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

Percentage Accurate: 93.2% → 99.6%

Time: 11.8s

Alternatives: 14

Speedup: 1.0×

• 24.7% 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: 93.2% 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: 99.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z - t\right) \cdot y\\ \mathbf{if}\;t_1 \leq -2 \cdot 10^{+303}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a}\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{+266}:\\ \;\;\;\;x + \frac{t_1}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (- z t) y)))
   (if (<= t_1 -2e+303)
     (+ x (* y (/ (- z t) a)))
     (if (<= t_1 2e+266) (+ x (/ t_1 a)) (+ x (/ y (/ a (- z t))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (z - t) * y;
	double tmp;
	if (t_1 <= -2e+303) {
		tmp = x + (y * ((z - t) / a));
	} else if (t_1 <= 2e+266) {
		tmp = x + (t_1 / a);
	} else {
		tmp = x + (y / (a / (z - t)));
	}
	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 = (z - t) * y
    if (t_1 <= (-2d+303)) then
        tmp = x + (y * ((z - t) / a))
    else if (t_1 <= 2d+266) then
        tmp = x + (t_1 / a)
    else
        tmp = x + (y / (a / (z - t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (z - t) * y;
	double tmp;
	if (t_1 <= -2e+303) {
		tmp = x + (y * ((z - t) / a));
	} else if (t_1 <= 2e+266) {
		tmp = x + (t_1 / a);
	} else {
		tmp = x + (y / (a / (z - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (z - t) * y
	tmp = 0
	if t_1 <= -2e+303:
		tmp = x + (y * ((z - t) / a))
	elif t_1 <= 2e+266:
		tmp = x + (t_1 / a)
	else:
		tmp = x + (y / (a / (z - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(z - t) * y)
	tmp = 0.0
	if (t_1 <= -2e+303)
		tmp = Float64(x + Float64(y * Float64(Float64(z - t) / a)));
	elseif (t_1 <= 2e+266)
		tmp = Float64(x + Float64(t_1 / a));
	else
		tmp = Float64(x + Float64(y / Float64(a / Float64(z - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (z - t) * y;
	tmp = 0.0;
	if (t_1 <= -2e+303)
		tmp = x + (y * ((z - t) / a));
	elseif (t_1 <= 2e+266)
		tmp = x + (t_1 / a);
	else
		tmp = x + (y / (a / (z - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z - t), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+303], N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+266], N[(x + N[(t$95$1 / a), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(a / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 y (-.f64 z t)) < -2e303

   1. Initial program 62.5%

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

      1. *-commutative 62.5%

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

      2. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

      1. associate-/r/ 99.8%

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

   6. Applied egg-rr 99.8%

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

   if -2e303 < (*.f64 y (-.f64 z t)) < 2.0000000000000001e266

   1. Initial program 99.0%

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

   if 2.0000000000000001e266 < (*.f64 y (-.f64 z t))

   1. Initial program 64.7%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

4. Final simplification 99.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(z - t\right) \cdot y \leq -2 \cdot 10^{+303}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a}\\ \mathbf{elif}\;\left(z - t\right) \cdot y \leq 2 \cdot 10^{+266}:\\ \;\;\;\;x + \frac{\left(z - t\right) \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 77.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{-y}{a}\\ \mathbf{if}\;t \leq -5.2 \cdot 10^{+119}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 3.95 \cdot 10^{+191}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq 2.75 \cdot 10^{+219} \lor \neg \left(t \leq 7.5 \cdot 10^{+263}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z \cdot y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y) a))))
   (if (<= t -5.2e+119)
     t_1
     (if (<= t 3.95e+191)
       (+ x (* z (/ y a)))
       (if (or (<= t 2.75e+219) (not (<= t 7.5e+263)))
         t_1
         (+ x (/ (* z y) a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (-y / a);
	double tmp;
	if (t <= -5.2e+119) {
		tmp = t_1;
	} else if (t <= 3.95e+191) {
		tmp = x + (z * (y / a));
	} else if ((t <= 2.75e+219) || !(t <= 7.5e+263)) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = t * (-y / a)
    if (t <= (-5.2d+119)) then
        tmp = t_1
    else if (t <= 3.95d+191) then
        tmp = x + (z * (y / a))
    else if ((t <= 2.75d+219) .or. (.not. (t <= 7.5d+263))) then
        tmp = t_1
    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 t_1 = t * (-y / a);
	double tmp;
	if (t <= -5.2e+119) {
		tmp = t_1;
	} else if (t <= 3.95e+191) {
		tmp = x + (z * (y / a));
	} else if ((t <= 2.75e+219) || !(t <= 7.5e+263)) {
		tmp = t_1;
	} else {
		tmp = x + ((z * y) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * (-y / a)
	tmp = 0
	if t <= -5.2e+119:
		tmp = t_1
	elif t <= 3.95e+191:
		tmp = x + (z * (y / a))
	elif (t <= 2.75e+219) or not (t <= 7.5e+263):
		tmp = t_1
	else:
		tmp = x + ((z * y) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(-y) / a))
	tmp = 0.0
	if (t <= -5.2e+119)
		tmp = t_1;
	elseif (t <= 3.95e+191)
		tmp = Float64(x + Float64(z * Float64(y / a)));
	elseif ((t <= 2.75e+219) || !(t <= 7.5e+263))
		tmp = t_1;
	else
		tmp = Float64(x + Float64(Float64(z * y) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * (-y / a);
	tmp = 0.0;
	if (t <= -5.2e+119)
		tmp = t_1;
	elseif (t <= 3.95e+191)
		tmp = x + (z * (y / a));
	elseif ((t <= 2.75e+219) || ~((t <= 7.5e+263)))
		tmp = t_1;
	else
		tmp = x + ((z * y) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[((-y) / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -5.2e+119], t$95$1, If[LessEqual[t, 3.95e+191], N[(x + N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t, 2.75e+219], N[Not[LessEqual[t, 7.5e+263]], $MachinePrecision]], t$95$1, N[(x + N[(N[(z * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -5.2e119 or 3.94999999999999985e191 < t < 2.74999999999999986e219 or 7.5000000000000001e263 < t

