Diagrams.Solve.Polynomial:cubForm from diagrams-solve-0.1, I

Percentage Accurate: 91.3% → 96.7%

Time: 9.7s

Alternatives: 8

Speedup: 0.5×

• 28.2% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ \frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (/ (- (* x y) (* (* z 9.0) t)) (* a 2.0)))

C

double code(double x, double y, double z, double t, double a) {
	return ((x * y) - ((z * 9.0) * t)) / (a * 2.0);
}

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 * 9.0d0) * t)) / (a * 2.0d0)
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return ((x * y) - ((z * 9.0) * t)) / (a * 2.0);
}

Python

def code(x, y, z, t, a):
	return ((x * y) - ((z * 9.0) * t)) / (a * 2.0)

Julia

function code(x, y, z, t, a)
	return Float64(Float64(Float64(x * y) - Float64(Float64(z * 9.0) * t)) / Float64(a * 2.0))
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = ((x * y) - ((z * 9.0) * t)) / (a * 2.0);
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(N[(N[(x * y), $MachinePrecision] - N[(N[(z * 9.0), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision]

Initial Program: 91.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (/ (- (* x y) (* (* z 9.0) t)) (* a 2.0)))

C

double code(double x, double y, double z, double t, double a) {
	return ((x * y) - ((z * 9.0) * t)) / (a * 2.0);
}

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 * 9.0d0) * t)) / (a * 2.0d0)
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return ((x * y) - ((z * 9.0) * t)) / (a * 2.0);
}

Python

def code(x, y, z, t, a):
	return ((x * y) - ((z * 9.0) * t)) / (a * 2.0)

Julia

function code(x, y, z, t, a)
	return Float64(Float64(Float64(x * y) - Float64(Float64(z * 9.0) * t)) / Float64(a * 2.0))
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = ((x * y) - ((z * 9.0) * t)) / (a * 2.0);
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(N[(N[(x * y), $MachinePrecision] - N[(N[(z * 9.0), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision]

Alternative 1: 96.7% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot y - \left(z \cdot 9\right) \cdot t\\ \mathbf{if}\;t_1 \leq -5 \cdot 10^{+226}:\\ \;\;\;\;\mathsf{fma}\left(-4.5, \frac{t}{\frac{a}{z}}, 0.5 \cdot \frac{x}{\frac{a}{y}}\right)\\ \mathbf{elif}\;t_1 \leq 5 \cdot 10^{+286}:\\ \;\;\;\;\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y \cdot \frac{0.5}{a}, x, z \cdot \frac{-4.5}{\frac{a}{t}}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (* x y) (* (* z 9.0) t))))
   (if (<= t_1 -5e+226)
     (fma -4.5 (/ t (/ a z)) (* 0.5 (/ x (/ a y))))
     (if (<= t_1 5e+286)
       (/ (- (* x y) (* z (* 9.0 t))) (* a 2.0))
       (fma (* y (/ 0.5 a)) x (* z (/ -4.5 (/ a t))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (x * y) - ((z * 9.0) * t);
	double tmp;
	if (t_1 <= -5e+226) {
		tmp = fma(-4.5, (t / (a / z)), (0.5 * (x / (a / y))));
	} else if (t_1 <= 5e+286) {
		tmp = ((x * y) - (z * (9.0 * t))) / (a * 2.0);
	} else {
		tmp = fma((y * (0.5 / a)), x, (z * (-4.5 / (a / t))));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(x * y) - Float64(Float64(z * 9.0) * t))
	tmp = 0.0
	if (t_1 <= -5e+226)
		tmp = fma(-4.5, Float64(t / Float64(a / z)), Float64(0.5 * Float64(x / Float64(a / y))));
	elseif (t_1 <= 5e+286)
		tmp = Float64(Float64(Float64(x * y) - Float64(z * Float64(9.0 * t))) / Float64(a * 2.0));
	else
		tmp = fma(Float64(y * Float64(0.5 / a)), x, Float64(z * Float64(-4.5 / Float64(a / t))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] - N[(N[(z * 9.0), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+226], N[(-4.5 * N[(t / N[(a / z), $MachinePrecision]), $MachinePrecision] + N[(0.5 * N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+286], N[(N[(N[(x * y), $MachinePrecision] - N[(z * N[(9.0 * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(y * N[(0.5 / a), $MachinePrecision]), $MachinePrecision] * x + N[(z * N[(-4.5 / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t)) < -5.0000000000000005e226

   1. Initial program 71.4%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Step-by-step derivation

      1. associate-*l* 73.3%

         \[\leadsto \frac{x \cdot y - \color{blue}{z \cdot \left(9 \cdot t\right)}}{a \cdot 2} \]

   3. Simplified 73.3%

      \[\leadsto \color{blue}{\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 71.2%

      \[\leadsto \color{blue}{-4.5 \cdot \frac{t \cdot z}{a} + 0.5 \cdot \frac{x \cdot y}{a}} \]
   6. Step-by-step derivation

      1. fma-def 71.2%

         \[\leadsto \color{blue}{\mathsf{fma}\left(-4.5, \frac{t \cdot z}{a}, 0.5 \cdot \frac{x \cdot y}{a}\right)} \]

      2. associate-/l* 82.5%

         \[\leadsto \mathsf{fma}\left(-4.5, \color{blue}{\frac{t}{\frac{a}{z}}}, 0.5 \cdot \frac{x \cdot y}{a}\right) \]

      3. associate-/l* 97.8%

         \[\leadsto \mathsf{fma}\left(-4.5, \frac{t}{\frac{a}{z}}, 0.5 \cdot \color{blue}{\frac{x}{\frac{a}{y}}}\right) \]

   7. Simplified 97.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-4.5, \frac{t}{\frac{a}{z}}, 0.5 \cdot \frac{x}{\frac{a}{y}}\right)} \]

   if -5.0000000000000005e226 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t)) < 5.0000000000000004e286

   1. Initial program 97.5%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Step-by-step derivation

      1. associate-*l* 97.5%

         \[\leadsto \frac{x \cdot y - \color{blue}{z \cdot \left(9 \cdot t\right)}}{a \cdot 2} \]

   3. Simplified 97.5%

      \[\leadsto \color{blue}{\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}} \]
   4. Add Preprocessing

   if 5.0000000000000004e286 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t))

   1. Initial program 56.4%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Step-by-step derivation

      1. associate-*l* 56.4%

         \[\leadsto \frac{x \cdot y - \color{blue}{z \cdot \left(9 \cdot t\right)}}{a \cdot 2} \]

   3. Simplified 56.4%

      \[\leadsto \color{blue}{\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 53.6%

      \[\leadsto \color{blue}{-4.5 \cdot \frac{t \cdot z}{a} + 0.5 \cdot \frac{x \cdot y}{a}} \]
   6. Step-by-step derivation

      1. fma-def 53.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(-4.5, \frac{t \cdot z}{a}, 0.5 \cdot \frac{x \cdot y}{a}\right)} \]

      2. associate-/l* 64.1%

         \[\leadsto \mathsf{fma}\left(-4.5, \color{blue}{\frac{t}{\frac{a}{z}}}, 0.5 \cdot \frac{x \cdot y}{a}\right) \]

      3. associate-/l* 91.4%

         \[\leadsto \mathsf{fma}\left(-4.5, \frac{t}{\frac{a}{z}}, 0.5 \cdot \color{blue}{\frac{x}{\frac{a}{y}}}\right) \]

