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

Percentage Accurate: 92.7% → 97.8%

Time: 6.5s

Alternatives: 11

Speedup: 1.0×

• 24.9% 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: 92.7% 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 92.4%

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

   1. associate-*l/ 96.9%

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

3. Simplified 96.9%

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

4. Final simplification 96.9%

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

Alternative 2: 74.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{-193} \lor \neg \left(z \leq 4 \cdot 10^{-245} \lor \neg \left(z \leq 2.5 \cdot 10^{-157}\right) \land z \leq 3.6 \cdot 10^{-117}\right):\\ \;\;\;\;x + \frac{y}{t} \cdot z\\ \mathbf{else}:\\ \;\;\;\;\left(-y\right) \cdot \frac{x}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -5.5e-193)
         (not (or (<= z 4e-245) (and (not (<= z 2.5e-157)) (<= z 3.6e-117)))))
   (+ x (* (/ y t) z))
   (* (- y) (/ x t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -5.5e-193) || !((z <= 4e-245) || (!(z <= 2.5e-157) && (z <= 3.6e-117)))) {
		tmp = x + ((y / t) * z);
	} else {
		tmp = -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 <= (-5.5d-193)) .or. (.not. (z <= 4d-245) .or. (.not. (z <= 2.5d-157)) .and. (z <= 3.6d-117))) then
        tmp = x + ((y / t) * z)
    else
        tmp = -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 <= -5.5e-193) || !((z <= 4e-245) || (!(z <= 2.5e-157) && (z <= 3.6e-117)))) {
		tmp = x + ((y / t) * z);
	} else {
		tmp = -y * (x / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -5.5e-193) or not ((z <= 4e-245) or (not (z <= 2.5e-157) and (z <= 3.6e-117))):
		tmp = x + ((y / t) * z)
	else:
		tmp = -y * (x / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -5.5e-193) || !((z <= 4e-245) || (!(z <= 2.5e-157) && (z <= 3.6e-117))))
		tmp = Float64(x + Float64(Float64(y / t) * z));
	else
		tmp = Float64(Float64(-y) * Float64(x / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -5.5e-193) || ~(((z <= 4e-245) || (~((z <= 2.5e-157)) && (z <= 3.6e-117)))))
		tmp = x + ((y / t) * z);
	else
		tmp = -y * (x / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -5.5e-193], N[Not[Or[LessEqual[z, 4e-245], And[N[Not[LessEqual[z, 2.5e-157]], $MachinePrecision], LessEqual[z, 3.6e-117]]]], $MachinePrecision]], N[(x + N[(N[(y / t), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], N[((-y) * N[(x / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.50000000000000014e-193 or 3.9999999999999997e-245 < z < 2.5000000000000001e-157 or 3.6e-117 < z

   1. Initial program 91.9%

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

      1. associate-*l/ 98.9%

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

   3. Simplified 98.9%

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

   4. Taylor expanded in z around inf 80.6%

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

      1. associate-*l/ 86.2%

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

      2. *-commutative 86.2%

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

   6. Simplified 86.2%

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

   if -5.50000000000000014e-193 < z < 3.9999999999999997e-245 or 2.5000000000000001e-157 < z < 3.6e-117

   1. Initial program 94.6%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around 0 99.8%

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

      1. associate-*r/ 99.8%

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

      2. neg-mul-1 99.8%

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

   6. Simplified 99.8%

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

      1. associate-/r/ 89.5%

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

      2. add-sqr-sqrt 46.6%

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

      3. sqrt-unprod 55.5%

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

      4. sqr-neg 55.5%

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

      5. sqrt-unprod 15.9%

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

      6. add-sqr-sqrt 25.4%

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

      7. frac-2neg 25.4%

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

      8. distribute-frac-neg 25.4%

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

      9. cancel-sign-sub-inv 25.4%

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

      10. *-commutative 25.4%

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

      11. add-sqr-sqrt 9.5%

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

      12. sqrt-unprod 48.7%

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

      13. sqr-neg 48.7%

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

      14. sqrt-unprod 42.8%

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

      15. add-sqr-sqrt 89.5%

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

   8. Applied egg-rr 89.5%

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

   9. Taylor expanded in y around inf 69.6%

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

       1. mul-1-neg 69.6%

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

       2. associate-*l/ 73.1%

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

       3. distribute-lft-neg-out 73.1%

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

       4. *-commutative 73.1%

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

       5. distribute-neg-frac 73.1%

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

   11. Simplified 73.1%

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

4. Final simplification 83.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{-193} \lor \neg \left(z \leq 4 \cdot 10^{-245} \lor \neg \left(z \leq 2.5 \cdot 10^{-157}\right) \land z \leq 3.6 \cdot 10^{-117}\right):\\ \;\;\;\;x + \frac{y}{t} \cdot z\\ \mathbf{else}:\\ \;\;\;\;\left(-y\right) \cdot \frac{x}{t}\\ \end{array} \]

