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

Percentage Accurate: 93.3% → 98.0%

Time: 7.8s

Alternatives: 12

Speedup: 1.0×

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

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 93.3% 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: 98.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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 + ((z - x) / (t / y))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 94.1%

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

   1. associate-*l/ 98.4%

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

3. Simplified 98.4%

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

   1. *-commutative 98.4%

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

   2. clear-num 98.3%

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

   3. un-div-inv 98.4%

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

5. Applied egg-rr 98.4%

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

6. Final simplification 98.4%

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

Alternative 2: 48.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{-x}{t}\\ \mathbf{if}\;t \leq -3.6 \cdot 10^{-56}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -1.9 \cdot 10^{-296}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 9.8 \cdot 10^{-300}:\\ \;\;\;\;\frac{x}{\frac{t}{y}}\\ \mathbf{elif}\;t \leq 8.2 \cdot 10^{-114}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (/ (- x) t))))
   (if (<= t -3.6e-56)
     x
     (if (<= t -1.9e-296)
       t_1
       (if (<= t 9.8e-300) (/ x (/ t y)) (if (<= t 8.2e-114) t_1 x))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (-x / t);
	double tmp;
	if (t <= -3.6e-56) {
		tmp = x;
	} else if (t <= -1.9e-296) {
		tmp = t_1;
	} else if (t <= 9.8e-300) {
		tmp = x / (t / y);
	} else if (t <= 8.2e-114) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = y * (-x / t)
    if (t <= (-3.6d-56)) then
        tmp = x
    else if (t <= (-1.9d-296)) then
        tmp = t_1
    else if (t <= 9.8d-300) then
        tmp = x / (t / y)
    else if (t <= 8.2d-114) then
        tmp = t_1
    else
        tmp = x
    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 (t <= -3.6e-56) {
		tmp = x;
	} else if (t <= -1.9e-296) {
		tmp = t_1;
	} else if (t <= 9.8e-300) {
		tmp = x / (t / y);
	} else if (t <= 8.2e-114) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (-x / t)
	tmp = 0
	if t <= -3.6e-56:
		tmp = x
	elif t <= -1.9e-296:
		tmp = t_1
	elif t <= 9.8e-300:
		tmp = x / (t / y)
	elif t <= 8.2e-114:
		tmp = t_1
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(Float64(-x) / t))
	tmp = 0.0
	if (t <= -3.6e-56)
		tmp = x;
	elseif (t <= -1.9e-296)
		tmp = t_1;
	elseif (t <= 9.8e-300)
		tmp = Float64(x / Float64(t / y));
	elseif (t <= 8.2e-114)
		tmp = t_1;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * (-x / t);
	tmp = 0.0;
	if (t <= -3.6e-56)
		tmp = x;
	elseif (t <= -1.9e-296)
		tmp = t_1;
	elseif (t <= 9.8e-300)
		tmp = x / (t / y);
	elseif (t <= 8.2e-114)
		tmp = t_1;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * N[((-x) / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.6e-56], x, If[LessEqual[t, -1.9e-296], t$95$1, If[LessEqual[t, 9.8e-300], N[(x / N[(t / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 8.2e-114], t$95$1, x]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.59999999999999978e-56 or 8.1999999999999993e-114 < t

   1. Initial program 90.9%

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

      1. +-commutative 90.9%

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

      2. associate-*r/ 98.6%

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

      3. fma-def 98.6%

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

   3. Simplified 98.6%

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

   4. Taylor expanded in y around 0 56.7%

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

   if -3.59999999999999978e-56 < t < -1.9000000000000001e-296 or 9.8e-300 < t < 8.1999999999999993e-114