   7. Simplified 91.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-4.5, \frac{t}{\frac{a}{z}}, 0.5 \cdot \frac{x}{\frac{a}{y}}\right)} \]
   8. Step-by-step derivation

      1. fma-udef 91.4%

         \[\leadsto \color{blue}{-4.5 \cdot \frac{t}{\frac{a}{z}} + 0.5 \cdot \frac{x}{\frac{a}{y}}} \]

      2. associate-/r/ 94.2%

         \[\leadsto -4.5 \cdot \color{blue}{\left(\frac{t}{a} \cdot z\right)} + 0.5 \cdot \frac{x}{\frac{a}{y}} \]

      3. +-commutative 94.2%

         \[\leadsto \color{blue}{0.5 \cdot \frac{x}{\frac{a}{y}} + -4.5 \cdot \left(\frac{t}{a} \cdot z\right)} \]

      4. *-commutative 94.2%

         \[\leadsto \color{blue}{\frac{x}{\frac{a}{y}} \cdot 0.5} + -4.5 \cdot \left(\frac{t}{a} \cdot z\right) \]

      5. div-inv 94.2%

         \[\leadsto \color{blue}{\left(x \cdot \frac{1}{\frac{a}{y}}\right)} \cdot 0.5 + -4.5 \cdot \left(\frac{t}{a} \cdot z\right) \]

      6. clear-num 94.2%

         \[\leadsto \left(x \cdot \color{blue}{\frac{y}{a}}\right) \cdot 0.5 + -4.5 \cdot \left(\frac{t}{a} \cdot z\right) \]

      7. associate-*l* 94.2%

         \[\leadsto \color{blue}{x \cdot \left(\frac{y}{a} \cdot 0.5\right)} + -4.5 \cdot \left(\frac{t}{a} \cdot z\right) \]

      8. associate-/r/ 91.3%

         \[\leadsto x \cdot \left(\frac{y}{a} \cdot 0.5\right) + -4.5 \cdot \color{blue}{\frac{t}{\frac{a}{z}}} \]

      9. *-commutative 91.3%

         \[\leadsto x \cdot \left(\frac{y}{a} \cdot 0.5\right) + \color{blue}{\frac{t}{\frac{a}{z}} \cdot -4.5} \]

      10. div-inv 91.3%

          \[\leadsto x \cdot \left(\frac{y}{a} \cdot 0.5\right) + \color{blue}{\left(t \cdot \frac{1}{\frac{a}{z}}\right)} \cdot -4.5 \]

      11. clear-num 91.3%

          \[\leadsto x \cdot \left(\frac{y}{a} \cdot 0.5\right) + \left(t \cdot \color{blue}{\frac{z}{a}}\right) \cdot -4.5 \]

      12. associate-*l* 91.3%

          \[\leadsto x \cdot \left(\frac{y}{a} \cdot 0.5\right) + \color{blue}{t \cdot \left(\frac{z}{a} \cdot -4.5\right)} \]

   9. Applied egg-rr 91.3%

      \[\leadsto \color{blue}{x \cdot \left(\frac{y}{a} \cdot 0.5\right) + t \cdot \left(\frac{z}{a} \cdot -4.5\right)} \]
   10. Step-by-step derivation

       1. *-commutative 91.3%

          \[\leadsto \color{blue}{\left(\frac{y}{a} \cdot 0.5\right) \cdot x} + t \cdot \left(\frac{z}{a} \cdot -4.5\right) \]

       2. fma-def 94.1%

          \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y}{a} \cdot 0.5, x, t \cdot \left(\frac{z}{a} \cdot -4.5\right)\right)} \]

       3. associate-*l/ 94.1%

          \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{y \cdot 0.5}{a}}, x, t \cdot \left(\frac{z}{a} \cdot -4.5\right)\right) \]

       4. associate-*r/ 94.1%

          \[\leadsto \mathsf{fma}\left(\color{blue}{y \cdot \frac{0.5}{a}}, x, t \cdot \left(\frac{z}{a} \cdot -4.5\right)\right) \]

       5. *-commutative 94.1%

          \[\leadsto \mathsf{fma}\left(y \cdot \frac{0.5}{a}, x, \color{blue}{\left(\frac{z}{a} \cdot -4.5\right) \cdot t}\right) \]

       6. *-commutative 94.1%

          \[\leadsto \mathsf{fma}\left(y \cdot \frac{0.5}{a}, x, \color{blue}{\left(-4.5 \cdot \frac{z}{a}\right)} \cdot t\right) \]

       7. associate-*r/ 94.0%

          \[\leadsto \mathsf{fma}\left(y \cdot \frac{0.5}{a}, x, \color{blue}{\frac{-4.5 \cdot z}{a}} \cdot t\right) \]

       8. associate-/r/ 96.9%

          \[\leadsto \mathsf{fma}\left(y \cdot \frac{0.5}{a}, x, \color{blue}{\frac{-4.5 \cdot z}{\frac{a}{t}}}\right) \]

       9. associate-/l* 96.9%

          \[\leadsto \mathsf{fma}\left(y \cdot \frac{0.5}{a}, x, \color{blue}{\frac{-4.5}{\frac{\frac{a}{t}}{z}}}\right) \]

       10. associate-/r/ 96.8%

           \[\leadsto \mathsf{fma}\left(y \cdot \frac{0.5}{a}, x, \color{blue}{\frac{-4.5}{\frac{a}{t}} \cdot z}\right) \]

   11. Applied egg-rr 96.8%

       \[\leadsto \color{blue}{\mathsf{fma}\left(y \cdot \frac{0.5}{a}, x, \frac{-4.5}{\frac{a}{t}} \cdot z\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 97.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - \left(z \cdot 9\right) \cdot t \leq -5 \cdot 10^{+226}:\\ \;\;\;\;\mathsf{fma}\left(-4.5, \frac{t}{\frac{a}{z}}, 0.5 \cdot \frac{x}{\frac{a}{y}}\right)\\ \mathbf{elif}\;x \cdot y - \left(z \cdot 9\right) \cdot t \leq 5 \cdot 10^{+286}:\\ \;\;\;\;\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y \cdot \frac{0.5}{a}, x, z \cdot \frac{-4.5}{\frac{a}{t}}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 95.2% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot y - \left(z \cdot 9\right) \cdot t\\ \mathbf{if}\;t_1 \leq -5 \cdot 10^{+226} \lor \neg \left(t_1 \leq 4 \cdot 10^{+117}\right):\\ \;\;\;\;\mathsf{fma}\left(-4.5, \frac{t}{\frac{a}{z}}, 0.5 \cdot \frac{x}{\frac{a}{y}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (* x y) (* (* z 9.0) t))))
   (if (or (<= t_1 -5e+226) (not (<= t_1 4e+117)))
     (fma -4.5 (/ t (/ a z)) (* 0.5 (/ x (/ a y))))
     (/ (- (* x y) (* z (* 9.0 t))) (* a 2.0)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (x * y) - ((z * 9.0) * t);
	double tmp;
	if ((t_1 <= -5e+226) || !(t_1 <= 4e+117)) {
		tmp = fma(-4.5, (t / (a / z)), (0.5 * (x / (a / y))));
	} else {
		tmp = ((x * y) - (z * (9.0 * t))) / (a * 2.0);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(x * y) - Float64(Float64(z * 9.0) * t))
	tmp = 0.0
	if ((t_1 <= -5e+226) || !(t_1 <= 4e+117))
		tmp = fma(-4.5, Float64(t / Float64(a / z)), Float64(0.5 * Float64(x / Float64(a / y))));
	else
		tmp = Float64(Float64(Float64(x * y) - Float64(z * Float64(9.0 * t))) / Float64(a * 2.0));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] - N[(N[(z * 9.0), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -5e+226], N[Not[LessEqual[t$95$1, 4e+117]], $MachinePrecision]], N[(-4.5 * N[(t / N[(a / z), $MachinePrecision]), $MachinePrecision] + N[(0.5 * N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x * y), $MachinePrecision] - N[(z * N[(9.0 * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t)) < -5.0000000000000005e226 or 4.0000000000000002e117 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t))

