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

Percentage Accurate: 79.0% → 91.8%

Time: 14.9s

Alternatives: 14

Speedup: 0.8×

• 37.0% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	return ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c);
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    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), intent (in) :: b
    real(8), intent (in) :: c
    code = ((((x * 9.0d0) * y) - (((z * 4.0d0) * t) * a)) + b) / (z * c)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	return ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c);
}

Python

def code(x, y, z, t, a, b, c):
	return ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c)

Julia

function code(x, y, z, t, a, b, c)
	return Float64(Float64(Float64(Float64(Float64(x * 9.0) * y) - Float64(Float64(Float64(z * 4.0) * t) * a)) + b) / Float64(z * c))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c)
	tmp = ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c);
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := N[(N[(N[(N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision] - N[(N[(N[(z * 4.0), $MachinePrecision] * t), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]

Initial Program: 79.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	return ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c);
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    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), intent (in) :: b
    real(8), intent (in) :: c
    code = ((((x * 9.0d0) * y) - (((z * 4.0d0) * t) * a)) + b) / (z * c)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	return ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c);
}

Python

def code(x, y, z, t, a, b, c):
	return ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c)

Julia

function code(x, y, z, t, a, b, c)
	return Float64(Float64(Float64(Float64(Float64(x * 9.0) * y) - Float64(Float64(Float64(z * 4.0) * t) * a)) + b) / Float64(z * c))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c)
	tmp = ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c);
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := N[(N[(N[(N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision] - N[(N[(N[(z * 4.0), $MachinePrecision] * t), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]

Alternative 1: 91.8% accurate, 0.2× speedup

Math

\[\begin{array}{l} [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} t_1 := \frac{a}{\frac{c}{t}}\\ t_2 := \frac{\frac{b}{z}}{c}\\ \mathbf{if}\;z \leq -1.85 \cdot 10^{+101}:\\ \;\;\;\;t_2 + \mathsf{fma}\left(-4, t_1, 9 \cdot \frac{\frac{y}{\frac{z}{x}}}{c}\right)\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{+38}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(9 \cdot x\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;t_2 + \mathsf{fma}\left(-4, t_1, \frac{\frac{9}{\frac{\frac{z}{x}}{y}}}{c}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ a (/ c t))) (t_2 (/ (/ b z) c)))
   (if (<= z -1.85e+101)
     (+ t_2 (fma -4.0 t_1 (* 9.0 (/ (/ y (/ z x)) c))))
     (if (<= z 1.45e+38)
       (/ (+ b (- (* y (* 9.0 x)) (* a (* t (* z 4.0))))) (* z c))
       (+ t_2 (fma -4.0 t_1 (/ (/ 9.0 (/ (/ z x) y)) c)))))))

C

assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = a / (c / t);
	double t_2 = (b / z) / c;
	double tmp;
	if (z <= -1.85e+101) {
		tmp = t_2 + fma(-4.0, t_1, (9.0 * ((y / (z / x)) / c)));
	} else if (z <= 1.45e+38) {
		tmp = (b + ((y * (9.0 * x)) - (a * (t * (z * 4.0))))) / (z * c);
	} else {
		tmp = t_2 + fma(-4.0, t_1, ((9.0 / ((z / x) / y)) / c));
	}
	return tmp;
}

Julia

t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(a / Float64(c / t))
	t_2 = Float64(Float64(b / z) / c)
	tmp = 0.0
	if (z <= -1.85e+101)
		tmp = Float64(t_2 + fma(-4.0, t_1, Float64(9.0 * Float64(Float64(y / Float64(z / x)) / c))));
	elseif (z <= 1.45e+38)
		tmp = Float64(Float64(b + Float64(Float64(y * Float64(9.0 * x)) - Float64(a * Float64(t * Float64(z * 4.0))))) / Float64(z * c));
	else
		tmp = Float64(t_2 + fma(-4.0, t_1, Float64(Float64(9.0 / Float64(Float64(z / x) / y)) / c)));
	end
	return tmp
end

Wolfram

NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(a / N[(c / t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b / z), $MachinePrecision] / c), $MachinePrecision]}, If[LessEqual[z, -1.85e+101], N[(t$95$2 + N[(-4.0 * t$95$1 + N[(9.0 * N[(N[(y / N[(z / x), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.45e+38], N[(N[(b + N[(N[(y * N[(9.0 * x), $MachinePrecision]), $MachinePrecision] - N[(a * N[(t * N[(z * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(t$95$2 + N[(-4.0 * t$95$1 + N[(N[(9.0 / N[(N[(z / x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.8499999999999999e101

   1. Initial program 58.2%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-/r* 71.3%

         \[\leadsto \color{blue}{\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}}{c}} \]

   3. Simplified 88.4%

      \[\leadsto \color{blue}{\frac{\frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z} + t \cdot \left(a \cdot -4\right)}{c}} \]
   4. Step-by-step derivation

      1. fma-udef 88.4%

         \[\leadsto \frac{\frac{\color{blue}{x \cdot \left(9 \cdot y\right) + b}}{z} + t \cdot \left(a \cdot -4\right)}{c} \]

   5. Applied egg-rr 88.4%

      \[\leadsto \frac{\frac{\color{blue}{x \cdot \left(9 \cdot y\right) + b}}{z} + t \cdot \left(a \cdot -4\right)}{c} \]
   6. Step-by-step derivation

      1. clear-num 88.4%

         \[\leadsto \frac{\color{blue}{\frac{1}{\frac{z}{x \cdot \left(9 \cdot y\right) + b}}} + t \cdot \left(a \cdot -4\right)}{c} \]

      2. inv-pow 88.4%

         \[\leadsto \frac{\color{blue}{{\left(\frac{z}{x \cdot \left(9 \cdot y\right) + b}\right)}^{-1}} + t \cdot \left(a \cdot -4\right)}{c} \]

      3. associate-*r* 88.4%

         \[\leadsto \frac{{\left(\frac{z}{\color{blue}{\left(x \cdot 9\right) \cdot y} + b}\right)}^{-1} + t \cdot \left(a \cdot -4\right)}{c} \]

      4. fma-def 88.4%

         \[\leadsto \frac{{\left(\frac{z}{\color{blue}{\mathsf{fma}\left(x \cdot 9, y, b\right)}}\right)}^{-1} + t \cdot \left(a \cdot -4\right)}{c} \]

   7. Applied egg-rr 88.4%

      \[\leadsto \frac{\color{blue}{{\left(\frac{z}{\mathsf{fma}\left(x \cdot 9, y, b\right)}\right)}^{-1}} + t \cdot \left(a \cdot -4\right)}{c} \]

   8. Taylor expanded in z around 0 77.2%

      \[\leadsto \color{blue}{\frac{b}{c \cdot z} + \left(-4 \cdot \frac{a \cdot t}{c} + 9 \cdot \frac{y \cdot x}{c \cdot z}\right)} \]
   9. Step-by-step derivation

      1. associate-/l/ 79.1%

         \[\leadsto \color{blue}{\frac{\frac{b}{z}}{c}} + \left(-4 \cdot \frac{a \cdot t}{c} + 9 \cdot \frac{y \cdot x}{c \cdot z}\right) \]

      2. fma-def 79.1%

         \[\leadsto \frac{\frac{b}{z}}{c} + \color{blue}{\mathsf{fma}\left(-4, \frac{a \cdot t}{c}, 9 \cdot \frac{y \cdot x}{c \cdot z}\right)} \]

      3. associate-/l* 73.5%

         \[\leadsto \frac{\frac{b}{z}}{c} + \mathsf{fma}\left(-4, \color{blue}{\frac{a}{\frac{c}{t}}}, 9 \cdot \frac{y \cdot x}{c \cdot z}\right) \]

      4. *-commutative 73.5%

         \[\leadsto \frac{\frac{b}{z}}{c} + \mathsf{fma}\left(-4, \frac{a}{\frac{c}{t}}, 9 \cdot \frac{y \cdot x}{\color{blue}{z \cdot c}}\right) \]

      5. times-frac 86.0%

         \[\leadsto \frac{\frac{b}{z}}{c} + \mathsf{fma}\left(-4, \frac{a}{\frac{c}{t}}, 9 \cdot \color{blue}{\left(\frac{y}{z} \cdot \frac{x}{c}\right)}\right) \]

      6. associate-*r/ 86.4%

         \[\leadsto \frac{\frac{b}{z}}{c} + \mathsf{fma}\left(-4, \frac{a}{\frac{c}{t}}, 9 \cdot \color{blue}{\frac{\frac{y}{z} \cdot x}{c}}\right) \]

      7. associate-*l/ 78.8%

         \[\leadsto \frac{\frac{b}{z}}{c} + \mathsf{fma}\left(-4, \frac{a}{\frac{c}{t}}, 9 \cdot \frac{\color{blue}{\frac{y \cdot x}{z}}}{c}\right) \]

      8. associate-/l* 86.9%

         \[\leadsto \frac{\frac{b}{z}}{c} + \mathsf{fma}\left(-4, \frac{a}{\frac{c}{t}}, 9 \cdot \frac{\color{blue}{\frac{y}{\frac{z}{x}}}}{c}\right) \]

   10. Simplified 86.9%

       \[\leadsto \color{blue}{\frac{\frac{b}{z}}{c} + \mathsf{fma}\left(-4, \frac{a}{\frac{c}{t}}, 9 \cdot \frac{\frac{y}{\frac{z}{x}}}{c}\right)} \]

   if -1.8499999999999999e101 < z < 1.45000000000000003e38

   1. Initial program 92.5%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

   if 1.45000000000000003e38 < z

   1. Initial program 45.3%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-/r* 55.6%

         \[\leadsto \color{blue}{\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}}{c}} \]

   3. Simplified 80.9%

      \[\leadsto \color{blue}{\frac{\frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z} + t \cdot \left(a \cdot -4\right)}{c}} \]
   4. Step-by-step derivation

      1. fma-udef 80.9%

         \[\leadsto \frac{\frac{\color{blue}{x \cdot \left(9 \cdot y\right) + b}}{z} + t \cdot \left(a \cdot -4\right)}{c} \]

   5. Applied egg-rr 80.9%

      \[\leadsto \frac{\frac{\color{blue}{x \cdot \left(9 \cdot y\right) + b}}{z} + t \cdot \left(a \cdot -4\right)}{c} \]
   6. Step-by-step derivation

      1. clear-num 80.7%

         \[\leadsto \frac{\color{blue}{\frac{1}{\frac{z}{x \cdot \left(9 \cdot y\right) + b}}} + t \cdot \left(a \cdot -4\right)}{c} \]

      2. inv-pow 80.7%

         \[\leadsto \frac{\color{blue}{{\left(\frac{z}{x \cdot \left(9 \cdot y\right) + b}\right)}^{-1}} + t \cdot \left(a \cdot -4\right)}{c} \]

      3. associate-*r* 80.7%

         \[\leadsto \frac{{\left(\frac{z}{\color{blue}{\left(x \cdot 9\right) \cdot y} + b}\right)}^{-1} + t \cdot \left(a \cdot -4\right)}{c} \]

      4. fma-def 80.7%

         \[\leadsto \frac{{\left(\frac{z}{\color{blue}{\mathsf{fma}\left(x \cdot 9, y, b\right)}}\right)}^{-1} + t \cdot \left(a \cdot -4\right)}{c} \]

   7. Applied egg-rr 80.7%

      \[\leadsto \frac{\color{blue}{{\left(\frac{z}{\mathsf{fma}\left(x \cdot 9, y, b\right)}\right)}^{-1}} + t \cdot \left(a \cdot -4\right)}{c} \]

   8. Taylor expanded in z around 0 76.8%

      \[\leadsto \color{blue}{\frac{b}{c \cdot z} + \left(-4 \cdot \frac{a \cdot t}{c} + 9 \cdot \frac{y \cdot x}{c \cdot z}\right)} \]
   9. Step-by-step derivation

      1. associate-/l/ 78.7%

         \[\leadsto \color{blue}{\frac{\frac{b}{z}}{c}} + \left(-4 \cdot \frac{a \cdot t}{c} + 9 \cdot \frac{y \cdot x}{c \cdot z}\right) \]

      2. fma-def 78.7%

         \[\leadsto \frac{\frac{b}{z}}{c} + \color{blue}{\mathsf{fma}\left(-4, \frac{a \cdot t}{c}, 9 \cdot \frac{y \cdot x}{c \cdot z}\right)} \]

      3. associate-/l* 84.3%

         \[\leadsto \frac{\frac{b}{z}}{c} + \mathsf{fma}\left(-4, \color{blue}{\frac{a}{\frac{c}{t}}}, 9 \cdot \frac{y \cdot x}{c \cdot z}\right) \]

      4. *-commutative 84.3%

         \[\leadsto \frac{\frac{b}{z}}{c} + \mathsf{fma}\left(-4, \frac{a}{\frac{c}{t}}, 9 \cdot \frac{y \cdot x}{\color{blue}{z \cdot c}}\right) \]

      5. times-frac 90.5%

         \[\leadsto \frac{\frac{b}{z}}{c} + \mathsf{fma}\left(-4, \frac{a}{\frac{c}{t}}, 9 \cdot \color{blue}{\left(\frac{y}{z} \cdot \frac{x}{c}\right)}\right) \]

      6. associate-*r/ 94.7%

         \[\leadsto \frac{\frac{b}{z}}{c} + \mathsf{fma}\left(-4, \frac{a}{\frac{c}{t}}, 9 \cdot \color{blue}{\frac{\frac{y}{z} \cdot x}{c}}\right) \]

      7. associate-*l/ 86.5%

         \[\leadsto \frac{\frac{b}{z}}{c} + \mathsf{fma}\left(-4, \frac{a}{\frac{c}{t}}, 9 \cdot \frac{\color{blue}{\frac{y \cdot x}{z}}}{c}\right) \]

      8. associate-/l* 95.9%

         \[\leadsto \frac{\frac{b}{z}}{c} + \mathsf{fma}\left(-4, \frac{a}{\frac{c}{t}}, 9 \cdot \frac{\color{blue}{\frac{y}{\frac{z}{x}}}}{c}\right) \]

   10. Simplified 95.9%

       \[\leadsto \color{blue}{\frac{\frac{b}{z}}{c} + \mathsf{fma}\left(-4, \frac{a}{\frac{c}{t}}, 9 \cdot \frac{\frac{y}{\frac{z}{x}}}{c}\right)} \]
   11. Step-by-step derivation

       1. associate-*r/ 95.8%

          \[\leadsto \frac{\frac{b}{z}}{c} + \mathsf{fma}\left(-4, \frac{a}{\frac{c}{t}}, \color{blue}{\frac{9 \cdot \frac{y}{\frac{z}{x}}}{c}}\right) \]

       2. clear-num 95.8%

          \[\leadsto \frac{\frac{b}{z}}{c} + \mathsf{fma}\left(-4, \frac{a}{\frac{c}{t}}, \frac{9 \cdot \color{blue}{\frac{1}{\frac{\frac{z}{x}}{y}}}}{c}\right) \]

       3. un-div-inv 95.9%

          \[\leadsto \frac{\frac{b}{z}}{c} + \mathsf{fma}\left(-4, \frac{a}{\frac{c}{t}}, \frac{\color{blue}{\frac{9}{\frac{\frac{z}{x}}{y}}}}{c}\right) \]

   12. Applied egg-rr 95.9%

       \[\leadsto \frac{\frac{b}{z}}{c} + \mathsf{fma}\left(-4, \frac{a}{\frac{c}{t}}, \color{blue}{\frac{\frac{9}{\frac{\frac{z}{x}}{y}}}{c}}\right) \]
3. Recombined 3 regimes into one program.