   1. Initial program 99.2%

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

      1. associate-/l* 88.3%

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

   3. Simplified 88.3%

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

   4. Taylor expanded in z around 0 51.0%

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

      1. associate-*r/ 51.0%

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

      2. neg-mul-1 51.0%

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

   6. Simplified 51.0%

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

   7. Taylor expanded in x around 0 58.2%

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

      1. mul-1-neg 58.2%

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

      2. sub-neg 58.2%

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

      3. *-commutative 58.2%

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

   9. Simplified 58.2%

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

   10. Taylor expanded in y around inf 47.3%

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

       1. associate-*r/ 47.3%

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

       2. neg-mul-1 47.3%

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

       3. distribute-lft-neg-in 47.3%

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

       4. associate-*r/ 44.7%

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

   12. Simplified 44.7%

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

   if -1.9000000000000001e-296 < t < 9.8e-300

   1. Initial program 99.8%

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

      1. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in z around 0 7.9%

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

      1. associate-*r/ 7.9%

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

      2. neg-mul-1 7.9%

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

   6. Simplified 7.9%

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

   7. Taylor expanded in x around 0 21.3%

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

      1. mul-1-neg 21.3%

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

      2. sub-neg 21.3%

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

      3. *-commutative 21.3%

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

   9. Simplified 21.3%

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

   10. Taylor expanded in y around inf 7.9%

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

       1. associate-*r/ 7.9%

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

       2. neg-mul-1 7.9%

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

       3. distribute-lft-neg-in 7.9%

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

       4. associate-*r/ 7.9%

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

   12. Simplified 7.9%

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

       1. add-sqr-sqrt 7.9%

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

       2. sqrt-unprod 49.9%

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

       3. sqr-neg 49.9%

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

       4. sqrt-unprod 16.3%

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

       5. add-sqr-sqrt 46.4%

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

       6. associate-*r/ 46.4%

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

       7. *-commutative 46.4%

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

       8. associate-/l* 71.6%

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

   14. Applied egg-rr 71.6%

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

4. Final simplification 52.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.6 \cdot 10^{-56}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -1.9 \cdot 10^{-296}:\\ \;\;\;\;y \cdot \frac{-x}{t}\\ \mathbf{elif}\;t \leq 9.8 \cdot 10^{-300}:\\ \;\;\;\;\frac{x}{\frac{t}{y}}\\ \mathbf{elif}\;t \leq 8.2 \cdot 10^{-114}:\\ \;\;\;\;y \cdot \frac{-x}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 3: 86.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.4 \cdot 10^{-80} \lor \neg \left(z \leq 8 \cdot 10^{-106}\right):\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -5.4e-80) (not (<= z 8e-106)))
   (+ x (* z (/ y t)))
   (* x (- 1.0 (/ y t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -5.4e-80) || !(z <= 8e-106)) {
		tmp = x + (z * (y / 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 <= (-5.4d-80)) .or. (.not. (z <= 8d-106))) then
        tmp = x + (z * (y / 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 <= -5.4e-80) || !(z <= 8e-106)) {
		tmp = x + (z * (y / t));
	} else {
		tmp = x * (1.0 - (y / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -5.4e-80) or not (z <= 8e-106):
		tmp = x + (z * (y / t))
	else:
		tmp = x * (1.0 - (y / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -5.4e-80) || !(z <= 8e-106))
		tmp = Float64(x + Float64(z * Float64(y / 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 <= -5.4e-80) || ~((z <= 8e-106)))
		tmp = x + (z * (y / t));
	else
		tmp = x * (1.0 - (y / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -5.4e-80], N[Not[LessEqual[z, 8e-106]], $MachinePrecision]], N[(x + N[(z * N[(y / 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 < -5.4000000000000004e-80 or 7.99999999999999953e-106 < z

   1. Initial program 92.7%

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

      1. associate-*l/ 98.7%

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

   3. Simplified 98.7%

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

   4. Taylor expanded in z around inf 85.4%

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

      1. associate-*l/ 89.6%

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

      2. *-commutative 89.6%

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

   6. Simplified 89.6%

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

   if -5.4000000000000004e-80 < z < 7.99999999999999953e-106

   1. Initial program 96.8%

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

      1. associate-/l* 95.8%

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

   3. Simplified 95.8%

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

   4. Taylor expanded in z around 0 89.0%

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

      1. associate-*r/ 89.0%

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

      2. neg-mul-1 89.0%

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

   6. Simplified 89.0%

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

   7. Taylor expanded in x around 0 90.9%

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

      1. mul-1-neg 90.9%

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

      2. sub-neg 90.9%

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

      3. *-commutative 90.9%

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

   9. Simplified 90.9%

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

4. Final simplification 90.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.4 \cdot 10^{-80} \lor \neg \left(z \leq 8 \cdot 10^{-106}\right):\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \end{array} \]