Alternative 3: 73.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.4 \cdot 10^{-193}:\\ \;\;\;\;x + \frac{z}{\frac{t}{y}}\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-245} \lor \neg \left(z \leq 2.4 \cdot 10^{-157}\right) \land z \leq 3.6 \cdot 10^{-117}:\\ \;\;\;\;\left(-y\right) \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{t} \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -5.4e-193)
   (+ x (/ z (/ t y)))
   (if (or (<= z 4.5e-245) (and (not (<= z 2.4e-157)) (<= z 3.6e-117)))
     (* (- y) (/ x t))
     (+ x (* (/ y t) z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -5.4e-193) {
		tmp = x + (z / (t / y));
	} else if ((z <= 4.5e-245) || (!(z <= 2.4e-157) && (z <= 3.6e-117))) {
		tmp = -y * (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 (z <= (-5.4d-193)) then
        tmp = x + (z / (t / y))
    else if ((z <= 4.5d-245) .or. (.not. (z <= 2.4d-157)) .and. (z <= 3.6d-117)) then
        tmp = -y * (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 (z <= -5.4e-193) {
		tmp = x + (z / (t / y));
	} else if ((z <= 4.5e-245) || (!(z <= 2.4e-157) && (z <= 3.6e-117))) {
		tmp = -y * (x / t);
	} else {
		tmp = x + ((y / t) * z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -5.4e-193:
		tmp = x + (z / (t / y))
	elif (z <= 4.5e-245) or (not (z <= 2.4e-157) and (z <= 3.6e-117)):
		tmp = -y * (x / t)
	else:
		tmp = x + ((y / t) * z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -5.4e-193)
		tmp = Float64(x + Float64(z / Float64(t / y)));
	elseif ((z <= 4.5e-245) || (!(z <= 2.4e-157) && (z <= 3.6e-117)))
		tmp = Float64(Float64(-y) * Float64(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 (z <= -5.4e-193)
		tmp = x + (z / (t / y));
	elseif ((z <= 4.5e-245) || (~((z <= 2.4e-157)) && (z <= 3.6e-117)))
		tmp = -y * (x / t);
	else
		tmp = x + ((y / t) * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -5.4e-193], N[(x + N[(z / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, 4.5e-245], And[N[Not[LessEqual[z, 2.4e-157]], $MachinePrecision], LessEqual[z, 3.6e-117]]], N[((-y) * N[(x / t), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y / t), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.3999999999999998e-193

   1. Initial program 92.1%

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

      1. associate-*l/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 76.7%

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

      1. associate-*l/ 84.3%

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

      2. *-commutative 84.3%

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

   6. Simplified 84.3%

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

      1. clear-num 84.2%

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

      2. un-div-inv 84.4%

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

   8. Applied egg-rr 84.4%

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

   if -5.3999999999999998e-193 < z < 4.49999999999999969e-245 or 2.4e-157 < z < 3.6e-117