4. Final simplification 92.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.85 \cdot 10^{+101}:\\ \;\;\;\;\frac{\frac{b}{z}}{c} + \mathsf{fma}\left(-4, \frac{a}{\frac{c}{t}}, 9 \cdot \frac{\frac{y}{\frac{z}{x}}}{c}\right)\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{+38}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(9 \cdot x\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{z}}{c} + \mathsf{fma}\left(-4, \frac{a}{\frac{c}{t}}, \frac{\frac{9}{\frac{\frac{z}{x}}{y}}}{c}\right)\\ \end{array} \]

Alternative 2: 91.8% accurate, 0.2× speedup

Math

\[\begin{array}{l} [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -2.65 \cdot 10^{+101} \lor \neg \left(z \leq 1.56 \cdot 10^{+38}\right):\\ \;\;\;\;\frac{\frac{b}{z}}{c} + \mathsf{fma}\left(-4, \frac{a}{\frac{c}{t}}, 9 \cdot \frac{\frac{y}{\frac{z}{x}}}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(9 \cdot x\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c}\\ \end{array} \end{array} \]

FPCore

NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= z -2.65e+101) (not (<= z 1.56e+38)))
   (+ (/ (/ b z) c) (fma -4.0 (/ a (/ c t)) (* 9.0 (/ (/ y (/ z x)) c))))
   (/ (+ b (- (* y (* 9.0 x)) (* a (* t (* z 4.0))))) (* z c))))

C

assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((z <= -2.65e+101) || !(z <= 1.56e+38)) {
		tmp = ((b / z) / c) + fma(-4.0, (a / (c / t)), (9.0 * ((y / (z / x)) / c)));
	} else {
		tmp = (b + ((y * (9.0 * x)) - (a * (t * (z * 4.0))))) / (z * c);
	}
	return tmp;
}

Julia

t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((z <= -2.65e+101) || !(z <= 1.56e+38))
		tmp = Float64(Float64(Float64(b / z) / c) + fma(-4.0, Float64(a / Float64(c / t)), Float64(9.0 * Float64(Float64(y / Float64(z / x)) / c))));
	else
		tmp = Float64(Float64(b + Float64(Float64(y * Float64(9.0 * x)) - Float64(a * Float64(t * Float64(z * 4.0))))) / Float64(z * c));
	end
	return tmp
end

Wolfram

NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[z, -2.65e+101], N[Not[LessEqual[z, 1.56e+38]], $MachinePrecision]], N[(N[(N[(b / z), $MachinePrecision] / c), $MachinePrecision] + N[(-4.0 * N[(a / N[(c / t), $MachinePrecision]), $MachinePrecision] + N[(9.0 * N[(N[(y / N[(z / x), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b + N[(N[(y * N[(9.0 * x), $MachinePrecision]), $MachinePrecision] - N[(a * N[(t * N[(z * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.65000000000000003e101 or 1.5599999999999999e38 < z

   1. Initial program 51.7%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-/r* 63.5%

         \[\leadsto \color{blue}{\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}}{c}} \]

   3. Simplified 84.6%

      \[\leadsto \color{blue}{\frac{\frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z} + t \cdot \left(a \cdot -4\right)}{c}} \]
   4. Step-by-step derivation

      1. fma-udef 84.6%

         \[\leadsto \frac{\frac{\color{blue}{x \cdot \left(9 \cdot y\right) + b}}{z} + t \cdot \left(a \cdot -4\right)}{c} \]

   5. Applied egg-rr 84.6%

      \[\leadsto \frac{\frac{\color{blue}{x \cdot \left(9 \cdot y\right) + b}}{z} + t \cdot \left(a \cdot -4\right)}{c} \]
   6. Step-by-step derivation

      1. clear-num 84.6%

         \[\leadsto \frac{\color{blue}{\frac{1}{\frac{z}{x \cdot \left(9 \cdot y\right) + b}}} + t \cdot \left(a \cdot -4\right)}{c} \]

      2. inv-pow 84.6%

         \[\leadsto \frac{\color{blue}{{\left(\frac{z}{x \cdot \left(9 \cdot y\right) + b}\right)}^{-1}} + t \cdot \left(a \cdot -4\right)}{c} \]

      3. associate-*r* 84.6%

         \[\leadsto \frac{{\left(\frac{z}{\color{blue}{\left(x \cdot 9\right) \cdot y} + b}\right)}^{-1} + t \cdot \left(a \cdot -4\right)}{c} \]

      4. fma-def 84.6%

         \[\leadsto \frac{{\left(\frac{z}{\color{blue}{\mathsf{fma}\left(x \cdot 9, y, b\right)}}\right)}^{-1} + t \cdot \left(a \cdot -4\right)}{c} \]

   7. Applied egg-rr 84.6%

      \[\leadsto \frac{\color{blue}{{\left(\frac{z}{\mathsf{fma}\left(x \cdot 9, y, b\right)}\right)}^{-1}} + t \cdot \left(a \cdot -4\right)}{c} \]

   8. Taylor expanded in z around 0 77.0%

      \[\leadsto \color{blue}{\frac{b}{c \cdot z} + \left(-4 \cdot \frac{a \cdot t}{c} + 9 \cdot \frac{y \cdot x}{c \cdot z}\right)} \]
   9. Step-by-step derivation

      1. associate-/l/ 78.9%

         \[\leadsto \color{blue}{\frac{\frac{b}{z}}{c}} + \left(-4 \cdot \frac{a \cdot t}{c} + 9 \cdot \frac{y \cdot x}{c \cdot z}\right) \]

      2. fma-def 78.9%

         \[\leadsto \frac{\frac{b}{z}}{c} + \color{blue}{\mathsf{fma}\left(-4, \frac{a \cdot t}{c}, 9 \cdot \frac{y \cdot x}{c \cdot z}\right)} \]

      3. associate-/l* 78.9%

         \[\leadsto \frac{\frac{b}{z}}{c} + \mathsf{fma}\left(-4, \color{blue}{\frac{a}{\frac{c}{t}}}, 9 \cdot \frac{y \cdot x}{c \cdot z}\right) \]

      4. *-commutative 78.9%

         \[\leadsto \frac{\frac{b}{z}}{c} + \mathsf{fma}\left(-4, \frac{a}{\frac{c}{t}}, 9 \cdot \frac{y \cdot x}{\color{blue}{z \cdot c}}\right) \]

      5. times-frac 88.2%

         \[\leadsto \frac{\frac{b}{z}}{c} + \mathsf{fma}\left(-4, \frac{a}{\frac{c}{t}}, 9 \cdot \color{blue}{\left(\frac{y}{z} \cdot \frac{x}{c}\right)}\right) \]

      6. associate-*r/ 90.5%

         \[\leadsto \frac{\frac{b}{z}}{c} + \mathsf{fma}\left(-4, \frac{a}{\frac{c}{t}}, 9 \cdot \color{blue}{\frac{\frac{y}{z} \cdot x}{c}}\right) \]

      7. associate-*l/ 82.7%

         \[\leadsto \frac{\frac{b}{z}}{c} + \mathsf{fma}\left(-4, \frac{a}{\frac{c}{t}}, 9 \cdot \frac{\color{blue}{\frac{y \cdot x}{z}}}{c}\right) \]

      8. associate-/l* 91.4%

         \[\leadsto \frac{\frac{b}{z}}{c} + \mathsf{fma}\left(-4, \frac{a}{\frac{c}{t}}, 9 \cdot \frac{\color{blue}{\frac{y}{\frac{z}{x}}}}{c}\right) \]

   10. Simplified 91.4%

       \[\leadsto \color{blue}{\frac{\frac{b}{z}}{c} + \mathsf{fma}\left(-4, \frac{a}{\frac{c}{t}}, 9 \cdot \frac{\frac{y}{\frac{z}{x}}}{c}\right)} \]

   if -2.65000000000000003e101 < z < 1.5599999999999999e38

   1. Initial program 92.5%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
3. Recombined 2 regimes into one program.

4. Final simplification 92.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.65 \cdot 10^{+101} \lor \neg \left(z \leq 1.56 \cdot 10^{+38}\right):\\ \;\;\;\;\frac{\frac{b}{z}}{c} + \mathsf{fma}\left(-4, \frac{a}{\frac{c}{t}}, 9 \cdot \frac{\frac{y}{\frac{z}{x}}}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(9 \cdot x\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c}\\ \end{array} \]

Alternative 3: 87.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;y \cdot \left(9 \cdot x\right) \leq 5 \cdot 10^{+190}:\\ \;\;\;\;\frac{\frac{b + x \cdot \left(9 \cdot y\right)}{z} + t \cdot \left(-4 \cdot a\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;9 \cdot \frac{y}{z \cdot \frac{c}{x}}\\ \end{array} \end{array} \]

FPCore

NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= (* y (* 9.0 x)) 5e+190)
   (/ (+ (/ (+ b (* x (* 9.0 y))) z) (* t (* -4.0 a))) c)
   (* 9.0 (/ y (* z (/ c x))))))

C

assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((y * (9.0 * x)) <= 5e+190) {
		tmp = (((b + (x * (9.0 * y))) / z) + (t * (-4.0 * a))) / c;
	} else {
		tmp = 9.0 * (y / (z * (c / x)));
	}
	return tmp;
}

Fortran

NOTE: t and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    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), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if ((y * (9.0d0 * x)) <= 5d+190) then
        tmp = (((b + (x * (9.0d0 * y))) / z) + (t * ((-4.0d0) * a))) / c
    else
        tmp = 9.0d0 * (y / (z * (c / x)))
    end if
    code = tmp
end function

Java

assert t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((y * (9.0 * x)) <= 5e+190) {
		tmp = (((b + (x * (9.0 * y))) / z) + (t * (-4.0 * a))) / c;
	} else {
		tmp = 9.0 * (y / (z * (c / x)));
	}
	return tmp;
}

Python

[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if (y * (9.0 * x)) <= 5e+190:
		tmp = (((b + (x * (9.0 * y))) / z) + (t * (-4.0 * a))) / c
	else:
		tmp = 9.0 * (y / (z * (c / x)))
	return tmp

Julia

t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (Float64(y * Float64(9.0 * x)) <= 5e+190)
		tmp = Float64(Float64(Float64(Float64(b + Float64(x * Float64(9.0 * y))) / z) + Float64(t * Float64(-4.0 * a))) / c);
	else
		tmp = Float64(9.0 * Float64(y / Float64(z * Float64(c / x))));
	end
	return tmp
end

MATLAB

t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((y * (9.0 * x)) <= 5e+190)
		tmp = (((b + (x * (9.0 * y))) / z) + (t * (-4.0 * a))) / c;
	else
		tmp = 9.0 * (y / (z * (c / x)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[N[(y * N[(9.0 * x), $MachinePrecision]), $MachinePrecision], 5e+190], N[(N[(N[(N[(b + N[(x * N[(9.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] + N[(t * N[(-4.0 * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], N[(9.0 * N[(y / N[(z * N[(c / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 x 9) y) < 5.00000000000000036e190

   1. Initial program 77.3%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-/r* 80.8%

         \[\leadsto \color{blue}{\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}}{c}} \]

   3. Simplified 90.2%

      \[\leadsto \color{blue}{\frac{\frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z} + t \cdot \left(a \cdot -4\right)}{c}} \]
   4. Step-by-step derivation

      1. fma-udef 90.2%

         \[\leadsto \frac{\frac{\color{blue}{x \cdot \left(9 \cdot y\right) + b}}{z} + t \cdot \left(a \cdot -4\right)}{c} \]

   5. Applied egg-rr 90.2%

      \[\leadsto \frac{\frac{\color{blue}{x \cdot \left(9 \cdot y\right) + b}}{z} + t \cdot \left(a \cdot -4\right)}{c} \]

   if 5.00000000000000036e190 < (*.f64 (*.f64 x 9) y)

   1. Initial program 71.5%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-/r* 63.0%

         \[\leadsto \color{blue}{\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}}{c}} \]

   3. Simplified 63.4%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(t, a \cdot -4, \frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z}\right)}{c}} \]

   4. Taylor expanded in x around inf 68.7%

      \[\leadsto \color{blue}{9 \cdot \frac{y \cdot x}{c \cdot z}} \]
   5. Step-by-step derivation

      1. *-commutative 68.7%

         \[\leadsto 9 \cdot \frac{y \cdot x}{\color{blue}{z \cdot c}} \]

      2. times-frac 90.2%

         \[\leadsto 9 \cdot \color{blue}{\left(\frac{y}{z} \cdot \frac{x}{c}\right)} \]

   6. Simplified 90.2%

      \[\leadsto \color{blue}{9 \cdot \left(\frac{y}{z} \cdot \frac{x}{c}\right)} \]
   7. Step-by-step derivation

      1. *-commutative 90.2%

         \[\leadsto 9 \cdot \color{blue}{\left(\frac{x}{c} \cdot \frac{y}{z}\right)} \]

      2. clear-num 90.2%

         \[\leadsto 9 \cdot \left(\color{blue}{\frac{1}{\frac{c}{x}}} \cdot \frac{y}{z}\right) \]

      3. frac-times 87.0%

         \[\leadsto 9 \cdot \color{blue}{\frac{1 \cdot y}{\frac{c}{x} \cdot z}} \]

      4. *-un-lft-identity 87.0%

         \[\leadsto 9 \cdot \frac{\color{blue}{y}}{\frac{c}{x} \cdot z} \]

   8. Applied egg-rr 87.0%

      \[\leadsto 9 \cdot \color{blue}{\frac{y}{\frac{c}{x} \cdot z}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 89.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \left(9 \cdot x\right) \leq 5 \cdot 10^{+190}:\\ \;\;\;\;\frac{\frac{b + x \cdot \left(9 \cdot y\right)}{z} + t \cdot \left(-4 \cdot a\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;9 \cdot \frac{y}{z \cdot \frac{c}{x}}\\ \end{array} \]

Alternative 4: 75.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} t_1 := 9 \cdot \left(y \cdot x\right)\\ t_2 := t \cdot \left(-4 \cdot a\right)\\ t_3 := \frac{\frac{b}{z} + t_2}{c}\\ \mathbf{if}\;z \leq -2000000000000:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{-36}:\\ \;\;\;\;\frac{b + t_1}{z \cdot c}\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{+133}:\\ \;\;\;\;\frac{t_2 + \frac{t_1}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* 9.0 (* y x)))
        (t_2 (* t (* -4.0 a)))
        (t_3 (/ (+ (/ b z) t_2) c)))
   (if (<= z -2000000000000.0)
     t_3
     (if (<= z 1.95e-36)
       (/ (+ b t_1) (* z c))
       (if (<= z 2.8e+133) (/ (+ t_2 (/ t_1 z)) c) t_3)))))

C

assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = 9.0 * (y * x);
	double t_2 = t * (-4.0 * a);
	double t_3 = ((b / z) + t_2) / c;
	double tmp;
	if (z <= -2000000000000.0) {
		tmp = t_3;
	} else if (z <= 1.95e-36) {
		tmp = (b + t_1) / (z * c);
	} else if (z <= 2.8e+133) {
		tmp = (t_2 + (t_1 / z)) / c;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

