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

Percentage Accurate: 80.0% → 88.3%

Time: 20.9s

Alternatives: 16

Speedup: 0.7×

• 37.7% 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: 80.0% 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: 88.3% accurate, 0.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \frac{b}{z \cdot c}\\ \mathbf{if}\;z \leq -1.95 \cdot 10^{+183}:\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right) + 9 \cdot \left(x \cdot \frac{y}{z}\right)}{c}\\ \mathbf{elif}\;z \leq -5.8 \cdot 10^{-69}:\\ \;\;\;\;\mathsf{fma}\left(-4, t \cdot \frac{a}{c}, \mathsf{fma}\left(9, \frac{y}{z} \cdot \frac{x}{c}, t\_1\right)\right)\\ \mathbf{elif}\;z \leq 9 \cdot 10^{+79}:\\ \;\;\;\;\left(b + \mathsf{fma}\left(x, 9 \cdot y, a \cdot \left(\left(t \cdot 4\right) \cdot \left(-z\right)\right)\right)\right) \cdot \frac{1}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\left(t\_1 + 9 \cdot \frac{x \cdot y}{z \cdot c}\right) - 4 \cdot \frac{a \cdot t}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ b (* z c))))
   (if (<= z -1.95e+183)
     (/ (+ (* -4.0 (* a t)) (* 9.0 (* x (/ y z)))) c)
     (if (<= z -5.8e-69)
       (fma -4.0 (* t (/ a c)) (fma 9.0 (* (/ y z) (/ x c)) t_1))
       (if (<= z 9e+79)
         (* (+ b (fma x (* 9.0 y) (* a (* (* t 4.0) (- z))))) (/ 1.0 (* z c)))
         (- (+ t_1 (* 9.0 (/ (* x y) (* z c)))) (* 4.0 (/ (* a t) c))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = b / (z * c);
	double tmp;
	if (z <= -1.95e+183) {
		tmp = ((-4.0 * (a * t)) + (9.0 * (x * (y / z)))) / c;
	} else if (z <= -5.8e-69) {
		tmp = fma(-4.0, (t * (a / c)), fma(9.0, ((y / z) * (x / c)), t_1));
	} else if (z <= 9e+79) {
		tmp = (b + fma(x, (9.0 * y), (a * ((t * 4.0) * -z)))) * (1.0 / (z * c));
	} else {
		tmp = (t_1 + (9.0 * ((x * y) / (z * c)))) - (4.0 * ((a * t) / c));
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(b / Float64(z * c))
	tmp = 0.0
	if (z <= -1.95e+183)
		tmp = Float64(Float64(Float64(-4.0 * Float64(a * t)) + Float64(9.0 * Float64(x * Float64(y / z)))) / c);
	elseif (z <= -5.8e-69)
		tmp = fma(-4.0, Float64(t * Float64(a / c)), fma(9.0, Float64(Float64(y / z) * Float64(x / c)), t_1));
	elseif (z <= 9e+79)
		tmp = Float64(Float64(b + fma(x, Float64(9.0 * y), Float64(a * Float64(Float64(t * 4.0) * Float64(-z))))) * Float64(1.0 / Float64(z * c)));
	else
		tmp = Float64(Float64(t_1 + Float64(9.0 * Float64(Float64(x * y) / Float64(z * c)))) - Float64(4.0 * Float64(Float64(a * t) / c)));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.95e+183], N[(N[(N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision] + N[(9.0 * N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[z, -5.8e-69], N[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision] + N[(9.0 * N[(N[(y / z), $MachinePrecision] * N[(x / c), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9e+79], N[(N[(b + N[(x * N[(9.0 * y), $MachinePrecision] + N[(a * N[(N[(t * 4.0), $MachinePrecision] * (-z)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(1.0 / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t$95$1 + N[(9.0 * N[(N[(x * y), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * N[(N[(a * t), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.9499999999999999e183

   1. Initial program 60.0%

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

   3. Taylor expanded in b around 0 52.8%

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

   4. Taylor expanded in x around 0 81.6%

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

   5. Taylor expanded in c around 0 81.8%

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

      1. add0 81.8%

         \[\leadsto \frac{-4 \cdot \left(a \cdot t\right) + 9 \cdot \color{blue}{\left(\frac{x \cdot y}{z} + 0\right)}}{c} \]

      2. associate-/l* 92.5%

         \[\leadsto \frac{-4 \cdot \left(a \cdot t\right) + 9 \cdot \left(\color{blue}{\frac{x}{\frac{z}{y}}} + 0\right)}{c} \]

   7. Applied egg-rr 92.5%

      \[\leadsto \frac{-4 \cdot \left(a \cdot t\right) + 9 \cdot \color{blue}{\left(\frac{x}{\frac{z}{y}} + 0\right)}}{c} \]
   8. Step-by-step derivation

      1. associate-/l* 81.8%

         \[\leadsto \frac{-4 \cdot \left(a \cdot t\right) + 9 \cdot \left(\color{blue}{\frac{x \cdot y}{z}} + 0\right)}{c} \]

      2. associate-*r/ 92.5%

         \[\leadsto \frac{-4 \cdot \left(a \cdot t\right) + 9 \cdot \left(\color{blue}{x \cdot \frac{y}{z}} + 0\right)}{c} \]

      3. add0 92.5%

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

   9. Simplified 92.5%

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

   if -1.9499999999999999e183 < z < -5.7999999999999997e-69

   1. Initial program 82.9%

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

      1. add0 82.9%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a + 0\right)}\right) + b}{z \cdot c} \]

      2. associate-*l* 86.4%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)} + 0\right)\right) + b}{z \cdot c} \]

   4. Applied egg-rr 86.4%

      \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot \left(t \cdot a\right) + 0\right)}\right) + b}{z \cdot c} \]