   1. Initial program 86.2%

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

      1. +-commutative 86.2%

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

      2. associate-*r/ 88.2%

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

      3. fma-udef 88.2%

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

   3. Simplified 88.2%

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

      1. fma-udef 88.2%

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

      2. associate-*r/ 86.2%

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

      3. div-inv 86.2%

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

      4. div-inv 86.2%

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

      5. *-commutative 86.2%

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

      6. associate-*r/ 97.7%

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

   6. Applied egg-rr 97.7%

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

   7. Taylor expanded in z around 0 76.1%

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

      1. mul-1-neg 76.1%

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

      2. associate-*l/ 80.0%

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

      3. *-commutative 80.0%

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

      4. distribute-lft-neg-out 80.0%

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

      5. cancel-sign-sub-inv 80.0%

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

      6. *-commutative 80.0%

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

      7. associate-*l/ 76.1%

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

      8. associate-*r/ 87.6%

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

   9. Simplified 87.6%

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

   10. Taylor expanded in x around 0 59.9%

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

       1. mul-1-neg 59.9%

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

       2. associate-*l/ 65.6%

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

       3. distribute-lft-neg-in 65.6%

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

       4. *-lft-identity 65.6%

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

       5. metadata-eval 65.6%

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

       6. times-frac 65.6%

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

       7. neg-mul-1 65.6%

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

       8. neg-mul-1 65.6%

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

       9. distribute-frac-neg 65.6%

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

       10. remove-double-neg 65.6%

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

       11. *-commutative 65.6%

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

   12. Simplified 65.6%

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

   13. Taylor expanded in y around 0 59.9%

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

       1. mul-1-neg 59.9%

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

       2. associate-*r/ 71.4%

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

       3. *-commutative 71.4%

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

       4. distribute-rgt-neg-in 71.4%

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

   15. Simplified 71.4%

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

   if -5.2e119 < t < 3.94999999999999985e191

   1. Initial program 92.5%

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

      1. +-commutative 92.5%

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

      2. associate-*r/ 91.9%

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

      3. fma-udef 91.9%

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

   3. Simplified 91.9%

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

      1. fma-udef 91.9%

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

      2. associate-*r/ 92.5%

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

      3. div-inv 92.5%

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

      4. div-inv 92.5%

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

      5. *-commutative 92.5%

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

      6. associate-*r/ 96.3%

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

   6. Applied egg-rr 96.3%

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

   7. Taylor expanded in z around inf 76.9%

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

      1. associate-*l/ 82.4%

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

      2. *-commutative 82.4%

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

   9. Simplified 82.4%

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

   if 2.74999999999999986e219 < t < 7.5000000000000001e263

   1. Initial program 86.8%

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

      1. *-commutative 86.8%

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

      2. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around inf 100.0%

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

4. Final simplification 80.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.2 \cdot 10^{+119}:\\ \;\;\;\;t \cdot \frac{-y}{a}\\ \mathbf{elif}\;t \leq 3.95 \cdot 10^{+191}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq 2.75 \cdot 10^{+219} \lor \neg \left(t \leq 7.5 \cdot 10^{+263}\right):\\ \;\;\;\;t \cdot \frac{-y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z \cdot y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 77.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{-y}{a}\\ \mathbf{if}\;t \leq -9.2 \cdot 10^{+119}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{+191}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y}}\\ \mathbf{elif}\;t \leq 1.22 \cdot 10^{+219} \lor \neg \left(t \leq 7.5 \cdot 10^{+263}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z \cdot y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y) a))))
   (if (<= t -9.2e+119)
     t_1
     (if (<= t 2.6e+191)
       (+ x (/ z (/ a y)))
       (if (or (<= t 1.22e+219) (not (<= t 7.5e+263)))
         t_1
         (+ x (/ (* z y) a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (-y / a);
	double tmp;
	if (t <= -9.2e+119) {
		tmp = t_1;
	} else if (t <= 2.6e+191) {
		tmp = x + (z / (a / y));
	} else if ((t <= 1.22e+219) || !(t <= 7.5e+263)) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = t * (-y / a)
    if (t <= (-9.2d+119)) then
        tmp = t_1
    else if (t <= 2.6d+191) then
        tmp = x + (z / (a / y))
    else if ((t <= 1.22d+219) .or. (.not. (t <= 7.5d+263))) then
        tmp = t_1
    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 t_1 = t * (-y / a);
	double tmp;
	if (t <= -9.2e+119) {
		tmp = t_1;
	} else if (t <= 2.6e+191) {
		tmp = x + (z / (a / y));
	} else if ((t <= 1.22e+219) || !(t <= 7.5e+263)) {
		tmp = t_1;
	} else {
		tmp = x + ((z * y) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * (-y / a)
	tmp = 0
	if t <= -9.2e+119:
		tmp = t_1
	elif t <= 2.6e+191:
		tmp = x + (z / (a / y))
	elif (t <= 1.22e+219) or not (t <= 7.5e+263):
		tmp = t_1
	else:
		tmp = x + ((z * y) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(-y) / a))
	tmp = 0.0
	if (t <= -9.2e+119)
		tmp = t_1;
	elseif (t <= 2.6e+191)
		tmp = Float64(x + Float64(z / Float64(a / y)));
	elseif ((t <= 1.22e+219) || !(t <= 7.5e+263))
		tmp = t_1;
	else
		tmp = Float64(x + Float64(Float64(z * y) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * (-y / a);
	tmp = 0.0;
	if (t <= -9.2e+119)
		tmp = t_1;
	elseif (t <= 2.6e+191)
		tmp = x + (z / (a / y));
	elseif ((t <= 1.22e+219) || ~((t <= 7.5e+263)))
		tmp = t_1;
	else
		tmp = x + ((z * y) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[((-y) / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -9.2e+119], t$95$1, If[LessEqual[t, 2.6e+191], N[(x + N[(z / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t, 1.22e+219], N[Not[LessEqual[t, 7.5e+263]], $MachinePrecision]], t$95$1, N[(x + N[(N[(z * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -9.2000000000000003e119 or 2.6e191 < t < 1.22000000000000004e219 or 7.5000000000000001e263 < t