NOTE: t and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    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), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = 9.0d0 * (y * x)
    t_2 = t * ((-4.0d0) * a)
    t_3 = ((b / z) + t_2) / c
    if (z <= (-2000000000000.0d0)) then
        tmp = t_3
    else if (z <= 1.95d-36) then
        tmp = (b + t_1) / (z * c)
    else if (z <= 2.8d+133) then
        tmp = (t_2 + (t_1 / z)) / c
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

assert t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = 9.0 * (y * x);
	double t_2 = t * (-4.0 * a);
	double t_3 = ((b / z) + t_2) / c;
	double tmp;
	if (z <= -2000000000000.0) {
		tmp = t_3;
	} else if (z <= 1.95e-36) {
		tmp = (b + t_1) / (z * c);
	} else if (z <= 2.8e+133) {
		tmp = (t_2 + (t_1 / z)) / c;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	t_1 = 9.0 * (y * x)
	t_2 = t * (-4.0 * a)
	t_3 = ((b / z) + t_2) / c
	tmp = 0
	if z <= -2000000000000.0:
		tmp = t_3
	elif z <= 1.95e-36:
		tmp = (b + t_1) / (z * c)
	elif z <= 2.8e+133:
		tmp = (t_2 + (t_1 / z)) / c
	else:
		tmp = t_3
	return tmp

Julia

t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(9.0 * Float64(y * x))
	t_2 = Float64(t * Float64(-4.0 * a))
	t_3 = Float64(Float64(Float64(b / z) + t_2) / c)
	tmp = 0.0
	if (z <= -2000000000000.0)
		tmp = t_3;
	elseif (z <= 1.95e-36)
		tmp = Float64(Float64(b + t_1) / Float64(z * c));
	elseif (z <= 2.8e+133)
		tmp = Float64(Float64(t_2 + Float64(t_1 / z)) / c);
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = 9.0 * (y * x);
	t_2 = t * (-4.0 * a);
	t_3 = ((b / z) + t_2) / c;
	tmp = 0.0;
	if (z <= -2000000000000.0)
		tmp = t_3;
	elseif (z <= 1.95e-36)
		tmp = (b + t_1) / (z * c);
	elseif (z <= 2.8e+133)
		tmp = (t_2 + (t_1 / z)) / c;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(9.0 * N[(y * x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(-4.0 * a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(b / z), $MachinePrecision] + t$95$2), $MachinePrecision] / c), $MachinePrecision]}, If[LessEqual[z, -2000000000000.0], t$95$3, If[LessEqual[z, 1.95e-36], N[(N[(b + t$95$1), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.8e+133], N[(N[(t$95$2 + N[(t$95$1 / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], t$95$3]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2e12 or 2.80000000000000016e133 < z

   1. Initial program 57.9%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-/r* 69.5%

         \[\leadsto \color{blue}{\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}}{c}} \]

   3. Simplified 87.5%

      \[\leadsto \color{blue}{\frac{\frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z} + t \cdot \left(a \cdot -4\right)}{c}} \]

   4. Taylor expanded in x around 0 80.0%

      \[\leadsto \frac{\color{blue}{\frac{b}{z}} + t \cdot \left(a \cdot -4\right)}{c} \]

   if -2e12 < z < 1.95e-36

   1. Initial program 93.7%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-/r* 86.8%

         \[\leadsto \color{blue}{\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}}{c}} \]

   3. Simplified 86.8%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(t, a \cdot -4, \frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z}\right)}{c}} \]

   4. Taylor expanded in z around 0 83.8%

      \[\leadsto \color{blue}{\frac{9 \cdot \left(y \cdot x\right) + b}{c \cdot z}} \]

   if 1.95e-36 < z < 2.80000000000000016e133

   1. Initial program 70.5%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-/r* 76.4%

         \[\leadsto \color{blue}{\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}}{c}} \]

   3. Simplified 88.4%

      \[\leadsto \color{blue}{\frac{\frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z} + t \cdot \left(a \cdot -4\right)}{c}} \]

   4. Taylor expanded in x around inf 78.4%

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

4. Final simplification 81.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2000000000000:\\ \;\;\;\;\frac{\frac{b}{z} + t \cdot \left(-4 \cdot a\right)}{c}\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{-36}:\\ \;\;\;\;\frac{b + 9 \cdot \left(y \cdot x\right)}{z \cdot c}\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{+133}:\\ \;\;\;\;\frac{t \cdot \left(-4 \cdot a\right) + \frac{9 \cdot \left(y \cdot x\right)}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{z} + t \cdot \left(-4 \cdot a\right)}{c}\\ \end{array} \]

Alternative 5: 50.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} t_1 := 9 \cdot \left(\frac{x}{c} \cdot \frac{y}{z}\right)\\ \mathbf{if}\;b \leq -3.35 \cdot 10^{-15}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;b \leq -4.6 \cdot 10^{-246}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;b \leq 1.15 \cdot 10^{-257}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 1.6 \cdot 10^{-19}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;b \leq 6 \cdot 10^{+50}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \end{array} \end{array} \]

FPCore

NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* 9.0 (* (/ x c) (/ y z)))))
   (if (<= b -3.35e-15)
     (/ b (* z c))
     (if (<= b -4.6e-246)
       (* -4.0 (* t (/ a c)))
       (if (<= b 1.15e-257)
         t_1
         (if (<= b 1.6e-19)
           (* -4.0 (/ a (/ c t)))
           (if (<= b 6e+50) t_1 (/ (/ b c) z))))))))

C

assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = 9.0 * ((x / c) * (y / z));
	double tmp;
	if (b <= -3.35e-15) {
		tmp = b / (z * c);
	} else if (b <= -4.6e-246) {
		tmp = -4.0 * (t * (a / c));
	} else if (b <= 1.15e-257) {
		tmp = t_1;
	} else if (b <= 1.6e-19) {
		tmp = -4.0 * (a / (c / t));
	} else if (b <= 6e+50) {
		tmp = t_1;
	} else {
		tmp = (b / c) / z;
	}
	return tmp;
}

Fortran

NOTE: t and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    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), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 9.0d0 * ((x / c) * (y / z))
    if (b <= (-3.35d-15)) then
        tmp = b / (z * c)
    else if (b <= (-4.6d-246)) then
        tmp = (-4.0d0) * (t * (a / c))
    else if (b <= 1.15d-257) then
        tmp = t_1
    else if (b <= 1.6d-19) then
        tmp = (-4.0d0) * (a / (c / t))
    else if (b <= 6d+50) then
        tmp = t_1
    else
        tmp = (b / c) / z
    end if
    code = tmp
end function

Java

assert t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = 9.0 * ((x / c) * (y / z));
	double tmp;
	if (b <= -3.35e-15) {
		tmp = b / (z * c);
	} else if (b <= -4.6e-246) {
		tmp = -4.0 * (t * (a / c));
	} else if (b <= 1.15e-257) {
		tmp = t_1;
	} else if (b <= 1.6e-19) {
		tmp = -4.0 * (a / (c / t));
	} else if (b <= 6e+50) {
		tmp = t_1;
	} else {
		tmp = (b / c) / z;
	}
	return tmp;
}

Python

[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	t_1 = 9.0 * ((x / c) * (y / z))
	tmp = 0
	if b <= -3.35e-15:
		tmp = b / (z * c)
	elif b <= -4.6e-246:
		tmp = -4.0 * (t * (a / c))
	elif b <= 1.15e-257:
		tmp = t_1
	elif b <= 1.6e-19:
		tmp = -4.0 * (a / (c / t))
	elif b <= 6e+50:
		tmp = t_1
	else:
		tmp = (b / c) / z
	return tmp

Julia

t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(9.0 * Float64(Float64(x / c) * Float64(y / z)))
	tmp = 0.0
	if (b <= -3.35e-15)
		tmp = Float64(b / Float64(z * c));
	elseif (b <= -4.6e-246)
		tmp = Float64(-4.0 * Float64(t * Float64(a / c)));
	elseif (b <= 1.15e-257)
		tmp = t_1;
	elseif (b <= 1.6e-19)
		tmp = Float64(-4.0 * Float64(a / Float64(c / t)));
	elseif (b <= 6e+50)
		tmp = t_1;
	else
		tmp = Float64(Float64(b / c) / z);
	end
	return tmp
end

MATLAB

t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = 9.0 * ((x / c) * (y / z));
	tmp = 0.0;
	if (b <= -3.35e-15)
		tmp = b / (z * c);
	elseif (b <= -4.6e-246)
		tmp = -4.0 * (t * (a / c));
	elseif (b <= 1.15e-257)
		tmp = t_1;
	elseif (b <= 1.6e-19)
		tmp = -4.0 * (a / (c / t));
	elseif (b <= 6e+50)
		tmp = t_1;
	else
		tmp = (b / c) / z;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(9.0 * N[(N[(x / c), $MachinePrecision] * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -3.35e-15], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -4.6e-246], N[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.15e-257], t$95$1, If[LessEqual[b, 1.6e-19], N[(-4.0 * N[(a / N[(c / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 6e+50], t$95$1, N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -3.35e-15

   1. Initial program 83.8%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-/r* 80.6%

         \[\leadsto \color{blue}{\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}}{c}} \]

   3. Simplified 86.5%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(t, a \cdot -4, \frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z}\right)}{c}} \]

   4. Taylor expanded in b around inf 61.3%

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
   5. Step-by-step derivation

      1. *-commutative 61.3%

         \[\leadsto \frac{b}{\color{blue}{z \cdot c}} \]

   6. Simplified 61.3%

      \[\leadsto \color{blue}{\frac{b}{z \cdot c}} \]

   if -3.35e-15 < b < -4.5999999999999995e-246

   1. Initial program 70.3%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-/r* 79.3%

         \[\leadsto \color{blue}{\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}}{c}} \]

   3. Simplified 88.4%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(t, a \cdot -4, \frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z}\right)}{c}} \]

   4. Taylor expanded in t around inf 58.7%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   5. Step-by-step derivation

      1. associate-/l* 63.1%

         \[\leadsto -4 \cdot \color{blue}{\frac{a}{\frac{c}{t}}} \]

      2. associate-/r/ 60.9%

         \[\leadsto -4 \cdot \color{blue}{\left(\frac{a}{c} \cdot t\right)} \]

   6. Simplified 60.9%

      \[\leadsto \color{blue}{-4 \cdot \left(\frac{a}{c} \cdot t\right)} \]

   if -4.5999999999999995e-246 < b < 1.15e-257 or 1.59999999999999991e-19 < b < 5.9999999999999996e50

   1. Initial program 72.6%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-/r* 83.6%

         \[\leadsto \color{blue}{\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}}{c}} \]

   3. Simplified 90.6%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(t, a \cdot -4, \frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z}\right)}{c}} \]

   4. Taylor expanded in x around inf 59.6%

      \[\leadsto \color{blue}{9 \cdot \frac{y \cdot x}{c \cdot z}} \]
   5. Step-by-step derivation

      1. *-commutative 59.6%

         \[\leadsto 9 \cdot \frac{y \cdot x}{\color{blue}{z \cdot c}} \]

      2. times-frac 68.0%

         \[\leadsto 9 \cdot \color{blue}{\left(\frac{y}{z} \cdot \frac{x}{c}\right)} \]

   6. Simplified 68.0%

      \[\leadsto \color{blue}{9 \cdot \left(\frac{y}{z} \cdot \frac{x}{c}\right)} \]

   if 1.15e-257 < b < 1.59999999999999991e-19

   1. Initial program 72.1%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-/r* 70.8%

         \[\leadsto \color{blue}{\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}}{c}} \]

   3. Simplified 84.5%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(t, a \cdot -4, \frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z}\right)}{c}} \]

   4. Taylor expanded in t around inf 54.0%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   5. Step-by-step derivation

      1. associate-/l* 57.8%

         \[\leadsto -4 \cdot \color{blue}{\frac{a}{\frac{c}{t}}} \]

   6. Simplified 57.8%

      \[\leadsto \color{blue}{-4 \cdot \frac{a}{\frac{c}{t}}} \]

   if 5.9999999999999996e50 < b

   1. Initial program 78.0%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-/r* 78.4%

         \[\leadsto \color{blue}{\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}}{c}} \]

   3. Simplified 88.0%

      \[\leadsto \color{blue}{\frac{\frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z} + t \cdot \left(a \cdot -4\right)}{c}} \]

   4. Taylor expanded in x around 0 77.1%

      \[\leadsto \frac{\color{blue}{\frac{b}{z}} + t \cdot \left(a \cdot -4\right)}{c} \]

   5. Taylor expanded in b around inf 57.6%

      \[\leadsto \frac{\color{blue}{\frac{b}{z}}}{c} \]
   6. Step-by-step derivation

      1. div-inv 57.7%

         \[\leadsto \color{blue}{\frac{b}{z} \cdot \frac{1}{c}} \]

   7. Applied egg-rr 57.7%

      \[\leadsto \color{blue}{\frac{b}{z} \cdot \frac{1}{c}} \]

   8. Taylor expanded in b around 0 55.2%

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
   9. Step-by-step derivation

      1. associate-/r* 57.7%

         \[\leadsto \color{blue}{\frac{\frac{b}{c}}{z}} \]

   10. Simplified 57.7%

       \[\leadsto \color{blue}{\frac{\frac{b}{c}}{z}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 61.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.35 \cdot 10^{-15}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;b \leq -4.6 \cdot 10^{-246}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;b \leq 1.15 \cdot 10^{-257}:\\ \;\;\;\;9 \cdot \left(\frac{x}{c} \cdot \frac{y}{z}\right)\\ \mathbf{elif}\;b \leq 1.6 \cdot 10^{-19}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;b \leq 6 \cdot 10^{+50}:\\ \;\;\;\;9 \cdot \left(\frac{x}{c} \cdot \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \end{array} \]

Alternative 6: 50.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;b \leq -1.55 \cdot 10^{-15}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;b \leq -1.12 \cdot 10^{-242}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;b \leq 9.8 \cdot 10^{-260}:\\ \;\;\;\;9 \cdot \left(\frac{x}{c} \cdot \frac{y}{z}\right)\\ \mathbf{elif}\;b \leq 9 \cdot 10^{-24}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;b \leq 1.05 \cdot 10^{+52}:\\ \;\;\;\;9 \cdot \frac{x}{c \cdot \frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \end{array} \end{array} \]

FPCore

NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= b -1.55e-15)
   (/ b (* z c))
   (if (<= b -1.12e-242)
     (* -4.0 (* t (/ a c)))
     (if (<= b 9.8e-260)
       (* 9.0 (* (/ x c) (/ y z)))
       (if (<= b 9e-24)
         (* -4.0 (/ a (/ c t)))
         (if (<= b 1.05e+52) (* 9.0 (/ x (* c (/ z y)))) (/ (/ b c) z)))))))

C

assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (b <= -1.55e-15) {
		tmp = b / (z * c);
	} else if (b <= -1.12e-242) {
		tmp = -4.0 * (t * (a / c));
	} else if (b <= 9.8e-260) {
		tmp = 9.0 * ((x / c) * (y / z));
	} else if (b <= 9e-24) {
		tmp = -4.0 * (a / (c / t));
	} else if (b <= 1.05e+52) {
		tmp = 9.0 * (x / (c * (z / y)));
	} else {
		tmp = (b / c) / z;
	}
	return tmp;
}