   1. Initial program 94.6%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around 0 99.8%

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

      1. associate-*r/ 99.8%

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

      2. neg-mul-1 99.8%

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

   6. Simplified 99.8%

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

      1. associate-/r/ 89.5%

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

      2. add-sqr-sqrt 46.6%

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

      3. sqrt-unprod 55.5%

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

      4. sqr-neg 55.5%

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

      5. sqrt-unprod 15.9%

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

      6. add-sqr-sqrt 25.4%

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

      7. frac-2neg 25.4%

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

      8. distribute-frac-neg 25.4%

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

      9. cancel-sign-sub-inv 25.4%

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

      10. *-commutative 25.4%

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

      11. add-sqr-sqrt 9.5%

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

      12. sqrt-unprod 48.7%

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

      13. sqr-neg 48.7%

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

      14. sqrt-unprod 42.8%

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

      15. add-sqr-sqrt 89.5%

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

   8. Applied egg-rr 89.5%

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

   9. Taylor expanded in y around inf 69.6%

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

       1. mul-1-neg 69.6%

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

       2. associate-*l/ 73.1%

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

       3. distribute-lft-neg-out 73.1%

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

       4. *-commutative 73.1%

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

       5. distribute-neg-frac 73.1%

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

   11. Simplified 73.1%

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

   if 4.49999999999999969e-245 < z < 2.4e-157 or 3.6e-117 < z

   1. Initial program 91.7%

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

      1. associate-*l/ 98.0%

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

   3. Simplified 98.0%

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

   4. Taylor expanded in z around inf 84.2%

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

      1. associate-*l/ 87.9%

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

      2. *-commutative 87.9%

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

   6. Simplified 87.9%

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

4. Final simplification 83.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.4 \cdot 10^{-193}:\\ \;\;\;\;x + \frac{z}{\frac{t}{y}}\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-245} \lor \neg \left(z \leq 2.4 \cdot 10^{-157}\right) \land z \leq 3.6 \cdot 10^{-117}:\\ \;\;\;\;\left(-y\right) \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{t} \cdot z\\ \end{array} \]

Alternative 4: 73.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(-y\right) \cdot \frac{x}{t}\\ \mathbf{if}\;z \leq -5.4 \cdot 10^{-193}:\\ \;\;\;\;x + \frac{z}{\frac{t}{y}}\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-244}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-157}:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \mathbf{elif}\;z \leq 1.22 \cdot 10^{-115}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{t} \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- y) (/ x t))))
   (if (<= z -5.4e-193)
     (+ x (/ z (/ t y)))
     (if (<= z 8e-244)
       t_1
       (if (<= z 2.5e-157)
         (+ x (/ (* y z) t))
         (if (<= z 1.22e-115) t_1 (+ x (* (/ y t) z))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = -y * (x / t);
	double tmp;
	if (z <= -5.4e-193) {
		tmp = x + (z / (t / y));
	} else if (z <= 8e-244) {
		tmp = t_1;
	} else if (z <= 2.5e-157) {
		tmp = x + ((y * z) / t);
	} else if (z <= 1.22e-115) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = -y * (x / t)
    if (z <= (-5.4d-193)) then
        tmp = x + (z / (t / y))
    else if (z <= 8d-244) then
        tmp = t_1
    else if (z <= 2.5d-157) then
        tmp = x + ((y * z) / t)
    else if (z <= 1.22d-115) then
        tmp = t_1
    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 t_1 = -y * (x / t);
	double tmp;
	if (z <= -5.4e-193) {
		tmp = x + (z / (t / y));
	} else if (z <= 8e-244) {
		tmp = t_1;
	} else if (z <= 2.5e-157) {
		tmp = x + ((y * z) / t);
	} else if (z <= 1.22e-115) {
		tmp = t_1;
	} else {
		tmp = x + ((y / t) * z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = -y * (x / t)
	tmp = 0
	if z <= -5.4e-193:
		tmp = x + (z / (t / y))
	elif z <= 8e-244:
		tmp = t_1
	elif z <= 2.5e-157:
		tmp = x + ((y * z) / t)
	elif z <= 1.22e-115:
		tmp = t_1
	else:
		tmp = x + ((y / t) * z)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(-y) * Float64(x / t))
	tmp = 0.0
	if (z <= -5.4e-193)
		tmp = Float64(x + Float64(z / Float64(t / y)));
	elseif (z <= 8e-244)
		tmp = t_1;
	elseif (z <= 2.5e-157)
		tmp = Float64(x + Float64(Float64(y * z) / t));
	elseif (z <= 1.22e-115)
		tmp = t_1;
	else
		tmp = Float64(x + Float64(Float64(y / t) * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = -y * (x / t);
	tmp = 0.0;
	if (z <= -5.4e-193)
		tmp = x + (z / (t / y));
	elseif (z <= 8e-244)
		tmp = t_1;
	elseif (z <= 2.5e-157)
		tmp = x + ((y * z) / t);
	elseif (z <= 1.22e-115)
		tmp = t_1;
	else
		tmp = x + ((y / t) * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[((-y) * N[(x / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.4e-193], N[(x + N[(z / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8e-244], t$95$1, If[LessEqual[z, 2.5e-157], N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.22e-115], t$95$1, N[(x + N[(N[(y / t), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -5.3999999999999998e-193

   1. Initial program 92.1%

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

      1. associate-*l/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 76.7%

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

      1. associate-*l/ 84.3%

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

      2. *-commutative 84.3%

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

   6. Simplified 84.3%

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

      1. clear-num 84.2%

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

      2. un-div-inv 84.4%

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

   8. Applied egg-rr 84.4%

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

   if -5.3999999999999998e-193 < z < 7.9999999999999994e-244 or 2.5000000000000001e-157 < z < 1.22000000000000009e-115