Alternative 4: 85.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.35 \cdot 10^{-83}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-104}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -2.35e-83)
   (+ x (/ y (/ t z)))
   (if (<= z 3.5e-104) (* x (- 1.0 (/ y t))) (+ x (* z (/ y t))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.35e-83) {
		tmp = x + (y / (t / z));
	} else if (z <= 3.5e-104) {
		tmp = x * (1.0 - (y / t));
	} else {
		tmp = 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 (z <= (-2.35d-83)) then
        tmp = x + (y / (t / z))
    else if (z <= 3.5d-104) then
        tmp = x * (1.0d0 - (y / t))
    else
        tmp = 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 (z <= -2.35e-83) {
		tmp = x + (y / (t / z));
	} else if (z <= 3.5e-104) {
		tmp = x * (1.0 - (y / t));
	} else {
		tmp = x + (z * (y / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -2.35e-83:
		tmp = x + (y / (t / z))
	elif z <= 3.5e-104:
		tmp = x * (1.0 - (y / t))
	else:
		tmp = x + (z * (y / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -2.35e-83)
		tmp = Float64(x + Float64(y / Float64(t / z)));
	elseif (z <= 3.5e-104)
		tmp = Float64(x * Float64(1.0 - Float64(y / t)));
	else
		tmp = Float64(x + Float64(z * Float64(y / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -2.35e-83)
		tmp = x + (y / (t / z));
	elseif (z <= 3.5e-104)
		tmp = x * (1.0 - (y / t));
	else
		tmp = x + (z * (y / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -2.35e-83], N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.5e-104], N[(x * N[(1.0 - N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.3500000000000002e-83

   1. Initial program 92.2%

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

      1. associate-/l* 96.0%

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

   3. Simplified 96.0%

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

   4. Taylor expanded in z around inf 89.4%

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

   if -2.3500000000000002e-83 < z < 3.50000000000000029e-104

   1. Initial program 96.8%

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

      1. associate-/l* 95.8%

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

   3. Simplified 95.8%

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

   4. Taylor expanded in z around 0 89.0%

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

      1. associate-*r/ 89.0%

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

      2. neg-mul-1 89.0%

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

   6. Simplified 89.0%

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

   7. Taylor expanded in x around 0 90.9%

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

      1. mul-1-neg 90.9%

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

      2. sub-neg 90.9%

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

      3. *-commutative 90.9%

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

   9. Simplified 90.9%

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

   if 3.50000000000000029e-104 < z

   1. Initial program 93.0%

      \[x + \frac{y \cdot \left(z - x\right)}{t} \]
   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 87.1%

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

      1. associate-*l/ 91.8%

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

      2. *-commutative 91.8%

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

   6. Simplified 91.8%

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

4. Final simplification 90.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.35 \cdot 10^{-83}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-104}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \end{array} \]

Alternative 5: 85.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.58 \cdot 10^{-80}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \mathbf{elif}\;z \leq 4.3 \cdot 10^{-104}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{\frac{t}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.58e-80)
   (+ x (/ y (/ t z)))
   (if (<= z 4.3e-104) (* x (- 1.0 (/ y t))) (+ x (/ z (/ t y))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.58e-80) {
		tmp = x + (y / (t / z));
	} else if (z <= 4.3e-104) {
		tmp = x * (1.0 - (y / t));
	} else {
		tmp = x + (z / (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 <= (-1.58d-80)) then
        tmp = x + (y / (t / z))
    else if (z <= 4.3d-104) then
        tmp = x * (1.0d0 - (y / t))
    else
        tmp = x + (z / (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 <= -1.58e-80) {
		tmp = x + (y / (t / z));
	} else if (z <= 4.3e-104) {
		tmp = x * (1.0 - (y / t));
	} else {
		tmp = x + (z / (t / y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.58e-80:
		tmp = x + (y / (t / z))
	elif z <= 4.3e-104:
		tmp = x * (1.0 - (y / t))
	else:
		tmp = x + (z / (t / y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.58e-80)
		tmp = Float64(x + Float64(y / Float64(t / z)));
	elseif (z <= 4.3e-104)
		tmp = Float64(x * Float64(1.0 - Float64(y / t)));
	else
		tmp = Float64(x + Float64(z / Float64(t / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.58e-80)
		tmp = x + (y / (t / z));
	elseif (z <= 4.3e-104)
		tmp = x * (1.0 - (y / t));
	else
		tmp = x + (z / (t / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.58e-80], N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.3e-104], N[(x * N[(1.0 - N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.58000000000000003e-80