   1. Initial program 73.3%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Step-by-step derivation

      1. associate-*l* 74.2%

         \[\leadsto \frac{x \cdot y - \color{blue}{z \cdot \left(9 \cdot t\right)}}{a \cdot 2} \]

   3. Simplified 74.2%

      \[\leadsto \color{blue}{\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 72.3%

      \[\leadsto \color{blue}{-4.5 \cdot \frac{t \cdot z}{a} + 0.5 \cdot \frac{x \cdot y}{a}} \]
   6. Step-by-step derivation

      1. fma-def 72.3%

         \[\leadsto \color{blue}{\mathsf{fma}\left(-4.5, \frac{t \cdot z}{a}, 0.5 \cdot \frac{x \cdot y}{a}\right)} \]

      2. associate-/l* 80.8%

         \[\leadsto \mathsf{fma}\left(-4.5, \color{blue}{\frac{t}{\frac{a}{z}}}, 0.5 \cdot \frac{x \cdot y}{a}\right) \]

      3. associate-/l* 95.4%

         \[\leadsto \mathsf{fma}\left(-4.5, \frac{t}{\frac{a}{z}}, 0.5 \cdot \color{blue}{\frac{x}{\frac{a}{y}}}\right) \]

   7. Simplified 95.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-4.5, \frac{t}{\frac{a}{z}}, 0.5 \cdot \frac{x}{\frac{a}{y}}\right)} \]

   if -5.0000000000000005e226 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t)) < 4.0000000000000002e117

   1. Initial program 97.1%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Step-by-step derivation

      1. associate-*l* 97.1%

         \[\leadsto \frac{x \cdot y - \color{blue}{z \cdot \left(9 \cdot t\right)}}{a \cdot 2} \]

   3. Simplified 97.1%

      \[\leadsto \color{blue}{\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}} \]
   4. Add Preprocessing
3. Recombined 2 regimes into one program.

4. Final simplification 96.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - \left(z \cdot 9\right) \cdot t \leq -5 \cdot 10^{+226} \lor \neg \left(x \cdot y - \left(z \cdot 9\right) \cdot t \leq 4 \cdot 10^{+117}\right):\\ \;\;\;\;\mathsf{fma}\left(-4.5, \frac{t}{\frac{a}{z}}, 0.5 \cdot \frac{x}{\frac{a}{y}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 96.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot y - \left(z \cdot 9\right) \cdot t\\ \mathbf{if}\;t_1 \leq -\infty \lor \neg \left(t_1 \leq 5 \cdot 10^{+261}\right):\\ \;\;\;\;x \cdot \left(0.5 \cdot \frac{y}{a}\right) + t \cdot \left(-4.5 \cdot \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (* x y) (* (* z 9.0) t))))
   (if (or (<= t_1 (- INFINITY)) (not (<= t_1 5e+261)))
     (+ (* x (* 0.5 (/ y a))) (* t (* -4.5 (/ z a))))
     (/ (- (* x y) (* z (* 9.0 t))) (* a 2.0)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (x * y) - ((z * 9.0) * t);
	double tmp;
	if ((t_1 <= -((double) INFINITY)) || !(t_1 <= 5e+261)) {
		tmp = (x * (0.5 * (y / a))) + (t * (-4.5 * (z / a)));
	} else {
		tmp = ((x * y) - (z * (9.0 * t))) / (a * 2.0);
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (x * y) - ((z * 9.0) * t);
	double tmp;
	if ((t_1 <= -Double.POSITIVE_INFINITY) || !(t_1 <= 5e+261)) {
		tmp = (x * (0.5 * (y / a))) + (t * (-4.5 * (z / a)));
	} else {
		tmp = ((x * y) - (z * (9.0 * t))) / (a * 2.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (x * y) - ((z * 9.0) * t)
	tmp = 0
	if (t_1 <= -math.inf) or not (t_1 <= 5e+261):
		tmp = (x * (0.5 * (y / a))) + (t * (-4.5 * (z / a)))
	else:
		tmp = ((x * y) - (z * (9.0 * t))) / (a * 2.0)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(x * y) - Float64(Float64(z * 9.0) * t))
	tmp = 0.0
	if ((t_1 <= Float64(-Inf)) || !(t_1 <= 5e+261))
		tmp = Float64(Float64(x * Float64(0.5 * Float64(y / a))) + Float64(t * Float64(-4.5 * Float64(z / a))));
	else
		tmp = Float64(Float64(Float64(x * y) - Float64(z * Float64(9.0 * t))) / Float64(a * 2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (x * y) - ((z * 9.0) * t);
	tmp = 0.0;
	if ((t_1 <= -Inf) || ~((t_1 <= 5e+261)))
		tmp = (x * (0.5 * (y / a))) + (t * (-4.5 * (z / a)));
	else
		tmp = ((x * y) - (z * (9.0 * t))) / (a * 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] - N[(N[(z * 9.0), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, (-Infinity)], N[Not[LessEqual[t$95$1, 5e+261]], $MachinePrecision]], N[(N[(x * N[(0.5 * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * N[(-4.5 * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x * y), $MachinePrecision] - N[(z * N[(9.0 * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t)) < -inf.0 or 5.0000000000000001e261 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t))

   1. Initial program 60.1%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Step-by-step derivation

      1. associate-*l* 61.4%

         \[\leadsto \frac{x \cdot y - \color{blue}{z \cdot \left(9 \cdot t\right)}}{a \cdot 2} \]

   3. Simplified 61.4%

      \[\leadsto \color{blue}{\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 58.7%

      \[\leadsto \color{blue}{-4.5 \cdot \frac{t \cdot z}{a} + 0.5 \cdot \frac{x \cdot y}{a}} \]
   6. Step-by-step derivation

      1. fma-def 58.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(-4.5, \frac{t \cdot z}{a}, 0.5 \cdot \frac{x \cdot y}{a}\right)} \]

      2. associate-/l* 71.3%

         \[\leadsto \mathsf{fma}\left(-4.5, \color{blue}{\frac{t}{\frac{a}{z}}}, 0.5 \cdot \frac{x \cdot y}{a}\right) \]

      3. associate-/l* 93.1%

         \[\leadsto \mathsf{fma}\left(-4.5, \frac{t}{\frac{a}{z}}, 0.5 \cdot \color{blue}{\frac{x}{\frac{a}{y}}}\right) \]

   7. Simplified 93.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-4.5, \frac{t}{\frac{a}{z}}, 0.5 \cdot \frac{x}{\frac{a}{y}}\right)} \]
   8. Step-by-step derivation

      1. fma-udef 93.1%

         \[\leadsto \color{blue}{-4.5 \cdot \frac{t}{\frac{a}{z}} + 0.5 \cdot \frac{x}{\frac{a}{y}}} \]