   1. Initial program 94.6%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around 0 99.8%

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

      1. associate-*r/ 99.8%

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

      2. neg-mul-1 99.8%

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

   6. Simplified 99.8%

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

      1. associate-/r/ 89.5%

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

      2. add-sqr-sqrt 46.6%

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

      3. sqrt-unprod 55.5%

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

      4. sqr-neg 55.5%

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

      5. sqrt-unprod 15.9%

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

      6. add-sqr-sqrt 25.4%

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

      7. frac-2neg 25.4%

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

      8. distribute-frac-neg 25.4%

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

      9. cancel-sign-sub-inv 25.4%

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

      10. *-commutative 25.4%

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

      11. add-sqr-sqrt 9.5%

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

      12. sqrt-unprod 48.7%

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

      13. sqr-neg 48.7%

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

      14. sqrt-unprod 42.8%

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

      15. add-sqr-sqrt 89.5%

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

   8. Applied egg-rr 89.5%

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

   9. Taylor expanded in y around inf 69.6%

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

       1. mul-1-neg 69.6%

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

       2. associate-*l/ 73.1%

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

       3. distribute-lft-neg-out 73.1%

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

       4. *-commutative 73.1%

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

       5. distribute-neg-frac 73.1%

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

   11. Simplified 73.1%

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

   if 7.9999999999999994e-244 < z < 2.5000000000000001e-157

   1. Initial program 94.0%

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

      1. associate-*l/ 94.3%

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

   3. Simplified 94.3%

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

   4. Taylor expanded in z around inf 81.5%

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

   if 1.22000000000000009e-115 < z

   1. Initial program 91.3%

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

      1. associate-*l/ 98.6%

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

   3. Simplified 98.6%

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

   4. Taylor expanded in z around inf 84.7%

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

      1. associate-*l/ 90.0%

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

      2. *-commutative 90.0%

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

   6. Simplified 90.0%

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

4. Final simplification 83.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.4 \cdot 10^{-193}:\\ \;\;\;\;x + \frac{z}{\frac{t}{y}}\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-244}:\\ \;\;\;\;\left(-y\right) \cdot \frac{x}{t}\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-157}:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \mathbf{elif}\;z \leq 1.22 \cdot 10^{-115}:\\ \;\;\;\;\left(-y\right) \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{t} \cdot z\\ \end{array} \]

Alternative 5: 86.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{-97}:\\ \;\;\;\;x + \frac{z}{\frac{t}{y}}\\ \mathbf{elif}\;z \leq 10^{-59}:\\ \;\;\;\;x - x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{t} \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -7e-97)
   (+ x (/ z (/ t y)))
   (if (<= z 1e-59) (- x (* x (/ y t))) (+ x (* (/ y t) z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -7e-97) {
		tmp = x + (z / (t / y));
	} else if (z <= 1e-59) {
		tmp = x - (x * (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 (z <= (-7d-97)) then
        tmp = x + (z / (t / y))
    else if (z <= 1d-59) then
        tmp = x - (x * (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 (z <= -7e-97) {
		tmp = x + (z / (t / y));
	} else if (z <= 1e-59) {
		tmp = x - (x * (y / t));
	} else {
		tmp = x + ((y / t) * z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -7e-97:
		tmp = x + (z / (t / y))
	elif z <= 1e-59:
		tmp = x - (x * (y / t))
	else:
		tmp = x + ((y / t) * z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -7e-97)
		tmp = Float64(x + Float64(z / Float64(t / y)));
	elseif (z <= 1e-59)
		tmp = Float64(x - Float64(x * 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 (z <= -7e-97)
		tmp = x + (z / (t / y));
	elseif (z <= 1e-59)
		tmp = x - (x * (y / t));
	else
		tmp = x + ((y / t) * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -7e-97], N[(x + N[(z / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1e-59], N[(x - N[(x * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y / t), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.00000000000000038e-97

   1. Initial program 91.5%

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

      1. associate-*l/ 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around inf 79.9%