   5. Taylor expanded in x around 0 86.9%

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

      1. cancel-sign-sub-inv 86.9%

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

      2. metadata-eval 86.9%

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

      3. +-commutative 86.9%

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

      4. fma-define 86.9%

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

      5. associate-/l* 83.2%

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

      6. associate-/r/ 88.8%

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

      7. fma-define 88.8%

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

      8. times-frac 94.2%

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

      9. *-commutative 94.2%

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

   7. Simplified 94.2%

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

   if -5.7999999999999997e-69 < z < 8.99999999999999987e79

   1. Initial program 95.1%

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

      1. div-inv 95.0%

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

      2. associate-*l* 95.0%

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

      3. fma-neg 95.0%

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

      4. distribute-rgt-neg-in 95.0%

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

      5. associate-*l* 95.0%

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

   4. Applied egg-rr 95.0%

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

   if 8.99999999999999987e79 < z

   1. Initial program 56.0%

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

   3. Taylor expanded in x around 0 87.8%

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

4. Final simplification 93.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.95 \cdot 10^{+183}:\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right) + 9 \cdot \left(x \cdot \frac{y}{z}\right)}{c}\\ \mathbf{elif}\;z \leq -5.8 \cdot 10^{-69}:\\ \;\;\;\;\mathsf{fma}\left(-4, t \cdot \frac{a}{c}, \mathsf{fma}\left(9, \frac{y}{z} \cdot \frac{x}{c}, \frac{b}{z \cdot c}\right)\right)\\ \mathbf{elif}\;z \leq 9 \cdot 10^{+79}:\\ \;\;\;\;\left(b + \mathsf{fma}\left(x, 9 \cdot y, a \cdot \left(\left(t \cdot 4\right) \cdot \left(-z\right)\right)\right)\right) \cdot \frac{1}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{b}{z \cdot c} + 9 \cdot \frac{x \cdot y}{z \cdot c}\right) - 4 \cdot \frac{a \cdot t}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 49.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \frac{1}{z \cdot \frac{c}{b}}\\ t_2 := 9 \cdot \left(\frac{y}{z} \cdot \frac{x}{c}\right)\\ t_3 := -4 \cdot \frac{a \cdot t}{c}\\ \mathbf{if}\;x \leq -2.1 \cdot 10^{+107}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq -6.4 \cdot 10^{-15}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -5.4 \cdot 10^{-166}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;x \leq 6.9 \cdot 10^{-270}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;x \leq 4.3 \cdot 10^{-142}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;x \leq 3.1 \cdot 10^{-97}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ 1.0 (* z (/ c b))))
        (t_2 (* 9.0 (* (/ y z) (/ x c))))
        (t_3 (* -4.0 (/ (* a t) c))))
   (if (<= x -2.1e+107)
     t_2
     (if (<= x -6.4e-15)
       t_1
       (if (<= x -5.4e-166)
         t_3
         (if (<= x 6.9e-270)
           (/ (/ b c) z)
           (if (<= x 4.3e-142) t_3 (if (<= x 3.1e-97) t_1 t_2))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = 1.0 / (z * (c / b));
	double t_2 = 9.0 * ((y / z) * (x / c));
	double t_3 = -4.0 * ((a * t) / c);
	double tmp;
	if (x <= -2.1e+107) {
		tmp = t_2;
	} else if (x <= -6.4e-15) {
		tmp = t_1;
	} else if (x <= -5.4e-166) {
		tmp = t_3;
	} else if (x <= 6.9e-270) {
		tmp = (b / c) / z;
	} else if (x <= 4.3e-142) {
		tmp = t_3;
	} else if (x <= 3.1e-97) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c 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 = 1.0d0 / (z * (c / b))
    t_2 = 9.0d0 * ((y / z) * (x / c))
    t_3 = (-4.0d0) * ((a * t) / c)
    if (x <= (-2.1d+107)) then
        tmp = t_2
    else if (x <= (-6.4d-15)) then
        tmp = t_1
    else if (x <= (-5.4d-166)) then
        tmp = t_3
    else if (x <= 6.9d-270) then
        tmp = (b / c) / z
    else if (x <= 4.3d-142) then
        tmp = t_3
    else if (x <= 3.1d-97) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = 1.0 / (z * (c / b));
	double t_2 = 9.0 * ((y / z) * (x / c));
	double t_3 = -4.0 * ((a * t) / c);
	double tmp;
	if (x <= -2.1e+107) {
		tmp = t_2;
	} else if (x <= -6.4e-15) {
		tmp = t_1;
	} else if (x <= -5.4e-166) {
		tmp = t_3;
	} else if (x <= 6.9e-270) {
		tmp = (b / c) / z;
	} else if (x <= 4.3e-142) {
		tmp = t_3;
	} else if (x <= 3.1e-97) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	t_1 = 1.0 / (z * (c / b))
	t_2 = 9.0 * ((y / z) * (x / c))
	t_3 = -4.0 * ((a * t) / c)
	tmp = 0
	if x <= -2.1e+107:
		tmp = t_2
	elif x <= -6.4e-15:
		tmp = t_1
	elif x <= -5.4e-166:
		tmp = t_3
	elif x <= 6.9e-270:
		tmp = (b / c) / z
	elif x <= 4.3e-142:
		tmp = t_3
	elif x <= 3.1e-97:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(1.0 / Float64(z * Float64(c / b)))
	t_2 = Float64(9.0 * Float64(Float64(y / z) * Float64(x / c)))
	t_3 = Float64(-4.0 * Float64(Float64(a * t) / c))
	tmp = 0.0
	if (x <= -2.1e+107)
		tmp = t_2;
	elseif (x <= -6.4e-15)
		tmp = t_1;
	elseif (x <= -5.4e-166)
		tmp = t_3;
	elseif (x <= 6.9e-270)
		tmp = Float64(Float64(b / c) / z);
	elseif (x <= 4.3e-142)
		tmp = t_3;
	elseif (x <= 3.1e-97)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = 1.0 / (z * (c / b));
	t_2 = 9.0 * ((y / z) * (x / c));
	t_3 = -4.0 * ((a * t) / c);
	tmp = 0.0;
	if (x <= -2.1e+107)
		tmp = t_2;
	elseif (x <= -6.4e-15)
		tmp = t_1;
	elseif (x <= -5.4e-166)
		tmp = t_3;
	elseif (x <= 6.9e-270)
		tmp = (b / c) / z;
	elseif (x <= 4.3e-142)
		tmp = t_3;
	elseif (x <= 3.1e-97)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(1.0 / N[(z * N[(c / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(9.0 * N[(N[(y / z), $MachinePrecision] * N[(x / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(-4.0 * N[(N[(a * t), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.1e+107], t$95$2, If[LessEqual[x, -6.4e-15], t$95$1, If[LessEqual[x, -5.4e-166], t$95$3, If[LessEqual[x, 6.9e-270], N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[x, 4.3e-142], t$95$3, If[LessEqual[x, 3.1e-97], t$95$1, t$95$2]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -2.1e107 or 3.10000000000000002e-97 < x

   1. Initial program 80.4%

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

   3. Taylor expanded in x around inf 56.4%

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

      1. times-frac 59.3%

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

   5. Simplified 59.3%

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

   if -2.1e107 < x < -6.3999999999999999e-15 or 4.2999999999999997e-142 < x < 3.10000000000000002e-97

   1. Initial program 83.0%

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

      1. div-inv 83.2%

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

      2. associate-*l* 83.2%

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

      3. fma-neg 85.6%

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

      4. distribute-rgt-neg-in 85.6%

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

      5. associate-*l* 85.6%

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

   4. Applied egg-rr 85.6%

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

   5. Taylor expanded in b around inf 47.8%

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

      1. *-commutative 47.8%

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

      2. associate-/r* 48.0%

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

   7. Simplified 48.0%

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

      1. div-inv 47.9%

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

   9. Applied egg-rr 47.9%

      \[\leadsto \color{blue}{\frac{b}{z} \cdot \frac{1}{c}} \]
   10. Step-by-step derivation

       1. associate-*l/ 50.0%

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

       2. div-inv 50.1%

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

       3. div-inv 50.1%

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

       4. clear-num 50.2%

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

       5. frac-times 50.2%

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

       6. metadata-eval 50.2%

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

   11. Applied egg-rr 50.2%

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

   if -6.3999999999999999e-15 < x < -5.40000000000000013e-166 or 6.90000000000000041e-270 < x < 4.2999999999999997e-142

   1. Initial program 87.7%

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

   3. Taylor expanded in z around inf 55.4%

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

   if -5.40000000000000013e-166 < x < 6.90000000000000041e-270

   1. Initial program 82.3%

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

      1. add0 82.3%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a + 0\right)}\right) + b}{z \cdot c} \]

      2. associate-*l* 86.0%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)} + 0\right)\right) + b}{z \cdot c} \]

   4. Applied egg-rr 86.0%

      \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot \left(t \cdot a\right) + 0\right)}\right) + b}{z \cdot c} \]

