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

      1. associate-*r/ 86.0%

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

      2. *-commutative 86.0%

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

      3. associate-/r/ 90.9%

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

   8. Simplified 90.9%

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

   if -2.45e-83 < z < 1.65999999999999986e27

   1. Initial program 94.5%

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

      1. associate-/l* 97.9%

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

   3. Simplified 97.9%

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

   4. Taylor expanded in x around inf 86.1%

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

      1. associate-*r/ 86.1%

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

      2. associate-*l/ 86.1%

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

      3. distribute-rgt-in 86.1%

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

      4. *-lft-identity 86.1%

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

      5. associate-*l/ 86.1%

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

      6. associate-*r/ 86.1%

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

      7. mul-1-neg 86.1%

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

      8. distribute-lft-neg-in 86.1%

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

      9. distribute-rgt-neg-out 86.1%

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

      10. distribute-rgt-neg-out 86.1%

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

      11. associate-*l/ 85.3%

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

      12. *-commutative 85.3%

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

      13. unsub-neg 85.3%

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

      14. *-commutative 85.3%

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

      15. associate-*l/ 86.1%

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

      16. *-commutative 86.1%

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

   6. Simplified 86.1%

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

      1. *-commutative 86.1%

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

      2. associate-/r/ 88.3%

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

   8. Applied egg-rr 88.3%

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

4. Final simplification 89.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.45 \cdot 10^{-83} \lor \neg \left(z \leq 1.66 \cdot 10^{+27}\right):\\ \;\;\;\;x + \frac{z}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{t}{x}}\\ \end{array} \]

Alternative 9: 97.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{+79}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z - x}}\\ \mathbf{else}:\\ \;\;\;\;x - \left(x - z\right) \cdot \frac{y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -4e+79) (+ x (/ y (/ t (- z x)))) (- x (* (- x z) (/ y t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -4e+79) {
		tmp = x + (y / (t / (z - x)));
	} else {
		tmp = x - ((x - z) * (y / 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 (y <= (-4d+79)) then
        tmp = x + (y / (t / (z - x)))
    else
        tmp = x - ((x - z) * (y / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -4e+79) {
		tmp = x + (y / (t / (z - x)));
	} else {
		tmp = x - ((x - z) * (y / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -4e+79:
		tmp = x + (y / (t / (z - x)))
	else:
		tmp = x - ((x - z) * (y / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -4e+79)
		tmp = Float64(x + Float64(y / Float64(t / Float64(z - x))));
	else
		tmp = Float64(x - Float64(Float64(x - z) * Float64(y / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -4e+79)
		tmp = x + (y / (t / (z - x)));
	else
		tmp = x - ((x - z) * (y / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -4e+79], N[(x + N[(y / N[(t / N[(z - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(x - z), $MachinePrecision] * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.99999999999999987e79

   1. Initial program 86.0%

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

      1. associate-/l* 97.3%

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

   3. Simplified 97.3%

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

   if -3.99999999999999987e79 < y

   1. Initial program 93.7%

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

      1. associate-/l* 95.0%

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

   3. Simplified 95.0%

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

      1. associate-/r/ 98.6%

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

   5. Applied egg-rr 98.6%

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

4. Final simplification 98.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{+79}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z - x}}\\ \mathbf{else}:\\ \;\;\;\;x - \left(x - z\right) \cdot \frac{y}{t}\\ \end{array} \]

Alternative 10: 97.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{+79}:\\ \;\;\;\;x + y \cdot \frac{z - x}{t}\\ \mathbf{else}:\\ \;\;\;\;x - \left(x - z\right) \cdot \frac{y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.15e+79) (+ x (* y (/ (- z x) t))) (- x (* (- x z) (/ y t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.15e+79) {
		tmp = x + (y * ((z - x) / t));
	} else {
		tmp = x - ((x - z) * (y / 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 (y <= (-1.15d+79)) then
        tmp = x + (y * ((z - x) / t))
    else
        tmp = x - ((x - z) * (y / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.15e+79) {
		tmp = x + (y * ((z - x) / t));
	} else {
		tmp = x - ((x - z) * (y / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.15e+79:
		tmp = x + (y * ((z - x) / t))
	else:
		tmp = x - ((x - z) * (y / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.15e+79)
		tmp = Float64(x + Float64(y * Float64(Float64(z - x) / t)));
	else
		tmp = Float64(x - Float64(Float64(x - z) * Float64(y / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.15e+79)
		tmp = x + (y * ((z - x) / t));
	else
		tmp = x - ((x - z) * (y / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.15e+79], N[(x + N[(y * N[(N[(z - x), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(x - z), $MachinePrecision] * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.15e79