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

      1. associate-*l/ 88.3%

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

      2. *-commutative 88.3%

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

   6. Simplified 88.3%

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

      1. clear-num 88.2%

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

      2. un-div-inv 88.3%

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

   8. Applied egg-rr 88.3%

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

   if -7.00000000000000038e-97 < z < 1e-59

   1. Initial program 93.5%

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

      1. associate-/l* 96.1%

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

   3. Simplified 96.1%

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

   4. Taylor expanded in z around 0 91.6%

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

      1. associate-*r/ 91.6%

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

      2. neg-mul-1 91.6%

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

   6. Simplified 91.6%

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

      1. associate-/r/ 89.1%

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

      2. add-sqr-sqrt 46.5%

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

      3. sqrt-unprod 60.1%

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

      4. sqr-neg 60.1%

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

      5. sqrt-unprod 21.8%

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

      6. add-sqr-sqrt 42.2%

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

      7. frac-2neg 42.2%

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

      8. distribute-frac-neg 42.2%

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

      9. cancel-sign-sub-inv 42.2%

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

      10. *-commutative 42.2%

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

      11. add-sqr-sqrt 20.4%

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

      12. sqrt-unprod 56.0%

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

      13. sqr-neg 56.0%

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

      14. sqrt-unprod 42.5%

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

      15. add-sqr-sqrt 89.1%

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

   8. Applied egg-rr 89.1%

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

   if 1e-59 < z

   1. Initial program 92.0%

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

      1. associate-*l/ 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in z around inf 86.8%

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

      1. associate-*l/ 93.1%

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

      2. *-commutative 93.1%

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

   6. Simplified 93.1%

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

4. Final simplification 90.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{-97}:\\ \;\;\;\;x + \frac{z}{\frac{t}{y}}\\ \mathbf{elif}\;z \leq 10^{-59}:\\ \;\;\;\;x - x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{t} \cdot z\\ \end{array} \]

Alternative 6: 85.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{-98}:\\ \;\;\;\;x + \frac{z}{\frac{t}{y}}\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-60}:\\ \;\;\;\;x - \frac{y}{\frac{t}{x}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{t} \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -7e-98)
   (+ x (/ z (/ t y)))
   (if (<= z 8.5e-60) (- x (/ y (/ t x))) (+ x (* (/ y t) z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -7e-98) {
		tmp = x + (z / (t / y));
	} else if (z <= 8.5e-60) {
		tmp = x - (y / (t / x));
	} 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 (z <= (-7d-98)) then
        tmp = x + (z / (t / y))
    else if (z <= 8.5d-60) then
        tmp = x - (y / (t / x))
    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 (z <= -7e-98) {
		tmp = x + (z / (t / y));
	} else if (z <= 8.5e-60) {
		tmp = x - (y / (t / x));
	} else {
		tmp = x + ((y / t) * z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -7e-98:
		tmp = x + (z / (t / y))
	elif z <= 8.5e-60:
		tmp = x - (y / (t / x))
	else:
		tmp = x + ((y / t) * z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -7e-98)
		tmp = Float64(x + Float64(z / Float64(t / y)));
	elseif (z <= 8.5e-60)
		tmp = Float64(x - Float64(y / Float64(t / x)));
	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 (z <= -7e-98)
		tmp = x + (z / (t / y));
	elseif (z <= 8.5e-60)
		tmp = x - (y / (t / x));
	else
		tmp = x + ((y / t) * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -7e-98], N[(x + N[(z / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8.5e-60], N[(x - N[(y / N[(t / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y / t), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.0000000000000004e-98

   1. Initial program 91.5%

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

      1. associate-*l/ 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around inf 79.9%

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

      1. associate-*l/ 88.3%

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

      2. *-commutative 88.3%

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

   6. Simplified 88.3%

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

      1. clear-num 88.2%

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

      2. un-div-inv 88.3%

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

   8. Applied egg-rr 88.3%

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

   if -7.0000000000000004e-98 < z < 8.50000000000000044e-60

   1. Initial program 93.5%

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

      1. associate-/l* 96.1%

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

   3. Simplified 96.1%

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

   4. Taylor expanded in z around 0 91.6%

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

      1. associate-*r/ 91.6%

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

      2. neg-mul-1 91.6%

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

   6. Simplified 91.6%

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

   7. Taylor expanded in x around 0 89.1%

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

      1. distribute-lft-in 89.1%

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

      2. mul-1-neg 89.1%

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

      3. distribute-rgt-neg-in 89.1%

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

      4. unsub-neg 89.1%

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

      5. *-rgt-identity 89.1%

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

      6. *-commutative 89.1%

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

      7. associate-/r/ 91.6%

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

   9. Simplified 91.6%

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

   if 8.50000000000000044e-60 < z

   1. Initial program 92.0%

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

      1. associate-*l/ 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in z around inf 86.8%

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

      1. associate-*l/ 93.1%

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

      2. *-commutative 93.1%

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

   6. Simplified 93.1%

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

4. Final simplification 91.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{-98}:\\ \;\;\;\;x + \frac{z}{\frac{t}{y}}\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-60}:\\ \;\;\;\;x - \frac{y}{\frac{t}{x}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{t} \cdot z\\ \end{array} \]