      2. associate-/r/ 93.1%

         \[\leadsto -4.5 \cdot \color{blue}{\left(\frac{t}{a} \cdot z\right)} + 0.5 \cdot \frac{x}{\frac{a}{y}} \]

      3. +-commutative 93.1%

         \[\leadsto \color{blue}{0.5 \cdot \frac{x}{\frac{a}{y}} + -4.5 \cdot \left(\frac{t}{a} \cdot z\right)} \]

      4. *-commutative 93.1%

         \[\leadsto \color{blue}{\frac{x}{\frac{a}{y}} \cdot 0.5} + -4.5 \cdot \left(\frac{t}{a} \cdot z\right) \]

      5. div-inv 93.0%

         \[\leadsto \color{blue}{\left(x \cdot \frac{1}{\frac{a}{y}}\right)} \cdot 0.5 + -4.5 \cdot \left(\frac{t}{a} \cdot z\right) \]

      6. clear-num 93.1%

         \[\leadsto \left(x \cdot \color{blue}{\frac{y}{a}}\right) \cdot 0.5 + -4.5 \cdot \left(\frac{t}{a} \cdot z\right) \]

      7. associate-*l* 93.1%

         \[\leadsto \color{blue}{x \cdot \left(\frac{y}{a} \cdot 0.5\right)} + -4.5 \cdot \left(\frac{t}{a} \cdot z\right) \]

      8. associate-/r/ 93.1%

         \[\leadsto x \cdot \left(\frac{y}{a} \cdot 0.5\right) + -4.5 \cdot \color{blue}{\frac{t}{\frac{a}{z}}} \]

      9. *-commutative 93.1%

         \[\leadsto x \cdot \left(\frac{y}{a} \cdot 0.5\right) + \color{blue}{\frac{t}{\frac{a}{z}} \cdot -4.5} \]

      10. div-inv 93.1%

          \[\leadsto x \cdot \left(\frac{y}{a} \cdot 0.5\right) + \color{blue}{\left(t \cdot \frac{1}{\frac{a}{z}}\right)} \cdot -4.5 \]

      11. clear-num 93.1%

          \[\leadsto x \cdot \left(\frac{y}{a} \cdot 0.5\right) + \left(t \cdot \color{blue}{\frac{z}{a}}\right) \cdot -4.5 \]

      12. associate-*l* 93.1%

          \[\leadsto x \cdot \left(\frac{y}{a} \cdot 0.5\right) + \color{blue}{t \cdot \left(\frac{z}{a} \cdot -4.5\right)} \]

   9. Applied egg-rr 93.1%

      \[\leadsto \color{blue}{x \cdot \left(\frac{y}{a} \cdot 0.5\right) + t \cdot \left(\frac{z}{a} \cdot -4.5\right)} \]

   if -inf.0 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t)) < 5.0000000000000001e261

   1. Initial program 97.6%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Step-by-step derivation

      1. associate-*l* 97.6%

         \[\leadsto \frac{x \cdot y - \color{blue}{z \cdot \left(9 \cdot t\right)}}{a \cdot 2} \]

   3. Simplified 97.6%

      \[\leadsto \color{blue}{\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}} \]
   4. Add Preprocessing
3. Recombined 2 regimes into one program.

4. Final simplification 96.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - \left(z \cdot 9\right) \cdot t \leq -\infty \lor \neg \left(x \cdot y - \left(z \cdot 9\right) \cdot t \leq 5 \cdot 10^{+261}\right):\\ \;\;\;\;x \cdot \left(0.5 \cdot \frac{y}{a}\right) + t \cdot \left(-4.5 \cdot \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 72.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 0.5 \cdot \frac{x}{\frac{a}{y}}\\ \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{-17}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot y \leq 4 \cdot 10^{-268}:\\ \;\;\;\;-4.5 \cdot \frac{t}{\frac{a}{z}}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-224}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot y \leq 10^{+30}:\\ \;\;\;\;-4.5 \cdot \left(z \cdot \frac{t}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \left(y \cdot \frac{x}{a}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* 0.5 (/ x (/ a y)))))
   (if (<= (* x y) -1e-17)
     t_1
     (if (<= (* x y) 4e-268)
       (* -4.5 (/ t (/ a z)))
       (if (<= (* x y) 5e-224)
         t_1
         (if (<= (* x y) 1e+30)
           (* -4.5 (* z (/ t a)))
           (* 0.5 (* y (/ x a)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = 0.5 * (x / (a / y));
	double tmp;
	if ((x * y) <= -1e-17) {
		tmp = t_1;
	} else if ((x * y) <= 4e-268) {
		tmp = -4.5 * (t / (a / z));
	} else if ((x * y) <= 5e-224) {
		tmp = t_1;
	} else if ((x * y) <= 1e+30) {
		tmp = -4.5 * (z * (t / a));
	} else {
		tmp = 0.5 * (y * (x / 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 = 0.5d0 * (x / (a / y))
    if ((x * y) <= (-1d-17)) then
        tmp = t_1
    else if ((x * y) <= 4d-268) then
        tmp = (-4.5d0) * (t / (a / z))
    else if ((x * y) <= 5d-224) then
        tmp = t_1
    else if ((x * y) <= 1d+30) then
        tmp = (-4.5d0) * (z * (t / a))
    else
        tmp = 0.5d0 * (y * (x / 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 = 0.5 * (x / (a / y));
	double tmp;
	if ((x * y) <= -1e-17) {
		tmp = t_1;
	} else if ((x * y) <= 4e-268) {
		tmp = -4.5 * (t / (a / z));
	} else if ((x * y) <= 5e-224) {
		tmp = t_1;
	} else if ((x * y) <= 1e+30) {
		tmp = -4.5 * (z * (t / a));
	} else {
		tmp = 0.5 * (y * (x / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = 0.5 * (x / (a / y))
	tmp = 0
	if (x * y) <= -1e-17:
		tmp = t_1
	elif (x * y) <= 4e-268:
		tmp = -4.5 * (t / (a / z))
	elif (x * y) <= 5e-224:
		tmp = t_1
	elif (x * y) <= 1e+30:
		tmp = -4.5 * (z * (t / a))
	else:
		tmp = 0.5 * (y * (x / a))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(0.5 * Float64(x / Float64(a / y)))
	tmp = 0.0
	if (Float64(x * y) <= -1e-17)
		tmp = t_1;
	elseif (Float64(x * y) <= 4e-268)
		tmp = Float64(-4.5 * Float64(t / Float64(a / z)));
	elseif (Float64(x * y) <= 5e-224)
		tmp = t_1;
	elseif (Float64(x * y) <= 1e+30)
		tmp = Float64(-4.5 * Float64(z * Float64(t / a)));
	else
		tmp = Float64(0.5 * Float64(y * Float64(x / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = 0.5 * (x / (a / y));
	tmp = 0.0;
	if ((x * y) <= -1e-17)
		tmp = t_1;
	elseif ((x * y) <= 4e-268)
		tmp = -4.5 * (t / (a / z));
	elseif ((x * y) <= 5e-224)
		tmp = t_1;
	elseif ((x * y) <= 1e+30)
		tmp = -4.5 * (z * (t / a));
	else
		tmp = 0.5 * (y * (x / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(0.5 * N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -1e-17], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 4e-268], N[(-4.5 * N[(t / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 5e-224], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 1e+30], N[(-4.5 * N[(z * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(0.5 * N[(y * N[(x / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 x y) < -1.00000000000000007e-17 or 3.99999999999999983e-268 < (*.f64 x y) < 4.9999999999999999e-224