   1. Initial program 86.0%

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

      1. associate-/l* 97.3%

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

   3. Simplified 97.3%

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

      1. frac-2neg 97.3%

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

      2. distribute-frac-neg 97.3%

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

      3. remove-double-neg 97.3%

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

      4. distribute-frac-neg 97.3%

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

      5. frac-2neg 97.3%

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

      6. associate-/l* 86.0%

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

      7. unsub-neg 86.0%

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

      8. associate-/l* 97.3%

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

      9. frac-2neg 97.3%

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

      10. distribute-frac-neg 97.3%

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

      11. remove-double-neg 97.3%

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

      12. div-inv 97.3%

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

      13. distribute-neg-frac 97.3%

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

      14. clear-num 97.4%

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

      15. frac-2neg 97.4%

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

      16. neg-sub0 97.4%

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

      17. sub-neg 97.4%

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

      18. +-commutative 97.4%

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

      19. associate--r+ 97.4%

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

      20. neg-sub0 97.4%

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

      21. remove-double-neg 97.4%

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

      22. remove-double-neg 97.4%

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

   5. Applied egg-rr 97.4%

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

   if -1.15e79 < y

   1. Initial program 93.7%

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

      1. associate-/l* 95.0%

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

   3. Simplified 95.0%

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

      1. associate-/r/ 98.6%

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

   5. Applied egg-rr 98.6%

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

4. Final simplification 98.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{+79}:\\ \;\;\;\;x + y \cdot \frac{z - x}{t}\\ \mathbf{else}:\\ \;\;\;\;x - \left(x - z\right) \cdot \frac{y}{t}\\ \end{array} \]

Alternative 11: 50.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.62 \cdot 10^{-108}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{-22}:\\ \;\;\;\;x \cdot \frac{y}{-t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -1.62e-108) x (if (<= t 1.9e-22) (* x (/ y (- t))) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.62e-108) {
		tmp = x;
	} else if (t <= 1.9e-22) {
		tmp = x * (y / -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 (t <= (-1.62d-108)) then
        tmp = x
    else if (t <= 1.9d-22) then
        tmp = x * (y / -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 (t <= -1.62e-108) {
		tmp = x;
	} else if (t <= 1.9e-22) {
		tmp = x * (y / -t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -1.62e-108:
		tmp = x
	elif t <= 1.9e-22:
		tmp = x * (y / -t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -1.62e-108)
		tmp = x;
	elseif (t <= 1.9e-22)
		tmp = Float64(x * Float64(y / Float64(-t)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -1.62e-108)
		tmp = x;
	elseif (t <= 1.9e-22)
		tmp = x * (y / -t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -1.62e-108], x, If[LessEqual[t, 1.9e-22], N[(x * N[(y / (-t)), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if t < -1.62e-108 or 1.90000000000000012e-22 < t