Alternative 7: 85.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{-97}:\\ \;\;\;\;x + \frac{z}{\frac{t}{y}}\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-60}:\\ \;\;\;\;x - y \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{t} \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -5.5e-97)
   (+ x (/ z (/ t y)))
   (if (<= z 1.8e-60) (- x (* y (/ x t))) (+ x (* (/ y t) z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -5.5e-97) {
		tmp = x + (z / (t / y));
	} else if (z <= 1.8e-60) {
		tmp = x - (y * (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 (z <= (-5.5d-97)) then
        tmp = x + (z / (t / y))
    else if (z <= 1.8d-60) then
        tmp = x - (y * (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 (z <= -5.5e-97) {
		tmp = x + (z / (t / y));
	} else if (z <= 1.8e-60) {
		tmp = x - (y * (x / t));
	} else {
		tmp = x + ((y / t) * z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -5.5e-97:
		tmp = x + (z / (t / y))
	elif z <= 1.8e-60:
		tmp = x - (y * (x / t))
	else:
		tmp = x + ((y / t) * z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -5.5e-97)
		tmp = Float64(x + Float64(z / Float64(t / y)));
	elseif (z <= 1.8e-60)
		tmp = Float64(x - Float64(y * Float64(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 (z <= -5.5e-97)
		tmp = x + (z / (t / y));
	elseif (z <= 1.8e-60)
		tmp = x - (y * (x / t));
	else
		tmp = x + ((y / t) * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -5.5e-97], N[(x + N[(z / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.8e-60], N[(x - N[(y * N[(x / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y / t), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.49999999999999948e-97

   1. Initial program 91.5%

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

      1. associate-*l/ 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around inf 79.9%

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

      1. associate-*l/ 88.3%

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

      2. *-commutative 88.3%

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

   6. Simplified 88.3%

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

      1. clear-num 88.2%

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

      2. un-div-inv 88.3%

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

   8. Applied egg-rr 88.3%

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

   if -5.49999999999999948e-97 < z < 1.8e-60

   1. Initial program 93.5%

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

      1. associate-/l* 96.1%

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

   3. Simplified 96.1%

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

   4. Taylor expanded in z around 0 91.6%

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

      1. associate-*r/ 91.6%

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

      2. neg-mul-1 91.6%

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

   6. Simplified 91.6%

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

      1. frac-2neg 91.6%

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

      2. div-inv 91.6%

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

      3. distribute-frac-neg 91.6%

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

      4. remove-double-neg 91.6%

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

      5. clear-num 92.4%

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

   8. Applied egg-rr 92.4%

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

   if 1.8e-60 < z

   1. Initial program 92.0%

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

      1. associate-*l/ 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in z around inf 86.8%

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

      1. associate-*l/ 93.1%

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

      2. *-commutative 93.1%

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

   6. Simplified 93.1%

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

4. Final simplification 91.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{-97}:\\ \;\;\;\;x + \frac{z}{\frac{t}{y}}\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-60}:\\ \;\;\;\;x - y \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{t} \cdot z\\ \end{array} \]

Alternative 8: 49.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5.6 \cdot 10^{+19}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 4.7 \cdot 10^{+83}:\\ \;\;\;\;\frac{-x}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -5.6e+19) x (if (<= t 4.7e+83) (/ (- x) (/ t y)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -5.6e+19) {
		tmp = x;
	} else if (t <= 4.7e+83) {
		tmp = -x / (t / y);
	} 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 <= (-5.6d+19)) then
        tmp = x
    else if (t <= 4.7d+83) then
        tmp = -x / (t / y)
    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 <= -5.6e+19) {
		tmp = x;
	} else if (t <= 4.7e+83) {
		tmp = -x / (t / y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -5.6e+19:
		tmp = x
	elif t <= 4.7e+83:
		tmp = -x / (t / y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -5.6e+19)
		tmp = x;
	elseif (t <= 4.7e+83)
		tmp = Float64(Float64(-x) / Float64(t / y));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -5.6e+19)
		tmp = x;
	elseif (t <= 4.7e+83)
		tmp = -x / (t / y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -5.6e+19], x, If[LessEqual[t, 4.7e+83], N[((-x) / N[(t / y), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if t < -5.6e19 or 4.6999999999999999e83 < t

