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

Percentage Accurate: 93.0% → 99.1%

Time: 10.1s

Alternatives: 10

Speedup: 1.0×

• 24.1% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 93.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.1% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(z - t\right)\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+130}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{a}, z - t, x\right)\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+118}:\\ \;\;\;\;x + \frac{t\_1}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z - t}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (- z t))))
   (if (<= t_1 -5e+130)
     (fma (/ y a) (- z t) x)
     (if (<= t_1 5e+118) (+ x (/ t_1 a)) (+ x (/ (- z t) (/ a y)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (z - t);
	double tmp;
	if (t_1 <= -5e+130) {
		tmp = fma((y / a), (z - t), x);
	} else if (t_1 <= 5e+118) {
		tmp = x + (t_1 / a);
	} else {
		tmp = x + ((z - t) / (a / y));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(z - t))
	tmp = 0.0
	if (t_1 <= -5e+130)
		tmp = fma(Float64(y / a), Float64(z - t), x);
	elseif (t_1 <= 5e+118)
		tmp = Float64(x + Float64(t_1 / a));
	else
		tmp = Float64(x + Float64(Float64(z - t) / Float64(a / y)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+130], N[(N[(y / a), $MachinePrecision] * N[(z - t), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[t$95$1, 5e+118], N[(x + N[(t$95$1 / a), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(z - t), $MachinePrecision] / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 y (-.f64 z t)) < -4.9999999999999996e130

   1. Initial program 90.8%

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

      1. +-commutative 90.8%

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

      2. associate-*l/ 99.8%

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

      3. fma-define 99.8%

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

   3. Simplified 99.8%

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

   if -4.9999999999999996e130 < (*.f64 y (-.f64 z t)) < 4.99999999999999972e118

   1. Initial program 98.5%

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

   if 4.99999999999999972e118 < (*.f64 y (-.f64 z t))

   1. Initial program 86.8%

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

      1. +-commutative 86.8%

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

      2. associate-*l/ 99.9%

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

      3. fma-define 99.9%

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

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y}{a}, z - t, x\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. fma-undefine 99.9%

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

      2. *-commutative 99.9%

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

      3. clear-num 99.9%

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

      4. un-div-inv 100.0%

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

   6. Applied egg-rr 100.0%

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

4. Final simplification 99.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \left(z - t\right) \leq -5 \cdot 10^{+130}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{a}, z - t, x\right)\\ \mathbf{elif}\;y \cdot \left(z - t\right) \leq 5 \cdot 10^{+118}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z - t}{\frac{a}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 71.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{z}{\frac{a}{y}}\\ t_2 := y \cdot \left(-\frac{t}{a}\right)\\ \mathbf{if}\;t \leq -8.8 \cdot 10^{+110}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -1.45 \cdot 10^{+21}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -70:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -2.1 \cdot 10^{-276}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{+15}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ z (/ a y)))) (t_2 (* y (- (/ t a)))))
   (if (<= t -8.8e+110)
     t_2
     (if (<= t -1.45e+21)
       t_1
       (if (<= t -70.0)
         t_2
         (if (<= t -2.1e-276)
           (+ x (/ (* y z) a))
           (if (<= t 3.4e+15) t_1 t_2)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (z / (a / y));
	double t_2 = y * -(t / a);
	double tmp;
	if (t <= -8.8e+110) {
		tmp = t_2;
	} else if (t <= -1.45e+21) {
		tmp = t_1;
	} else if (t <= -70.0) {
		tmp = t_2;
	} else if (t <= -2.1e-276) {
		tmp = x + ((y * z) / a);
	} else if (t <= 3.4e+15) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + (z / (a / y))
    t_2 = y * -(t / a)
    if (t <= (-8.8d+110)) then
        tmp = t_2
    else if (t <= (-1.45d+21)) then
        tmp = t_1
    else if (t <= (-70.0d0)) then
        tmp = t_2
    else if (t <= (-2.1d-276)) then
        tmp = x + ((y * z) / a)
    else if (t <= 3.4d+15) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (z / (a / y));
	double t_2 = y * -(t / a);
	double tmp;
	if (t <= -8.8e+110) {
		tmp = t_2;
	} else if (t <= -1.45e+21) {
		tmp = t_1;
	} else if (t <= -70.0) {
		tmp = t_2;
	} else if (t <= -2.1e-276) {
		tmp = x + ((y * z) / a);
	} else if (t <= 3.4e+15) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (z / (a / y))
	t_2 = y * -(t / a)
	tmp = 0
	if t <= -8.8e+110:
		tmp = t_2
	elif t <= -1.45e+21:
		tmp = t_1
	elif t <= -70.0:
		tmp = t_2
	elif t <= -2.1e-276:
		tmp = x + ((y * z) / a)
	elif t <= 3.4e+15:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(z / Float64(a / y)))
	t_2 = Float64(y * Float64(-Float64(t / a)))
	tmp = 0.0
	if (t <= -8.8e+110)
		tmp = t_2;
	elseif (t <= -1.45e+21)
		tmp = t_1;
	elseif (t <= -70.0)
		tmp = t_2;
	elseif (t <= -2.1e-276)
		tmp = Float64(x + Float64(Float64(y * z) / a));
	elseif (t <= 3.4e+15)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (z / (a / y));
	t_2 = y * -(t / a);
	tmp = 0.0;
	if (t <= -8.8e+110)
		tmp = t_2;
	elseif (t <= -1.45e+21)
		tmp = t_1;
	elseif (t <= -70.0)
		tmp = t_2;
	elseif (t <= -2.1e-276)
		tmp = x + ((y * z) / a);
	elseif (t <= 3.4e+15)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(z / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * (-N[(t / a), $MachinePrecision])), $MachinePrecision]}, If[LessEqual[t, -8.8e+110], t$95$2, If[LessEqual[t, -1.45e+21], t$95$1, If[LessEqual[t, -70.0], t$95$2, If[LessEqual[t, -2.1e-276], N[(x + N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.4e+15], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -8.79999999999999967e110 or -1.45e21 < t < -70 or 3.4e15 < t