   1. Initial program 92.2%

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

      1. associate-/l* 96.0%

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

   3. Simplified 96.0%

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

   4. Taylor expanded in z around inf 89.4%

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

   if -1.58000000000000003e-80 < z < 4.3000000000000001e-104

   1. Initial program 96.8%

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

      1. associate-/l* 95.8%

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

   3. Simplified 95.8%

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

   4. Taylor expanded in z around 0 89.0%

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

      1. associate-*r/ 89.0%

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

      2. neg-mul-1 89.0%

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

   6. Simplified 89.0%

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

   7. Taylor expanded in x around 0 90.9%

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

      1. mul-1-neg 90.9%

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

      2. sub-neg 90.9%

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

      3. *-commutative 90.9%

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

   9. Simplified 90.9%

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

   if 4.3000000000000001e-104 < z

   1. Initial program 93.0%

      \[x + \frac{y \cdot \left(z - x\right)}{t} \]
   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 87.1%

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

      1. associate-*l/ 91.8%

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

      2. *-commutative 91.8%

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

   6. Simplified 91.8%

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

      1. clear-num 91.7%

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

      2. div-inv 91.8%

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

   8. Applied egg-rr 91.8%

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

4. Final simplification 90.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.58 \cdot 10^{-80}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \mathbf{elif}\;z \leq 4.3 \cdot 10^{-104}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{\frac{t}{y}}\\ \end{array} \]

Alternative 6: 85.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.3 \cdot 10^{-80}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-104}:\\ \;\;\;\;x - x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{\frac{t}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -3.3e-80)
   (+ x (/ y (/ t z)))
   (if (<= z 3e-104) (- x (* x (/ y t))) (+ x (/ z (/ t y))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -3.3e-80) {
		tmp = x + (y / (t / z));
	} else if (z <= 3e-104) {
		tmp = x - (x * (y / t));
	} else {
		tmp = x + (z / (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 <= (-3.3d-80)) then
        tmp = x + (y / (t / z))
    else if (z <= 3d-104) then
        tmp = x - (x * (y / t))
    else
        tmp = x + (z / (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 <= -3.3e-80) {
		tmp = x + (y / (t / z));
	} else if (z <= 3e-104) {
		tmp = x - (x * (y / t));
	} else {
		tmp = x + (z / (t / y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -3.3e-80:
		tmp = x + (y / (t / z))
	elif z <= 3e-104:
		tmp = x - (x * (y / t))
	else:
		tmp = x + (z / (t / y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -3.3e-80)
		tmp = Float64(x + Float64(y / Float64(t / z)));
	elseif (z <= 3e-104)
		tmp = Float64(x - Float64(x * Float64(y / t)));
	else
		tmp = Float64(x + Float64(z / Float64(t / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -3.3e-80)
		tmp = x + (y / (t / z));
	elseif (z <= 3e-104)
		tmp = x - (x * (y / t));
	else
		tmp = x + (z / (t / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -3.3e-80], N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3e-104], N[(x - N[(x * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.3e-80

   1. Initial program 92.2%

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

      1. associate-/l* 96.0%

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

   3. Simplified 96.0%

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

   4. Taylor expanded in z around inf 89.4%

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

   if -3.3e-80 < z < 3.0000000000000002e-104

   1. Initial program 96.8%

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

      1. +-commutative 96.8%

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

      2. associate-*r/ 95.8%

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

      3. fma-def 95.7%

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

   3. Simplified 95.7%

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

   4. Taylor expanded in z around 0 88.9%

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

      1. +-commutative 88.9%

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

      2. mul-1-neg 88.9%

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

      3. unsub-neg 88.9%

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

      4. *-commutative 88.9%

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

      5. associate-*r/ 90.9%

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

   6. Simplified 90.9%

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

   if 3.0000000000000002e-104 < z

   1. Initial program 93.0%

      \[x + \frac{y \cdot \left(z - x\right)}{t} \]
   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 87.1%

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

      1. associate-*l/ 91.8%

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

      2. *-commutative 91.8%

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

   6. Simplified 91.8%

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

      1. clear-num 91.7%

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

      2. div-inv 91.8%

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

   8. Applied egg-rr 91.8%

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

4. Final simplification 90.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.3 \cdot 10^{-80}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-104}:\\ \;\;\;\;x - x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{\frac{t}{y}}\\ \end{array} \]