   1. Initial program 86.5%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Step-by-step derivation

      1. associate-*l* 86.5%

         \[\leadsto \frac{x \cdot y - \color{blue}{z \cdot \left(9 \cdot t\right)}}{a \cdot 2} \]

   3. Simplified 86.5%

      \[\leadsto \color{blue}{\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 71.1%

      \[\leadsto \color{blue}{0.5 \cdot \frac{x \cdot y}{a}} \]
   6. Step-by-step derivation

      1. associate-/l* 77.0%

         \[\leadsto 0.5 \cdot \color{blue}{\frac{x}{\frac{a}{y}}} \]

   7. Simplified 77.0%

      \[\leadsto \color{blue}{0.5 \cdot \frac{x}{\frac{a}{y}}} \]

   if -1.00000000000000007e-17 < (*.f64 x y) < 3.99999999999999983e-268

   1. Initial program 91.0%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Step-by-step derivation

      1. associate-*l* 91.1%

         \[\leadsto \frac{x \cdot y - \color{blue}{z \cdot \left(9 \cdot t\right)}}{a \cdot 2} \]

   3. Simplified 91.1%

      \[\leadsto \color{blue}{\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 77.7%

      \[\leadsto \color{blue}{-4.5 \cdot \frac{t \cdot z}{a}} \]
   6. Step-by-step derivation

      1. associate-/l* 77.0%

         \[\leadsto -4.5 \cdot \color{blue}{\frac{t}{\frac{a}{z}}} \]

   7. Simplified 77.0%

      \[\leadsto \color{blue}{-4.5 \cdot \frac{t}{\frac{a}{z}}} \]

   if 4.9999999999999999e-224 < (*.f64 x y) < 1e30

   1. Initial program 92.8%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Step-by-step derivation

      1. associate-*l* 95.3%

         \[\leadsto \frac{x \cdot y - \color{blue}{z \cdot \left(9 \cdot t\right)}}{a \cdot 2} \]

   3. Simplified 95.3%

      \[\leadsto \color{blue}{\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 68.4%

      \[\leadsto \color{blue}{-4.5 \cdot \frac{t \cdot z}{a}} \]
   6. Step-by-step derivation

      1. associate-/l* 68.6%

         \[\leadsto -4.5 \cdot \color{blue}{\frac{t}{\frac{a}{z}}} \]

      2. associate-/r/ 68.4%

         \[\leadsto -4.5 \cdot \color{blue}{\left(\frac{t}{a} \cdot z\right)} \]

   7. Simplified 68.4%

      \[\leadsto \color{blue}{-4.5 \cdot \left(\frac{t}{a} \cdot z\right)} \]

   if 1e30 < (*.f64 x y)

   1. Initial program 74.2%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Step-by-step derivation

      1. associate-*l* 74.2%

         \[\leadsto \frac{x \cdot y - \color{blue}{z \cdot \left(9 \cdot t\right)}}{a \cdot 2} \]

   3. Simplified 74.2%

      \[\leadsto \color{blue}{\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 63.5%

      \[\leadsto \color{blue}{0.5 \cdot \frac{x \cdot y}{a}} \]
   6. Step-by-step derivation

      1. associate-/l* 75.3%

         \[\leadsto 0.5 \cdot \color{blue}{\frac{x}{\frac{a}{y}}} \]

   7. Simplified 75.3%

      \[\leadsto \color{blue}{0.5 \cdot \frac{x}{\frac{a}{y}}} \]
   8. Step-by-step derivation

      1. associate-/r/ 77.1%

         \[\leadsto 0.5 \cdot \color{blue}{\left(\frac{x}{a} \cdot y\right)} \]

   9. Applied egg-rr 77.1%

      \[\leadsto 0.5 \cdot \color{blue}{\left(\frac{x}{a} \cdot y\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 75.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{-17}:\\ \;\;\;\;0.5 \cdot \frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;x \cdot y \leq 4 \cdot 10^{-268}:\\ \;\;\;\;-4.5 \cdot \frac{t}{\frac{a}{z}}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-224}:\\ \;\;\;\;0.5 \cdot \frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;x \cdot y \leq 10^{+30}:\\ \;\;\;\;-4.5 \cdot \left(z \cdot \frac{t}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \left(y \cdot \frac{x}{a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 64.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5.6 \cdot 10^{-75}:\\ \;\;\;\;-4.5 \cdot \frac{z}{\frac{a}{t}}\\ \mathbf{elif}\;t \leq 3.9 \cdot 10^{+86}:\\ \;\;\;\;0.5 \cdot \left(x \cdot \frac{y}{a}\right)\\ \mathbf{elif}\;t \leq 2 \cdot 10^{+170}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \mathbf{elif}\;t \leq 8.1 \cdot 10^{+192}:\\ \;\;\;\;0.5 \cdot \left(y \cdot \frac{x}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \left(z \cdot \frac{t}{a}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -5.6e-75)
   (* -4.5 (/ z (/ a t)))
   (if (<= t 3.9e+86)
     (* 0.5 (* x (/ y a)))
     (if (<= t 2e+170)
       (* -4.5 (/ (* z t) a))
       (if (<= t 8.1e+192) (* 0.5 (* y (/ x a))) (* -4.5 (* z (/ t a))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -5.6e-75) {
		tmp = -4.5 * (z / (a / t));
	} else if (t <= 3.9e+86) {
		tmp = 0.5 * (x * (y / a));
	} else if (t <= 2e+170) {
		tmp = -4.5 * ((z * t) / a);
	} else if (t <= 8.1e+192) {
		tmp = 0.5 * (y * (x / a));
	} else {
		tmp = -4.5 * (z * (t / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-5.6d-75)) then
        tmp = (-4.5d0) * (z / (a / t))
    else if (t <= 3.9d+86) then
        tmp = 0.5d0 * (x * (y / a))
    else if (t <= 2d+170) then
        tmp = (-4.5d0) * ((z * t) / a)
    else if (t <= 8.1d+192) then
        tmp = 0.5d0 * (y * (x / a))
    else
        tmp = (-4.5d0) * (z * (t / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -5.6e-75) {
		tmp = -4.5 * (z / (a / t));
	} else if (t <= 3.9e+86) {
		tmp = 0.5 * (x * (y / a));
	} else if (t <= 2e+170) {
		tmp = -4.5 * ((z * t) / a);
	} else if (t <= 8.1e+192) {
		tmp = 0.5 * (y * (x / a));
	} else {
		tmp = -4.5 * (z * (t / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -5.6e-75:
		tmp = -4.5 * (z / (a / t))
	elif t <= 3.9e+86:
		tmp = 0.5 * (x * (y / a))
	elif t <= 2e+170:
		tmp = -4.5 * ((z * t) / a)
	elif t <= 8.1e+192:
		tmp = 0.5 * (y * (x / a))
	else:
		tmp = -4.5 * (z * (t / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -5.6e-75)
		tmp = Float64(-4.5 * Float64(z / Float64(a / t)));
	elseif (t <= 3.9e+86)
		tmp = Float64(0.5 * Float64(x * Float64(y / a)));
	elseif (t <= 2e+170)
		tmp = Float64(-4.5 * Float64(Float64(z * t) / a));
	elseif (t <= 8.1e+192)
		tmp = Float64(0.5 * Float64(y * Float64(x / a)));
	else
		tmp = Float64(-4.5 * Float64(z * Float64(t / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -5.6e-75)
		tmp = -4.5 * (z / (a / t));
	elseif (t <= 3.9e+86)
		tmp = 0.5 * (x * (y / a));
	elseif (t <= 2e+170)
		tmp = -4.5 * ((z * t) / a);
	elseif (t <= 8.1e+192)
		tmp = 0.5 * (y * (x / a));
	else
		tmp = -4.5 * (z * (t / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -5.6e-75], N[(-4.5 * N[(z / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.9e+86], N[(0.5 * N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2e+170], N[(-4.5 * N[(N[(z * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 8.1e+192], N[(0.5 * N[(y * N[(x / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-4.5 * N[(z * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -5.59999999999999996e-75