   1. Initial program 94.1%

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

      1. +-commutative 94.1%

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

      2. associate-*l/ 96.1%

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

      3. fma-define 96.1%

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

   3. Simplified 96.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y}{a}, z - t, x\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. fma-undefine 96.1%

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

      2. *-commutative 96.1%

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

      3. clear-num 96.0%

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

      4. un-div-inv 96.0%

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

   6. Applied egg-rr 96.0%

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

   7. Taylor expanded in z around 0 83.2%

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

      1. associate-*r/ 84.2%

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

      2. neg-mul-1 84.2%

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

      3. distribute-lft-neg-in 84.2%

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

      4. cancel-sign-sub-inv 84.2%

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

      5. associate-*r/ 83.2%

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

      6. associate-/l* 84.2%

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

   9. Simplified 84.2%

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

       1. *-un-lft-identity 84.2%

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

       2. associate-*l/ 84.1%

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

       3. clear-num 84.2%

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

   11. Applied egg-rr 84.2%

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

   12. Taylor expanded in x around 0 65.9%

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

       1. mul-1-neg 65.9%

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

       2. associate-*r/ 65.1%

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

       3. *-commutative 65.1%

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

       4. associate-*l/ 65.9%

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

       5. associate-*r/ 61.3%

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

       6. distribute-rgt-neg-in 61.3%

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

       7. distribute-neg-frac 61.3%

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

   14. Simplified 61.3%

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

   if -8.79999999999999967e110 < t < -1.45e21 or -2.1e-276 < t < 3.4e15

   1. Initial program 93.7%

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

      1. associate-*l/ 96.9%

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

   3. Simplified 96.9%

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

   5. Taylor expanded in z around inf 80.8%

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

      1. associate-*l/ 85.8%

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

      2. *-commutative 85.8%

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

   7. Simplified 85.8%

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

      1. clear-num 85.7%

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

      2. un-div-inv 86.8%

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

   9. Applied egg-rr 86.8%

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

   if -70 < t < -2.1e-276

   1. Initial program 96.5%

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

      1. associate-*l/ 90.5%

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

   3. Simplified 90.5%

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

   5. Taylor expanded in z around inf 85.3%

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

4. Final simplification 76.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.8 \cdot 10^{+110}:\\ \;\;\;\;y \cdot \left(-\frac{t}{a}\right)\\ \mathbf{elif}\;t \leq -1.45 \cdot 10^{+21}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y}}\\ \mathbf{elif}\;t \leq -70:\\ \;\;\;\;y \cdot \left(-\frac{t}{a}\right)\\ \mathbf{elif}\;t \leq -2.1 \cdot 10^{-276}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{+15}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-\frac{t}{a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 73.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -9.8 \cdot 10^{+110} \lor \neg \left(t \leq 3.4 \cdot 10^{+15}\right):\\ \;\;\;\;y \cdot \left(-\frac{t}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -9.8e+110) (not (<= t 3.4e+15)))
   (* y (- (/ t a)))
   (+ x (* z (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -9.8e+110) || !(t <= 3.4e+15)) {
		tmp = y * -(t / a);
	} else {
		tmp = x + (z * (y / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-9.8d+110)) .or. (.not. (t <= 3.4d+15))) then
        tmp = y * -(t / a)
    else
        tmp = x + (z * (y / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -9.8e+110) || !(t <= 3.4e+15)) {
		tmp = y * -(t / a);
	} else {
		tmp = x + (z * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -9.8e+110) or not (t <= 3.4e+15):
		tmp = y * -(t / a)
	else:
		tmp = x + (z * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -9.8e+110) || !(t <= 3.4e+15))
		tmp = Float64(y * Float64(-Float64(t / a)));