Alternative 7: 51.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.35 \cdot 10^{-55}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 6 \cdot 10^{-96}:\\ \;\;\;\;x \cdot \frac{-y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -1.35e-55) x (if (<= t 6e-96) (* x (/ (- y) t)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.35e-55) {
		tmp = x;
	} else if (t <= 6e-96) {
		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 <= (-1.35d-55)) then
        tmp = x
    else if (t <= 6d-96) 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 <= -1.35e-55) {
		tmp = x;
	} else if (t <= 6e-96) {
		tmp = x * (-y / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -1.35e-55:
		tmp = x
	elif t <= 6e-96:
		tmp = x * (-y / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -1.35e-55)
		tmp = x;
	elseif (t <= 6e-96)
		tmp = Float64(x * Float64(Float64(-y) / t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -1.35e-55)
		tmp = x;
	elseif (t <= 6e-96)
		tmp = x * (-y / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -1.35e-55], x, If[LessEqual[t, 6e-96], N[(x * N[((-y) / t), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if t < -1.35000000000000002e-55 or 6e-96 < t

   1. Initial program 90.6%

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

      1. +-commutative 90.6%

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

      2. associate-*r/ 98.6%

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

      3. fma-def 98.5%

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

   3. Simplified 98.5%

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

   4. Taylor expanded in y around 0 57.5%

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

   if -1.35000000000000002e-55 < t < 6e-96

   1. Initial program 99.3%

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

      1. associate-/l* 89.5%

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

   3. Simplified 89.5%

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

   4. Taylor expanded in z around 0 47.2%

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

      1. associate-*r/ 47.2%

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

      2. neg-mul-1 47.2%

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

   6. Simplified 47.2%

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

   7. Taylor expanded in x around 0 55.5%

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

      1. mul-1-neg 55.5%

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

      2. sub-neg 55.5%

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

      3. *-commutative 55.5%

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

   9. Simplified 55.5%

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

   10. Taylor expanded in y around inf 42.9%

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

       1. associate-*r/ 42.9%

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

       2. neg-mul-1 42.9%

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

       3. distribute-rgt-neg-in 42.9%

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

       4. associate-*l/ 45.7%

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

   12. Simplified 45.7%

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

4. Final simplification 52.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.35 \cdot 10^{-55}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 6 \cdot 10^{-96}:\\ \;\;\;\;x \cdot \frac{-y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 8: 51.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.4 \cdot 10^{-54}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{-97}:\\ \;\;\;\;\frac{-x}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -4.4e-54) x (if (<= t 2.1e-97) (/ (- x) (/ t y)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -4.4e-54) {
		tmp = x;
	} else if (t <= 2.1e-97) {
		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 <= (-4.4d-54)) then
        tmp = x
    else if (t <= 2.1d-97) 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 <= -4.4e-54) {
		tmp = x;
	} else if (t <= 2.1e-97) {
		tmp = -x / (t / y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -4.4e-54:
		tmp = x
	elif t <= 2.1e-97:
		tmp = -x / (t / y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -4.4e-54)
		tmp = x;
	elseif (t <= 2.1e-97)
		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 <= -4.4e-54)
		tmp = x;
	elseif (t <= 2.1e-97)
		tmp = -x / (t / y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -4.4e-54], x, If[LessEqual[t, 2.1e-97], N[((-x) / N[(t / y), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if t < -4.3999999999999999e-54 or 2.1000000000000001e-97 < t