   5. Taylor expanded in b around inf 59.5%

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

      1. associate-/r* 59.6%

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

   7. Simplified 59.6%

      \[\leadsto \color{blue}{\frac{\frac{b}{c}}{z}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 57.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.1 \cdot 10^{+107}:\\ \;\;\;\;9 \cdot \left(\frac{y}{z} \cdot \frac{x}{c}\right)\\ \mathbf{elif}\;x \leq -6.4 \cdot 10^{-15}:\\ \;\;\;\;\frac{1}{z \cdot \frac{c}{b}}\\ \mathbf{elif}\;x \leq -5.4 \cdot 10^{-166}:\\ \;\;\;\;-4 \cdot \frac{a \cdot t}{c}\\ \mathbf{elif}\;x \leq 6.9 \cdot 10^{-270}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;x \leq 4.3 \cdot 10^{-142}:\\ \;\;\;\;-4 \cdot \frac{a \cdot t}{c}\\ \mathbf{elif}\;x \leq 3.1 \cdot 10^{-97}:\\ \;\;\;\;\frac{1}{z \cdot \frac{c}{b}}\\ \mathbf{else}:\\ \;\;\;\;9 \cdot \left(\frac{y}{z} \cdot \frac{x}{c}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 49.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \frac{1}{z \cdot \frac{c}{b}}\\ t_2 := -4 \cdot \frac{a \cdot t}{c}\\ \mathbf{if}\;x \leq -2.1 \cdot 10^{+107}:\\ \;\;\;\;9 \cdot \left(\frac{y}{z} \cdot \frac{x}{c}\right)\\ \mathbf{elif}\;x \leq -6.6 \cdot 10^{-15}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -9 \cdot 10^{-163}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 4.5 \cdot 10^{-271}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;x \leq 2.1 \cdot 10^{-141}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{-97}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;9 \cdot \frac{x \cdot y}{z \cdot c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ 1.0 (* z (/ c b)))) (t_2 (* -4.0 (/ (* a t) c))))
   (if (<= x -2.1e+107)
     (* 9.0 (* (/ y z) (/ x c)))
     (if (<= x -6.6e-15)
       t_1
       (if (<= x -9e-163)
         t_2
         (if (<= x 4.5e-271)
           (/ (/ b c) z)
           (if (<= x 2.1e-141)
             t_2
             (if (<= x 7.5e-97) t_1 (* 9.0 (/ (* x y) (* z c)))))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = 1.0 / (z * (c / b));
	double t_2 = -4.0 * ((a * t) / c);
	double tmp;
	if (x <= -2.1e+107) {
		tmp = 9.0 * ((y / z) * (x / c));
	} else if (x <= -6.6e-15) {
		tmp = t_1;
	} else if (x <= -9e-163) {
		tmp = t_2;
	} else if (x <= 4.5e-271) {
		tmp = (b / c) / z;
	} else if (x <= 2.1e-141) {
		tmp = t_2;
	} else if (x <= 7.5e-97) {
		tmp = t_1;
	} else {
		tmp = 9.0 * ((x * y) / (z * c));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c 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) :: tmp
    t_1 = 1.0d0 / (z * (c / b))
    t_2 = (-4.0d0) * ((a * t) / c)
    if (x <= (-2.1d+107)) then
        tmp = 9.0d0 * ((y / z) * (x / c))
    else if (x <= (-6.6d-15)) then
        tmp = t_1
    else if (x <= (-9d-163)) then
        tmp = t_2
    else if (x <= 4.5d-271) then
        tmp = (b / c) / z
    else if (x <= 2.1d-141) then
        tmp = t_2
    else if (x <= 7.5d-97) then
        tmp = t_1
    else
        tmp = 9.0d0 * ((x * y) / (z * c))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = 1.0 / (z * (c / b));
	double t_2 = -4.0 * ((a * t) / c);
	double tmp;
	if (x <= -2.1e+107) {
		tmp = 9.0 * ((y / z) * (x / c));
	} else if (x <= -6.6e-15) {
		tmp = t_1;
	} else if (x <= -9e-163) {
		tmp = t_2;
	} else if (x <= 4.5e-271) {
		tmp = (b / c) / z;
	} else if (x <= 2.1e-141) {
		tmp = t_2;
	} else if (x <= 7.5e-97) {
		tmp = t_1;
	} else {
		tmp = 9.0 * ((x * y) / (z * c));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	t_1 = 1.0 / (z * (c / b))
	t_2 = -4.0 * ((a * t) / c)
	tmp = 0
	if x <= -2.1e+107:
		tmp = 9.0 * ((y / z) * (x / c))
	elif x <= -6.6e-15:
		tmp = t_1
	elif x <= -9e-163:
		tmp = t_2
	elif x <= 4.5e-271:
		tmp = (b / c) / z
	elif x <= 2.1e-141:
		tmp = t_2
	elif x <= 7.5e-97:
		tmp = t_1
	else:
		tmp = 9.0 * ((x * y) / (z * c))
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(1.0 / Float64(z * Float64(c / b)))
	t_2 = Float64(-4.0 * Float64(Float64(a * t) / c))
	tmp = 0.0
	if (x <= -2.1e+107)
		tmp = Float64(9.0 * Float64(Float64(y / z) * Float64(x / c)));
	elseif (x <= -6.6e-15)
		tmp = t_1;
	elseif (x <= -9e-163)
		tmp = t_2;
	elseif (x <= 4.5e-271)
		tmp = Float64(Float64(b / c) / z);
	elseif (x <= 2.1e-141)
		tmp = t_2;
	elseif (x <= 7.5e-97)
		tmp = t_1;
	else
		tmp = Float64(9.0 * Float64(Float64(x * y) / Float64(z * c)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = 1.0 / (z * (c / b));
	t_2 = -4.0 * ((a * t) / c);
	tmp = 0.0;
	if (x <= -2.1e+107)
		tmp = 9.0 * ((y / z) * (x / c));
	elseif (x <= -6.6e-15)
		tmp = t_1;
	elseif (x <= -9e-163)
		tmp = t_2;
	elseif (x <= 4.5e-271)
		tmp = (b / c) / z;
	elseif (x <= 2.1e-141)
		tmp = t_2;
	elseif (x <= 7.5e-97)
		tmp = t_1;
	else
		tmp = 9.0 * ((x * y) / (z * c));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(1.0 / N[(z * N[(c / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(-4.0 * N[(N[(a * t), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.1e+107], N[(9.0 * N[(N[(y / z), $MachinePrecision] * N[(x / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -6.6e-15], t$95$1, If[LessEqual[x, -9e-163], t$95$2, If[LessEqual[x, 4.5e-271], N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[x, 2.1e-141], t$95$2, If[LessEqual[x, 7.5e-97], t$95$1, N[(9.0 * N[(N[(x * y), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -2.1e107

   1. Initial program 78.6%

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

   3. Taylor expanded in x around inf 64.2%

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

      1. times-frac 74.2%

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

   5. Simplified 74.2%

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

   if -2.1e107 < x < -6.6e-15 or 2.0999999999999999e-141 < x < 7.5e-97

   1. Initial program 83.0%

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

      1. div-inv 83.2%

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

      2. associate-*l* 83.2%

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

      3. fma-neg 85.6%

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

      4. distribute-rgt-neg-in 85.6%

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

      5. associate-*l* 85.6%

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

   4. Applied egg-rr 85.6%

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

   5. Taylor expanded in b around inf 47.8%

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

      1. *-commutative 47.8%

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

      2. associate-/r* 48.0%

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

   7. Simplified 48.0%

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

      1. div-inv 47.9%

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

   9. Applied egg-rr 47.9%

      \[\leadsto \color{blue}{\frac{b}{z} \cdot \frac{1}{c}} \]
   10. Step-by-step derivation

       1. associate-*l/ 50.0%

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

       2. div-inv 50.1%

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

       3. div-inv 50.1%

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

       4. clear-num 50.2%

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

       5. frac-times 50.2%

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

       6. metadata-eval 50.2%

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

   11. Applied egg-rr 50.2%

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

   if -6.6e-15 < x < -8.9999999999999995e-163 or 4.4999999999999998e-271 < x < 2.0999999999999999e-141

   1. Initial program 87.7%

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

   3. Taylor expanded in z around inf 55.4%

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

   if -8.9999999999999995e-163 < x < 4.4999999999999998e-271

   1. Initial program 82.3%

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

      1. add0 82.3%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a + 0\right)}\right) + b}{z \cdot c} \]

      2. associate-*l* 86.0%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)} + 0\right)\right) + b}{z \cdot c} \]

   4. Applied egg-rr 86.0%

      \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot \left(t \cdot a\right) + 0\right)}\right) + b}{z \cdot c} \]