	else
		tmp = Float64(x + Float64(z * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -9.8e+110) || ~((t <= 3.4e+15)))
		tmp = y * -(t / a);
	else
		tmp = x + (z * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -9.8e+110], N[Not[LessEqual[t, 3.4e+15]], $MachinePrecision]], N[(y * (-N[(t / a), $MachinePrecision])), $MachinePrecision], N[(x + N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -9.80000000000000003e110 or 3.4e15 < t

   1. Initial program 94.0%

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

      1. +-commutative 94.0%

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

      2. associate-*l/ 96.0%

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

      3. fma-define 96.0%

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

   3. Simplified 96.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y}{a}, z - t, x\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. fma-undefine 96.0%

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

      2. *-commutative 96.0%

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

      3. clear-num 95.9%

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

      4. un-div-inv 95.9%

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

   6. Applied egg-rr 95.9%

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

   7. Taylor expanded in z around 0 82.6%

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

      1. associate-*r/ 83.8%

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

      2. neg-mul-1 83.8%

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

      3. distribute-lft-neg-in 83.8%

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

      4. cancel-sign-sub-inv 83.8%

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

      5. associate-*r/ 82.6%

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

      6. associate-/l* 83.7%

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

   9. Simplified 83.7%

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

       1. *-un-lft-identity 83.7%

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

       2. associate-*l/ 83.6%

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

       3. clear-num 83.8%

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

   11. Applied egg-rr 83.8%

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

   12. Taylor expanded in x around 0 64.9%

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

       1. mul-1-neg 64.9%

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

       2. associate-*r/ 64.1%

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

       3. *-commutative 64.1%

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

       4. associate-*l/ 64.9%

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

       5. associate-*r/ 60.2%

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

       6. distribute-rgt-neg-in 60.2%

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

       7. distribute-neg-frac 60.2%

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

   14. Simplified 60.2%

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

   if -9.80000000000000003e110 < t < 3.4e15

   1. Initial program 94.9%

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

      1. associate-*l/ 94.5%

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

   3. Simplified 94.5%

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

   5. Taylor expanded in z around inf 81.0%

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

      1. associate-*l/ 83.0%

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

      2. *-commutative 83.0%

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

   7. Simplified 83.0%

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

4. Final simplification 74.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9.8 \cdot 10^{+110} \lor \neg \left(t \leq 3.4 \cdot 10^{+15}\right):\\ \;\;\;\;y \cdot \left(-\frac{t}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 73.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -8.5 \cdot 10^{+110} \lor \neg \left(t \leq 3.35 \cdot 10^{+15}\right):\\ \;\;\;\;y \cdot \left(-\frac{t}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -8.5e+110) (not (<= t 3.35e+15)))
   (* y (- (/ t a)))
   (+ x (/ z (/ a y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -8.5e+110) || !(t <= 3.35e+15)) {
		tmp = y * -(t / a);
	} else {
		tmp = x + (z / (a / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-8.5d+110)) .or. (.not. (t <= 3.35d+15))) then
        tmp = y * -(t / a)
    else
        tmp = x + (z / (a / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -8.5e+110) || !(t <= 3.35e+15)) {
		tmp = y * -(t / a);
	} else {
		tmp = x + (z / (a / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -8.5e+110) or not (t <= 3.35e+15):
		tmp = y * -(t / a)
	else:
		tmp = x + (z / (a / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -8.5e+110) || !(t <= 3.35e+15))
		tmp = Float64(y * Float64(-Float64(t / a)));
	else
		tmp = Float64(x + Float64(z / Float64(a / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -8.5e+110) || ~((t <= 3.35e+15)))
		tmp = y * -(t / a);
	else
		tmp = x + (z / (a / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -8.5e+110], N[Not[LessEqual[t, 3.35e+15]], $MachinePrecision]], N[(y * (-N[(t / a), $MachinePrecision])), $MachinePrecision], N[(x + N[(z / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -8.5000000000000004e110 or 3.35e15 < t