   1. Initial program 82.0%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Step-by-step derivation

      1. associate-*l* 82.0%

         \[\leadsto \frac{x \cdot y - \color{blue}{z \cdot \left(9 \cdot t\right)}}{a \cdot 2} \]

   3. Simplified 82.0%

      \[\leadsto \color{blue}{\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 56.4%

      \[\leadsto \color{blue}{-4.5 \cdot \frac{t \cdot z}{a}} \]
   6. Step-by-step derivation

      1. associate-/l* 62.0%

         \[\leadsto -4.5 \cdot \color{blue}{\frac{t}{\frac{a}{z}}} \]

      2. associate-/r/ 62.7%

         \[\leadsto -4.5 \cdot \color{blue}{\left(\frac{t}{a} \cdot z\right)} \]

   7. Simplified 62.7%

      \[\leadsto \color{blue}{-4.5 \cdot \left(\frac{t}{a} \cdot z\right)} \]
   8. Step-by-step derivation

      1. *-commutative 62.7%

         \[\leadsto -4.5 \cdot \color{blue}{\left(z \cdot \frac{t}{a}\right)} \]

      2. clear-num 62.6%

         \[\leadsto -4.5 \cdot \left(z \cdot \color{blue}{\frac{1}{\frac{a}{t}}}\right) \]

      3. un-div-inv 63.8%

         \[\leadsto -4.5 \cdot \color{blue}{\frac{z}{\frac{a}{t}}} \]

   9. Applied egg-rr 63.8%

      \[\leadsto -4.5 \cdot \color{blue}{\frac{z}{\frac{a}{t}}} \]

   if -5.59999999999999996e-75 < t < 3.9000000000000002e86

   1. Initial program 90.9%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Step-by-step derivation

      1. associate-*l* 91.7%

         \[\leadsto \frac{x \cdot y - \color{blue}{z \cdot \left(9 \cdot t\right)}}{a \cdot 2} \]

   3. Simplified 91.7%

      \[\leadsto \color{blue}{\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 65.3%

      \[\leadsto \color{blue}{0.5 \cdot \frac{x \cdot y}{a}} \]
   6. Step-by-step derivation

      1. associate-*r/ 67.0%

         \[\leadsto 0.5 \cdot \color{blue}{\left(x \cdot \frac{y}{a}\right)} \]

   7. Simplified 67.0%

      \[\leadsto \color{blue}{0.5 \cdot \left(x \cdot \frac{y}{a}\right)} \]

   if 3.9000000000000002e86 < t < 2.00000000000000007e170

   1. Initial program 87.2%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Step-by-step derivation

      1. associate-*l* 87.2%

         \[\leadsto \frac{x \cdot y - \color{blue}{z \cdot \left(9 \cdot t\right)}}{a \cdot 2} \]

   3. Simplified 87.2%

      \[\leadsto \color{blue}{\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 73.9%

      \[\leadsto \color{blue}{-4.5 \cdot \frac{t \cdot z}{a}} \]

   if 2.00000000000000007e170 < t < 8.10000000000000019e192

   1. Initial program 68.6%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Step-by-step derivation

      1. associate-*l* 68.6%

         \[\leadsto \frac{x \cdot y - \color{blue}{z \cdot \left(9 \cdot t\right)}}{a \cdot 2} \]

   3. Simplified 68.6%

      \[\leadsto \color{blue}{\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 35.6%

      \[\leadsto \color{blue}{0.5 \cdot \frac{x \cdot y}{a}} \]
   6. Step-by-step derivation

      1. associate-/l* 67.0%

         \[\leadsto 0.5 \cdot \color{blue}{\frac{x}{\frac{a}{y}}} \]

   7. Simplified 67.0%

      \[\leadsto \color{blue}{0.5 \cdot \frac{x}{\frac{a}{y}}} \]
   8. Step-by-step derivation

      1. associate-/r/ 67.0%

         \[\leadsto 0.5 \cdot \color{blue}{\left(\frac{x}{a} \cdot y\right)} \]

   9. Applied egg-rr 67.0%

      \[\leadsto 0.5 \cdot \color{blue}{\left(\frac{x}{a} \cdot y\right)} \]

   if 8.10000000000000019e192 < t

   1. Initial program 77.5%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Step-by-step derivation

      1. associate-*l* 77.6%

         \[\leadsto \frac{x \cdot y - \color{blue}{z \cdot \left(9 \cdot t\right)}}{a \cdot 2} \]

   3. Simplified 77.6%

      \[\leadsto \color{blue}{\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 69.5%

      \[\leadsto \color{blue}{-4.5 \cdot \frac{t \cdot z}{a}} \]
   6. Step-by-step derivation

      1. associate-/l* 81.8%

         \[\leadsto -4.5 \cdot \color{blue}{\frac{t}{\frac{a}{z}}} \]

      2. associate-/r/ 87.2%

         \[\leadsto -4.5 \cdot \color{blue}{\left(\frac{t}{a} \cdot z\right)} \]

   7. Simplified 87.2%

      \[\leadsto \color{blue}{-4.5 \cdot \left(\frac{t}{a} \cdot z\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 68.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.6 \cdot 10^{-75}:\\ \;\;\;\;-4.5 \cdot \frac{z}{\frac{a}{t}}\\ \mathbf{elif}\;t \leq 3.9 \cdot 10^{+86}:\\ \;\;\;\;0.5 \cdot \left(x \cdot \frac{y}{a}\right)\\ \mathbf{elif}\;t \leq 2 \cdot 10^{+170}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \mathbf{elif}\;t \leq 8.1 \cdot 10^{+192}:\\ \;\;\;\;0.5 \cdot \left(y \cdot \frac{x}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \left(z \cdot \frac{t}{a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 94.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{+306} \lor \neg \left(x \cdot y \leq 10^{+276}\right):\\ \;\;\;\;0.5 \cdot \left(y \cdot \frac{x}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= (* x y) -5e+306) (not (<= (* x y) 1e+276)))
   (* 0.5 (* y (/ x a)))
   (/ (- (* x y) (* z (* 9.0 t))) (* a 2.0))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((x * y) <= -5e+306) || !((x * y) <= 1e+276)) {
		tmp = 0.5 * (y * (x / a));
	} else {
		tmp = ((x * y) - (z * (9.0 * t))) / (a * 2.0);
	}
	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 (((x * y) <= (-5d+306)) .or. (.not. ((x * y) <= 1d+276))) then
        tmp = 0.5d0 * (y * (x / a))
    else
        tmp = ((x * y) - (z * (9.0d0 * t))) / (a * 2.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((x * y) <= -5e+306) || !((x * y) <= 1e+276)) {
		tmp = 0.5 * (y * (x / a));
	} else {
		tmp = ((x * y) - (z * (9.0 * t))) / (a * 2.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if ((x * y) <= -5e+306) or not ((x * y) <= 1e+276):
		tmp = 0.5 * (y * (x / a))
	else:
		tmp = ((x * y) - (z * (9.0 * t))) / (a * 2.0)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((Float64(x * y) <= -5e+306) || !(Float64(x * y) <= 1e+276))
		tmp = Float64(0.5 * Float64(y * Float64(x / a)));
	else
		tmp = Float64(Float64(Float64(x * y) - Float64(z * Float64(9.0 * t))) / Float64(a * 2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (((x * y) <= -5e+306) || ~(((x * y) <= 1e+276)))
		tmp = 0.5 * (y * (x / a));
	else
		tmp = ((x * y) - (z * (9.0 * t))) / (a * 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[N[(x * y), $MachinePrecision], -5e+306], N[Not[LessEqual[N[(x * y), $MachinePrecision], 1e+276]], $MachinePrecision]], N[(0.5 * N[(y * N[(x / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x * y), $MachinePrecision] - N[(z * N[(9.0 * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -4.99999999999999993e306 or 1.0000000000000001e276 < (*.f64 x y)