   1. Initial program 86.2%

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

      1. +-commutative 86.2%

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

      2. associate-*r/ 88.2%

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

      3. fma-udef 88.2%

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

   3. Simplified 88.2%

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

      1. fma-udef 88.2%

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

      2. associate-*r/ 86.2%

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

      3. div-inv 86.2%

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

      4. div-inv 86.2%

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

      5. *-commutative 86.2%

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

      6. associate-*r/ 97.7%

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

   6. Applied egg-rr 97.7%

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

   7. Taylor expanded in z around 0 76.1%

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

      1. mul-1-neg 76.1%

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

      2. associate-*l/ 80.0%

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

      3. *-commutative 80.0%

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

      4. distribute-lft-neg-out 80.0%

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

      5. cancel-sign-sub-inv 80.0%

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

      6. *-commutative 80.0%

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

      7. associate-*l/ 76.1%

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

      8. associate-*r/ 87.6%

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

   9. Simplified 87.6%

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

   10. Taylor expanded in x around 0 59.9%

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

       1. mul-1-neg 59.9%

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

       2. associate-*l/ 65.6%

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

       3. distribute-lft-neg-in 65.6%

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

       4. *-lft-identity 65.6%

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

       5. metadata-eval 65.6%

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

       6. times-frac 65.6%

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

       7. neg-mul-1 65.6%

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

       8. neg-mul-1 65.6%

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

       9. distribute-frac-neg 65.6%

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

       10. remove-double-neg 65.6%

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

       11. *-commutative 65.6%

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

   12. Simplified 65.6%

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

   13. Taylor expanded in y around 0 59.9%

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

       1. mul-1-neg 59.9%

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

       2. associate-*r/ 71.4%

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

       3. *-commutative 71.4%

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

       4. distribute-rgt-neg-in 71.4%

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

   15. Simplified 71.4%

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

   if -9.2000000000000003e119 < t < 2.6e191

   1. Initial program 92.5%

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

      1. +-commutative 92.5%

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

      2. associate-*r/ 91.9%

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

      3. fma-udef 91.9%

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

   3. Simplified 91.9%

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

      1. fma-udef 91.9%

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

      2. associate-*r/ 92.5%

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

      3. div-inv 92.5%

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

      4. div-inv 92.5%

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

      5. *-commutative 92.5%

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

      6. associate-*r/ 96.3%

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

   6. Applied egg-rr 96.3%

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

   7. Taylor expanded in z around inf 76.9%

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

      1. associate-*l/ 82.4%

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

      2. *-commutative 82.4%

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

   9. Simplified 82.4%

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

       1. clear-num 82.4%

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

       2. un-div-inv 82.9%

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

   11. Applied egg-rr 82.9%

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

   if 1.22000000000000004e219 < t < 7.5000000000000001e263

   1. Initial program 86.8%

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

      1. *-commutative 86.8%

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

      2. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around inf 100.0%

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

4. Final simplification 81.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9.2 \cdot 10^{+119}:\\ \;\;\;\;t \cdot \frac{-y}{a}\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{+191}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y}}\\ \mathbf{elif}\;t \leq 1.22 \cdot 10^{+219} \lor \neg \left(t \leq 7.5 \cdot 10^{+263}\right):\\ \;\;\;\;t \cdot \frac{-y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z \cdot y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 93.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{-242} \lor \neg \left(y \leq 6.8 \cdot 10^{-129}\right):\\ \;\;\;\;x + y \cdot \frac{z - t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -2e-242) (not (<= y 6.8e-129)))
   (+ x (* y (/ (- z t) a)))
   (+ x (/ z (/ a y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -2e-242) || !(y <= 6.8e-129)) {
		tmp = x + (y * ((z - 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 ((y <= (-2d-242)) .or. (.not. (y <= 6.8d-129))) then
        tmp = x + (y * ((z - 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 ((y <= -2e-242) || !(y <= 6.8e-129)) {
		tmp = x + (y * ((z - t) / a));
	} else {
		tmp = x + (z / (a / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -2e-242) or not (y <= 6.8e-129):
		tmp = x + (y * ((z - t) / a))
	else:
		tmp = x + (z / (a / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -2e-242) || !(y <= 6.8e-129))
		tmp = Float64(x + Float64(y * Float64(Float64(z - 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 ((y <= -2e-242) || ~((y <= 6.8e-129)))
		tmp = x + (y * ((z - t) / a));
	else
		tmp = x + (z / (a / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -2e-242], N[Not[LessEqual[y, 6.8e-129]], $MachinePrecision]], N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2e-242 or 6.80000000000000026e-129 < y

   1. Initial program 88.9%

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

      1. *-commutative 88.9%

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

      2. associate-/l* 95.8%

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

   3. Simplified 95.8%

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

      1. associate-/r/ 96.8%

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

   6. Applied egg-rr 96.8%

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

   if -2e-242 < y < 6.80000000000000026e-129

   1. Initial program 97.5%

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

      1. +-commutative 97.5%

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

      2. associate-*r/ 76.0%

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

      3. fma-udef 76.1%

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

   3. Simplified 76.1%

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

      1. fma-udef 76.0%

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

      2. associate-*r/ 97.5%

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

      3. div-inv 97.4%

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

      4. div-inv 97.5%

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

      5. *-commutative 97.5%

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

      6. associate-*r/ 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in z around inf 88.9%