   1. Initial program 94.0%

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

      1. +-commutative 94.0%

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

      2. associate-*l/ 96.0%

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

      3. fma-define 96.0%

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

   3. Simplified 96.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y}{a}, z - t, x\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. fma-undefine 96.0%

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

      2. *-commutative 96.0%

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

      3. clear-num 95.9%

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

      4. un-div-inv 95.9%

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

   6. Applied egg-rr 95.9%

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

   7. Taylor expanded in z around 0 82.6%

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

      1. associate-*r/ 83.8%

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

      2. neg-mul-1 83.8%

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

      3. distribute-lft-neg-in 83.8%

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

      4. cancel-sign-sub-inv 83.8%

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

      5. associate-*r/ 82.6%

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

      6. associate-/l* 83.7%

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

   9. Simplified 83.7%

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

       1. *-un-lft-identity 83.7%

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

       2. associate-*l/ 83.6%

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

       3. clear-num 83.8%

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

   11. Applied egg-rr 83.8%

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

   12. Taylor expanded in x around 0 64.9%

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

       1. mul-1-neg 64.9%

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

       2. associate-*r/ 64.1%

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

       3. *-commutative 64.1%

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

       4. associate-*l/ 64.9%

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

       5. associate-*r/ 60.2%

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

       6. distribute-rgt-neg-in 60.2%

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

       7. distribute-neg-frac 60.2%

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

   14. Simplified 60.2%

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

   if -8.5000000000000004e110 < t < 3.35e15

   1. Initial program 94.9%

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

      1. associate-*l/ 94.5%

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

   3. Simplified 94.5%

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

   5. Taylor expanded in z around inf 81.0%

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

      1. associate-*l/ 83.0%

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

      2. *-commutative 83.0%

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

   7. Simplified 83.0%

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

      1. clear-num 82.9%

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

      2. un-div-inv 83.6%

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

   9. Applied egg-rr 83.6%

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

4. Final simplification 74.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.5 \cdot 10^{+110} \lor \neg \left(t \leq 3.35 \cdot 10^{+15}\right):\\ \;\;\;\;y \cdot \left(-\frac{t}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 86.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7.2 \lor \neg \left(t \leq 19500000000000\right):\\ \;\;\;\;x - t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -7.2) (not (<= t 19500000000000.0)))
   (- x (* t (/ y a)))
   (+ x (/ z (/ a y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -7.2) || !(t <= 19500000000000.0)) {
		tmp = x - (t * (y / a));
	} else {
		tmp = x + (z / (a / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-7.2d0)) .or. (.not. (t <= 19500000000000.0d0))) then
        tmp = x - (t * (y / a))
    else
        tmp = x + (z / (a / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -7.2) || !(t <= 19500000000000.0)) {
		tmp = x - (t * (y / a));
	} else {
		tmp = x + (z / (a / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -7.2) or not (t <= 19500000000000.0):
		tmp = x - (t * (y / a))
	else:
		tmp = x + (z / (a / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -7.2) || !(t <= 19500000000000.0))
		tmp = Float64(x - Float64(t * Float64(y / a)));
	else
		tmp = Float64(x + Float64(z / Float64(a / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -7.2) || ~((t <= 19500000000000.0)))
		tmp = x - (t * (y / a));
	else
		tmp = x + (z / (a / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -7.2], N[Not[LessEqual[t, 19500000000000.0]], $MachinePrecision]], N[(x - N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -7.20000000000000018 or 1.95e13 < t

   1. Initial program 93.4%

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

      1. +-commutative 93.4%

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

      2. associate-*l/ 96.6%

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

      3. fma-define 96.6%

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

   3. Simplified 96.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y}{a}, z - t, x\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. fma-undefine 96.6%