   1. Initial program 54.4%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Step-by-step derivation

      1. associate-*l* 54.4%

         \[\leadsto \frac{x \cdot y - \color{blue}{z \cdot \left(9 \cdot t\right)}}{a \cdot 2} \]

   3. Simplified 54.4%

      \[\leadsto \color{blue}{\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 54.4%

      \[\leadsto \color{blue}{0.5 \cdot \frac{x \cdot y}{a}} \]
   6. Step-by-step derivation

      1. associate-/l* 92.3%

         \[\leadsto 0.5 \cdot \color{blue}{\frac{x}{\frac{a}{y}}} \]

   7. Simplified 92.3%

      \[\leadsto \color{blue}{0.5 \cdot \frac{x}{\frac{a}{y}}} \]
   8. Step-by-step derivation

      1. associate-/r/ 92.4%

         \[\leadsto 0.5 \cdot \color{blue}{\left(\frac{x}{a} \cdot y\right)} \]

   9. Applied egg-rr 92.4%

      \[\leadsto 0.5 \cdot \color{blue}{\left(\frac{x}{a} \cdot y\right)} \]

   if -4.99999999999999993e306 < (*.f64 x y) < 1.0000000000000001e276

   1. Initial program 92.8%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Step-by-step derivation

      1. associate-*l* 93.2%

         \[\leadsto \frac{x \cdot y - \color{blue}{z \cdot \left(9 \cdot t\right)}}{a \cdot 2} \]

   3. Simplified 93.2%

      \[\leadsto \color{blue}{\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}} \]
   4. Add Preprocessing
3. Recombined 2 regimes into one program.

4. Final simplification 93.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{+306} \lor \neg \left(x \cdot y \leq 10^{+276}\right):\\ \;\;\;\;0.5 \cdot \left(y \cdot \frac{x}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 65.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6.2 \cdot 10^{-75}:\\ \;\;\;\;-4.5 \cdot \frac{z}{\frac{a}{t}}\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{+87}:\\ \;\;\;\;0.5 \cdot \left(x \cdot \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \left(z \cdot \frac{t}{a}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -6.2e-75)
   (* -4.5 (/ z (/ a t)))
   (if (<= t 1.3e+87) (* 0.5 (* x (/ y a))) (* -4.5 (* z (/ t a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -6.2e-75) {
		tmp = -4.5 * (z / (a / t));
	} else if (t <= 1.3e+87) {
		tmp = 0.5 * (x * (y / a));
	} else {
		tmp = -4.5 * (z * (t / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-6.2d-75)) then
        tmp = (-4.5d0) * (z / (a / t))
    else if (t <= 1.3d+87) then
        tmp = 0.5d0 * (x * (y / a))
    else
        tmp = (-4.5d0) * (z * (t / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -6.2e-75) {
		tmp = -4.5 * (z / (a / t));
	} else if (t <= 1.3e+87) {
		tmp = 0.5 * (x * (y / a));
	} else {
		tmp = -4.5 * (z * (t / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -6.2e-75:
		tmp = -4.5 * (z / (a / t))
	elif t <= 1.3e+87:
		tmp = 0.5 * (x * (y / a))
	else:
		tmp = -4.5 * (z * (t / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -6.2e-75)
		tmp = Float64(-4.5 * Float64(z / Float64(a / t)));
	elseif (t <= 1.3e+87)
		tmp = Float64(0.5 * Float64(x * Float64(y / a)));
	else
		tmp = Float64(-4.5 * Float64(z * Float64(t / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -6.2e-75)
		tmp = -4.5 * (z / (a / t));
	elseif (t <= 1.3e+87)
		tmp = 0.5 * (x * (y / a));
	else
		tmp = -4.5 * (z * (t / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -6.2e-75], N[(-4.5 * N[(z / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.3e+87], N[(0.5 * N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-4.5 * N[(z * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -6.20000000000000013e-75

   1. Initial program 82.0%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Step-by-step derivation

      1. associate-*l* 82.0%

         \[\leadsto \frac{x \cdot y - \color{blue}{z \cdot \left(9 \cdot t\right)}}{a \cdot 2} \]

   3. Simplified 82.0%

      \[\leadsto \color{blue}{\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 56.4%

      \[\leadsto \color{blue}{-4.5 \cdot \frac{t \cdot z}{a}} \]
   6. Step-by-step derivation

      1. associate-/l* 62.0%

         \[\leadsto -4.5 \cdot \color{blue}{\frac{t}{\frac{a}{z}}} \]

      2. associate-/r/ 62.7%

         \[\leadsto -4.5 \cdot \color{blue}{\left(\frac{t}{a} \cdot z\right)} \]

   7. Simplified 62.7%

      \[\leadsto \color{blue}{-4.5 \cdot \left(\frac{t}{a} \cdot z\right)} \]
   8. Step-by-step derivation

      1. *-commutative 62.7%

         \[\leadsto -4.5 \cdot \color{blue}{\left(z \cdot \frac{t}{a}\right)} \]

      2. clear-num 62.6%

         \[\leadsto -4.5 \cdot \left(z \cdot \color{blue}{\frac{1}{\frac{a}{t}}}\right) \]

      3. un-div-inv 63.8%

         \[\leadsto -4.5 \cdot \color{blue}{\frac{z}{\frac{a}{t}}} \]

   9. Applied egg-rr 63.8%

      \[\leadsto -4.5 \cdot \color{blue}{\frac{z}{\frac{a}{t}}} \]

   if -6.20000000000000013e-75 < t < 1.29999999999999999e87

   1. Initial program 90.9%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Step-by-step derivation

      1. associate-*l* 91.7%

         \[\leadsto \frac{x \cdot y - \color{blue}{z \cdot \left(9 \cdot t\right)}}{a \cdot 2} \]

   3. Simplified 91.7%

      \[\leadsto \color{blue}{\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 65.3%

      \[\leadsto \color{blue}{0.5 \cdot \frac{x \cdot y}{a}} \]
   6. Step-by-step derivation

      1. associate-*r/ 67.0%

         \[\leadsto 0.5 \cdot \color{blue}{\left(x \cdot \frac{y}{a}\right)} \]