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

      1. associate-*l/ 90.2%

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

      2. *-commutative 90.2%

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

   9. Simplified 90.2%

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

       1. clear-num 90.1%

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

       2. un-div-inv 90.2%

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

   11. Applied egg-rr 90.2%

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

4. Final simplification 95.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{-242} \lor \neg \left(y \leq 6.8 \cdot 10^{-129}\right):\\ \;\;\;\;x + y \cdot \frac{z - t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 93.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9.4 \cdot 10^{-304} \lor \neg \left(y \leq 6.8 \cdot 10^{-129}\right):\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -9.4e-304) (not (<= y 6.8e-129)))
   (+ x (/ y (/ a (- z t))))
   (+ x (/ z (/ a y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -9.4e-304) || !(y <= 6.8e-129)) {
		tmp = x + (y / (a / (z - t)));
	} 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 ((y <= (-9.4d-304)) .or. (.not. (y <= 6.8d-129))) then
        tmp = x + (y / (a / (z - t)))
    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 ((y <= -9.4e-304) || !(y <= 6.8e-129)) {
		tmp = x + (y / (a / (z - t)));
	} else {
		tmp = x + (z / (a / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -9.4e-304) or not (y <= 6.8e-129):
		tmp = x + (y / (a / (z - t)))
	else:
		tmp = x + (z / (a / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -9.4e-304) || !(y <= 6.8e-129))
		tmp = Float64(x + Float64(y / Float64(a / Float64(z - t))));
	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 ((y <= -9.4e-304) || ~((y <= 6.8e-129)))
		tmp = x + (y / (a / (z - t)));
	else
		tmp = x + (z / (a / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -9.4e-304], N[Not[LessEqual[y, 6.8e-129]], $MachinePrecision]], N[(x + N[(y / N[(a / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -9.4000000000000001e-304 or 6.80000000000000026e-129 < y

   1. Initial program 89.7%

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

      1. associate-/l* 95.9%

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

   3. Simplified 95.9%

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

   if -9.4000000000000001e-304 < y < 6.80000000000000026e-129

   1. Initial program 97.8%

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

      1. +-commutative 97.8%

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

      2. associate-*r/ 74.0%

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

      3. fma-udef 74.1%

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

   3. Simplified 74.1%

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

      1. fma-udef 74.0%

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

      2. associate-*r/ 97.8%

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

      3. div-inv 97.7%

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

      4. div-inv 97.8%

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

      5. *-commutative 97.8%

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

      6. associate-*r/ 99.7%

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

   6. Applied egg-rr 99.7%

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

   7. Taylor expanded in z around inf 91.4%

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

      1. associate-*l/ 93.3%

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

      2. *-commutative 93.3%

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

   9. Simplified 93.3%

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

       1. clear-num 93.3%

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

       2. un-div-inv 93.4%

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

   11. Applied egg-rr 93.4%

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

4. Final simplification 95.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.4 \cdot 10^{-304} \lor \neg \left(y \leq 6.8 \cdot 10^{-129}\right):\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 85.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -34 \lor \neg \left(z \leq 0.0062\right):\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{t \cdot y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -34.0) (not (<= z 0.0062)))
   (+ x (* z (/ y a)))
   (- x (/ (* t y) a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -34.0) || !(z <= 0.0062)) {
		tmp = x + (z * (y / a));
	} else {
		tmp = x - ((t * 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 ((z <= (-34.0d0)) .or. (.not. (z <= 0.0062d0))) then
        tmp = x + (z * (y / a))
    else
        tmp = x - ((t * 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 ((z <= -34.0) || !(z <= 0.0062)) {
		tmp = x + (z * (y / a));
	} else {
		tmp = x - ((t * y) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -34.0) or not (z <= 0.0062):
		tmp = x + (z * (y / a))
	else:
		tmp = x - ((t * y) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -34.0) || !(z <= 0.0062))
		tmp = Float64(x + Float64(z * Float64(y / a)));
	else
		tmp = Float64(x - Float64(Float64(t * y) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -34.0) || ~((z <= 0.0062)))
		tmp = x + (z * (y / a));
	else
		tmp = x - ((t * y) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -34.0], N[Not[LessEqual[z, 0.0062]], $MachinePrecision]], N[(x + N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(t * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -34 or 0.00619999999999999978 < z

   1. Initial program 85.9%

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

      1. +-commutative 85.9%

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

      2. associate-*r/ 87.2%

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

      3. fma-udef 87.3%

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

   3. Simplified 87.3%

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

      1. fma-udef 87.2%

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

      2. associate-*r/ 85.9%

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

      3. div-inv 85.8%

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

      4. div-inv 85.9%

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

      5. *-commutative 85.9%

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

      6. associate-*r/ 99.0%

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

   6. Applied egg-rr 99.0%

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

   7. Taylor expanded in z around inf 79.1%

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

      1. associate-*l/ 87.1%

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

      2. *-commutative 87.1%

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

   9. Simplified 87.1%

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

   if -34 < z < 0.00619999999999999978

   1. Initial program 96.4%

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

      1. *-commutative 96.4%

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

      2. associate-/l* 94.7%

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

   3. Simplified 94.7%

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

   5. Taylor expanded in z around 0 90.3%

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

      1. mul-1-neg 90.3%

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

      2. associate-*r/ 88.9%

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

      3. unsub-neg 88.9%

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

      4. associate-*r/ 90.3%

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

      5. associate-/l* 89.3%

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

      6. associate-/r/ 89.3%

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

   7. Simplified 89.3%

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

   8. Taylor expanded in t around 0 90.3%

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

4. Final simplification 88.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -34 \lor \neg \left(z \leq 0.0062\right):\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{t \cdot y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 86.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{+54}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 0.0006:\\ \;\;\;\;x - t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -9e+54)
   (+ x (/ z (/ a y)))
   (if (<= z 0.0006) (- x (* t (/ y a))) (+ x (* z (/ y a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -9e+54) {
		tmp = x + (z / (a / y));
	} else if (z <= 0.0006) {
		tmp = x - (t * (y / 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 (z <= (-9d+54)) then
        tmp = x + (z / (a / y))
    else if (z <= 0.0006d0) then
        tmp = x - (t * (y / 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 (z <= -9e+54) {
		tmp = x + (z / (a / y));
	} else if (z <= 0.0006) {
		tmp = x - (t * (y / a));
	} else {
		tmp = x + (z * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -9e+54:
		tmp = x + (z / (a / y))
	elif z <= 0.0006:
		tmp = x - (t * (y / a))
	else:
		tmp = x + (z * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -9e+54)
		tmp = Float64(x + Float64(z / Float64(a / y)));
	elseif (z <= 0.0006)
		tmp = Float64(x - Float64(t * Float64(y / 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 (z <= -9e+54)
		tmp = x + (z / (a / y));
	elseif (z <= 0.0006)
		tmp = x - (t * (y / a));
	else
		tmp = x + (z * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -9e+54], N[(x + N[(z / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.0006], N[(x - N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.99999999999999968e54