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

      2. *-commutative 96.6%

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

      3. clear-num 96.5%

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

      4. un-div-inv 96.6%

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

   6. Applied egg-rr 96.6%

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

   7. Taylor expanded in z around 0 80.2%

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

      1. associate-*r/ 81.0%

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

      2. neg-mul-1 81.0%

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

      3. distribute-lft-neg-in 81.0%

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

      4. cancel-sign-sub-inv 81.0%

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

      5. associate-*r/ 80.2%

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

      6. associate-/l* 81.0%

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

   9. Simplified 81.0%

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

       1. *-un-lft-identity 81.0%

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

       2. associate-*l/ 80.9%

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

       3. clear-num 81.0%

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

   11. Applied egg-rr 81.0%

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

   if -7.20000000000000018 < t < 1.95e13

   1. Initial program 95.5%

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

      1. associate-*l/ 93.6%

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

   3. Simplified 93.6%

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

   5. Taylor expanded in z around inf 86.3%

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

      1. associate-*l/ 87.2%

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

      2. *-commutative 87.2%

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

   7. Simplified 87.2%

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

      1. clear-num 87.1%

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

      2. un-div-inv 87.9%

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

   9. Applied egg-rr 87.9%

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

4. Final simplification 84.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.2 \lor \neg \left(t \leq 19500000000000\right):\\ \;\;\;\;x - t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 84.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2000:\\ \;\;\;\;x - t \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{+15}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y \cdot t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -2000.0)
   (- x (* t (/ y a)))
   (if (<= t 1.4e+15) (+ x (/ z (/ a y))) (- x (/ (* y t) a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2000.0) {
		tmp = x - (t * (y / a));
	} else if (t <= 1.4e+15) {
		tmp = x + (z / (a / y));
	} else {
		tmp = x - ((y * t) / a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-2000.0d0)) then
        tmp = x - (t * (y / a))
    else if (t <= 1.4d+15) then
        tmp = x + (z / (a / y))
    else
        tmp = x - ((y * t) / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2000.0) {
		tmp = x - (t * (y / a));
	} else if (t <= 1.4e+15) {
		tmp = x + (z / (a / y));
	} else {
		tmp = x - ((y * t) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -2000.0:
		tmp = x - (t * (y / a))
	elif t <= 1.4e+15:
		tmp = x + (z / (a / y))
	else:
		tmp = x - ((y * t) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -2000.0)
		tmp = Float64(x - Float64(t * Float64(y / a)));
	elseif (t <= 1.4e+15)
		tmp = Float64(x + Float64(z / Float64(a / y)));
	else
		tmp = Float64(x - Float64(Float64(y * t) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -2000.0)
		tmp = x - (t * (y / a));
	elseif (t <= 1.4e+15)
		tmp = x + (z / (a / y));
	else
		tmp = x - ((y * t) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -2000.0], N[(x - N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.4e+15], N[(x + N[(z / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -2e3

   1. Initial program 89.8%

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

      1. +-commutative 89.8%

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

      2. associate-*l/ 98.0%

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

      3. fma-define 98.0%

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

   3. Simplified 98.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y}{a}, z - t, x\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. fma-undefine 98.0%

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

      2. *-commutative 98.0%

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

      3. clear-num 97.8%

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

      4. un-div-inv 98.0%

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

   6. Applied egg-rr 98.0%

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

   7. Taylor expanded in z around 0 78.0%

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

      1. associate-*r/ 82.9%

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

      2. neg-mul-1 82.9%

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

      3. distribute-lft-neg-in 82.9%

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

      4. cancel-sign-sub-inv 82.9%

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

      5. associate-*r/ 78.0%

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

      6. associate-/l* 82.9%

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

   9. Simplified 82.9%

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

       1. *-un-lft-identity 82.9%

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

       2. associate-*l/ 82.8%

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

       3. clear-num 82.9%

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

   11. Applied egg-rr 82.9%

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

   if -2e3 < t < 1.4e15

   1. Initial program 95.5%

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

      1. associate-*l/ 93.6%

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

   3. Simplified 93.6%

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

   5. Taylor expanded in z around inf 86.3%

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

      1. associate-*l/ 87.2%

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

      2. *-commutative 87.2%

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

   7. Simplified 87.2%

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

      1. clear-num 87.1%

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

      2. un-div-inv 87.9%

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

   9. Applied egg-rr 87.9%

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

   if 1.4e15 < t

   1. Initial program 96.8%

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

      1. +-commutative 96.8%

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

      2. associate-*l/ 95.3%

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

      3. fma-define 95.3%

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

   3. Simplified 95.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y}{a}, z - t, x\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. fma-undefine 95.3%