   5. Taylor expanded in b around inf 59.5%

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

      1. associate-/r* 59.6%

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

   7. Simplified 59.6%

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

   if 7.5e-97 < x

   1. Initial program 81.5%

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

   3. Taylor expanded in x around inf 52.0%

      \[\leadsto \color{blue}{9 \cdot \frac{x \cdot y}{c \cdot z}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 57.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.1 \cdot 10^{+107}:\\ \;\;\;\;9 \cdot \left(\frac{y}{z} \cdot \frac{x}{c}\right)\\ \mathbf{elif}\;x \leq -6.6 \cdot 10^{-15}:\\ \;\;\;\;\frac{1}{z \cdot \frac{c}{b}}\\ \mathbf{elif}\;x \leq -9 \cdot 10^{-163}:\\ \;\;\;\;-4 \cdot \frac{a \cdot t}{c}\\ \mathbf{elif}\;x \leq 4.5 \cdot 10^{-271}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;x \leq 2.1 \cdot 10^{-141}:\\ \;\;\;\;-4 \cdot \frac{a \cdot t}{c}\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{-97}:\\ \;\;\;\;\frac{1}{z \cdot \frac{c}{b}}\\ \mathbf{else}:\\ \;\;\;\;9 \cdot \frac{x \cdot y}{z \cdot c}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 49.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \frac{1}{z \cdot \frac{c}{b}}\\ t_2 := -4 \cdot \frac{a \cdot t}{c}\\ \mathbf{if}\;x \leq -2.1 \cdot 10^{+107}:\\ \;\;\;\;9 \cdot \left(\frac{y}{z} \cdot \frac{x}{c}\right)\\ \mathbf{elif}\;x \leq -3.8 \cdot 10^{-15}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -9.5 \cdot 10^{-164}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 1.85 \cdot 10^{-270}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;x \leq 4.9 \cdot 10^{-142}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{-97}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;9 \cdot \frac{\frac{x \cdot y}{c}}{z}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ 1.0 (* z (/ c b)))) (t_2 (* -4.0 (/ (* a t) c))))
   (if (<= x -2.1e+107)
     (* 9.0 (* (/ y z) (/ x c)))
     (if (<= x -3.8e-15)
       t_1
       (if (<= x -9.5e-164)
         t_2
         (if (<= x 1.85e-270)
           (/ (/ b c) z)
           (if (<= x 4.9e-142)
             t_2
             (if (<= x 1.5e-97) t_1 (* 9.0 (/ (/ (* x y) c) z))))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = 1.0 / (z * (c / b));
	double t_2 = -4.0 * ((a * t) / c);
	double tmp;
	if (x <= -2.1e+107) {
		tmp = 9.0 * ((y / z) * (x / c));
	} else if (x <= -3.8e-15) {
		tmp = t_1;
	} else if (x <= -9.5e-164) {
		tmp = t_2;
	} else if (x <= 1.85e-270) {
		tmp = (b / c) / z;
	} else if (x <= 4.9e-142) {
		tmp = t_2;
	} else if (x <= 1.5e-97) {
		tmp = t_1;
	} else {
		tmp = 9.0 * (((x * y) / c) / z);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c 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) :: tmp
    t_1 = 1.0d0 / (z * (c / b))
    t_2 = (-4.0d0) * ((a * t) / c)
    if (x <= (-2.1d+107)) then
        tmp = 9.0d0 * ((y / z) * (x / c))
    else if (x <= (-3.8d-15)) then
        tmp = t_1
    else if (x <= (-9.5d-164)) then
        tmp = t_2
    else if (x <= 1.85d-270) then
        tmp = (b / c) / z
    else if (x <= 4.9d-142) then
        tmp = t_2
    else if (x <= 1.5d-97) then
        tmp = t_1
    else
        tmp = 9.0d0 * (((x * y) / c) / z)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = 1.0 / (z * (c / b));
	double t_2 = -4.0 * ((a * t) / c);
	double tmp;
	if (x <= -2.1e+107) {
		tmp = 9.0 * ((y / z) * (x / c));
	} else if (x <= -3.8e-15) {
		tmp = t_1;
	} else if (x <= -9.5e-164) {
		tmp = t_2;
	} else if (x <= 1.85e-270) {
		tmp = (b / c) / z;
	} else if (x <= 4.9e-142) {
		tmp = t_2;
	} else if (x <= 1.5e-97) {
		tmp = t_1;
	} else {
		tmp = 9.0 * (((x * y) / c) / z);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	t_1 = 1.0 / (z * (c / b))
	t_2 = -4.0 * ((a * t) / c)
	tmp = 0
	if x <= -2.1e+107:
		tmp = 9.0 * ((y / z) * (x / c))
	elif x <= -3.8e-15:
		tmp = t_1
	elif x <= -9.5e-164:
		tmp = t_2
	elif x <= 1.85e-270:
		tmp = (b / c) / z
	elif x <= 4.9e-142:
		tmp = t_2
	elif x <= 1.5e-97:
		tmp = t_1
	else:
		tmp = 9.0 * (((x * y) / c) / z)
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(1.0 / Float64(z * Float64(c / b)))
	t_2 = Float64(-4.0 * Float64(Float64(a * t) / c))
	tmp = 0.0
	if (x <= -2.1e+107)
		tmp = Float64(9.0 * Float64(Float64(y / z) * Float64(x / c)));
	elseif (x <= -3.8e-15)
		tmp = t_1;
	elseif (x <= -9.5e-164)
		tmp = t_2;
	elseif (x <= 1.85e-270)
		tmp = Float64(Float64(b / c) / z);
	elseif (x <= 4.9e-142)
		tmp = t_2;
	elseif (x <= 1.5e-97)
		tmp = t_1;
	else
		tmp = Float64(9.0 * Float64(Float64(Float64(x * y) / c) / z));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = 1.0 / (z * (c / b));
	t_2 = -4.0 * ((a * t) / c);
	tmp = 0.0;
	if (x <= -2.1e+107)
		tmp = 9.0 * ((y / z) * (x / c));
	elseif (x <= -3.8e-15)
		tmp = t_1;
	elseif (x <= -9.5e-164)
		tmp = t_2;
	elseif (x <= 1.85e-270)
		tmp = (b / c) / z;
	elseif (x <= 4.9e-142)
		tmp = t_2;
	elseif (x <= 1.5e-97)
		tmp = t_1;
	else
		tmp = 9.0 * (((x * y) / c) / z);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(1.0 / N[(z * N[(c / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(-4.0 * N[(N[(a * t), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.1e+107], N[(9.0 * N[(N[(y / z), $MachinePrecision] * N[(x / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -3.8e-15], t$95$1, If[LessEqual[x, -9.5e-164], t$95$2, If[LessEqual[x, 1.85e-270], N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[x, 4.9e-142], t$95$2, If[LessEqual[x, 1.5e-97], t$95$1, N[(9.0 * N[(N[(N[(x * y), $MachinePrecision] / c), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -2.1e107

   1. Initial program 78.6%

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

   3. Taylor expanded in x around inf 64.2%

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

      1. times-frac 74.2%

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

   5. Simplified 74.2%

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

   if -2.1e107 < x < -3.8000000000000002e-15 or 4.9000000000000003e-142 < x < 1.50000000000000012e-97

   1. Initial program 83.0%

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

      1. div-inv 83.2%

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

      2. associate-*l* 83.2%

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

      3. fma-neg 85.6%

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

      4. distribute-rgt-neg-in 85.6%

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

      5. associate-*l* 85.6%

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

   4. Applied egg-rr 85.6%

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

   5. Taylor expanded in b around inf 47.8%

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

      1. *-commutative 47.8%

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

      2. associate-/r* 48.0%

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

   7. Simplified 48.0%

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

      1. div-inv 47.9%

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

   9. Applied egg-rr 47.9%

      \[\leadsto \color{blue}{\frac{b}{z} \cdot \frac{1}{c}} \]
   10. Step-by-step derivation

       1. associate-*l/ 50.0%

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

       2. div-inv 50.1%

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

       3. div-inv 50.1%

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

       4. clear-num 50.2%

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

       5. frac-times 50.2%

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

       6. metadata-eval 50.2%

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

   11. Applied egg-rr 50.2%

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

   if -3.8000000000000002e-15 < x < -9.5000000000000001e-164 or 1.8500000000000001e-270 < x < 4.9000000000000003e-142

   1. Initial program 87.7%

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

   3. Taylor expanded in z around inf 55.4%

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

   if -9.5000000000000001e-164 < x < 1.8500000000000001e-270

   1. Initial program 82.3%

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

      1. add0 82.3%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a + 0\right)}\right) + b}{z \cdot c} \]