   1. Initial program 82.5%

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

      1. +-commutative 82.5%

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

      2. associate-*r/ 85.0%

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

      3. fma-udef 85.0%

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

   3. Simplified 85.0%

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

      1. fma-udef 85.0%

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

      2. associate-*r/ 82.5%

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

      3. div-inv 82.5%

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

      4. div-inv 82.5%

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

      5. *-commutative 82.5%

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

      6. associate-*r/ 99.7%

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

   6. Applied egg-rr 99.7%

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

   7. Taylor expanded in z around inf 75.0%

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

      1. associate-*l/ 85.1%

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

      2. *-commutative 85.1%

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

   9. Simplified 85.1%

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

       1. clear-num 85.1%

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

       2. un-div-inv 85.1%

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

   11. Applied egg-rr 85.1%

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

   if -8.99999999999999968e54 < z < 5.99999999999999947e-4

   1. Initial program 95.9%

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

      1. +-commutative 95.9%

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

      2. associate-*r/ 95.8%

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

      3. fma-udef 95.8%

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

   3. Simplified 95.8%

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

      1. fma-udef 95.8%

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

      2. associate-*r/ 95.9%

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

      3. div-inv 95.9%

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

      4. div-inv 95.9%

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

      5. *-commutative 95.9%

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

      6. associate-*r/ 94.7%

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

   6. Applied egg-rr 94.7%

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

   7. Taylor expanded in z around 0 88.8%

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

      1. mul-1-neg 88.8%

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

      2. associate-*l/ 88.6%

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

      3. *-commutative 88.6%

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

      4. distribute-lft-neg-out 88.6%

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

      5. cancel-sign-sub-inv 88.6%

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

      6. *-commutative 88.6%

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

      7. associate-*l/ 88.8%

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

      8. associate-*r/ 88.2%

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

   9. Simplified 88.2%

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

   if 5.99999999999999947e-4 < z

   1. Initial program 89.4%

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

      1. +-commutative 89.4%

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

      2. associate-*r/ 87.7%

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

      3. fma-udef 87.8%

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

   3. Simplified 87.8%

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

      1. fma-udef 87.7%

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

      2. associate-*r/ 89.4%

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

      3. div-inv 89.2%

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

      4. div-inv 89.4%

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

      5. *-commutative 89.4%

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

      6. associate-*r/ 98.0%

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

   6. Applied egg-rr 98.0%

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

   7. Taylor expanded in z around inf 84.0%

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

      1. associate-*l/ 90.9%

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

      2. *-commutative 90.9%

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

   9. Simplified 90.9%

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

4. Final simplification 88.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{+54}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 0.0006:\\ \;\;\;\;x - t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 84.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.4 \cdot 10^{+54}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 0.000165:\\ \;\;\;\;x - y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -9.4e+54)
   (+ x (/ z (/ a y)))
   (if (<= z 0.000165) (- x (* y (/ t a))) (+ x (* z (/ y a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -9.4e+54) {
		tmp = x + (z / (a / y));
	} else if (z <= 0.000165) {
		tmp = x - (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 (z <= (-9.4d+54)) then
        tmp = x + (z / (a / y))
    else if (z <= 0.000165d0) then
        tmp = x - (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 (z <= -9.4e+54) {
		tmp = x + (z / (a / y));
	} else if (z <= 0.000165) {
		tmp = x - (y * (t / a));
	} else {
		tmp = x + (z * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -9.4e+54:
		tmp = x + (z / (a / y))
	elif z <= 0.000165:
		tmp = x - (y * (t / a))
	else:
		tmp = x + (z * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -9.4e+54)
		tmp = Float64(x + Float64(z / Float64(a / y)));
	elseif (z <= 0.000165)
		tmp = Float64(x - Float64(y * 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 (z <= -9.4e+54)
		tmp = x + (z / (a / y));
	elseif (z <= 0.000165)
		tmp = x - (y * (t / a));
	else
		tmp = x + (z * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -9.4e+54], N[(x + N[(z / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.000165], N[(x - N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -9.39999999999999985e54