   1. Initial program 88.2%

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

      1. associate-/l* 97.5%

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

   3. Simplified 97.5%

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

   4. Taylor expanded in y around 0 56.0%

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

   if -1.62e-108 < t < 1.90000000000000012e-22

   1. Initial program 97.2%

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

      1. associate-/l* 92.9%

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

   3. Simplified 92.9%

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

   4. Taylor expanded in x around inf 57.4%

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

      1. associate-*r/ 57.4%

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

      2. associate-*l/ 57.4%

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

      3. distribute-rgt-in 57.4%

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

      4. *-lft-identity 57.4%

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

      5. associate-*l/ 57.4%

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

      6. associate-*r/ 57.4%

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

      7. mul-1-neg 57.4%

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

      8. distribute-lft-neg-in 57.4%

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

      9. distribute-rgt-neg-out 57.4%

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

      10. distribute-rgt-neg-out 57.4%

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

      11. associate-*l/ 58.2%

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

      12. *-commutative 58.2%

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

      13. unsub-neg 58.2%

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

      14. *-commutative 58.2%

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

      15. associate-*l/ 57.4%

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

      16. *-commutative 57.4%

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

   6. Simplified 57.4%

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

      1. clear-num 57.4%

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

      2. un-div-inv 57.4%

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

   8. Applied egg-rr 57.4%

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

   9. Taylor expanded in t around 0 53.0%

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

       1. associate-*r/ 52.0%

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

       2. neg-mul-1 52.0%

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

       3. distribute-rgt-neg-in 52.0%

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

       4. mul-1-neg 52.0%

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

       5. metadata-eval 52.0%

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

       6. times-frac 52.0%

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

       7. *-lft-identity 52.0%

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

       8. neg-mul-1 52.0%

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

   11. Simplified 52.0%

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

4. Final simplification 54.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.62 \cdot 10^{-108}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{-22}:\\ \;\;\;\;x \cdot \frac{y}{-t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 12: 49.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.3 \cdot 10^{-108}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{-23}:\\ \;\;\;\;\left(-y\right) \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -3.3e-108) x (if (<= t 3.5e-23) (* (- y) (/ x t)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -3.3e-108) {
		tmp = x;
	} else if (t <= 3.5e-23) {
		tmp = -y * (x / 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 (t <= (-3.3d-108)) then
        tmp = x
    else if (t <= 3.5d-23) then
        tmp = -y * (x / 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 (t <= -3.3e-108) {
		tmp = x;
	} else if (t <= 3.5e-23) {
		tmp = -y * (x / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -3.3e-108:
		tmp = x
	elif t <= 3.5e-23:
		tmp = -y * (x / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -3.3e-108)
		tmp = x;
	elseif (t <= 3.5e-23)
		tmp = Float64(Float64(-y) * Float64(x / t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -3.3e-108)
		tmp = x;
	elseif (t <= 3.5e-23)
		tmp = -y * (x / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -3.3e-108], x, If[LessEqual[t, 3.5e-23], N[((-y) * N[(x / t), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if t < -3.3000000000000002e-108 or 3.49999999999999993e-23 < t

   1. Initial program 88.2%

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

      1. associate-/l* 97.5%

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

   3. Simplified 97.5%

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

   4. Taylor expanded in y around 0 56.0%

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

   if -3.3000000000000002e-108 < t < 3.49999999999999993e-23

   1. Initial program 97.2%

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

      1. associate-/l* 92.9%

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

   3. Simplified 92.9%

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

   4. Taylor expanded in x around inf 57.4%

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

      1. associate-*r/ 57.4%

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

      2. associate-*l/ 57.4%

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

      3. distribute-rgt-in 57.4%

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

      4. *-lft-identity 57.4%

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

      5. associate-*l/ 57.4%

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

      6. associate-*r/ 57.4%

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

      7. mul-1-neg 57.4%

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

      8. distribute-lft-neg-in 57.4%

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

      9. distribute-rgt-neg-out 57.4%

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

      10. distribute-rgt-neg-out 57.4%

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

      11. associate-*l/ 58.2%

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

      12. *-commutative 58.2%

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

      13. unsub-neg 58.2%

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

      14. *-commutative 58.2%

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

      15. associate-*l/ 57.4%

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

      16. *-commutative 57.4%

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

   6. Simplified 57.4%

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

   7. Taylor expanded in y around inf 53.0%

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

      1. associate-/l* 52.0%

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

      2. associate-*r/ 52.0%

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

      3. neg-mul-1 52.0%

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

      4. associate-/r/ 53.5%

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

      5. *-commutative 53.5%

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

   9. Simplified 53.5%

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

4. Final simplification 54.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.3 \cdot 10^{-108}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{-23}:\\ \;\;\;\;\left(-y\right) \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 13: 97.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 92.0%

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

   1. associate-/l* 95.5%

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

3. Simplified 95.5%

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

   1. associate-/r/ 96.3%

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

5. Applied egg-rr 96.3%

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

6. Final simplification 96.3%

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

Alternative 14: 65.1% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ x \cdot \left(1 - \frac{y}{t}\right) \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (* x (- 1.0 (/ y t))))

C

double code(double x, double y, double z, double t) {
	return x * (1.0 - (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 * (1.0d0 - (y / t))
end function

Java

public static double code(double x, double y, double z, double t) {
	return x * (1.0 - (y / t));
}

Python

def code(x, y, z, t):
	return x * (1.0 - (y / t))

Julia

function code(x, y, z, t)
	return Float64(x * Float64(1.0 - Float64(y / t)))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = x * (1.0 - (y / t));
end

Wolfram

code[x_, y_, z_, t_] := N[(x * N[(1.0 - N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 92.0%

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

   1. associate-/l* 95.5%

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

3. Simplified 95.5%

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

4. Taylor expanded in x around inf 65.3%

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

   1. associate-*r/ 65.3%

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

   2. associate-*l/ 65.3%

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

   3. distribute-rgt-in 65.3%

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

   4. *-lft-identity 65.3%

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

   5. associate-*l/ 65.3%

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

   6. associate-*r/ 65.3%

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

   7. mul-1-neg 65.3%

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

   8. distribute-lft-neg-in 65.3%

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

   9. distribute-rgt-neg-out 65.3%

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

   10. distribute-rgt-neg-out 65.3%

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

   11. associate-*l/ 61.5%

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

   12. *-commutative 61.5%

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

   13. unsub-neg 61.5%

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

   14. *-commutative 61.5%

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

   15. associate-*l/ 65.3%

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

   16. *-commutative 65.3%

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

6. Simplified 65.3%

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

7. Taylor expanded in x around 0 65.3%

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

8. Final simplification 65.3%

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

Alternative 15: 38.3% 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 92.0%

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

   1. associate-/l* 95.5%

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

3. Simplified 95.5%

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

4. Taylor expanded in y around 0 35.1%

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

5. Final simplification 35.1%

   \[\leadsto x \]

Developer target: 89.9% 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 2023297 
(FPCore (x y z t)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, D"
  :precision binary64

  :herbie-target
  (- x (+ (* x (/ y t)) (* (- z) (/ y t))))

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