Fortran

NOTE: t and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    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), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (b <= (-1.55d-15)) then
        tmp = b / (z * c)
    else if (b <= (-1.12d-242)) then
        tmp = (-4.0d0) * (t * (a / c))
    else if (b <= 9.8d-260) then
        tmp = 9.0d0 * ((x / c) * (y / z))
    else if (b <= 9d-24) then
        tmp = (-4.0d0) * (a / (c / t))
    else if (b <= 1.05d+52) then
        tmp = 9.0d0 * (x / (c * (z / y)))
    else
        tmp = (b / c) / z
    end if
    code = tmp
end function

Java

assert t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (b <= -1.55e-15) {
		tmp = b / (z * c);
	} else if (b <= -1.12e-242) {
		tmp = -4.0 * (t * (a / c));
	} else if (b <= 9.8e-260) {
		tmp = 9.0 * ((x / c) * (y / z));
	} else if (b <= 9e-24) {
		tmp = -4.0 * (a / (c / t));
	} else if (b <= 1.05e+52) {
		tmp = 9.0 * (x / (c * (z / y)));
	} else {
		tmp = (b / c) / z;
	}
	return tmp;
}

Python

[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if b <= -1.55e-15:
		tmp = b / (z * c)
	elif b <= -1.12e-242:
		tmp = -4.0 * (t * (a / c))
	elif b <= 9.8e-260:
		tmp = 9.0 * ((x / c) * (y / z))
	elif b <= 9e-24:
		tmp = -4.0 * (a / (c / t))
	elif b <= 1.05e+52:
		tmp = 9.0 * (x / (c * (z / y)))
	else:
		tmp = (b / c) / z
	return tmp

Julia

t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (b <= -1.55e-15)
		tmp = Float64(b / Float64(z * c));
	elseif (b <= -1.12e-242)
		tmp = Float64(-4.0 * Float64(t * Float64(a / c)));
	elseif (b <= 9.8e-260)
		tmp = Float64(9.0 * Float64(Float64(x / c) * Float64(y / z)));
	elseif (b <= 9e-24)
		tmp = Float64(-4.0 * Float64(a / Float64(c / t)));
	elseif (b <= 1.05e+52)
		tmp = Float64(9.0 * Float64(x / Float64(c * Float64(z / y))));
	else
		tmp = Float64(Float64(b / c) / z);
	end
	return tmp
end

MATLAB

t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (b <= -1.55e-15)
		tmp = b / (z * c);
	elseif (b <= -1.12e-242)
		tmp = -4.0 * (t * (a / c));
	elseif (b <= 9.8e-260)
		tmp = 9.0 * ((x / c) * (y / z));
	elseif (b <= 9e-24)
		tmp = -4.0 * (a / (c / t));
	elseif (b <= 1.05e+52)
		tmp = 9.0 * (x / (c * (z / y)));
	else
		tmp = (b / c) / z;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[b, -1.55e-15], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -1.12e-242], N[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 9.8e-260], N[(9.0 * N[(N[(x / c), $MachinePrecision] * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 9e-24], N[(-4.0 * N[(a / N[(c / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.05e+52], N[(9.0 * N[(x / N[(c * N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if b < -1.5499999999999999e-15

   1. Initial program 83.8%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-/r* 80.6%

         \[\leadsto \color{blue}{\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}}{c}} \]

   3. Simplified 86.5%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(t, a \cdot -4, \frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z}\right)}{c}} \]

   4. Taylor expanded in b around inf 61.3%

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
   5. Step-by-step derivation

      1. *-commutative 61.3%

         \[\leadsto \frac{b}{\color{blue}{z \cdot c}} \]

   6. Simplified 61.3%

      \[\leadsto \color{blue}{\frac{b}{z \cdot c}} \]

   if -1.5499999999999999e-15 < b < -1.11999999999999997e-242

   1. Initial program 70.3%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-/r* 79.3%

         \[\leadsto \color{blue}{\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}}{c}} \]

   3. Simplified 88.4%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(t, a \cdot -4, \frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z}\right)}{c}} \]

   4. Taylor expanded in t around inf 58.7%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   5. Step-by-step derivation

      1. associate-/l* 63.1%

         \[\leadsto -4 \cdot \color{blue}{\frac{a}{\frac{c}{t}}} \]

      2. associate-/r/ 60.9%

         \[\leadsto -4 \cdot \color{blue}{\left(\frac{a}{c} \cdot t\right)} \]

   6. Simplified 60.9%

      \[\leadsto \color{blue}{-4 \cdot \left(\frac{a}{c} \cdot t\right)} \]

   if -1.11999999999999997e-242 < b < 9.8000000000000005e-260

   1. Initial program 70.7%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-/r* 92.2%

         \[\leadsto \color{blue}{\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}}{c}} \]

   3. Simplified 92.3%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(t, a \cdot -4, \frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z}\right)}{c}} \]

   4. Taylor expanded in x around inf 57.2%

      \[\leadsto \color{blue}{9 \cdot \frac{y \cdot x}{c \cdot z}} \]
   5. Step-by-step derivation

      1. *-commutative 57.2%

         \[\leadsto 9 \cdot \frac{y \cdot x}{\color{blue}{z \cdot c}} \]

      2. times-frac 67.2%

         \[\leadsto 9 \cdot \color{blue}{\left(\frac{y}{z} \cdot \frac{x}{c}\right)} \]

   6. Simplified 67.2%

      \[\leadsto \color{blue}{9 \cdot \left(\frac{y}{z} \cdot \frac{x}{c}\right)} \]

   if 9.8000000000000005e-260 < b < 8.9999999999999995e-24

   1. Initial program 72.1%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-/r* 70.8%

         \[\leadsto \color{blue}{\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}}{c}} \]

   3. Simplified 84.5%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(t, a \cdot -4, \frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z}\right)}{c}} \]

   4. Taylor expanded in t around inf 54.0%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   5. Step-by-step derivation

      1. associate-/l* 57.8%

         \[\leadsto -4 \cdot \color{blue}{\frac{a}{\frac{c}{t}}} \]

   6. Simplified 57.8%

      \[\leadsto \color{blue}{-4 \cdot \frac{a}{\frac{c}{t}}} \]

   if 8.9999999999999995e-24 < b < 1.05e52

   1. Initial program 75.5%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-/r* 70.0%

         \[\leadsto \color{blue}{\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}}{c}} \]

   3. Simplified 88.1%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(t, a \cdot -4, \frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z}\right)}{c}} \]

   4. Taylor expanded in x around inf 63.3%

      \[\leadsto \color{blue}{9 \cdot \frac{y \cdot x}{c \cdot z}} \]
   5. Step-by-step derivation

      1. *-commutative 63.3%

         \[\leadsto 9 \cdot \frac{y \cdot x}{\color{blue}{z \cdot c}} \]

      2. times-frac 69.3%

         \[\leadsto 9 \cdot \color{blue}{\left(\frac{y}{z} \cdot \frac{x}{c}\right)} \]

   6. Simplified 69.3%

      \[\leadsto \color{blue}{9 \cdot \left(\frac{y}{z} \cdot \frac{x}{c}\right)} \]
   7. Step-by-step derivation

      1. clear-num 69.4%

         \[\leadsto 9 \cdot \left(\color{blue}{\frac{1}{\frac{z}{y}}} \cdot \frac{x}{c}\right) \]

      2. frac-times 69.4%

         \[\leadsto 9 \cdot \color{blue}{\frac{1 \cdot x}{\frac{z}{y} \cdot c}} \]

      3. *-un-lft-identity 69.4%

         \[\leadsto 9 \cdot \frac{\color{blue}{x}}{\frac{z}{y} \cdot c} \]

   8. Applied egg-rr 69.4%

      \[\leadsto 9 \cdot \color{blue}{\frac{x}{\frac{z}{y} \cdot c}} \]

   if 1.05e52 < b

   1. Initial program 78.0%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-/r* 78.4%

         \[\leadsto \color{blue}{\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}}{c}} \]

   3. Simplified 88.0%

      \[\leadsto \color{blue}{\frac{\frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z} + t \cdot \left(a \cdot -4\right)}{c}} \]

   4. Taylor expanded in x around 0 77.1%

      \[\leadsto \frac{\color{blue}{\frac{b}{z}} + t \cdot \left(a \cdot -4\right)}{c} \]

   5. Taylor expanded in b around inf 57.6%

      \[\leadsto \frac{\color{blue}{\frac{b}{z}}}{c} \]
   6. Step-by-step derivation

      1. div-inv 57.7%

         \[\leadsto \color{blue}{\frac{b}{z} \cdot \frac{1}{c}} \]

   7. Applied egg-rr 57.7%

      \[\leadsto \color{blue}{\frac{b}{z} \cdot \frac{1}{c}} \]

   8. Taylor expanded in b around 0 55.2%

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
   9. Step-by-step derivation

      1. associate-/r* 57.7%

         \[\leadsto \color{blue}{\frac{\frac{b}{c}}{z}} \]

   10. Simplified 57.7%

       \[\leadsto \color{blue}{\frac{\frac{b}{c}}{z}} \]
3. Recombined 6 regimes into one program.

4. Final simplification 61.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.55 \cdot 10^{-15}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;b \leq -1.12 \cdot 10^{-242}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;b \leq 9.8 \cdot 10^{-260}:\\ \;\;\;\;9 \cdot \left(\frac{x}{c} \cdot \frac{y}{z}\right)\\ \mathbf{elif}\;b \leq 9 \cdot 10^{-24}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;b \leq 1.05 \cdot 10^{+52}:\\ \;\;\;\;9 \cdot \frac{x}{c \cdot \frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \end{array} \]

Alternative 7: 50.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;b \leq -3.3 \cdot 10^{-16}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;b \leq -9.6 \cdot 10^{-244}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;b \leq 2 \cdot 10^{-258}:\\ \;\;\;\;9 \cdot \left(\frac{x}{c} \cdot \frac{y}{z}\right)\\ \mathbf{elif}\;b \leq 5 \cdot 10^{-25}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;b \leq 7.2 \cdot 10^{+52}:\\ \;\;\;\;9 \cdot \frac{x}{\frac{z}{\frac{y}{c}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \end{array} \end{array} \]

FPCore

NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= b -3.3e-16)
   (/ b (* z c))
   (if (<= b -9.6e-244)
     (* -4.0 (* t (/ a c)))
     (if (<= b 2e-258)
       (* 9.0 (* (/ x c) (/ y z)))
       (if (<= b 5e-25)
         (* -4.0 (/ a (/ c t)))
         (if (<= b 7.2e+52) (* 9.0 (/ x (/ z (/ y c)))) (/ (/ b c) z)))))))

C

assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (b <= -3.3e-16) {
		tmp = b / (z * c);
	} else if (b <= -9.6e-244) {
		tmp = -4.0 * (t * (a / c));
	} else if (b <= 2e-258) {
		tmp = 9.0 * ((x / c) * (y / z));
	} else if (b <= 5e-25) {
		tmp = -4.0 * (a / (c / t));
	} else if (b <= 7.2e+52) {
		tmp = 9.0 * (x / (z / (y / c)));
	} else {
		tmp = (b / c) / z;
	}
	return tmp;
}

Fortran

NOTE: t and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    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), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (b <= (-3.3d-16)) then
        tmp = b / (z * c)
    else if (b <= (-9.6d-244)) then
        tmp = (-4.0d0) * (t * (a / c))
    else if (b <= 2d-258) then
        tmp = 9.0d0 * ((x / c) * (y / z))
    else if (b <= 5d-25) then
        tmp = (-4.0d0) * (a / (c / t))
    else if (b <= 7.2d+52) then
        tmp = 9.0d0 * (x / (z / (y / c)))
    else
        tmp = (b / c) / z
    end if
    code = tmp
end function

Java

assert t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (b <= -3.3e-16) {
		tmp = b / (z * c);
	} else if (b <= -9.6e-244) {
		tmp = -4.0 * (t * (a / c));
	} else if (b <= 2e-258) {
		tmp = 9.0 * ((x / c) * (y / z));
	} else if (b <= 5e-25) {
		tmp = -4.0 * (a / (c / t));
	} else if (b <= 7.2e+52) {
		tmp = 9.0 * (x / (z / (y / c)));
	} else {
		tmp = (b / c) / z;
	}
	return tmp;
}

Python

[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if b <= -3.3e-16:
		tmp = b / (z * c)
	elif b <= -9.6e-244:
		tmp = -4.0 * (t * (a / c))
	elif b <= 2e-258:
		tmp = 9.0 * ((x / c) * (y / z))
	elif b <= 5e-25:
		tmp = -4.0 * (a / (c / t))
	elif b <= 7.2e+52:
		tmp = 9.0 * (x / (z / (y / c)))
	else:
		tmp = (b / c) / z
	return tmp

Julia

t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (b <= -3.3e-16)
		tmp = Float64(b / Float64(z * c));
	elseif (b <= -9.6e-244)
		tmp = Float64(-4.0 * Float64(t * Float64(a / c)));
	elseif (b <= 2e-258)
		tmp = Float64(9.0 * Float64(Float64(x / c) * Float64(y / z)));
	elseif (b <= 5e-25)
		tmp = Float64(-4.0 * Float64(a / Float64(c / t)));
	elseif (b <= 7.2e+52)
		tmp = Float64(9.0 * Float64(x / Float64(z / Float64(y / c))));
	else
		tmp = Float64(Float64(b / c) / z);
	end
	return tmp
end

MATLAB

t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (b <= -3.3e-16)
		tmp = b / (z * c);
	elseif (b <= -9.6e-244)
		tmp = -4.0 * (t * (a / c));
	elseif (b <= 2e-258)
		tmp = 9.0 * ((x / c) * (y / z));
	elseif (b <= 5e-25)
		tmp = -4.0 * (a / (c / t));
	elseif (b <= 7.2e+52)
		tmp = 9.0 * (x / (z / (y / c)));
	else
		tmp = (b / c) / z;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[b, -3.3e-16], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -9.6e-244], N[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2e-258], N[(9.0 * N[(N[(x / c), $MachinePrecision] * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 5e-25], N[(-4.0 * N[(a / N[(c / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 7.2e+52], N[(9.0 * N[(x / N[(z / N[(y / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if b < -3.29999999999999988e-16

   1. Initial program 83.8%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-/r* 80.6%

         \[\leadsto \color{blue}{\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}}{c}} \]

   3. Simplified 86.5%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(t, a \cdot -4, \frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z}\right)}{c}} \]

   4. Taylor expanded in b around inf 61.3%

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
   5. Step-by-step derivation

      1. *-commutative 61.3%

         \[\leadsto \frac{b}{\color{blue}{z \cdot c}} \]

   6. Simplified 61.3%

      \[\leadsto \color{blue}{\frac{b}{z \cdot c}} \]

   if -3.29999999999999988e-16 < b < -9.60000000000000063e-244

   1. Initial program 70.3%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-/r* 79.3%

         \[\leadsto \color{blue}{\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}}{c}} \]

   3. Simplified 88.4%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(t, a \cdot -4, \frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z}\right)}{c}} \]

   4. Taylor expanded in t around inf 58.7%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   5. Step-by-step derivation

      1. associate-/l* 63.1%

         \[\leadsto -4 \cdot \color{blue}{\frac{a}{\frac{c}{t}}} \]

      2. associate-/r/ 60.9%

         \[\leadsto -4 \cdot \color{blue}{\left(\frac{a}{c} \cdot t\right)} \]