      2. associate-*l* 86.0%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)} + 0\right)\right) + b}{z \cdot c} \]

   4. Applied egg-rr 86.0%

      \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot \left(t \cdot a\right) + 0\right)}\right) + b}{z \cdot c} \]

   5. Taylor expanded in b around inf 59.5%

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

      1. associate-/r* 59.6%

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

   7. Simplified 59.6%

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

   if 1.50000000000000012e-97 < x

   1. Initial program 81.5%

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

   3. Taylor expanded in x around inf 52.0%

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

      1. div-inv 51.9%

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

      2. *-commutative 51.9%

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

   5. Applied egg-rr 51.9%

      \[\leadsto 9 \cdot \color{blue}{\left(\left(x \cdot y\right) \cdot \frac{1}{z \cdot c}\right)} \]
   6. Step-by-step derivation

      1. *-commutative 51.9%

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

      2. div-inv 52.0%

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

      3. associate-/r* 51.1%

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

   7. Applied egg-rr 51.1%

      \[\leadsto 9 \cdot \color{blue}{\frac{\frac{x \cdot y}{c}}{z}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 57.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.1 \cdot 10^{+107}:\\ \;\;\;\;9 \cdot \left(\frac{y}{z} \cdot \frac{x}{c}\right)\\ \mathbf{elif}\;x \leq -3.8 \cdot 10^{-15}:\\ \;\;\;\;\frac{1}{z \cdot \frac{c}{b}}\\ \mathbf{elif}\;x \leq -9.5 \cdot 10^{-164}:\\ \;\;\;\;-4 \cdot \frac{a \cdot t}{c}\\ \mathbf{elif}\;x \leq 1.85 \cdot 10^{-270}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;x \leq 4.9 \cdot 10^{-142}:\\ \;\;\;\;-4 \cdot \frac{a \cdot t}{c}\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{-97}:\\ \;\;\;\;\frac{1}{z \cdot \frac{c}{b}}\\ \mathbf{else}:\\ \;\;\;\;9 \cdot \frac{\frac{x \cdot y}{c}}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 49.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \frac{1}{z \cdot \frac{c}{b}}\\ t_2 := -4 \cdot \frac{a \cdot t}{c}\\ \mathbf{if}\;x \leq -2.1 \cdot 10^{+107}:\\ \;\;\;\;9 \cdot \left(\frac{y}{z} \cdot \frac{x}{c}\right)\\ \mathbf{elif}\;x \leq -7.6 \cdot 10^{-15}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -8 \cdot 10^{-165}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 6 \cdot 10^{-270}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;x \leq 3.7 \cdot 10^{-142}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 7.6 \cdot 10^{-97}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot \frac{x}{c}\right) \cdot \frac{9}{z}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ 1.0 (* z (/ c b)))) (t_2 (* -4.0 (/ (* a t) c))))
   (if (<= x -2.1e+107)
     (* 9.0 (* (/ y z) (/ x c)))
     (if (<= x -7.6e-15)
       t_1
       (if (<= x -8e-165)
         t_2
         (if (<= x 6e-270)
           (/ (/ b c) z)
           (if (<= x 3.7e-142)
             t_2
             (if (<= x 7.6e-97) t_1 (* (* y (/ x c)) (/ 9.0 z))))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = 1.0 / (z * (c / b));
	double t_2 = -4.0 * ((a * t) / c);
	double tmp;
	if (x <= -2.1e+107) {
		tmp = 9.0 * ((y / z) * (x / c));
	} else if (x <= -7.6e-15) {
		tmp = t_1;
	} else if (x <= -8e-165) {
		tmp = t_2;
	} else if (x <= 6e-270) {
		tmp = (b / c) / z;
	} else if (x <= 3.7e-142) {
		tmp = t_2;
	} else if (x <= 7.6e-97) {
		tmp = t_1;
	} else {
		tmp = (y * (x / c)) * (9.0 / z);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c 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) :: tmp
    t_1 = 1.0d0 / (z * (c / b))
    t_2 = (-4.0d0) * ((a * t) / c)
    if (x <= (-2.1d+107)) then
        tmp = 9.0d0 * ((y / z) * (x / c))
    else if (x <= (-7.6d-15)) then
        tmp = t_1
    else if (x <= (-8d-165)) then
        tmp = t_2
    else if (x <= 6d-270) then
        tmp = (b / c) / z
    else if (x <= 3.7d-142) then
        tmp = t_2
    else if (x <= 7.6d-97) then
        tmp = t_1
    else
        tmp = (y * (x / c)) * (9.0d0 / z)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = 1.0 / (z * (c / b));
	double t_2 = -4.0 * ((a * t) / c);
	double tmp;
	if (x <= -2.1e+107) {
		tmp = 9.0 * ((y / z) * (x / c));
	} else if (x <= -7.6e-15) {
		tmp = t_1;
	} else if (x <= -8e-165) {
		tmp = t_2;
	} else if (x <= 6e-270) {
		tmp = (b / c) / z;
	} else if (x <= 3.7e-142) {
		tmp = t_2;
	} else if (x <= 7.6e-97) {
		tmp = t_1;
	} else {
		tmp = (y * (x / c)) * (9.0 / z);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	t_1 = 1.0 / (z * (c / b))
	t_2 = -4.0 * ((a * t) / c)
	tmp = 0
	if x <= -2.1e+107:
		tmp = 9.0 * ((y / z) * (x / c))
	elif x <= -7.6e-15:
		tmp = t_1
	elif x <= -8e-165:
		tmp = t_2
	elif x <= 6e-270:
		tmp = (b / c) / z
	elif x <= 3.7e-142:
		tmp = t_2
	elif x <= 7.6e-97:
		tmp = t_1
	else:
		tmp = (y * (x / c)) * (9.0 / z)
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(1.0 / Float64(z * Float64(c / b)))
	t_2 = Float64(-4.0 * Float64(Float64(a * t) / c))
	tmp = 0.0
	if (x <= -2.1e+107)
		tmp = Float64(9.0 * Float64(Float64(y / z) * Float64(x / c)));
	elseif (x <= -7.6e-15)
		tmp = t_1;
	elseif (x <= -8e-165)
		tmp = t_2;
	elseif (x <= 6e-270)
		tmp = Float64(Float64(b / c) / z);
	elseif (x <= 3.7e-142)
		tmp = t_2;
	elseif (x <= 7.6e-97)
		tmp = t_1;
	else
		tmp = Float64(Float64(y * Float64(x / c)) * Float64(9.0 / z));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = 1.0 / (z * (c / b));
	t_2 = -4.0 * ((a * t) / c);
	tmp = 0.0;
	if (x <= -2.1e+107)
		tmp = 9.0 * ((y / z) * (x / c));
	elseif (x <= -7.6e-15)
		tmp = t_1;
	elseif (x <= -8e-165)
		tmp = t_2;
	elseif (x <= 6e-270)
		tmp = (b / c) / z;
	elseif (x <= 3.7e-142)
		tmp = t_2;
	elseif (x <= 7.6e-97)
		tmp = t_1;
	else
		tmp = (y * (x / c)) * (9.0 / z);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(1.0 / N[(z * N[(c / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(-4.0 * N[(N[(a * t), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.1e+107], N[(9.0 * N[(N[(y / z), $MachinePrecision] * N[(x / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -7.6e-15], t$95$1, If[LessEqual[x, -8e-165], t$95$2, If[LessEqual[x, 6e-270], N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[x, 3.7e-142], t$95$2, If[LessEqual[x, 7.6e-97], t$95$1, N[(N[(y * N[(x / c), $MachinePrecision]), $MachinePrecision] * N[(9.0 / z), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -2.1e107

   1. Initial program 78.6%

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

   3. Taylor expanded in x around inf 64.2%

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

      1. times-frac 74.2%

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

   5. Simplified 74.2%

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

   if -2.1e107 < x < -7.6000000000000004e-15 or 3.69999999999999986e-142 < x < 7.6000000000000001e-97