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

      2. *-commutative 95.3%

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

      3. clear-num 95.3%

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

      4. un-div-inv 95.4%

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

   6. Applied egg-rr 95.4%

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

   7. Taylor expanded in z around 0 82.1%

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

      1. associate-*r/ 79.3%

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

      2. neg-mul-1 79.3%

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

      3. distribute-lft-neg-in 79.3%

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

      4. cancel-sign-sub-inv 79.3%

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

      5. associate-*r/ 82.1%

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

      6. associate-/l* 79.3%

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

   9. Simplified 79.3%

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

   10. Taylor expanded in t around 0 82.1%

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

4. Final simplification 85.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2000:\\ \;\;\;\;x - t \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{+15}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y \cdot t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 49.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.1 \cdot 10^{-12} \lor \neg \left(t \leq 3.6 \cdot 10^{+14}\right):\\ \;\;\;\;y \cdot \left(-\frac{t}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -2.1e-12) (not (<= t 3.6e+14))) (* y (- (/ t a))) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -2.1e-12) || !(t <= 3.6e+14)) {
		tmp = y * -(t / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-2.1d-12)) .or. (.not. (t <= 3.6d+14))) then
        tmp = y * -(t / a)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -2.1e-12) || !(t <= 3.6e+14)) {
		tmp = y * -(t / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -2.1e-12) or not (t <= 3.6e+14):
		tmp = y * -(t / a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -2.1e-12) || !(t <= 3.6e+14))
		tmp = Float64(y * Float64(-Float64(t / a)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -2.1e-12) || ~((t <= 3.6e+14)))
		tmp = y * -(t / a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -2.1e-12], N[Not[LessEqual[t, 3.6e+14]], $MachinePrecision]], N[(y * (-N[(t / a), $MachinePrecision])), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if t < -2.09999999999999994e-12 or 3.6e14 < t

   1. Initial program 93.5%

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

      1. +-commutative 93.5%

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

      2. associate-*l/ 96.7%

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

      3. fma-define 96.7%

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

   3. Simplified 96.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y}{a}, z - t, x\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. fma-undefine 96.7%

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

      2. *-commutative 96.7%

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

      3. clear-num 96.6%

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

      4. un-div-inv 96.7%

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

   6. Applied egg-rr 96.7%

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

   7. Taylor expanded in z around 0 79.7%

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

      1. associate-*r/ 80.6%

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

      2. neg-mul-1 80.6%

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

      3. distribute-lft-neg-in 80.6%

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

      4. cancel-sign-sub-inv 80.6%

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

      5. associate-*r/ 79.7%

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

      6. associate-/l* 80.6%

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

   9. Simplified 80.6%

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

       1. *-un-lft-identity 80.6%

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

       2. associate-*l/ 80.5%

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

       3. clear-num 80.6%

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

   11. Applied egg-rr 80.6%

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

   12. Taylor expanded in x around 0 61.3%

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

       1. mul-1-neg 61.3%

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

       2. associate-*r/ 60.7%

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

       3. *-commutative 60.7%

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

       4. associate-*l/ 61.3%

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

       5. associate-*r/ 57.5%

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

       6. distribute-rgt-neg-in 57.5%

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

       7. distribute-neg-frac 57.5%

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

   14. Simplified 57.5%

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

   if -2.09999999999999994e-12 < t < 3.6e14

   1. Initial program 95.5%

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

      1. associate-*l/ 93.6%

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

   3. Simplified 93.6%

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

   5. Taylor expanded in x around inf 48.1%

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

4. Final simplification 52.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.1 \cdot 10^{-12} \lor \neg \left(t \leq 3.6 \cdot 10^{+14}\right):\\ \;\;\;\;y \cdot \left(-\frac{t}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 96.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{-24}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -5e-24) (+ x (/ y (/ a (- z t)))) (+ x (/ (* y (- z t)) a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -5e-24) {
		tmp = x + (y / (a / (z - t)));
	} else {
		tmp = x + ((y * (z - t)) / a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (y <= (-5d-24)) then
        tmp = x + (y / (a / (z - t)))
    else
        tmp = x + ((y * (z - t)) / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -5e-24) {
		tmp = x + (y / (a / (z - t)));
	} else {
		tmp = x + ((y * (z - t)) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -5e-24:
		tmp = x + (y / (a / (z - t)))
	else:
		tmp = x + ((y * (z - t)) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -5e-24)
		tmp = Float64(x + Float64(y / Float64(a / Float64(z - t))));
	else
		tmp = Float64(x + Float64(Float64(y * Float64(z - t)) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -5e-24)
		tmp = x + (y / (a / (z - t)));
	else
		tmp = x + ((y * (z - t)) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -5e-24], N[(x + N[(y / N[(a / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.9999999999999998e-24