   1. Initial program 84.3%

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

      1. associate-*l/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 82.9%

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

      1. associate-*l/ 93.3%

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

      2. *-commutative 93.3%

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

   6. Simplified 93.3%

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

   7. Taylor expanded in x around inf 70.0%

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

   if -5.6e19 < t < 4.6999999999999999e83

   1. Initial program 98.5%

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

      1. associate-/l* 92.1%

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

   3. Simplified 92.1%

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

   4. Taylor expanded in z around 0 57.8%

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

      1. associate-*r/ 57.8%

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

      2. neg-mul-1 57.8%

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

   6. Simplified 57.8%

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

      1. associate-/r/ 58.6%

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

      2. add-sqr-sqrt 32.5%

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

      3. sqrt-unprod 35.9%

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

      4. sqr-neg 35.9%

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

      5. sqrt-unprod 7.9%

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

      6. add-sqr-sqrt 16.5%

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

      7. frac-2neg 16.5%

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

      8. distribute-frac-neg 16.5%

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

      9. cancel-sign-sub-inv 16.5%

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

      10. *-commutative 16.5%

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

      11. add-sqr-sqrt 8.6%

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

      12. sqrt-unprod 31.5%

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

      13. sqr-neg 31.5%

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

      14. sqrt-unprod 26.0%

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

      15. add-sqr-sqrt 58.6%

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

   8. Applied egg-rr 58.6%

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

   9. Taylor expanded in y around inf 48.0%

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

       1. mul-1-neg 48.0%

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

       2. associate-*r/ 46.2%

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

       3. distribute-rgt-neg-in 46.2%

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

       4. distribute-neg-frac 46.2%

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

   11. Simplified 46.2%

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

       1. distribute-frac-neg 46.2%

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

       2. distribute-rgt-neg-out 46.2%

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

       3. add-sqr-sqrt 28.4%

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

       4. sqrt-unprod 29.5%

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

       5. sqr-neg 29.5%

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

       6. sqrt-unprod 2.9%

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

       7. add-sqr-sqrt 6.6%

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

       8. clear-num 6.6%

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

       9. un-div-inv 6.6%

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

       10. add-sqr-sqrt 2.9%

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

       11. sqrt-unprod 30.1%

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

       12. sqr-neg 30.1%

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

       13. sqrt-unprod 29.6%

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

       14. add-sqr-sqrt 46.8%

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

   13. Applied egg-rr 46.8%

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

4. Final simplification 56.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.6 \cdot 10^{+19}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 4.7 \cdot 10^{+83}:\\ \;\;\;\;\frac{-x}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 9: 48.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.6 \cdot 10^{+18}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 4.3 \cdot 10^{+83}:\\ \;\;\;\;\frac{-y}{\frac{t}{x}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -4.6e+18) x (if (<= t 4.3e+83) (/ (- y) (/ t x)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -4.6e+18) {
		tmp = x;
	} else if (t <= 4.3e+83) {
		tmp = -y / (t / x);
	} 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 <= (-4.6d+18)) then
        tmp = x
    else if (t <= 4.3d+83) then
        tmp = -y / (t / x)
    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 <= -4.6e+18) {
		tmp = x;
	} else if (t <= 4.3e+83) {
		tmp = -y / (t / x);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -4.6e+18:
		tmp = x
	elif t <= 4.3e+83:
		tmp = -y / (t / x)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -4.6e+18)
		tmp = x;
	elseif (t <= 4.3e+83)
		tmp = Float64(Float64(-y) / Float64(t / x));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -4.6e+18)
		tmp = x;
	elseif (t <= 4.3e+83)
		tmp = -y / (t / x);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -4.6e+18], x, If[LessEqual[t, 4.3e+83], N[((-y) / N[(t / x), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if t < -4.6e18 or 4.3e83 < t