   1. Initial program 82.5%

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

      1. +-commutative 82.5%

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

      2. associate-*r/ 85.0%

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

      3. fma-udef 85.0%

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

   3. Simplified 85.0%

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

      1. fma-udef 85.0%

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

      2. associate-*r/ 82.5%

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

      3. div-inv 82.5%

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

      4. div-inv 82.5%

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

      5. *-commutative 82.5%

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

      6. associate-*r/ 99.7%

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

   6. Applied egg-rr 99.7%

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

   7. Taylor expanded in z around inf 75.0%

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

      1. associate-*l/ 85.1%

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

      2. *-commutative 85.1%

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

   9. Simplified 85.1%

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

       1. clear-num 85.1%

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

       2. un-div-inv 85.1%

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

   11. Applied egg-rr 85.1%

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

   if -9.39999999999999985e54 < z < 1.65e-4

   1. Initial program 95.9%

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

      1. *-commutative 95.9%

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

      2. associate-/l* 95.1%

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

   3. Simplified 95.1%

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

   5. Taylor expanded in z around 0 88.8%

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

      1. mul-1-neg 88.8%

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

      2. associate-*r/ 88.2%

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

      3. unsub-neg 88.2%

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

      4. associate-*r/ 88.8%

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

      5. associate-/l* 88.6%

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

      6. associate-/r/ 88.6%

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

   7. Simplified 88.6%

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

   if 1.65e-4 < z

   1. Initial program 89.4%

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

      1. +-commutative 89.4%

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

      2. associate-*r/ 87.7%

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

      3. fma-udef 87.8%

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

   3. Simplified 87.8%

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

      1. fma-udef 87.7%

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

      2. associate-*r/ 89.4%

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

      3. div-inv 89.2%

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

      4. div-inv 89.4%

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

      5. *-commutative 89.4%

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

      6. associate-*r/ 98.0%

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

   6. Applied egg-rr 98.0%

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

   7. Taylor expanded in z around inf 84.0%

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

      1. associate-*l/ 90.9%

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

      2. *-commutative 90.9%

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

   9. Simplified 90.9%

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

4. Final simplification 88.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.4 \cdot 10^{+54}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 0.000165:\\ \;\;\;\;x - y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 49.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{+68} \lor \neg \left(y \leq 2.6 \cdot 10^{+175}\right):\\ \;\;\;\;y \cdot \frac{t}{-a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -1.15e+68) (not (<= y 2.6e+175))) (* y (/ t (- a))) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -1.15e+68) || !(y <= 2.6e+175)) {
		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 ((y <= (-1.15d+68)) .or. (.not. (y <= 2.6d+175))) 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 ((y <= -1.15e+68) || !(y <= 2.6e+175)) {
		tmp = y * (t / -a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -1.15e+68) or not (y <= 2.6e+175):
		tmp = y * (t / -a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -1.15e+68) || !(y <= 2.6e+175))
		tmp = Float64(y * Float64(t / Float64(-a)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -1.15e+68) || ~((y <= 2.6e+175)))
		tmp = y * (t / -a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -1.15e+68], N[Not[LessEqual[y, 2.6e+175]], $MachinePrecision]], N[(y * N[(t / (-a)), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -1.15e68 or 2.6e175 < y

   1. Initial program 81.5%

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

      1. +-commutative 81.5%

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

      2. associate-*r/ 96.3%

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

      3. fma-udef 96.3%

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

   3. Simplified 96.3%

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

      1. fma-udef 96.3%

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

      2. associate-*r/ 81.5%

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

      3. div-inv 81.5%

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

      4. div-inv 81.5%

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

      5. *-commutative 81.5%

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

      6. associate-*r/ 96.4%

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

   6. Applied egg-rr 96.4%

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

   7. Taylor expanded in z around 0 64.2%

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

      1. mul-1-neg 64.2%

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

      2. associate-*l/ 68.7%

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

      3. *-commutative 68.7%

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

      4. distribute-lft-neg-out 68.7%

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

      5. cancel-sign-sub-inv 68.7%

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

      6. *-commutative 68.7%

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

      7. associate-*l/ 64.2%

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

      8. associate-*r/ 69.9%

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

   9. Simplified 69.9%

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

   10. Taylor expanded in x around 0 49.4%

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

       1. mul-1-neg 49.4%

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

       2. associate-*l/ 52.7%

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

       3. distribute-lft-neg-in 52.7%

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

       4. *-lft-identity 52.7%

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

       5. metadata-eval 52.7%

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

       6. times-frac 52.7%

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

       7. neg-mul-1 52.7%

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

       8. neg-mul-1 52.7%

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

       9. distribute-frac-neg 52.7%

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

       10. remove-double-neg 52.7%

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

       11. *-commutative 52.7%

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

   12. Simplified 52.7%

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

   if -1.15e68 < y < 2.6e175

   1. Initial program 95.7%

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

      1. *-commutative 95.7%

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

      2. associate-/l* 96.5%

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

   3. Simplified 96.5%

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

   5. Taylor expanded in x around inf 56.3%

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

4. Final simplification 55.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{+68} \lor \neg \left(y \leq 2.6 \cdot 10^{+175}\right):\\ \;\;\;\;y \cdot \frac{t}{-a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 49.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.85 \cdot 10^{+69}:\\ \;\;\;\;t \cdot \frac{-y}{a}\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{+175}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{t}{-a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -1.85e+69)
   (* t (/ (- y) a))
   (if (<= y 2.2e+175) x (* y (/ t (- a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -1.85e+69) {
		tmp = t * (-y / a);
	} else if (y <= 2.2e+175) {
		tmp = x;
	} else {
		tmp = 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 (y <= (-1.85d+69)) then
        tmp = t * (-y / a)
    else if (y <= 2.2d+175) then
        tmp = x
    else
        tmp = 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 (y <= -1.85e+69) {
		tmp = t * (-y / a);
	} else if (y <= 2.2e+175) {
		tmp = x;
	} else {
		tmp = y * (t / -a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -1.85e+69:
		tmp = t * (-y / a)
	elif y <= 2.2e+175:
		tmp = x
	else:
		tmp = y * (t / -a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -1.85e+69)
		tmp = Float64(t * Float64(Float64(-y) / a));
	elseif (y <= 2.2e+175)
		tmp = x;
	else
		tmp = Float64(y * Float64(t / Float64(-a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -1.85e+69)
		tmp = t * (-y / a);
	elseif (y <= 2.2e+175)
		tmp = x;
	else
		tmp = y * (t / -a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -1.85e+69], N[(t * N[((-y) / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.2e+175], x, N[(y * N[(t / (-a)), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.8499999999999999e69