   7. Simplified 67.0%

      \[\leadsto \color{blue}{0.5 \cdot \left(x \cdot \frac{y}{a}\right)} \]

   if 1.29999999999999999e87 < t

   1. Initial program 80.6%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Step-by-step derivation

      1. associate-*l* 80.6%

         \[\leadsto \frac{x \cdot y - \color{blue}{z \cdot \left(9 \cdot t\right)}}{a \cdot 2} \]

   3. Simplified 80.6%

      \[\leadsto \color{blue}{\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 68.6%

      \[\leadsto \color{blue}{-4.5 \cdot \frac{t \cdot z}{a}} \]
   6. Step-by-step derivation

      1. associate-/l* 72.7%

         \[\leadsto -4.5 \cdot \color{blue}{\frac{t}{\frac{a}{z}}} \]

      2. associate-/r/ 80.6%

         \[\leadsto -4.5 \cdot \color{blue}{\left(\frac{t}{a} \cdot z\right)} \]

   7. Simplified 80.6%

      \[\leadsto \color{blue}{-4.5 \cdot \left(\frac{t}{a} \cdot z\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 68.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.2 \cdot 10^{-75}:\\ \;\;\;\;-4.5 \cdot \frac{z}{\frac{a}{t}}\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{+87}:\\ \;\;\;\;0.5 \cdot \left(x \cdot \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \left(z \cdot \frac{t}{a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 51.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ -4.5 \cdot \left(z \cdot \frac{t}{a}\right) \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (* -4.5 (* z (/ t a))))

C

double code(double x, double y, double z, double t, double a) {
	return -4.5 * (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 = (-4.5d0) * (z * (t / a))
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return -4.5 * (z * (t / a));
}

Python

def code(x, y, z, t, a):
	return -4.5 * (z * (t / a))

Julia

function code(x, y, z, t, a)
	return Float64(-4.5 * Float64(z * Float64(t / a)))
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = -4.5 * (z * (t / a));
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(-4.5 * N[(z * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 86.8%

   \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
2. Step-by-step derivation

   1. associate-*l* 87.2%

      \[\leadsto \frac{x \cdot y - \color{blue}{z \cdot \left(9 \cdot t\right)}}{a \cdot 2} \]

3. Simplified 87.2%

   \[\leadsto \color{blue}{\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}} \]
4. Add Preprocessing

5. Taylor expanded in x around 0 48.0%

   \[\leadsto \color{blue}{-4.5 \cdot \frac{t \cdot z}{a}} \]
6. Step-by-step derivation

   1. associate-/l* 49.9%

      \[\leadsto -4.5 \cdot \color{blue}{\frac{t}{\frac{a}{z}}} \]

   2. associate-/r/ 51.8%

      \[\leadsto -4.5 \cdot \color{blue}{\left(\frac{t}{a} \cdot z\right)} \]

7. Simplified 51.8%

   \[\leadsto \color{blue}{-4.5 \cdot \left(\frac{t}{a} \cdot z\right)} \]

8. Final simplification 51.8%

   \[\leadsto -4.5 \cdot \left(z \cdot \frac{t}{a}\right) \]
9. Add Preprocessing

Developer target: 93.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a < -2.090464557976709 \cdot 10^{+86}:\\ \;\;\;\;0.5 \cdot \frac{y \cdot x}{a} - 4.5 \cdot \frac{t}{\frac{a}{z}}\\ \mathbf{elif}\;a < 2.144030707833976 \cdot 10^{+99}:\\ \;\;\;\;\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot \left(x \cdot 0.5\right) - \frac{t}{a} \cdot \left(z \cdot 4.5\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (< a -2.090464557976709e+86)
   (- (* 0.5 (/ (* y x) a)) (* 4.5 (/ t (/ a z))))
   (if (< a 2.144030707833976e+99)
     (/ (- (* x y) (* z (* 9.0 t))) (* a 2.0))
     (- (* (/ y a) (* x 0.5)) (* (/ t a) (* z 4.5))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a < -2.090464557976709e+86) {
		tmp = (0.5 * ((y * x) / a)) - (4.5 * (t / (a / z)));
	} else if (a < 2.144030707833976e+99) {
		tmp = ((x * y) - (z * (9.0 * t))) / (a * 2.0);
	} else {
		tmp = ((y / a) * (x * 0.5)) - ((t / a) * (z * 4.5));
	}
	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 (a < (-2.090464557976709d+86)) then
        tmp = (0.5d0 * ((y * x) / a)) - (4.5d0 * (t / (a / z)))
    else if (a < 2.144030707833976d+99) then
        tmp = ((x * y) - (z * (9.0d0 * t))) / (a * 2.0d0)
    else
        tmp = ((y / a) * (x * 0.5d0)) - ((t / a) * (z * 4.5d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a < -2.090464557976709e+86) {
		tmp = (0.5 * ((y * x) / a)) - (4.5 * (t / (a / z)));
	} else if (a < 2.144030707833976e+99) {
		tmp = ((x * y) - (z * (9.0 * t))) / (a * 2.0);
	} else {
		tmp = ((y / a) * (x * 0.5)) - ((t / a) * (z * 4.5));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a < -2.090464557976709e+86:
		tmp = (0.5 * ((y * x) / a)) - (4.5 * (t / (a / z)))
	elif a < 2.144030707833976e+99:
		tmp = ((x * y) - (z * (9.0 * t))) / (a * 2.0)
	else:
		tmp = ((y / a) * (x * 0.5)) - ((t / a) * (z * 4.5))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a < -2.090464557976709e+86)
		tmp = Float64(Float64(0.5 * Float64(Float64(y * x) / a)) - Float64(4.5 * Float64(t / Float64(a / z))));
	elseif (a < 2.144030707833976e+99)
		tmp = Float64(Float64(Float64(x * y) - Float64(z * Float64(9.0 * t))) / Float64(a * 2.0));
	else
		tmp = Float64(Float64(Float64(y / a) * Float64(x * 0.5)) - Float64(Float64(t / a) * Float64(z * 4.5)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a < -2.090464557976709e+86)
		tmp = (0.5 * ((y * x) / a)) - (4.5 * (t / (a / z)));
	elseif (a < 2.144030707833976e+99)
		tmp = ((x * y) - (z * (9.0 * t))) / (a * 2.0);
	else
		tmp = ((y / a) * (x * 0.5)) - ((t / a) * (z * 4.5));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Less[a, -2.090464557976709e+86], N[(N[(0.5 * N[(N[(y * x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] - N[(4.5 * N[(t / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Less[a, 2.144030707833976e+99], N[(N[(N[(x * y), $MachinePrecision] - N[(z * N[(9.0 * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(N[(y / a), $MachinePrecision] * N[(x * 0.5), $MachinePrecision]), $MachinePrecision] - N[(N[(t / a), $MachinePrecision] * N[(z * 4.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Reproduce

herbie shell --seed 2024018 
(FPCore (x y z t a)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, I"
  :precision binary64

  :herbie-target
  (if (< a -2.090464557976709e+86) (- (* 0.5 (/ (* y x) a)) (* 4.5 (/ t (/ a z)))) (if (< a 2.144030707833976e+99) (/ (- (* x y) (* z (* 9.0 t))) (* a 2.0)) (- (* (/ y a) (* x 0.5)) (* (/ t a) (* z 4.5)))))

  (/ (- (* x y) (* (* z 9.0) t)) (* a 2.0)))