   1. Initial program 83.0%

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

      1. div-inv 83.2%

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

      2. associate-*l* 83.2%

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

      3. fma-neg 85.6%

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

      4. distribute-rgt-neg-in 85.6%

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

      5. associate-*l* 85.6%

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

   4. Applied egg-rr 85.6%

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

   5. Taylor expanded in b around inf 47.8%

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

      1. *-commutative 47.8%

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

      2. associate-/r* 48.0%

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

   7. Simplified 48.0%

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

      1. div-inv 47.9%

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

   9. Applied egg-rr 47.9%

      \[\leadsto \color{blue}{\frac{b}{z} \cdot \frac{1}{c}} \]
   10. Step-by-step derivation

       1. associate-*l/ 50.0%

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

       2. div-inv 50.1%

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

       3. div-inv 50.1%

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

       4. clear-num 50.2%

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

       5. frac-times 50.2%

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

       6. metadata-eval 50.2%

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

   11. Applied egg-rr 50.2%

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

   if -7.6000000000000004e-15 < x < -8.0000000000000001e-165 or 6.00000000000000025e-270 < x < 3.69999999999999986e-142

   1. Initial program 87.7%

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

   3. Taylor expanded in z around inf 55.4%

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

   if -8.0000000000000001e-165 < x < 6.00000000000000025e-270

   1. Initial program 82.3%

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

      1. add0 82.3%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a + 0\right)}\right) + b}{z \cdot c} \]

      2. associate-*l* 86.0%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)} + 0\right)\right) + b}{z \cdot c} \]

   4. Applied egg-rr 86.0%

      \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot \left(t \cdot a\right) + 0\right)}\right) + b}{z \cdot c} \]

   5. Taylor expanded in b around inf 59.5%

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

      1. associate-/r* 59.6%

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

   7. Simplified 59.6%

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

   if 7.6000000000000001e-97 < x

   1. Initial program 81.5%

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

      1. add0 81.5%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a + 0\right)}\right) + b}{z \cdot c} \]

      2. associate-*l* 82.8%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)} + 0\right)\right) + b}{z \cdot c} \]

   4. Applied egg-rr 82.8%

      \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot \left(t \cdot a\right) + 0\right)}\right) + b}{z \cdot c} \]

   5. Taylor expanded in x around inf 52.0%

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

      1. associate-*r/ 52.0%

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

      2. *-commutative 52.0%

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

      3. times-frac 51.0%

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

      4. associate-/l* 53.4%

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

   7. Simplified 53.4%

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

      1. associate-/r/ 54.6%

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

   9. Applied egg-rr 54.6%

      \[\leadsto \color{blue}{\left(\frac{x}{c} \cdot y\right)} \cdot \frac{9}{z} \]
3. Recombined 5 regimes into one program.

4. Final simplification 58.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.1 \cdot 10^{+107}:\\ \;\;\;\;9 \cdot \left(\frac{y}{z} \cdot \frac{x}{c}\right)\\ \mathbf{elif}\;x \leq -7.6 \cdot 10^{-15}:\\ \;\;\;\;\frac{1}{z \cdot \frac{c}{b}}\\ \mathbf{elif}\;x \leq -8 \cdot 10^{-165}:\\ \;\;\;\;-4 \cdot \frac{a \cdot t}{c}\\ \mathbf{elif}\;x \leq 6 \cdot 10^{-270}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;x \leq 3.7 \cdot 10^{-142}:\\ \;\;\;\;-4 \cdot \frac{a \cdot t}{c}\\ \mathbf{elif}\;x \leq 7.6 \cdot 10^{-97}:\\ \;\;\;\;\frac{1}{z \cdot \frac{c}{b}}\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot \frac{x}{c}\right) \cdot \frac{9}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 49.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \frac{1}{z \cdot \frac{c}{b}}\\ t_2 := -4 \cdot \frac{a \cdot t}{c}\\ \mathbf{if}\;x \leq -6.6 \cdot 10^{+108}:\\ \;\;\;\;\frac{y}{z} \cdot \frac{9 \cdot x}{c}\\ \mathbf{elif}\;x \leq -3.4 \cdot 10^{-15}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -9 \cdot 10^{-164}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{-272}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;x \leq 5.1 \cdot 10^{-142}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 7.6 \cdot 10^{-97}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot \frac{x}{c}\right) \cdot \frac{9}{z}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ 1.0 (* z (/ c b)))) (t_2 (* -4.0 (/ (* a t) c))))
   (if (<= x -6.6e+108)
     (* (/ y z) (/ (* 9.0 x) c))
     (if (<= x -3.4e-15)
       t_1
       (if (<= x -9e-164)
         t_2
         (if (<= x 7.5e-272)
           (/ (/ b c) z)
           (if (<= x 5.1e-142)
             t_2
             (if (<= x 7.6e-97) t_1 (* (* y (/ x c)) (/ 9.0 z))))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = 1.0 / (z * (c / b));
	double t_2 = -4.0 * ((a * t) / c);
	double tmp;
	if (x <= -6.6e+108) {
		tmp = (y / z) * ((9.0 * x) / c);
	} else if (x <= -3.4e-15) {
		tmp = t_1;
	} else if (x <= -9e-164) {
		tmp = t_2;
	} else if (x <= 7.5e-272) {
		tmp = (b / c) / z;
	} else if (x <= 5.1e-142) {
		tmp = t_2;
	} else if (x <= 7.6e-97) {
		tmp = t_1;
	} else {
		tmp = (y * (x / c)) * (9.0 / z);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c 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) :: tmp
    t_1 = 1.0d0 / (z * (c / b))
    t_2 = (-4.0d0) * ((a * t) / c)
    if (x <= (-6.6d+108)) then
        tmp = (y / z) * ((9.0d0 * x) / c)
    else if (x <= (-3.4d-15)) then
        tmp = t_1
    else if (x <= (-9d-164)) then
        tmp = t_2
    else if (x <= 7.5d-272) then
        tmp = (b / c) / z
    else if (x <= 5.1d-142) then
        tmp = t_2
    else if (x <= 7.6d-97) then
        tmp = t_1
    else
        tmp = (y * (x / c)) * (9.0d0 / z)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = 1.0 / (z * (c / b));
	double t_2 = -4.0 * ((a * t) / c);
	double tmp;
	if (x <= -6.6e+108) {
		tmp = (y / z) * ((9.0 * x) / c);
	} else if (x <= -3.4e-15) {
		tmp = t_1;
	} else if (x <= -9e-164) {
		tmp = t_2;
	} else if (x <= 7.5e-272) {
		tmp = (b / c) / z;
	} else if (x <= 5.1e-142) {
		tmp = t_2;
	} else if (x <= 7.6e-97) {
		tmp = t_1;
	} else {
		tmp = (y * (x / c)) * (9.0 / z);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	t_1 = 1.0 / (z * (c / b))
	t_2 = -4.0 * ((a * t) / c)
	tmp = 0
	if x <= -6.6e+108:
		tmp = (y / z) * ((9.0 * x) / c)
	elif x <= -3.4e-15:
		tmp = t_1
	elif x <= -9e-164:
		tmp = t_2
	elif x <= 7.5e-272:
		tmp = (b / c) / z
	elif x <= 5.1e-142:
		tmp = t_2
	elif x <= 7.6e-97:
		tmp = t_1
	else:
		tmp = (y * (x / c)) * (9.0 / z)
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(1.0 / Float64(z * Float64(c / b)))
	t_2 = Float64(-4.0 * Float64(Float64(a * t) / c))
	tmp = 0.0
	if (x <= -6.6e+108)
		tmp = Float64(Float64(y / z) * Float64(Float64(9.0 * x) / c));
	elseif (x <= -3.4e-15)
		tmp = t_1;
	elseif (x <= -9e-164)
		tmp = t_2;
	elseif (x <= 7.5e-272)
		tmp = Float64(Float64(b / c) / z);
	elseif (x <= 5.1e-142)
		tmp = t_2;
	elseif (x <= 7.6e-97)
		tmp = t_1;
	else
		tmp = Float64(Float64(y * Float64(x / c)) * Float64(9.0 / z));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = 1.0 / (z * (c / b));
	t_2 = -4.0 * ((a * t) / c);
	tmp = 0.0;
	if (x <= -6.6e+108)
		tmp = (y / z) * ((9.0 * x) / c);
	elseif (x <= -3.4e-15)
		tmp = t_1;
	elseif (x <= -9e-164)
		tmp = t_2;
	elseif (x <= 7.5e-272)
		tmp = (b / c) / z;
	elseif (x <= 5.1e-142)
		tmp = t_2;
	elseif (x <= 7.6e-97)
		tmp = t_1;
	else
		tmp = (y * (x / c)) * (9.0 / z);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(1.0 / N[(z * N[(c / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(-4.0 * N[(N[(a * t), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -6.6e+108], N[(N[(y / z), $MachinePrecision] * N[(N[(9.0 * x), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -3.4e-15], t$95$1, If[LessEqual[x, -9e-164], t$95$2, If[LessEqual[x, 7.5e-272], N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[x, 5.1e-142], t$95$2, If[LessEqual[x, 7.6e-97], t$95$1, N[(N[(y * N[(x / c), $MachinePrecision]), $MachinePrecision] * N[(9.0 / z), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -6.60000000000000038e108