   1. Initial program 81.2%

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

      1. +-commutative 81.2%

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

      2. associate-*r/ 97.9%

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

      3. fma-udef 98.0%

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

   3. Simplified 98.0%

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

      1. fma-udef 97.9%

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

      2. associate-*r/ 81.2%

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

      3. div-inv 81.3%

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

      4. div-inv 81.2%

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

      5. *-commutative 81.2%

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

      6. associate-*r/ 97.9%

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

   6. Applied egg-rr 97.9%

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

   7. Taylor expanded in z around 0 69.0%

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

      1. mul-1-neg 69.0%

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

      2. associate-*l/ 76.5%

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

      3. *-commutative 76.5%

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

      4. distribute-lft-neg-out 76.5%

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

      5. cancel-sign-sub-inv 76.5%

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

      6. *-commutative 76.5%

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

      7. associate-*l/ 69.0%

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

      8. associate-*r/ 80.1%

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

   9. Simplified 80.1%

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

   10. Taylor expanded in x around 0 50.8%

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

       1. mul-1-neg 50.8%

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

       2. associate-*l/ 56.4%

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

       3. distribute-lft-neg-in 56.4%

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

       4. *-lft-identity 56.4%

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

       5. metadata-eval 56.4%

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

       6. times-frac 56.4%

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

       7. neg-mul-1 56.4%

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

       8. neg-mul-1 56.4%

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

       9. distribute-frac-neg 56.4%

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

       10. remove-double-neg 56.4%

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

       11. *-commutative 56.4%

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

   12. Simplified 56.4%

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

   13. Taylor expanded in y around 0 50.8%

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

       1. mul-1-neg 50.8%

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

       2. associate-*r/ 61.9%

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

       3. *-commutative 61.9%

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

       4. distribute-rgt-neg-in 61.9%

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

   15. Simplified 61.9%

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

   if -1.8499999999999999e69 < y < 2.1999999999999999e175

   1. Initial program 95.7%

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

      1. *-commutative 95.7%

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

      2. associate-/l* 96.5%

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

   3. Simplified 96.5%

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

   5. Taylor expanded in x around inf 56.3%

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

   if 2.1999999999999999e175 < y

   1. Initial program 81.9%

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

      1. +-commutative 81.9%

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

      2. associate-*r/ 93.6%

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

      3. fma-udef 93.6%

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

   3. Simplified 93.6%

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

      1. fma-udef 93.6%

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

      2. associate-*r/ 81.9%

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

      3. div-inv 81.9%

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

      4. div-inv 81.9%

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

      5. *-commutative 81.9%

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

      6. associate-*r/ 93.8%

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

   6. Applied egg-rr 93.8%

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

   7. Taylor expanded in z around 0 56.2%

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

      1. mul-1-neg 56.2%

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

      2. associate-*l/ 55.9%

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

      3. *-commutative 55.9%

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

      4. distribute-lft-neg-out 55.9%

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

      5. cancel-sign-sub-inv 55.9%

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

      6. *-commutative 55.9%

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

      7. associate-*l/ 56.2%

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

      8. associate-*r/ 53.1%

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

   9. Simplified 53.1%

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

   10. Taylor expanded in x around 0 46.9%

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

       1. mul-1-neg 46.9%

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

       2. associate-*l/ 46.6%

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

       3. distribute-lft-neg-in 46.6%

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

       4. *-lft-identity 46.6%

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

       5. metadata-eval 46.6%

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

       6. times-frac 46.6%

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

       7. neg-mul-1 46.6%

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

       8. neg-mul-1 46.6%

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

       9. distribute-frac-neg 46.6%

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

       10. remove-double-neg 46.6%

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

       11. *-commutative 46.6%

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

   12. Simplified 46.6%

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

4. Final simplification 56.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.85 \cdot 10^{+69}:\\ \;\;\;\;t \cdot \frac{-y}{a}\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{+175}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{t}{-a}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 49.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{+67}:\\ \;\;\;\;t \cdot \frac{-y}{a}\\ \mathbf{elif}\;y \leq 6.1 \cdot 10^{+177}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot \left(-y\right)}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -5.8e+67)
   (* t (/ (- y) a))
   (if (<= y 6.1e+177) x (/ (* t (- y)) a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -5.8e+67) {
		tmp = t * (-y / a);
	} else if (y <= 6.1e+177) {
		tmp = x;
	} else {
		tmp = (t * -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 (y <= (-5.8d+67)) then
        tmp = t * (-y / a)
    else if (y <= 6.1d+177) then
        tmp = x
    else
        tmp = (t * -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 (y <= -5.8e+67) {
		tmp = t * (-y / a);
	} else if (y <= 6.1e+177) {
		tmp = x;
	} else {
		tmp = (t * -y) / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -5.8e+67:
		tmp = t * (-y / a)
	elif y <= 6.1e+177:
		tmp = x
	else:
		tmp = (t * -y) / a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -5.8e+67)
		tmp = Float64(t * Float64(Float64(-y) / a));
	elseif (y <= 6.1e+177)
		tmp = x;
	else
		tmp = Float64(Float64(t * Float64(-y)) / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -5.8e+67)
		tmp = t * (-y / a);
	elseif (y <= 6.1e+177)
		tmp = x;
	else
		tmp = (t * -y) / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -5.8e+67], N[(t * N[((-y) / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.1e+177], x, N[(N[(t * (-y)), $MachinePrecision] / a), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.80000000000000047e67