   1. Initial program 88.8%

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

      1. associate-*l/ 97.1%

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

   3. Simplified 97.1%

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

      1. associate-/r/ 99.8%

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

   6. Applied egg-rr 99.8%

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

   if -4.9999999999999998e-24 < y

   1. Initial program 96.7%

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

4. Final simplification 97.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{-24}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 97.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 94.5%

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

   1. associate-*l/ 95.0%

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

3. Simplified 95.0%

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

5. Final simplification 95.0%

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

Alternative 10: 39.7% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 94.5%

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

   1. associate-*l/ 95.0%

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

3. Simplified 95.0%

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

5. Taylor expanded in x around inf 35.4%

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

6. Final simplification 35.4%

   \[\leadsto x \]
7. Add Preprocessing

Developer target: 99.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{a}{z - t}\\ \mathbf{if}\;y < -1.0761266216389975 \cdot 10^{-10}:\\ \;\;\;\;x + \frac{1}{\frac{t\_1}{y}}\\ \mathbf{elif}\;y < 2.894426862792089 \cdot 10^{-49}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{t\_1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ a (- z t))))
   (if (< y -1.0761266216389975e-10)
     (+ x (/ 1.0 (/ t_1 y)))
     (if (< y 2.894426862792089e-49)
       (+ x (/ (* y (- z t)) a))
       (+ x (/ y t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = a / (z - t);
	double tmp;
	if (y < -1.0761266216389975e-10) {
		tmp = x + (1.0 / (t_1 / y));
	} else if (y < 2.894426862792089e-49) {
		tmp = x + ((y * (z - t)) / a);
	} else {
		tmp = x + (y / t_1);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a / (z - t)
    if (y < (-1.0761266216389975d-10)) then
        tmp = x + (1.0d0 / (t_1 / y))
    else if (y < 2.894426862792089d-49) then
        tmp = x + ((y * (z - t)) / a)
    else
        tmp = x + (y / t_1)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = a / (z - t);
	double tmp;
	if (y < -1.0761266216389975e-10) {
		tmp = x + (1.0 / (t_1 / y));
	} else if (y < 2.894426862792089e-49) {
		tmp = x + ((y * (z - t)) / a);
	} else {
		tmp = x + (y / t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = a / (z - t)
	tmp = 0
	if y < -1.0761266216389975e-10:
		tmp = x + (1.0 / (t_1 / y))
	elif y < 2.894426862792089e-49:
		tmp = x + ((y * (z - t)) / a)
	else:
		tmp = x + (y / t_1)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(a / Float64(z - t))
	tmp = 0.0
	if (y < -1.0761266216389975e-10)
		tmp = Float64(x + Float64(1.0 / Float64(t_1 / y)));
	elseif (y < 2.894426862792089e-49)
		tmp = Float64(x + Float64(Float64(y * Float64(z - t)) / a));
	else
		tmp = Float64(x + Float64(y / t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = a / (z - t);
	tmp = 0.0;
	if (y < -1.0761266216389975e-10)
		tmp = x + (1.0 / (t_1 / y));
	elseif (y < 2.894426862792089e-49)
		tmp = x + ((y * (z - t)) / a);
	else
		tmp = x + (y / t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(a / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[Less[y, -1.0761266216389975e-10], N[(x + N[(1.0 / N[(t$95$1 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Less[y, 2.894426862792089e-49], N[(x + N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / t$95$1), $MachinePrecision]), $MachinePrecision]]]]

Reproduce

herbie shell --seed 2024034 
(FPCore (x y z t a)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, E"
  :precision binary64

  :herbie-target
  (if (< y -1.0761266216389975e-10) (+ x (/ 1.0 (/ (/ a (- z t)) y))) (if (< y 2.894426862792089e-49) (+ x (/ (* y (- z t)) a)) (+ x (/ y (/ a (- z t))))))

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