   6. Simplified 60.9%

      \[\leadsto \color{blue}{-4 \cdot \left(\frac{a}{c} \cdot t\right)} \]

   if -9.60000000000000063e-244 < b < 1.99999999999999991e-258

   1. Initial program 70.7%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-/r* 92.2%

         \[\leadsto \color{blue}{\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}}{c}} \]

   3. Simplified 92.3%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(t, a \cdot -4, \frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z}\right)}{c}} \]

   4. Taylor expanded in x around inf 57.2%

      \[\leadsto \color{blue}{9 \cdot \frac{y \cdot x}{c \cdot z}} \]
   5. Step-by-step derivation

      1. *-commutative 57.2%

         \[\leadsto 9 \cdot \frac{y \cdot x}{\color{blue}{z \cdot c}} \]

      2. times-frac 67.2%

         \[\leadsto 9 \cdot \color{blue}{\left(\frac{y}{z} \cdot \frac{x}{c}\right)} \]

   6. Simplified 67.2%

      \[\leadsto \color{blue}{9 \cdot \left(\frac{y}{z} \cdot \frac{x}{c}\right)} \]

   if 1.99999999999999991e-258 < b < 4.99999999999999962e-25

   1. Initial program 72.1%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-/r* 70.8%

         \[\leadsto \color{blue}{\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}}{c}} \]

   3. Simplified 84.5%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(t, a \cdot -4, \frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z}\right)}{c}} \]

   4. Taylor expanded in t around inf 54.0%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   5. Step-by-step derivation

      1. associate-/l* 57.8%

         \[\leadsto -4 \cdot \color{blue}{\frac{a}{\frac{c}{t}}} \]

   6. Simplified 57.8%

      \[\leadsto \color{blue}{-4 \cdot \frac{a}{\frac{c}{t}}} \]

   if 4.99999999999999962e-25 < b < 7.2e52

   1. Initial program 75.5%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-/r* 70.0%

         \[\leadsto \color{blue}{\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}}{c}} \]

   3. Simplified 88.1%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(t, a \cdot -4, \frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z}\right)}{c}} \]

   4. Taylor expanded in x around inf 63.3%

      \[\leadsto \color{blue}{9 \cdot \frac{y \cdot x}{c \cdot z}} \]
   5. Step-by-step derivation

      1. *-commutative 63.3%

         \[\leadsto 9 \cdot \frac{y \cdot x}{\color{blue}{z \cdot c}} \]

      2. times-frac 69.3%

         \[\leadsto 9 \cdot \color{blue}{\left(\frac{y}{z} \cdot \frac{x}{c}\right)} \]

   6. Simplified 69.3%

      \[\leadsto \color{blue}{9 \cdot \left(\frac{y}{z} \cdot \frac{x}{c}\right)} \]
   7. Step-by-step derivation

      1. clear-num 69.4%

         \[\leadsto 9 \cdot \left(\color{blue}{\frac{1}{\frac{z}{y}}} \cdot \frac{x}{c}\right) \]

      2. frac-times 69.4%

         \[\leadsto 9 \cdot \color{blue}{\frac{1 \cdot x}{\frac{z}{y} \cdot c}} \]

      3. *-un-lft-identity 69.4%

         \[\leadsto 9 \cdot \frac{\color{blue}{x}}{\frac{z}{y} \cdot c} \]

   8. Applied egg-rr 69.4%

      \[\leadsto 9 \cdot \color{blue}{\frac{x}{\frac{z}{y} \cdot c}} \]

   9. Taylor expanded in z around 0 63.5%

      \[\leadsto 9 \cdot \frac{x}{\color{blue}{\frac{c \cdot z}{y}}} \]
   10. Step-by-step derivation

       1. *-commutative 63.5%

          \[\leadsto 9 \cdot \frac{x}{\frac{\color{blue}{z \cdot c}}{y}} \]

       2. associate-/l* 69.5%

          \[\leadsto 9 \cdot \frac{x}{\color{blue}{\frac{z}{\frac{y}{c}}}} \]

   11. Simplified 69.5%

       \[\leadsto 9 \cdot \frac{x}{\color{blue}{\frac{z}{\frac{y}{c}}}} \]

   if 7.2e52 < b

   1. Initial program 78.0%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-/r* 78.4%

         \[\leadsto \color{blue}{\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}}{c}} \]

   3. Simplified 88.0%

      \[\leadsto \color{blue}{\frac{\frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z} + t \cdot \left(a \cdot -4\right)}{c}} \]

   4. Taylor expanded in x around 0 77.1%

      \[\leadsto \frac{\color{blue}{\frac{b}{z}} + t \cdot \left(a \cdot -4\right)}{c} \]

   5. Taylor expanded in b around inf 57.6%

      \[\leadsto \frac{\color{blue}{\frac{b}{z}}}{c} \]
   6. Step-by-step derivation

      1. div-inv 57.7%

         \[\leadsto \color{blue}{\frac{b}{z} \cdot \frac{1}{c}} \]

   7. Applied egg-rr 57.7%

      \[\leadsto \color{blue}{\frac{b}{z} \cdot \frac{1}{c}} \]

   8. Taylor expanded in b around 0 55.2%

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
   9. Step-by-step derivation

      1. associate-/r* 57.7%

         \[\leadsto \color{blue}{\frac{\frac{b}{c}}{z}} \]

   10. Simplified 57.7%

       \[\leadsto \color{blue}{\frac{\frac{b}{c}}{z}} \]
3. Recombined 6 regimes into one program.

4. Final simplification 61.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.3 \cdot 10^{-16}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;b \leq -9.6 \cdot 10^{-244}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;b \leq 2 \cdot 10^{-258}:\\ \;\;\;\;9 \cdot \left(\frac{x}{c} \cdot \frac{y}{z}\right)\\ \mathbf{elif}\;b \leq 5 \cdot 10^{-25}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;b \leq 7.2 \cdot 10^{+52}:\\ \;\;\;\;9 \cdot \frac{x}{\frac{z}{\frac{y}{c}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \end{array} \]

Alternative 8: 50.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;b \leq -2.3 \cdot 10^{-15}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;b \leq -8.5 \cdot 10^{-241}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;b \leq 9.8 \cdot 10^{-262}:\\ \;\;\;\;9 \cdot \frac{y}{z \cdot \frac{c}{x}}\\ \mathbf{elif}\;b \leq 4 \cdot 10^{-19}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;b \leq 7.8 \cdot 10^{+51}:\\ \;\;\;\;9 \cdot \frac{x}{\frac{z}{\frac{y}{c}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \end{array} \end{array} \]

FPCore

NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= b -2.3e-15)
   (/ b (* z c))
   (if (<= b -8.5e-241)
     (* -4.0 (* t (/ a c)))
     (if (<= b 9.8e-262)
       (* 9.0 (/ y (* z (/ c x))))
       (if (<= b 4e-19)
         (* -4.0 (/ a (/ c t)))
         (if (<= b 7.8e+51) (* 9.0 (/ x (/ z (/ y c)))) (/ (/ b c) z)))))))

C

assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (b <= -2.3e-15) {
		tmp = b / (z * c);
	} else if (b <= -8.5e-241) {
		tmp = -4.0 * (t * (a / c));
	} else if (b <= 9.8e-262) {
		tmp = 9.0 * (y / (z * (c / x)));
	} else if (b <= 4e-19) {
		tmp = -4.0 * (a / (c / t));
	} else if (b <= 7.8e+51) {
		tmp = 9.0 * (x / (z / (y / c)));
	} else {
		tmp = (b / c) / z;
	}
	return tmp;
}

Fortran

NOTE: t and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    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), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (b <= (-2.3d-15)) then
        tmp = b / (z * c)
    else if (b <= (-8.5d-241)) then
        tmp = (-4.0d0) * (t * (a / c))
    else if (b <= 9.8d-262) then
        tmp = 9.0d0 * (y / (z * (c / x)))
    else if (b <= 4d-19) then
        tmp = (-4.0d0) * (a / (c / t))
    else if (b <= 7.8d+51) then
        tmp = 9.0d0 * (x / (z / (y / c)))
    else
        tmp = (b / c) / z
    end if
    code = tmp
end function

Java

assert t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (b <= -2.3e-15) {
		tmp = b / (z * c);
	} else if (b <= -8.5e-241) {
		tmp = -4.0 * (t * (a / c));
	} else if (b <= 9.8e-262) {
		tmp = 9.0 * (y / (z * (c / x)));
	} else if (b <= 4e-19) {
		tmp = -4.0 * (a / (c / t));
	} else if (b <= 7.8e+51) {
		tmp = 9.0 * (x / (z / (y / c)));
	} else {
		tmp = (b / c) / z;
	}
	return tmp;
}

Python

[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if b <= -2.3e-15:
		tmp = b / (z * c)
	elif b <= -8.5e-241:
		tmp = -4.0 * (t * (a / c))
	elif b <= 9.8e-262:
		tmp = 9.0 * (y / (z * (c / x)))
	elif b <= 4e-19:
		tmp = -4.0 * (a / (c / t))
	elif b <= 7.8e+51:
		tmp = 9.0 * (x / (z / (y / c)))
	else:
		tmp = (b / c) / z
	return tmp

Julia

t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (b <= -2.3e-15)
		tmp = Float64(b / Float64(z * c));
	elseif (b <= -8.5e-241)
		tmp = Float64(-4.0 * Float64(t * Float64(a / c)));
	elseif (b <= 9.8e-262)
		tmp = Float64(9.0 * Float64(y / Float64(z * Float64(c / x))));
	elseif (b <= 4e-19)
		tmp = Float64(-4.0 * Float64(a / Float64(c / t)));
	elseif (b <= 7.8e+51)
		tmp = Float64(9.0 * Float64(x / Float64(z / Float64(y / c))));
	else
		tmp = Float64(Float64(b / c) / z);
	end
	return tmp
end

MATLAB

t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (b <= -2.3e-15)
		tmp = b / (z * c);
	elseif (b <= -8.5e-241)
		tmp = -4.0 * (t * (a / c));
	elseif (b <= 9.8e-262)
		tmp = 9.0 * (y / (z * (c / x)));
	elseif (b <= 4e-19)
		tmp = -4.0 * (a / (c / t));
	elseif (b <= 7.8e+51)
		tmp = 9.0 * (x / (z / (y / c)));
	else
		tmp = (b / c) / z;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[b, -2.3e-15], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -8.5e-241], N[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 9.8e-262], N[(9.0 * N[(y / N[(z * N[(c / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 4e-19], N[(-4.0 * N[(a / N[(c / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 7.8e+51], N[(9.0 * N[(x / N[(z / N[(y / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if b < -2.2999999999999999e-15

   1. Initial program 83.8%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-/r* 80.6%

         \[\leadsto \color{blue}{\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}}{c}} \]

   3. Simplified 86.5%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(t, a \cdot -4, \frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z}\right)}{c}} \]

   4. Taylor expanded in b around inf 61.3%

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
   5. Step-by-step derivation

      1. *-commutative 61.3%

         \[\leadsto \frac{b}{\color{blue}{z \cdot c}} \]

   6. Simplified 61.3%

      \[\leadsto \color{blue}{\frac{b}{z \cdot c}} \]

   if -2.2999999999999999e-15 < b < -8.49999999999999974e-241

   1. Initial program 70.3%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-/r* 79.3%

         \[\leadsto \color{blue}{\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}}{c}} \]

   3. Simplified 88.4%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(t, a \cdot -4, \frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z}\right)}{c}} \]

   4. Taylor expanded in t around inf 58.7%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   5. Step-by-step derivation

      1. associate-/l* 63.1%

         \[\leadsto -4 \cdot \color{blue}{\frac{a}{\frac{c}{t}}} \]

      2. associate-/r/ 60.9%

         \[\leadsto -4 \cdot \color{blue}{\left(\frac{a}{c} \cdot t\right)} \]

   6. Simplified 60.9%

      \[\leadsto \color{blue}{-4 \cdot \left(\frac{a}{c} \cdot t\right)} \]

   if -8.49999999999999974e-241 < b < 9.8000000000000005e-262

   1. Initial program 70.7%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-/r* 92.2%

         \[\leadsto \color{blue}{\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}}{c}} \]

   3. Simplified 92.3%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(t, a \cdot -4, \frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z}\right)}{c}} \]

   4. Taylor expanded in x around inf 57.2%

      \[\leadsto \color{blue}{9 \cdot \frac{y \cdot x}{c \cdot z}} \]
   5. Step-by-step derivation

      1. *-commutative 57.2%

         \[\leadsto 9 \cdot \frac{y \cdot x}{\color{blue}{z \cdot c}} \]

      2. times-frac 67.2%

         \[\leadsto 9 \cdot \color{blue}{\left(\frac{y}{z} \cdot \frac{x}{c}\right)} \]

   6. Simplified 67.2%

      \[\leadsto \color{blue}{9 \cdot \left(\frac{y}{z} \cdot \frac{x}{c}\right)} \]
   7. Step-by-step derivation

      1. *-commutative 67.2%

         \[\leadsto 9 \cdot \color{blue}{\left(\frac{x}{c} \cdot \frac{y}{z}\right)} \]

      2. clear-num 67.2%

         \[\leadsto 9 \cdot \left(\color{blue}{\frac{1}{\frac{c}{x}}} \cdot \frac{y}{z}\right) \]

      3. frac-times 68.4%

         \[\leadsto 9 \cdot \color{blue}{\frac{1 \cdot y}{\frac{c}{x} \cdot z}} \]

      4. *-un-lft-identity 68.4%

         \[\leadsto 9 \cdot \frac{\color{blue}{y}}{\frac{c}{x} \cdot z} \]

   8. Applied egg-rr 68.4%

      \[\leadsto 9 \cdot \color{blue}{\frac{y}{\frac{c}{x} \cdot z}} \]

   if 9.8000000000000005e-262 < b < 3.9999999999999999e-19

   1. Initial program 72.1%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-/r* 70.8%

         \[\leadsto \color{blue}{\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}}{c}} \]

   3. Simplified 84.5%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(t, a \cdot -4, \frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z}\right)}{c}} \]

   4. Taylor expanded in t around inf 54.0%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   5. Step-by-step derivation

      1. associate-/l* 57.8%

         \[\leadsto -4 \cdot \color{blue}{\frac{a}{\frac{c}{t}}} \]

   6. Simplified 57.8%

      \[\leadsto \color{blue}{-4 \cdot \frac{a}{\frac{c}{t}}} \]

   if 3.9999999999999999e-19 < b < 7.79999999999999968e51

   1. Initial program 75.5%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-/r* 70.0%

         \[\leadsto \color{blue}{\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}}{c}} \]

   3. Simplified 88.1%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(t, a \cdot -4, \frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z}\right)}{c}} \]

   4. Taylor expanded in x around inf 63.3%

      \[\leadsto \color{blue}{9 \cdot \frac{y \cdot x}{c \cdot z}} \]
   5. Step-by-step derivation

      1. *-commutative 63.3%

         \[\leadsto 9 \cdot \frac{y \cdot x}{\color{blue}{z \cdot c}} \]

      2. times-frac 69.3%

         \[\leadsto 9 \cdot \color{blue}{\left(\frac{y}{z} \cdot \frac{x}{c}\right)} \]