   1. Initial program 78.6%

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

   3. Taylor expanded in x around inf 64.2%

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

      1. associate-*r/ 64.2%

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

      2. *-commutative 64.2%

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

      3. *-commutative 64.2%

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

      4. associate-*l* 64.2%

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

      5. *-commutative 64.2%

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

      6. times-frac 74.2%

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

      7. *-commutative 74.2%

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

   5. Simplified 74.2%

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

   if -6.60000000000000038e108 < x < -3.4e-15 or 5.1000000000000001e-142 < x < 7.6000000000000001e-97

   1. Initial program 83.0%

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

      1. div-inv 83.2%

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

      2. associate-*l* 83.2%

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

      3. fma-neg 85.6%

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

      4. distribute-rgt-neg-in 85.6%

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

      5. associate-*l* 85.6%

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

   4. Applied egg-rr 85.6%

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

   5. Taylor expanded in b around inf 47.8%

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

      1. *-commutative 47.8%

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

      2. associate-/r* 48.0%

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

   7. Simplified 48.0%

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

      1. div-inv 47.9%

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

   9. Applied egg-rr 47.9%

      \[\leadsto \color{blue}{\frac{b}{z} \cdot \frac{1}{c}} \]
   10. Step-by-step derivation

       1. associate-*l/ 50.0%

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

       2. div-inv 50.1%

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

       3. div-inv 50.1%

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

       4. clear-num 50.2%

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

       5. frac-times 50.2%

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

       6. metadata-eval 50.2%

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

   11. Applied egg-rr 50.2%

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

   if -3.4e-15 < x < -8.9999999999999995e-164 or 7.50000000000000005e-272 < x < 5.1000000000000001e-142

   1. Initial program 87.9%

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

   3. Taylor expanded in z around inf 54.5%

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

   if -8.9999999999999995e-164 < x < 7.50000000000000005e-272

   1. Initial program 81.7%

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

      1. add0 81.7%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a + 0\right)}\right) + b}{z \cdot c} \]

      2. associate-*l* 85.5%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)} + 0\right)\right) + b}{z \cdot c} \]

   4. Applied egg-rr 85.5%

      \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot \left(t \cdot a\right) + 0\right)}\right) + b}{z \cdot c} \]

   5. Taylor expanded in b around inf 58.2%

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

      1. associate-/r* 58.4%

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

   7. Simplified 58.4%

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

   if 7.6000000000000001e-97 < x

   1. Initial program 81.5%

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

      1. add0 81.5%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a + 0\right)}\right) + b}{z \cdot c} \]

      2. associate-*l* 82.8%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)} + 0\right)\right) + b}{z \cdot c} \]

   4. Applied egg-rr 82.8%

      \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot \left(t \cdot a\right) + 0\right)}\right) + b}{z \cdot c} \]

   5. Taylor expanded in x around inf 52.0%

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

      1. associate-*r/ 52.0%

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

      2. *-commutative 52.0%

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

      3. times-frac 51.0%

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

      4. associate-/l* 53.4%

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

   7. Simplified 53.4%

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

      1. associate-/r/ 54.6%

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

   9. Applied egg-rr 54.6%

      \[\leadsto \color{blue}{\left(\frac{x}{c} \cdot y\right)} \cdot \frac{9}{z} \]
3. Recombined 5 regimes into one program.

4. Final simplification 57.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.6 \cdot 10^{+108}:\\ \;\;\;\;\frac{y}{z} \cdot \frac{9 \cdot x}{c}\\ \mathbf{elif}\;x \leq -3.4 \cdot 10^{-15}:\\ \;\;\;\;\frac{1}{z \cdot \frac{c}{b}}\\ \mathbf{elif}\;x \leq -9 \cdot 10^{-164}:\\ \;\;\;\;-4 \cdot \frac{a \cdot t}{c}\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{-272}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;x \leq 5.1 \cdot 10^{-142}:\\ \;\;\;\;-4 \cdot \frac{a \cdot t}{c}\\ \mathbf{elif}\;x \leq 7.6 \cdot 10^{-97}:\\ \;\;\;\;\frac{1}{z \cdot \frac{c}{b}}\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot \frac{x}{c}\right) \cdot \frac{9}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 88.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{+134}:\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right) + 9 \cdot \left(x \cdot \frac{y}{z}\right)}{c}\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+72}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(9 \cdot x\right) - t \cdot \left(a \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{b}{z \cdot c} + 9 \cdot \frac{x \cdot y}{z \cdot c}\right) - 4 \cdot \frac{a \cdot t}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= z -8e+134)
   (/ (+ (* -4.0 (* a t)) (* 9.0 (* x (/ y z)))) c)
   (if (<= z 2e+72)
     (/ (+ b (- (* y (* 9.0 x)) (* t (* a (* z 4.0))))) (* z c))
     (- (+ (/ b (* z c)) (* 9.0 (/ (* x y) (* z c)))) (* 4.0 (/ (* a t) c))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (z <= -8e+134) {
		tmp = ((-4.0 * (a * t)) + (9.0 * (x * (y / z)))) / c;
	} else if (z <= 2e+72) {
		tmp = (b + ((y * (9.0 * x)) - (t * (a * (z * 4.0))))) / (z * c);
	} else {
		tmp = ((b / (z * c)) + (9.0 * ((x * y) / (z * c)))) - (4.0 * ((a * t) / c));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c 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 <= (-8d+134)) then
        tmp = (((-4.0d0) * (a * t)) + (9.0d0 * (x * (y / z)))) / c
    else if (z <= 2d+72) then
        tmp = (b + ((y * (9.0d0 * x)) - (t * (a * (z * 4.0d0))))) / (z * c)
    else
        tmp = ((b / (z * c)) + (9.0d0 * ((x * y) / (z * c)))) - (4.0d0 * ((a * t) / c))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (z <= -8e+134) {
		tmp = ((-4.0 * (a * t)) + (9.0 * (x * (y / z)))) / c;
	} else if (z <= 2e+72) {
		tmp = (b + ((y * (9.0 * x)) - (t * (a * (z * 4.0))))) / (z * c);
	} else {
		tmp = ((b / (z * c)) + (9.0 * ((x * y) / (z * c)))) - (4.0 * ((a * t) / c));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if z <= -8e+134:
		tmp = ((-4.0 * (a * t)) + (9.0 * (x * (y / z)))) / c
	elif z <= 2e+72:
		tmp = (b + ((y * (9.0 * x)) - (t * (a * (z * 4.0))))) / (z * c)
	else:
		tmp = ((b / (z * c)) + (9.0 * ((x * y) / (z * c)))) - (4.0 * ((a * t) / c))
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (z <= -8e+134)
		tmp = Float64(Float64(Float64(-4.0 * Float64(a * t)) + Float64(9.0 * Float64(x * Float64(y / z)))) / c);
	elseif (z <= 2e+72)
		tmp = Float64(Float64(b + Float64(Float64(y * Float64(9.0 * x)) - Float64(t * Float64(a * Float64(z * 4.0))))) / Float64(z * c));
	else
		tmp = Float64(Float64(Float64(b / Float64(z * c)) + Float64(9.0 * Float64(Float64(x * y) / Float64(z * c)))) - Float64(4.0 * Float64(Float64(a * t) / c)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (z <= -8e+134)
		tmp = ((-4.0 * (a * t)) + (9.0 * (x * (y / z)))) / c;
	elseif (z <= 2e+72)
		tmp = (b + ((y * (9.0 * x)) - (t * (a * (z * 4.0))))) / (z * c);
	else
		tmp = ((b / (z * c)) + (9.0 * ((x * y) / (z * c)))) - (4.0 * ((a * t) / c));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[z, -8e+134], N[(N[(N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision] + N[(9.0 * N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[z, 2e+72], N[(N[(b + N[(N[(y * N[(9.0 * x), $MachinePrecision]), $MachinePrecision] - N[(t * N[(a * N[(z * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(N[(N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision] + N[(9.0 * N[(N[(x * y), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * N[(N[(a * t), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.99999999999999937e134