   1. Initial program 81.2%

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

      1. +-commutative 81.2%

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

      2. associate-*r/ 97.9%

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

      3. fma-udef 98.0%

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

   3. Simplified 98.0%

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

      1. fma-udef 97.9%

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

      2. associate-*r/ 81.2%

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

      3. div-inv 81.3%

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

      4. div-inv 81.2%

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

      5. *-commutative 81.2%

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

      6. associate-*r/ 97.9%

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

   6. Applied egg-rr 97.9%

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

   7. Taylor expanded in z around 0 69.0%

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

      1. mul-1-neg 69.0%

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

      2. associate-*l/ 76.5%

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

      3. *-commutative 76.5%

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

      4. distribute-lft-neg-out 76.5%

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

      5. cancel-sign-sub-inv 76.5%

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

      6. *-commutative 76.5%

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

      7. associate-*l/ 69.0%

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

      8. associate-*r/ 80.1%

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

   9. Simplified 80.1%

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

   10. Taylor expanded in x around 0 50.8%

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

       1. mul-1-neg 50.8%

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

       2. associate-*l/ 56.4%

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

       3. distribute-lft-neg-in 56.4%

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

       4. *-lft-identity 56.4%

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

       5. metadata-eval 56.4%

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

       6. times-frac 56.4%

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

       7. neg-mul-1 56.4%

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

       8. neg-mul-1 56.4%

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

       9. distribute-frac-neg 56.4%

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

       10. remove-double-neg 56.4%

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

       11. *-commutative 56.4%

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

   12. Simplified 56.4%

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

   13. Taylor expanded in y around 0 50.8%

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

       1. mul-1-neg 50.8%

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

       2. associate-*r/ 61.9%

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

       3. *-commutative 61.9%

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

       4. distribute-rgt-neg-in 61.9%

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

   15. Simplified 61.9%

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

   if -5.80000000000000047e67 < y < 6.0999999999999997e177

   1. Initial program 95.7%

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

      1. *-commutative 95.7%

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

      2. associate-/l* 96.5%

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

   3. Simplified 96.5%

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

   5. Taylor expanded in x around inf 56.3%

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

   if 6.0999999999999997e177 < y

   1. Initial program 81.9%

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

      1. +-commutative 81.9%

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

      2. associate-*r/ 93.6%

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

      3. fma-udef 93.6%

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

   3. Simplified 93.6%

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

      1. fma-udef 93.6%

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

      2. associate-*r/ 81.9%

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

      3. div-inv 81.9%

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

      4. div-inv 81.9%

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

      5. *-commutative 81.9%

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

      6. associate-*r/ 93.8%

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

   6. Applied egg-rr 93.8%

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

   7. Taylor expanded in z around 0 56.2%

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

      1. mul-1-neg 56.2%

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

      2. associate-*l/ 55.9%

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

      3. *-commutative 55.9%

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

      4. distribute-lft-neg-out 55.9%

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

      5. cancel-sign-sub-inv 55.9%

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

      6. *-commutative 55.9%

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

      7. associate-*l/ 56.2%

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

      8. associate-*r/ 53.1%

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

   9. Simplified 53.1%

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

   10. Taylor expanded in x around 0 46.9%

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

       1. associate-*r/ 46.9%

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

       2. *-commutative 46.9%

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

       3. neg-mul-1 46.9%

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

       4. distribute-rgt-neg-out 46.9%

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

   12. Simplified 46.9%

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

4. Final simplification 56.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{+67}:\\ \;\;\;\;t \cdot \frac{-y}{a}\\ \mathbf{elif}\;y \leq 6.1 \cdot 10^{+177}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot \left(-y\right)}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 67.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.9 \cdot 10^{+69}:\\ \;\;\;\;t \cdot \frac{-y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z \cdot y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -2.9e+69) (* t (/ (- y) a)) (+ x (/ (* z y) a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -2.9e+69) {
		tmp = t * (-y / 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 (y <= (-2.9d+69)) then
        tmp = t * (-y / 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 (y <= -2.9e+69) {
		tmp = t * (-y / a);
	} else {
		tmp = x + ((z * y) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -2.9e+69:
		tmp = t * (-y / a)
	else:
		tmp = x + ((z * y) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -2.9e+69)
		tmp = Float64(t * Float64(Float64(-y) / a));
	else
		tmp = Float64(x + Float64(Float64(z * y) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -2.9e+69)
		tmp = t * (-y / a);
	else
		tmp = x + ((z * y) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -2.9e+69], N[(t * N[((-y) / a), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(z * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.8999999999999998e69

   1. Initial program 81.2%

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

      1. +-commutative 81.2%

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

      2. associate-*r/ 97.9%

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

      3. fma-udef 98.0%

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

   3. Simplified 98.0%

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

      1. fma-udef 97.9%

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

      2. associate-*r/ 81.2%

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

      3. div-inv 81.3%

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

      4. div-inv 81.2%

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

      5. *-commutative 81.2%

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

      6. associate-*r/ 97.9%

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

   6. Applied egg-rr 97.9%

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

   7. Taylor expanded in z around 0 69.0%

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

      1. mul-1-neg 69.0%

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

      2. associate-*l/ 76.5%

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

      3. *-commutative 76.5%

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

      4. distribute-lft-neg-out 76.5%

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

      5. cancel-sign-sub-inv 76.5%

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

      6. *-commutative 76.5%

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

      7. associate-*l/ 69.0%

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

      8. associate-*r/ 80.1%

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

   9. Simplified 80.1%

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

   10. Taylor expanded in x around 0 50.8%

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

       1. mul-1-neg 50.8%

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

       2. associate-*l/ 56.4%

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

       3. distribute-lft-neg-in 56.4%

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

       4. *-lft-identity 56.4%

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

       5. metadata-eval 56.4%

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

       6. times-frac 56.4%

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

       7. neg-mul-1 56.4%

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

       8. neg-mul-1 56.4%

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

       9. distribute-frac-neg 56.4%

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

       10. remove-double-neg 56.4%

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

       11. *-commutative 56.4%

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

   12. Simplified 56.4%

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

   13. Taylor expanded in y around 0 50.8%

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

       1. mul-1-neg 50.8%

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

       2. associate-*r/ 61.9%

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

       3. *-commutative 61.9%

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

       4. distribute-rgt-neg-in 61.9%

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

   15. Simplified 61.9%

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

   if -2.8999999999999998e69 < y

   1. Initial program 93.6%

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

      1. *-commutative 93.6%

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

      2. associate-/l* 96.1%

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

   3. Simplified 96.1%

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

   5. Taylor expanded in z around inf 76.7%

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

4. Final simplification 73.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.9 \cdot 10^{+69}:\\ \;\;\;\;t \cdot \frac{-y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z \cdot y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 97.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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) / (a / y))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 91.2%

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

   1. *-commutative 91.2%

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

   2. associate-/l* 96.9%

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

3. Simplified 96.9%

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

5. Final simplification 96.9%

   \[\leadsto x + \frac{z - t}{\frac{a}{y}} \]
6. Add Preprocessing

Alternative 14: 39.6% 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 91.2%

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

   1. *-commutative 91.2%

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

   2. associate-/l* 96.9%

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

3. Simplified 96.9%

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

5. Taylor expanded in x around inf 44.1%

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

6. Final simplification 44.1%

   \[\leadsto x \]
7. Add Preprocessing

Developer target: 99.3% 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 2024018 
(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)))