   6. Simplified 69.3%

      \[\leadsto \color{blue}{9 \cdot \left(\frac{y}{z} \cdot \frac{x}{c}\right)} \]
   7. Step-by-step derivation

      1. clear-num 69.4%

         \[\leadsto 9 \cdot \left(\color{blue}{\frac{1}{\frac{z}{y}}} \cdot \frac{x}{c}\right) \]

      2. frac-times 69.4%

         \[\leadsto 9 \cdot \color{blue}{\frac{1 \cdot x}{\frac{z}{y} \cdot c}} \]

      3. *-un-lft-identity 69.4%

         \[\leadsto 9 \cdot \frac{\color{blue}{x}}{\frac{z}{y} \cdot c} \]

   8. Applied egg-rr 69.4%

      \[\leadsto 9 \cdot \color{blue}{\frac{x}{\frac{z}{y} \cdot c}} \]

   9. Taylor expanded in z around 0 63.5%

      \[\leadsto 9 \cdot \frac{x}{\color{blue}{\frac{c \cdot z}{y}}} \]
   10. Step-by-step derivation

       1. *-commutative 63.5%

          \[\leadsto 9 \cdot \frac{x}{\frac{\color{blue}{z \cdot c}}{y}} \]

       2. associate-/l* 69.5%

          \[\leadsto 9 \cdot \frac{x}{\color{blue}{\frac{z}{\frac{y}{c}}}} \]

   11. Simplified 69.5%

       \[\leadsto 9 \cdot \frac{x}{\color{blue}{\frac{z}{\frac{y}{c}}}} \]

   if 7.79999999999999968e51 < b

   1. Initial program 78.0%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-/r* 78.4%

         \[\leadsto \color{blue}{\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}}{c}} \]

   3. Simplified 88.0%

      \[\leadsto \color{blue}{\frac{\frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z} + t \cdot \left(a \cdot -4\right)}{c}} \]

   4. Taylor expanded in x around 0 77.1%

      \[\leadsto \frac{\color{blue}{\frac{b}{z}} + t \cdot \left(a \cdot -4\right)}{c} \]

   5. Taylor expanded in b around inf 57.6%

      \[\leadsto \frac{\color{blue}{\frac{b}{z}}}{c} \]
   6. Step-by-step derivation

      1. div-inv 57.7%

         \[\leadsto \color{blue}{\frac{b}{z} \cdot \frac{1}{c}} \]

   7. Applied egg-rr 57.7%

      \[\leadsto \color{blue}{\frac{b}{z} \cdot \frac{1}{c}} \]

   8. Taylor expanded in b around 0 55.2%

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
   9. Step-by-step derivation

      1. associate-/r* 57.7%

         \[\leadsto \color{blue}{\frac{\frac{b}{c}}{z}} \]

   10. Simplified 57.7%

       \[\leadsto \color{blue}{\frac{\frac{b}{c}}{z}} \]
3. Recombined 6 regimes into one program.

4. Final simplification 61.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.3 \cdot 10^{-15}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;b \leq -8.5 \cdot 10^{-241}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;b \leq 9.8 \cdot 10^{-262}:\\ \;\;\;\;9 \cdot \frac{y}{z \cdot \frac{c}{x}}\\ \mathbf{elif}\;b \leq 4 \cdot 10^{-19}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;b \leq 7.8 \cdot 10^{+51}:\\ \;\;\;\;9 \cdot \frac{x}{\frac{z}{\frac{y}{c}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \end{array} \]

Alternative 9: 50.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;b \leq -2.15 \cdot 10^{-15}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;b \leq -6.8 \cdot 10^{-242}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;b \leq 9.8 \cdot 10^{-258}:\\ \;\;\;\;9 \cdot \frac{y \cdot \frac{x}{c}}{z}\\ \mathbf{elif}\;b \leq 3.3 \cdot 10^{-18}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;b \leq 5 \cdot 10^{+51}:\\ \;\;\;\;9 \cdot \frac{x}{\frac{z}{\frac{y}{c}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \end{array} \end{array} \]

FPCore

NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= b -2.15e-15)
   (/ b (* z c))
   (if (<= b -6.8e-242)
     (* -4.0 (* t (/ a c)))
     (if (<= b 9.8e-258)
       (* 9.0 (/ (* y (/ x c)) z))
       (if (<= b 3.3e-18)
         (* -4.0 (/ a (/ c t)))
         (if (<= b 5e+51) (* 9.0 (/ x (/ z (/ y c)))) (/ (/ b c) z)))))))

C

assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (b <= -2.15e-15) {
		tmp = b / (z * c);
	} else if (b <= -6.8e-242) {
		tmp = -4.0 * (t * (a / c));
	} else if (b <= 9.8e-258) {
		tmp = 9.0 * ((y * (x / c)) / z);
	} else if (b <= 3.3e-18) {
		tmp = -4.0 * (a / (c / t));
	} else if (b <= 5e+51) {
		tmp = 9.0 * (x / (z / (y / c)));
	} else {
		tmp = (b / c) / z;
	}
	return tmp;
}

Fortran

NOTE: t and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    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), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (b <= (-2.15d-15)) then
        tmp = b / (z * c)
    else if (b <= (-6.8d-242)) then
        tmp = (-4.0d0) * (t * (a / c))
    else if (b <= 9.8d-258) then
        tmp = 9.0d0 * ((y * (x / c)) / z)
    else if (b <= 3.3d-18) then
        tmp = (-4.0d0) * (a / (c / t))
    else if (b <= 5d+51) then
        tmp = 9.0d0 * (x / (z / (y / c)))
    else
        tmp = (b / c) / z
    end if
    code = tmp
end function

Java

assert t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (b <= -2.15e-15) {
		tmp = b / (z * c);
	} else if (b <= -6.8e-242) {
		tmp = -4.0 * (t * (a / c));
	} else if (b <= 9.8e-258) {
		tmp = 9.0 * ((y * (x / c)) / z);
	} else if (b <= 3.3e-18) {
		tmp = -4.0 * (a / (c / t));
	} else if (b <= 5e+51) {
		tmp = 9.0 * (x / (z / (y / c)));
	} else {
		tmp = (b / c) / z;
	}
	return tmp;
}

Python

[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if b <= -2.15e-15:
		tmp = b / (z * c)
	elif b <= -6.8e-242:
		tmp = -4.0 * (t * (a / c))
	elif b <= 9.8e-258:
		tmp = 9.0 * ((y * (x / c)) / z)
	elif b <= 3.3e-18:
		tmp = -4.0 * (a / (c / t))
	elif b <= 5e+51:
		tmp = 9.0 * (x / (z / (y / c)))
	else:
		tmp = (b / c) / z
	return tmp

Julia

t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (b <= -2.15e-15)
		tmp = Float64(b / Float64(z * c));
	elseif (b <= -6.8e-242)
		tmp = Float64(-4.0 * Float64(t * Float64(a / c)));
	elseif (b <= 9.8e-258)
		tmp = Float64(9.0 * Float64(Float64(y * Float64(x / c)) / z));
	elseif (b <= 3.3e-18)
		tmp = Float64(-4.0 * Float64(a / Float64(c / t)));
	elseif (b <= 5e+51)
		tmp = Float64(9.0 * Float64(x / Float64(z / Float64(y / c))));
	else
		tmp = Float64(Float64(b / c) / z);
	end
	return tmp
end

MATLAB

t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (b <= -2.15e-15)
		tmp = b / (z * c);
	elseif (b <= -6.8e-242)
		tmp = -4.0 * (t * (a / c));
	elseif (b <= 9.8e-258)
		tmp = 9.0 * ((y * (x / c)) / z);
	elseif (b <= 3.3e-18)
		tmp = -4.0 * (a / (c / t));
	elseif (b <= 5e+51)
		tmp = 9.0 * (x / (z / (y / c)));
	else
		tmp = (b / c) / z;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[b, -2.15e-15], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -6.8e-242], N[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 9.8e-258], N[(9.0 * N[(N[(y * N[(x / c), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.3e-18], N[(-4.0 * N[(a / N[(c / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 5e+51], N[(9.0 * N[(x / N[(z / N[(y / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if b < -2.1499999999999998e-15

   1. Initial program 83.8%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-/r* 80.6%

         \[\leadsto \color{blue}{\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}}{c}} \]

   3. Simplified 86.5%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(t, a \cdot -4, \frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z}\right)}{c}} \]

   4. Taylor expanded in b around inf 61.3%

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
   5. Step-by-step derivation

      1. *-commutative 61.3%

         \[\leadsto \frac{b}{\color{blue}{z \cdot c}} \]

   6. Simplified 61.3%

      \[\leadsto \color{blue}{\frac{b}{z \cdot c}} \]

   if -2.1499999999999998e-15 < b < -6.8000000000000001e-242

   1. Initial program 70.3%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-/r* 79.3%

         \[\leadsto \color{blue}{\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}}{c}} \]

   3. Simplified 88.4%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(t, a \cdot -4, \frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z}\right)}{c}} \]

   4. Taylor expanded in t around inf 58.7%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   5. Step-by-step derivation

      1. associate-/l* 63.1%

         \[\leadsto -4 \cdot \color{blue}{\frac{a}{\frac{c}{t}}} \]

      2. associate-/r/ 60.9%

         \[\leadsto -4 \cdot \color{blue}{\left(\frac{a}{c} \cdot t\right)} \]

   6. Simplified 60.9%

      \[\leadsto \color{blue}{-4 \cdot \left(\frac{a}{c} \cdot t\right)} \]

   if -6.8000000000000001e-242 < b < 9.8000000000000002e-258

   1. Initial program 70.7%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-/r* 92.2%

         \[\leadsto \color{blue}{\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}}{c}} \]

   3. Simplified 92.3%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(t, a \cdot -4, \frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z}\right)}{c}} \]

   4. Taylor expanded in x around inf 57.2%

      \[\leadsto \color{blue}{9 \cdot \frac{y \cdot x}{c \cdot z}} \]
   5. Step-by-step derivation

      1. *-commutative 57.2%

         \[\leadsto 9 \cdot \frac{y \cdot x}{\color{blue}{z \cdot c}} \]

      2. times-frac 67.2%

         \[\leadsto 9 \cdot \color{blue}{\left(\frac{y}{z} \cdot \frac{x}{c}\right)} \]

   6. Simplified 67.2%

      \[\leadsto \color{blue}{9 \cdot \left(\frac{y}{z} \cdot \frac{x}{c}\right)} \]
   7. Step-by-step derivation

      1. associate-*l/ 74.7%

         \[\leadsto 9 \cdot \color{blue}{\frac{y \cdot \frac{x}{c}}{z}} \]

   8. Applied egg-rr 74.7%

      \[\leadsto 9 \cdot \color{blue}{\frac{y \cdot \frac{x}{c}}{z}} \]

   if 9.8000000000000002e-258 < b < 3.3000000000000002e-18

   1. Initial program 72.1%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-/r* 70.8%

         \[\leadsto \color{blue}{\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}}{c}} \]

   3. Simplified 84.5%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(t, a \cdot -4, \frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z}\right)}{c}} \]

   4. Taylor expanded in t around inf 54.0%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   5. Step-by-step derivation

      1. associate-/l* 57.8%

         \[\leadsto -4 \cdot \color{blue}{\frac{a}{\frac{c}{t}}} \]

   6. Simplified 57.8%

      \[\leadsto \color{blue}{-4 \cdot \frac{a}{\frac{c}{t}}} \]

   if 3.3000000000000002e-18 < b < 5e51

   1. Initial program 75.5%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-/r* 70.0%

         \[\leadsto \color{blue}{\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}}{c}} \]

   3. Simplified 88.1%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(t, a \cdot -4, \frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z}\right)}{c}} \]

   4. Taylor expanded in x around inf 63.3%

      \[\leadsto \color{blue}{9 \cdot \frac{y \cdot x}{c \cdot z}} \]
   5. Step-by-step derivation

      1. *-commutative 63.3%

         \[\leadsto 9 \cdot \frac{y \cdot x}{\color{blue}{z \cdot c}} \]

      2. times-frac 69.3%

         \[\leadsto 9 \cdot \color{blue}{\left(\frac{y}{z} \cdot \frac{x}{c}\right)} \]

   6. Simplified 69.3%

      \[\leadsto \color{blue}{9 \cdot \left(\frac{y}{z} \cdot \frac{x}{c}\right)} \]
   7. Step-by-step derivation

      1. clear-num 69.4%

         \[\leadsto 9 \cdot \left(\color{blue}{\frac{1}{\frac{z}{y}}} \cdot \frac{x}{c}\right) \]

      2. frac-times 69.4%

         \[\leadsto 9 \cdot \color{blue}{\frac{1 \cdot x}{\frac{z}{y} \cdot c}} \]

      3. *-un-lft-identity 69.4%

         \[\leadsto 9 \cdot \frac{\color{blue}{x}}{\frac{z}{y} \cdot c} \]

   8. Applied egg-rr 69.4%

      \[\leadsto 9 \cdot \color{blue}{\frac{x}{\frac{z}{y} \cdot c}} \]

   9. Taylor expanded in z around 0 63.5%

      \[\leadsto 9 \cdot \frac{x}{\color{blue}{\frac{c \cdot z}{y}}} \]
   10. Step-by-step derivation

       1. *-commutative 63.5%

          \[\leadsto 9 \cdot \frac{x}{\frac{\color{blue}{z \cdot c}}{y}} \]

       2. associate-/l* 69.5%

          \[\leadsto 9 \cdot \frac{x}{\color{blue}{\frac{z}{\frac{y}{c}}}} \]

   11. Simplified 69.5%

       \[\leadsto 9 \cdot \frac{x}{\color{blue}{\frac{z}{\frac{y}{c}}}} \]

   if 5e51 < b

   1. Initial program 78.0%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-/r* 78.4%

         \[\leadsto \color{blue}{\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}}{c}} \]

   3. Simplified 88.0%

      \[\leadsto \color{blue}{\frac{\frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z} + t \cdot \left(a \cdot -4\right)}{c}} \]

   4. Taylor expanded in x around 0 77.1%

      \[\leadsto \frac{\color{blue}{\frac{b}{z}} + t \cdot \left(a \cdot -4\right)}{c} \]

   5. Taylor expanded in b around inf 57.6%

      \[\leadsto \frac{\color{blue}{\frac{b}{z}}}{c} \]
   6. Step-by-step derivation

      1. div-inv 57.7%

         \[\leadsto \color{blue}{\frac{b}{z} \cdot \frac{1}{c}} \]

   7. Applied egg-rr 57.7%

      \[\leadsto \color{blue}{\frac{b}{z} \cdot \frac{1}{c}} \]

   8. Taylor expanded in b around 0 55.2%

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
   9. Step-by-step derivation

      1. associate-/r* 57.7%

         \[\leadsto \color{blue}{\frac{\frac{b}{c}}{z}} \]

   10. Simplified 57.7%

       \[\leadsto \color{blue}{\frac{\frac{b}{c}}{z}} \]
3. Recombined 6 regimes into one program.