   1. Initial program 90.6%

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

      1. +-commutative 90.6%

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

      2. associate-*r/ 98.6%

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

      3. fma-def 98.5%

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

   3. Simplified 98.5%

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

   4. Taylor expanded in y around 0 57.5%

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

   if -4.3999999999999999e-54 < t < 2.1000000000000001e-97

   1. Initial program 99.3%

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

      1. associate-/l* 89.5%

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

   3. Simplified 89.5%

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

   4. Taylor expanded in z around 0 47.2%

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

      1. associate-*r/ 47.2%

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

      2. neg-mul-1 47.2%

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

   6. Simplified 47.2%

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

   7. Taylor expanded in x around 0 55.5%

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

      1. mul-1-neg 55.5%

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

      2. sub-neg 55.5%

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

      3. *-commutative 55.5%

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

   9. Simplified 55.5%

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

   10. Taylor expanded in y around inf 42.9%

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

       1. associate-*r/ 42.9%

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

       2. neg-mul-1 42.9%

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

       3. distribute-lft-neg-in 42.9%

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

       4. associate-*r/ 40.7%

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

   12. Simplified 40.7%

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

   13. Taylor expanded in y around 0 42.9%

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

       1. mul-1-neg 42.9%

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

       2. *-commutative 42.9%

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

       3. associate-/l* 45.7%

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

       4. distribute-neg-frac 45.7%

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

   15. Simplified 45.7%

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

4. Final simplification 52.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.4 \cdot 10^{-54}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{-97}:\\ \;\;\;\;\frac{-x}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 9: 39.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -8.8 \cdot 10^{-200}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 3 \cdot 10^{-214}:\\ \;\;\;\;\frac{x}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -8.8e-200) x (if (<= t 3e-214) (/ x (/ t y)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -8.8e-200) {
		tmp = x;
	} else if (t <= 3e-214) {
		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 <= (-8.8d-200)) then
        tmp = x
    else if (t <= 3d-214) 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 <= -8.8e-200) {
		tmp = x;
	} else if (t <= 3e-214) {
		tmp = x / (t / y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -8.8e-200:
		tmp = x
	elif t <= 3e-214:
		tmp = x / (t / y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -8.8e-200)
		tmp = x;
	elseif (t <= 3e-214)
		tmp = 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 <= -8.8e-200)
		tmp = x;
	elseif (t <= 3e-214)
		tmp = x / (t / y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -8.8e-200], x, If[LessEqual[t, 3e-214], N[(x / N[(t / y), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if t < -8.80000000000000054e-200 or 2.99999999999999994e-214 < t

   1. Initial program 93.0%

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

      1. +-commutative 93.0%

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

      2. associate-*r/ 96.7%

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

      3. fma-def 96.7%

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

   3. Simplified 96.7%

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

   4. Taylor expanded in y around 0 46.4%

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

   if -8.80000000000000054e-200 < t < 2.99999999999999994e-214

   1. Initial program 99.8%

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

      1. associate-/l* 85.8%

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

   3. Simplified 85.8%

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

   4. Taylor expanded in z around 0 30.4%

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

      1. associate-*r/ 30.4%

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

      2. neg-mul-1 30.4%

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

   6. Simplified 30.4%

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

   7. Taylor expanded in x around 0 39.7%

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

      1. mul-1-neg 39.7%

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

      2. sub-neg 39.7%

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

      3. *-commutative 39.7%

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

   9. Simplified 39.7%

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

   10. Taylor expanded in y around inf 35.9%

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

       1. associate-*r/ 35.9%

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

       2. neg-mul-1 35.9%

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

       3. distribute-lft-neg-in 35.9%

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

       4. associate-*r/ 30.4%

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

   12. Simplified 30.4%

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

       1. add-sqr-sqrt 16.0%

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

       2. sqrt-unprod 29.9%

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

       3. sqr-neg 29.9%

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

       4. sqrt-unprod 10.4%

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

       5. add-sqr-sqrt 23.1%

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

       6. associate-*r/ 21.1%

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

       7. *-commutative 21.1%

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

       8. associate-/l* 27.3%

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

   14. Applied egg-rr 27.3%

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

4. Final simplification 43.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.8 \cdot 10^{-200}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 3 \cdot 10^{-214}:\\ \;\;\;\;\frac{x}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 10: 97.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 94.1%

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

   1. associate-*l/ 98.4%

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

3. Simplified 98.4%

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

4. Final simplification 98.4%

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

Alternative 11: 65.5% 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 94.1%

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

   1. associate-/l* 94.9%

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

3. Simplified 94.9%

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

4. Taylor expanded in z around 0 59.7%

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

   1. associate-*r/ 59.7%

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

   2. neg-mul-1 59.7%

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

6. Simplified 59.7%

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

7. Taylor expanded in x around 0 62.6%

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

   1. mul-1-neg 62.6%

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

   2. sub-neg 62.6%

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

   3. *-commutative 62.6%

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

9. Simplified 62.6%

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

10. Final simplification 62.6%

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

Alternative 12: 38.6% 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 94.1%

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

   1. +-commutative 94.1%

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

   2. associate-*r/ 94.7%

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

   3. fma-def 94.7%

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

3. Simplified 94.7%

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

4. Taylor expanded in y around 0 39.0%

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

5. Final simplification 39.0%

   \[\leadsto x \]

Developer target: 91.3% 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 2023194 
(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)))