   1. Initial program 84.3%

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

      1. associate-*l/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 82.9%

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

      1. associate-*l/ 93.3%

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

      2. *-commutative 93.3%

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

   6. Simplified 93.3%

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

   7. Taylor expanded in x around inf 70.0%

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

   if -4.6e18 < t < 4.3e83

   1. Initial program 98.5%

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

      1. associate-/l* 92.1%

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

   3. Simplified 92.1%

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

   4. Taylor expanded in z around 0 57.8%

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

      1. associate-*r/ 57.8%

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

      2. neg-mul-1 57.8%

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

   6. Simplified 57.8%

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

      1. associate-/r/ 58.6%

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

      2. add-sqr-sqrt 32.5%

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

      3. sqrt-unprod 35.9%

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

      4. sqr-neg 35.9%

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

      5. sqrt-unprod 7.9%

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

      6. add-sqr-sqrt 16.5%

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

      7. frac-2neg 16.5%

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

      8. distribute-frac-neg 16.5%

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

      9. cancel-sign-sub-inv 16.5%

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

      10. *-commutative 16.5%

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

      11. add-sqr-sqrt 8.6%

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

      12. sqrt-unprod 31.5%

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

      13. sqr-neg 31.5%

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

      14. sqrt-unprod 26.0%

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

      15. add-sqr-sqrt 58.6%

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

   8. Applied egg-rr 58.6%

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

   9. Taylor expanded in y around inf 48.0%

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

       1. mul-1-neg 48.0%

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

       2. associate-*r/ 46.2%

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

       3. distribute-rgt-neg-in 46.2%

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

       4. distribute-neg-frac 46.2%

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

   11. Simplified 46.2%

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

   12. Taylor expanded in x around 0 48.0%

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

       1. mul-1-neg 48.0%

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

       2. *-commutative 48.0%

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

       3. associate-*l/ 46.2%

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

       4. associate-/r/ 47.8%

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

   14. Simplified 47.8%

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

4. Final simplification 57.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.6 \cdot 10^{+18}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 4.3 \cdot 10^{+83}:\\ \;\;\;\;\frac{-y}{\frac{t}{x}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 10: 48.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.16 \cdot 10^{+21}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 4.3 \cdot 10^{+83}:\\ \;\;\;\;\left(-y\right) \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -1.16e+21) x (if (<= t 4.3e+83) (* (- y) (/ x t)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.16e+21) {
		tmp = x;
	} else if (t <= 4.3e+83) {
		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 <= (-1.16d+21)) then
        tmp = x
    else if (t <= 4.3d+83) 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 <= -1.16e+21) {
		tmp = x;
	} else if (t <= 4.3e+83) {
		tmp = -y * (x / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -1.16e+21:
		tmp = x
	elif t <= 4.3e+83:
		tmp = -y * (x / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -1.16e+21)
		tmp = x;
	elseif (t <= 4.3e+83)
		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 <= -1.16e+21)
		tmp = x;
	elseif (t <= 4.3e+83)
		tmp = -y * (x / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -1.16e+21], x, If[LessEqual[t, 4.3e+83], N[((-y) * N[(x / t), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if t < -1.16e21 or 4.3e83 < t

   1. Initial program 84.3%

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

      1. associate-*l/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 82.9%

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

      1. associate-*l/ 93.3%

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

      2. *-commutative 93.3%

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

   6. Simplified 93.3%

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

   7. Taylor expanded in x around inf 70.0%

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

   if -1.16e21 < t < 4.3e83

   1. Initial program 98.5%

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

      1. associate-/l* 92.1%

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

   3. Simplified 92.1%

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

   4. Taylor expanded in z around 0 57.8%

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

      1. associate-*r/ 57.8%

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

      2. neg-mul-1 57.8%

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

   6. Simplified 57.8%

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

      1. associate-/r/ 58.6%

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

      2. add-sqr-sqrt 32.5%

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

      3. sqrt-unprod 35.9%

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

      4. sqr-neg 35.9%

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

      5. sqrt-unprod 7.9%

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

      6. add-sqr-sqrt 16.5%

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

      7. frac-2neg 16.5%

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

      8. distribute-frac-neg 16.5%

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

      9. cancel-sign-sub-inv 16.5%

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

      10. *-commutative 16.5%

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

      11. add-sqr-sqrt 8.6%

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

      12. sqrt-unprod 31.5%

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

      13. sqr-neg 31.5%

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

      14. sqrt-unprod 26.0%

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

      15. add-sqr-sqrt 58.6%

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

   8. Applied egg-rr 58.6%

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

   9. Taylor expanded in y around inf 48.0%

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

       1. mul-1-neg 48.0%

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

       2. associate-*l/ 48.5%

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

       3. distribute-lft-neg-out 48.5%

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

       4. *-commutative 48.5%

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

       5. distribute-neg-frac 48.5%

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

   11. Simplified 48.5%

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

4. Final simplification 57.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.16 \cdot 10^{+21}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 4.3 \cdot 10^{+83}:\\ \;\;\;\;\left(-y\right) \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 11: 38.8% 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 92.4%

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

   1. associate-*l/ 96.9%

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

3. Simplified 96.9%

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

4. Taylor expanded in z around inf 69.5%

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

   1. associate-*l/ 74.5%

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

   2. *-commutative 74.5%

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

6. Simplified 74.5%

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

7. Taylor expanded in x around inf 37.4%

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

8. Final simplification 37.4%

   \[\leadsto x \]

Developer target: 91.0% 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 2023290 
(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)))