4. Final simplification 61.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.15 \cdot 10^{-15}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;b \leq -6.8 \cdot 10^{-242}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;b \leq 9.8 \cdot 10^{-258}:\\ \;\;\;\;9 \cdot \frac{y \cdot \frac{x}{c}}{z}\\ \mathbf{elif}\;b \leq 3.3 \cdot 10^{-18}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;b \leq 5 \cdot 10^{+51}:\\ \;\;\;\;9 \cdot \frac{x}{\frac{z}{\frac{y}{c}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \end{array} \]

Alternative 10: 75.5% accurate, 1.3× speedup

Math

\[\begin{array}{l} [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -6500 \lor \neg \left(z \leq 23000000000000\right):\\ \;\;\;\;\frac{\frac{b}{z} + t \cdot \left(-4 \cdot a\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + 9 \cdot \left(y \cdot x\right)}{z \cdot c}\\ \end{array} \end{array} \]

FPCore

NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= z -6500.0) (not (<= z 23000000000000.0)))
   (/ (+ (/ b z) (* t (* -4.0 a))) c)
   (/ (+ b (* 9.0 (* y x))) (* z c))))

C

assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((z <= -6500.0) || !(z <= 23000000000000.0)) {
		tmp = ((b / z) + (t * (-4.0 * a))) / c;
	} else {
		tmp = (b + (9.0 * (y * x))) / (z * c);
	}
	return tmp;
}

Fortran

NOTE: t and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    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), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if ((z <= (-6500.0d0)) .or. (.not. (z <= 23000000000000.0d0))) then
        tmp = ((b / z) + (t * ((-4.0d0) * a))) / c
    else
        tmp = (b + (9.0d0 * (y * x))) / (z * c)
    end if
    code = tmp
end function

Java

assert t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((z <= -6500.0) || !(z <= 23000000000000.0)) {
		tmp = ((b / z) + (t * (-4.0 * a))) / c;
	} else {
		tmp = (b + (9.0 * (y * x))) / (z * c);
	}
	return tmp;
}

Python

[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if (z <= -6500.0) or not (z <= 23000000000000.0):
		tmp = ((b / z) + (t * (-4.0 * a))) / c
	else:
		tmp = (b + (9.0 * (y * x))) / (z * c)
	return tmp

Julia

t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((z <= -6500.0) || !(z <= 23000000000000.0))
		tmp = Float64(Float64(Float64(b / z) + Float64(t * Float64(-4.0 * a))) / c);
	else
		tmp = Float64(Float64(b + Float64(9.0 * Float64(y * x))) / Float64(z * c));
	end
	return tmp
end

MATLAB

t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((z <= -6500.0) || ~((z <= 23000000000000.0)))
		tmp = ((b / z) + (t * (-4.0 * a))) / c;
	else
		tmp = (b + (9.0 * (y * x))) / (z * c);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[z, -6500.0], N[Not[LessEqual[z, 23000000000000.0]], $MachinePrecision]], N[(N[(N[(b / z), $MachinePrecision] + N[(t * N[(-4.0 * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], N[(N[(b + N[(9.0 * N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -6500 or 2.3e13 < z

   1. Initial program 59.1%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-/r* 69.9%

         \[\leadsto \color{blue}{\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}}{c}} \]

   3. Simplified 86.9%

      \[\leadsto \color{blue}{\frac{\frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z} + t \cdot \left(a \cdot -4\right)}{c}} \]

   4. Taylor expanded in x around 0 76.2%

      \[\leadsto \frac{\color{blue}{\frac{b}{z}} + t \cdot \left(a \cdot -4\right)}{c} \]

   if -6500 < z < 2.3e13

   1. Initial program 93.3%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-/r* 86.9%

         \[\leadsto \color{blue}{\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}}{c}} \]

   3. Simplified 87.7%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(t, a \cdot -4, \frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z}\right)}{c}} \]

   4. Taylor expanded in z around 0 83.3%

      \[\leadsto \color{blue}{\frac{9 \cdot \left(y \cdot x\right) + b}{c \cdot z}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 79.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6500 \lor \neg \left(z \leq 23000000000000\right):\\ \;\;\;\;\frac{\frac{b}{z} + t \cdot \left(-4 \cdot a\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + 9 \cdot \left(y \cdot x\right)}{z \cdot c}\\ \end{array} \]

Alternative 11: 67.6% accurate, 1.3× speedup

Math

\[\begin{array}{l} [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -3.3 \cdot 10^{+97}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+16}:\\ \;\;\;\;\frac{b + 9 \cdot \left(y \cdot x\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(-4 \cdot \frac{t}{c}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= z -3.3e+97)
   (* -4.0 (/ a (/ c t)))
   (if (<= z 1.25e+16)
     (/ (+ b (* 9.0 (* y x))) (* z c))
     (* a (* -4.0 (/ t c))))))

C

assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (z <= -3.3e+97) {
		tmp = -4.0 * (a / (c / t));
	} else if (z <= 1.25e+16) {
		tmp = (b + (9.0 * (y * x))) / (z * c);
	} else {
		tmp = a * (-4.0 * (t / c));
	}
	return tmp;
}

Fortran

NOTE: t and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    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), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (z <= (-3.3d+97)) then
        tmp = (-4.0d0) * (a / (c / t))
    else if (z <= 1.25d+16) then
        tmp = (b + (9.0d0 * (y * x))) / (z * c)
    else
        tmp = a * ((-4.0d0) * (t / c))
    end if
    code = tmp
end function

Java

assert t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (z <= -3.3e+97) {
		tmp = -4.0 * (a / (c / t));
	} else if (z <= 1.25e+16) {
		tmp = (b + (9.0 * (y * x))) / (z * c);
	} else {
		tmp = a * (-4.0 * (t / c));
	}
	return tmp;
}

Python

[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if z <= -3.3e+97:
		tmp = -4.0 * (a / (c / t))
	elif z <= 1.25e+16:
		tmp = (b + (9.0 * (y * x))) / (z * c)
	else:
		tmp = a * (-4.0 * (t / c))
	return tmp

Julia

t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (z <= -3.3e+97)
		tmp = Float64(-4.0 * Float64(a / Float64(c / t)));
	elseif (z <= 1.25e+16)
		tmp = Float64(Float64(b + Float64(9.0 * Float64(y * x))) / Float64(z * c));
	else
		tmp = Float64(a * Float64(-4.0 * Float64(t / c)));
	end
	return tmp
end

MATLAB

t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (z <= -3.3e+97)
		tmp = -4.0 * (a / (c / t));
	elseif (z <= 1.25e+16)
		tmp = (b + (9.0 * (y * x))) / (z * c);
	else
		tmp = a * (-4.0 * (t / c));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[z, -3.3e+97], N[(-4.0 * N[(a / N[(c / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.25e+16], N[(N[(b + N[(9.0 * N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(a * N[(-4.0 * N[(t / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.3000000000000001e97

   1. Initial program 59.0%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-/r* 71.9%

         \[\leadsto \color{blue}{\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}}{c}} \]

   3. Simplified 88.7%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(t, a \cdot -4, \frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z}\right)}{c}} \]

   4. Taylor expanded in t around inf 64.3%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   5. Step-by-step derivation

      1. associate-/l* 62.5%

         \[\leadsto -4 \cdot \color{blue}{\frac{a}{\frac{c}{t}}} \]

   6. Simplified 62.5%

      \[\leadsto \color{blue}{-4 \cdot \frac{a}{\frac{c}{t}}} \]

   if -3.3000000000000001e97 < z < 1.25e16

   1. Initial program 92.3%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-/r* 87.9%

         \[\leadsto \color{blue}{\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}}{c}} \]

   3. Simplified 88.6%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(t, a \cdot -4, \frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z}\right)}{c}} \]

   4. Taylor expanded in z around 0 80.4%

      \[\leadsto \color{blue}{\frac{9 \cdot \left(y \cdot x\right) + b}{c \cdot z}} \]

   if 1.25e16 < z

   1. Initial program 50.2%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-/r* 59.6%

         \[\leadsto \color{blue}{\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}}{c}} \]

   3. Simplified 82.6%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(t, a \cdot -4, \frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z}\right)}{c}} \]

   4. Taylor expanded in t around inf 63.4%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   5. Step-by-step derivation

      1. associate-/l* 70.0%

         \[\leadsto -4 \cdot \color{blue}{\frac{a}{\frac{c}{t}}} \]

      2. associate-/r/ 59.9%

         \[\leadsto -4 \cdot \color{blue}{\left(\frac{a}{c} \cdot t\right)} \]

   6. Simplified 59.9%

      \[\leadsto \color{blue}{-4 \cdot \left(\frac{a}{c} \cdot t\right)} \]

   7. Taylor expanded in a around 0 63.4%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   8. Step-by-step derivation

      1. associate-*r/ 71.8%

         \[\leadsto -4 \cdot \color{blue}{\left(a \cdot \frac{t}{c}\right)} \]

      2. *-commutative 71.8%

         \[\leadsto \color{blue}{\left(a \cdot \frac{t}{c}\right) \cdot -4} \]

      3. associate-*l* 71.8%

         \[\leadsto \color{blue}{a \cdot \left(\frac{t}{c} \cdot -4\right)} \]

   9. Simplified 71.8%

      \[\leadsto \color{blue}{a \cdot \left(\frac{t}{c} \cdot -4\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 75.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.3 \cdot 10^{+97}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+16}:\\ \;\;\;\;\frac{b + 9 \cdot \left(y \cdot x\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(-4 \cdot \frac{t}{c}\right)\\ \end{array} \]

Alternative 12: 50.4% accurate, 1.7× speedup

Math

\[\begin{array}{l} [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;b \leq -1 \cdot 10^{-15}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;b \leq 4.3 \cdot 10^{+95}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \end{array} \end{array} \]

FPCore

NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= b -1e-15)
   (/ b (* z c))
   (if (<= b 4.3e+95) (* -4.0 (* t (/ a c))) (/ (/ b c) z))))

C

assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (b <= -1e-15) {
		tmp = b / (z * c);
	} else if (b <= 4.3e+95) {
		tmp = -4.0 * (t * (a / c));
	} else {
		tmp = (b / c) / z;
	}
	return tmp;
}

Fortran

NOTE: t and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    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), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (b <= (-1d-15)) then
        tmp = b / (z * c)
    else if (b <= 4.3d+95) then
        tmp = (-4.0d0) * (t * (a / c))
    else
        tmp = (b / c) / z
    end if
    code = tmp
end function

Java

assert t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (b <= -1e-15) {
		tmp = b / (z * c);
	} else if (b <= 4.3e+95) {
		tmp = -4.0 * (t * (a / c));
	} else {
		tmp = (b / c) / z;
	}
	return tmp;
}

Python

[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if b <= -1e-15:
		tmp = b / (z * c)
	elif b <= 4.3e+95:
		tmp = -4.0 * (t * (a / c))
	else:
		tmp = (b / c) / z
	return tmp

Julia

t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (b <= -1e-15)
		tmp = Float64(b / Float64(z * c));
	elseif (b <= 4.3e+95)
		tmp = Float64(-4.0 * Float64(t * Float64(a / c)));
	else
		tmp = Float64(Float64(b / c) / z);
	end
	return tmp
end

MATLAB

t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (b <= -1e-15)
		tmp = b / (z * c);
	elseif (b <= 4.3e+95)
		tmp = -4.0 * (t * (a / c));
	else
		tmp = (b / c) / z;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[b, -1e-15], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 4.3e+95], N[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.0000000000000001e-15

   1. Initial program 83.8%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-/r* 80.6%

         \[\leadsto \color{blue}{\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}}{c}} \]

   3. Simplified 86.5%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(t, a \cdot -4, \frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z}\right)}{c}} \]

   4. Taylor expanded in b around inf 61.3%

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
   5. Step-by-step derivation

      1. *-commutative 61.3%

         \[\leadsto \frac{b}{\color{blue}{z \cdot c}} \]

   6. Simplified 61.3%

      \[\leadsto \color{blue}{\frac{b}{z \cdot c}} \]

   if -1.0000000000000001e-15 < b < 4.3e95

   1. Initial program 71.5%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-/r* 76.3%

         \[\leadsto \color{blue}{\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}}{c}} \]

   3. Simplified 87.8%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(t, a \cdot -4, \frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z}\right)}{c}} \]

   4. Taylor expanded in t around inf 50.9%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   5. Step-by-step derivation

      1. associate-/l* 54.1%

         \[\leadsto -4 \cdot \color{blue}{\frac{a}{\frac{c}{t}}} \]

      2. associate-/r/ 51.7%

         \[\leadsto -4 \cdot \color{blue}{\left(\frac{a}{c} \cdot t\right)} \]

   6. Simplified 51.7%

      \[\leadsto \color{blue}{-4 \cdot \left(\frac{a}{c} \cdot t\right)} \]

   if 4.3e95 < b

   1. Initial program 80.7%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-/r* 84.1%

         \[\leadsto \color{blue}{\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}}{c}} \]

   3. Simplified 87.3%

      \[\leadsto \color{blue}{\frac{\frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z} + t \cdot \left(a \cdot -4\right)}{c}} \]

   4. Taylor expanded in x around 0 76.1%

      \[\leadsto \frac{\color{blue}{\frac{b}{z}} + t \cdot \left(a \cdot -4\right)}{c} \]

   5. Taylor expanded in b around inf 62.9%

      \[\leadsto \frac{\color{blue}{\frac{b}{z}}}{c} \]
   6. Step-by-step derivation

      1. div-inv 63.0%

         \[\leadsto \color{blue}{\frac{b}{z} \cdot \frac{1}{c}} \]

   7. Applied egg-rr 63.0%

      \[\leadsto \color{blue}{\frac{b}{z} \cdot \frac{1}{c}} \]

   8. Taylor expanded in b around 0 59.7%

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
   9. Step-by-step derivation

      1. associate-/r* 62.9%

         \[\leadsto \color{blue}{\frac{\frac{b}{c}}{z}} \]

   10. Simplified 62.9%

       \[\leadsto \color{blue}{\frac{\frac{b}{c}}{z}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 56.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1 \cdot 10^{-15}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;b \leq 4.3 \cdot 10^{+95}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \end{array} \]

Alternative 13: 50.4% accurate, 1.7× speedup

Math

\[\begin{array}{l} [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;b \leq -1.75 \cdot 10^{-16}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;b \leq 2.85 \cdot 10^{+48}:\\ \;\;\;\;a \cdot \left(-4 \cdot \frac{t}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \end{array} \end{array} \]

FPCore

NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= b -1.75e-16)
   (/ b (* z c))
   (if (<= b 2.85e+48) (* a (* -4.0 (/ t c))) (/ (/ b c) z))))

C

assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (b <= -1.75e-16) {
		tmp = b / (z * c);
	} else if (b <= 2.85e+48) {
		tmp = a * (-4.0 * (t / c));
	} else {
		tmp = (b / c) / z;
	}
	return tmp;
}

Fortran

NOTE: t and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    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), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (b <= (-1.75d-16)) then
        tmp = b / (z * c)
    else if (b <= 2.85d+48) then
        tmp = a * ((-4.0d0) * (t / c))
    else
        tmp = (b / c) / z
    end if
    code = tmp
end function

Java

assert t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (b <= -1.75e-16) {
		tmp = b / (z * c);
	} else if (b <= 2.85e+48) {
		tmp = a * (-4.0 * (t / c));
	} else {
		tmp = (b / c) / z;
	}
	return tmp;
}

Python

[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if b <= -1.75e-16:
		tmp = b / (z * c)
	elif b <= 2.85e+48:
		tmp = a * (-4.0 * (t / c))
	else:
		tmp = (b / c) / z
	return tmp

Julia

t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (b <= -1.75e-16)
		tmp = Float64(b / Float64(z * c));
	elseif (b <= 2.85e+48)
		tmp = Float64(a * Float64(-4.0 * Float64(t / c)));
	else
		tmp = Float64(Float64(b / c) / z);
	end
	return tmp
end

MATLAB

t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (b <= -1.75e-16)
		tmp = b / (z * c);
	elseif (b <= 2.85e+48)
		tmp = a * (-4.0 * (t / c));
	else
		tmp = (b / c) / z;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[b, -1.75e-16], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.85e+48], N[(a * N[(-4.0 * N[(t / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.75000000000000009e-16

   1. Initial program 83.8%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-/r* 80.6%

         \[\leadsto \color{blue}{\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}}{c}} \]

   3. Simplified 86.5%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(t, a \cdot -4, \frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z}\right)}{c}} \]

   4. Taylor expanded in b around inf 61.3%

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
   5. Step-by-step derivation

      1. *-commutative 61.3%

         \[\leadsto \frac{b}{\color{blue}{z \cdot c}} \]

   6. Simplified 61.3%

      \[\leadsto \color{blue}{\frac{b}{z \cdot c}} \]

   if -1.75000000000000009e-16 < b < 2.84999999999999984e48

   1. Initial program 71.0%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-/r* 76.9%

         \[\leadsto \color{blue}{\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}}{c}} \]

   3. Simplified 87.3%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(t, a \cdot -4, \frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z}\right)}{c}} \]

   4. Taylor expanded in t around inf 52.8%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   5. Step-by-step derivation

      1. associate-/l* 56.3%

         \[\leadsto -4 \cdot \color{blue}{\frac{a}{\frac{c}{t}}} \]

      2. associate-/r/ 52.9%

         \[\leadsto -4 \cdot \color{blue}{\left(\frac{a}{c} \cdot t\right)} \]

   6. Simplified 52.9%

      \[\leadsto \color{blue}{-4 \cdot \left(\frac{a}{c} \cdot t\right)} \]

   7. Taylor expanded in a around 0 52.8%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   8. Step-by-step derivation

      1. associate-*r/ 57.4%

         \[\leadsto -4 \cdot \color{blue}{\left(a \cdot \frac{t}{c}\right)} \]

      2. *-commutative 57.4%

         \[\leadsto \color{blue}{\left(a \cdot \frac{t}{c}\right) \cdot -4} \]

      3. associate-*l* 57.4%

         \[\leadsto \color{blue}{a \cdot \left(\frac{t}{c} \cdot -4\right)} \]

   9. Simplified 57.4%

      \[\leadsto \color{blue}{a \cdot \left(\frac{t}{c} \cdot -4\right)} \]

   if 2.84999999999999984e48 < b

   1. Initial program 79.5%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-/r* 80.0%

         \[\leadsto \color{blue}{\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}}{c}} \]

   3. Simplified 88.9%

      \[\leadsto \color{blue}{\frac{\frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z} + t \cdot \left(a \cdot -4\right)}{c}} \]

   4. Taylor expanded in x around 0 72.0%

      \[\leadsto \frac{\color{blue}{\frac{b}{z}} + t \cdot \left(a \cdot -4\right)}{c} \]

   5. Taylor expanded in b around inf 53.9%

      \[\leadsto \frac{\color{blue}{\frac{b}{z}}}{c} \]
   6. Step-by-step derivation

      1. div-inv 54.0%

         \[\leadsto \color{blue}{\frac{b}{z} \cdot \frac{1}{c}} \]

   7. Applied egg-rr 54.0%

      \[\leadsto \color{blue}{\frac{b}{z} \cdot \frac{1}{c}} \]

   8. Taylor expanded in b around 0 51.7%

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
   9. Step-by-step derivation

      1. associate-/r* 54.0%

         \[\leadsto \color{blue}{\frac{\frac{b}{c}}{z}} \]

   10. Simplified 54.0%

       \[\leadsto \color{blue}{\frac{\frac{b}{c}}{z}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 58.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.75 \cdot 10^{-16}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;b \leq 2.85 \cdot 10^{+48}:\\ \;\;\;\;a \cdot \left(-4 \cdot \frac{t}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \end{array} \]

Alternative 14: 35.0% accurate, 3.8× speedup

Math

\[\begin{array}{l} [t, a] = \mathsf{sort}([t, a])\\ \\ \frac{b}{z \cdot c} \end{array} \]

FPCore

NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c) :precision binary64 (/ b (* z c)))

C

assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	return b / (z * c);
}

Fortran

NOTE: t and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    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), intent (in) :: b
    real(8), intent (in) :: c
    code = b / (z * c)
end function

Java

assert t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	return b / (z * c);
}

Python

[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	return b / (z * c)

Julia

t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	return Float64(b / Float64(z * c))
end

MATLAB

t, a = num2cell(sort([t, a])){:}
function tmp = code(x, y, z, t, a, b, c)
	tmp = b / (z * c);
end

Wolfram

NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 76.6%

   \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
2. Step-by-step derivation

   1. associate-/r* 78.6%

      \[\leadsto \color{blue}{\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}}{c}} \]

3. Simplified 87.3%

   \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(t, a \cdot -4, \frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z}\right)}{c}} \]

4. Taylor expanded in b around inf 38.8%

   \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
5. Step-by-step derivation

   1. *-commutative 38.8%

      \[\leadsto \frac{b}{\color{blue}{z \cdot c}} \]

6. Simplified 38.8%

   \[\leadsto \color{blue}{\frac{b}{z \cdot c}} \]

7. Final simplification 38.8%

   \[\leadsto \frac{b}{z \cdot c} \]

Developer target: 80.3% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{b}{c \cdot z}\\ t_2 := 4 \cdot \frac{a \cdot t}{c}\\ t_3 := \left(x \cdot 9\right) \cdot y\\ t_4 := \left(t_3 - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b\\ t_5 := \frac{t_4}{z \cdot c}\\ t_6 := \frac{\left(t_3 - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}\\ \mathbf{if}\;t_5 < -1.100156740804105 \cdot 10^{-171}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;t_5 < 0:\\ \;\;\;\;\frac{\frac{t_4}{z}}{c}\\ \mathbf{elif}\;t_5 < 1.1708877911747488 \cdot 10^{-53}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;t_5 < 2.876823679546137 \cdot 10^{+130}:\\ \;\;\;\;\left(\left(9 \cdot \frac{y}{c}\right) \cdot \frac{x}{z} + t_1\right) - t_2\\ \mathbf{elif}\;t_5 < 1.3838515042456319 \cdot 10^{+158}:\\ \;\;\;\;t_6\\ \mathbf{else}:\\ \;\;\;\;\left(9 \cdot \left(\frac{y}{c \cdot z} \cdot x\right) + t_1\right) - t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ b (* c z)))
        (t_2 (* 4.0 (/ (* a t) c)))
        (t_3 (* (* x 9.0) y))
        (t_4 (+ (- t_3 (* (* (* z 4.0) t) a)) b))
        (t_5 (/ t_4 (* z c)))
        (t_6 (/ (+ (- t_3 (* (* z 4.0) (* t a))) b) (* z c))))
   (if (< t_5 -1.100156740804105e-171)
     t_6
     (if (< t_5 0.0)
       (/ (/ t_4 z) c)
       (if (< t_5 1.1708877911747488e-53)
         t_6
         (if (< t_5 2.876823679546137e+130)
           (- (+ (* (* 9.0 (/ y c)) (/ x z)) t_1) t_2)
           (if (< t_5 1.3838515042456319e+158)
             t_6
             (- (+ (* 9.0 (* (/ y (* c z)) x)) t_1) t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = b / (c * z);
	double t_2 = 4.0 * ((a * t) / c);
	double t_3 = (x * 9.0) * y;
	double t_4 = (t_3 - (((z * 4.0) * t) * a)) + b;
	double t_5 = t_4 / (z * c);
	double t_6 = ((t_3 - ((z * 4.0) * (t * a))) + b) / (z * c);
	double tmp;
	if (t_5 < -1.100156740804105e-171) {
		tmp = t_6;
	} else if (t_5 < 0.0) {
		tmp = (t_4 / z) / c;
	} else if (t_5 < 1.1708877911747488e-53) {
		tmp = t_6;
	} else if (t_5 < 2.876823679546137e+130) {
		tmp = (((9.0 * (y / c)) * (x / z)) + t_1) - t_2;
	} else if (t_5 < 1.3838515042456319e+158) {
		tmp = t_6;
	} else {
		tmp = ((9.0 * ((y / (c * z)) * x)) + t_1) - t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    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), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: tmp
    t_1 = b / (c * z)
    t_2 = 4.0d0 * ((a * t) / c)
    t_3 = (x * 9.0d0) * y
    t_4 = (t_3 - (((z * 4.0d0) * t) * a)) + b
    t_5 = t_4 / (z * c)
    t_6 = ((t_3 - ((z * 4.0d0) * (t * a))) + b) / (z * c)
    if (t_5 < (-1.100156740804105d-171)) then
        tmp = t_6
    else if (t_5 < 0.0d0) then
        tmp = (t_4 / z) / c
    else if (t_5 < 1.1708877911747488d-53) then
        tmp = t_6
    else if (t_5 < 2.876823679546137d+130) then
        tmp = (((9.0d0 * (y / c)) * (x / z)) + t_1) - t_2
    else if (t_5 < 1.3838515042456319d+158) then
        tmp = t_6
    else
        tmp = ((9.0d0 * ((y / (c * z)) * x)) + t_1) - t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = b / (c * z);
	double t_2 = 4.0 * ((a * t) / c);
	double t_3 = (x * 9.0) * y;
	double t_4 = (t_3 - (((z * 4.0) * t) * a)) + b;
	double t_5 = t_4 / (z * c);
	double t_6 = ((t_3 - ((z * 4.0) * (t * a))) + b) / (z * c);
	double tmp;
	if (t_5 < -1.100156740804105e-171) {
		tmp = t_6;
	} else if (t_5 < 0.0) {
		tmp = (t_4 / z) / c;
	} else if (t_5 < 1.1708877911747488e-53) {
		tmp = t_6;
	} else if (t_5 < 2.876823679546137e+130) {
		tmp = (((9.0 * (y / c)) * (x / z)) + t_1) - t_2;
	} else if (t_5 < 1.3838515042456319e+158) {
		tmp = t_6;
	} else {
		tmp = ((9.0 * ((y / (c * z)) * x)) + t_1) - t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = b / (c * z)
	t_2 = 4.0 * ((a * t) / c)
	t_3 = (x * 9.0) * y
	t_4 = (t_3 - (((z * 4.0) * t) * a)) + b
	t_5 = t_4 / (z * c)
	t_6 = ((t_3 - ((z * 4.0) * (t * a))) + b) / (z * c)
	tmp = 0
	if t_5 < -1.100156740804105e-171:
		tmp = t_6
	elif t_5 < 0.0:
		tmp = (t_4 / z) / c
	elif t_5 < 1.1708877911747488e-53:
		tmp = t_6
	elif t_5 < 2.876823679546137e+130:
		tmp = (((9.0 * (y / c)) * (x / z)) + t_1) - t_2
	elif t_5 < 1.3838515042456319e+158:
		tmp = t_6
	else:
		tmp = ((9.0 * ((y / (c * z)) * x)) + t_1) - t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(b / Float64(c * z))
	t_2 = Float64(4.0 * Float64(Float64(a * t) / c))
	t_3 = Float64(Float64(x * 9.0) * y)
	t_4 = Float64(Float64(t_3 - Float64(Float64(Float64(z * 4.0) * t) * a)) + b)
	t_5 = Float64(t_4 / Float64(z * c))
	t_6 = Float64(Float64(Float64(t_3 - Float64(Float64(z * 4.0) * Float64(t * a))) + b) / Float64(z * c))
	tmp = 0.0
	if (t_5 < -1.100156740804105e-171)
		tmp = t_6;
	elseif (t_5 < 0.0)
		tmp = Float64(Float64(t_4 / z) / c);
	elseif (t_5 < 1.1708877911747488e-53)
		tmp = t_6;
	elseif (t_5 < 2.876823679546137e+130)
		tmp = Float64(Float64(Float64(Float64(9.0 * Float64(y / c)) * Float64(x / z)) + t_1) - t_2);
	elseif (t_5 < 1.3838515042456319e+158)
		tmp = t_6;
	else
		tmp = Float64(Float64(Float64(9.0 * Float64(Float64(y / Float64(c * z)) * x)) + t_1) - t_2);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = b / (c * z);
	t_2 = 4.0 * ((a * t) / c);
	t_3 = (x * 9.0) * y;
	t_4 = (t_3 - (((z * 4.0) * t) * a)) + b;
	t_5 = t_4 / (z * c);
	t_6 = ((t_3 - ((z * 4.0) * (t * a))) + b) / (z * c);
	tmp = 0.0;
	if (t_5 < -1.100156740804105e-171)
		tmp = t_6;
	elseif (t_5 < 0.0)
		tmp = (t_4 / z) / c;
	elseif (t_5 < 1.1708877911747488e-53)
		tmp = t_6;
	elseif (t_5 < 2.876823679546137e+130)
		tmp = (((9.0 * (y / c)) * (x / z)) + t_1) - t_2;
	elseif (t_5 < 1.3838515042456319e+158)
		tmp = t_6;
	else
		tmp = ((9.0 * ((y / (c * z)) * x)) + t_1) - t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(b / N[(c * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(4.0 * N[(N[(a * t), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision]}, Block[{t$95$4 = N[(N[(t$95$3 - N[(N[(N[(z * 4.0), $MachinePrecision] * t), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]}, Block[{t$95$5 = N[(t$95$4 / N[(z * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(N[(N[(t$95$3 - N[(N[(z * 4.0), $MachinePrecision] * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]}, If[Less[t$95$5, -1.100156740804105e-171], t$95$6, If[Less[t$95$5, 0.0], N[(N[(t$95$4 / z), $MachinePrecision] / c), $MachinePrecision], If[Less[t$95$5, 1.1708877911747488e-53], t$95$6, If[Less[t$95$5, 2.876823679546137e+130], N[(N[(N[(N[(9.0 * N[(y / c), $MachinePrecision]), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision] - t$95$2), $MachinePrecision], If[Less[t$95$5, 1.3838515042456319e+158], t$95$6, N[(N[(N[(9.0 * N[(N[(y / N[(c * z), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision] - t$95$2), $MachinePrecision]]]]]]]]]]]]

Reproduce

herbie shell --seed 2023230 
(FPCore (x y z t a b c)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, J"
  :precision binary64

  :herbie-target
  (if (< (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)) -1.100156740804105e-171) (/ (+ (- (* (* x 9.0) y) (* (* z 4.0) (* t a))) b) (* z c)) (if (< (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)) 0.0) (/ (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) z) c) (if (< (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)) 1.1708877911747488e-53) (/ (+ (- (* (* x 9.0) y) (* (* z 4.0) (* t a))) b) (* z c)) (if (< (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)) 2.876823679546137e+130) (- (+ (* (* 9.0 (/ y c)) (/ x z)) (/ b (* c z))) (* 4.0 (/ (* a t) c))) (if (< (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)) 1.3838515042456319e+158) (/ (+ (- (* (* x 9.0) y) (* (* z 4.0) (* t a))) b) (* z c)) (- (+ (* 9.0 (* (/ y (* c z)) x)) (/ b (* c z))) (* 4.0 (/ (* a t) c))))))))

  (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)))