   1. Initial program 57.2%

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

   3. Taylor expanded in b around 0 51.2%

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

   4. Taylor expanded in x around 0 78.4%

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

   5. Taylor expanded in c around 0 78.5%

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

      1. add0 78.5%

         \[\leadsto \frac{-4 \cdot \left(a \cdot t\right) + 9 \cdot \color{blue}{\left(\frac{x \cdot y}{z} + 0\right)}}{c} \]

      2. associate-/l* 90.7%

         \[\leadsto \frac{-4 \cdot \left(a \cdot t\right) + 9 \cdot \left(\color{blue}{\frac{x}{\frac{z}{y}}} + 0\right)}{c} \]

   7. Applied egg-rr 90.7%

      \[\leadsto \frac{-4 \cdot \left(a \cdot t\right) + 9 \cdot \color{blue}{\left(\frac{x}{\frac{z}{y}} + 0\right)}}{c} \]
   8. Step-by-step derivation

      1. associate-/l* 78.5%

         \[\leadsto \frac{-4 \cdot \left(a \cdot t\right) + 9 \cdot \left(\color{blue}{\frac{x \cdot y}{z}} + 0\right)}{c} \]

      2. associate-*r/ 90.7%

         \[\leadsto \frac{-4 \cdot \left(a \cdot t\right) + 9 \cdot \left(\color{blue}{x \cdot \frac{y}{z}} + 0\right)}{c} \]

      3. add0 90.7%

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

   9. Simplified 90.7%

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

   if -7.99999999999999937e134 < z < 1.99999999999999989e72

   1. Initial program 93.0%

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

   3. Taylor expanded in z around 0 93.0%

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

      1. *-commutative 93.0%

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

      2. associate-*r* 89.3%

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

      3. *-commutative 89.3%

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

      4. associate-*r* 89.3%

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

      5. associate-*l* 93.5%

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

      6. *-commutative 93.5%

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

   5. Simplified 93.5%

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

   if 1.99999999999999989e72 < z

   1. Initial program 56.0%

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

   3. Taylor expanded in x around 0 87.8%

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

4. Final simplification 92.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{+134}:\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right) + 9 \cdot \left(x \cdot \frac{y}{z}\right)}{c}\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+72}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(9 \cdot x\right) - t \cdot \left(a \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{b}{z \cdot c} + 9 \cdot \frac{x \cdot y}{z \cdot c}\right) - 4 \cdot \frac{a \cdot t}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 87.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+134} \lor \neg \left(z \leq 1.4 \cdot 10^{+151}\right):\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right) + 9 \cdot \left(x \cdot \frac{y}{z}\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(9 \cdot x\right) - t \cdot \left(a \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= z -4.5e+134) (not (<= z 1.4e+151)))
   (/ (+ (* -4.0 (* a t)) (* 9.0 (* x (/ y z)))) c)
   (/ (+ b (- (* y (* 9.0 x)) (* t (* a (* z 4.0))))) (* z c))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((z <= -4.5e+134) || !(z <= 1.4e+151)) {
		tmp = ((-4.0 * (a * t)) + (9.0 * (x * (y / z)))) / c;
	} else {
		tmp = (b + ((y * (9.0 * x)) - (t * (a * (z * 4.0))))) / (z * c);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c 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 <= (-4.5d+134)) .or. (.not. (z <= 1.4d+151))) then
        tmp = (((-4.0d0) * (a * t)) + (9.0d0 * (x * (y / z)))) / c
    else
        tmp = (b + ((y * (9.0d0 * x)) - (t * (a * (z * 4.0d0))))) / (z * c)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((z <= -4.5e+134) || !(z <= 1.4e+151)) {
		tmp = ((-4.0 * (a * t)) + (9.0 * (x * (y / z)))) / c;
	} else {
		tmp = (b + ((y * (9.0 * x)) - (t * (a * (z * 4.0))))) / (z * c);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if (z <= -4.5e+134) or not (z <= 1.4e+151):
		tmp = ((-4.0 * (a * t)) + (9.0 * (x * (y / z)))) / c
	else:
		tmp = (b + ((y * (9.0 * x)) - (t * (a * (z * 4.0))))) / (z * c)
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((z <= -4.5e+134) || !(z <= 1.4e+151))
		tmp = Float64(Float64(Float64(-4.0 * Float64(a * t)) + Float64(9.0 * Float64(x * Float64(y / z)))) / c);
	else
		tmp = Float64(Float64(b + Float64(Float64(y * Float64(9.0 * x)) - Float64(t * Float64(a * Float64(z * 4.0))))) / Float64(z * c));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((z <= -4.5e+134) || ~((z <= 1.4e+151)))
		tmp = ((-4.0 * (a * t)) + (9.0 * (x * (y / z)))) / c;
	else
		tmp = (b + ((y * (9.0 * x)) - (t * (a * (z * 4.0))))) / (z * c);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[z, -4.5e+134], N[Not[LessEqual[z, 1.4e+151]], $MachinePrecision]], N[(N[(N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision] + N[(9.0 * N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], N[(N[(b + N[(N[(y * N[(9.0 * x), $MachinePrecision]), $MachinePrecision] - N[(t * N[(a * N[(z * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.4999999999999997e134 or 1.39999999999999994e151 < z

   1. Initial program 51.9%

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

   3. Taylor expanded in b around 0 43.2%

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

   4. Taylor expanded in x around 0 76.1%

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

   5. Taylor expanded in c around 0 77.7%

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

      1. add0 77.7%

         \[\leadsto \frac{-4 \cdot \left(a \cdot t\right) + 9 \cdot \color{blue}{\left(\frac{x \cdot y}{z} + 0\right)}}{c} \]

      2. associate-/l* 83.8%

         \[\leadsto \frac{-4 \cdot \left(a \cdot t\right) + 9 \cdot \left(\color{blue}{\frac{x}{\frac{z}{y}}} + 0\right)}{c} \]

   7. Applied egg-rr 83.8%

      \[\leadsto \frac{-4 \cdot \left(a \cdot t\right) + 9 \cdot \color{blue}{\left(\frac{x}{\frac{z}{y}} + 0\right)}}{c} \]
   8. Step-by-step derivation

      1. associate-/l* 77.7%

         \[\leadsto \frac{-4 \cdot \left(a \cdot t\right) + 9 \cdot \left(\color{blue}{\frac{x \cdot y}{z}} + 0\right)}{c} \]

      2. associate-*r/ 83.8%

         \[\leadsto \frac{-4 \cdot \left(a \cdot t\right) + 9 \cdot \left(\color{blue}{x \cdot \frac{y}{z}} + 0\right)}{c} \]

      3. add0 83.8%

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

   9. Simplified 83.8%

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

   if -4.4999999999999997e134 < z < 1.39999999999999994e151

   1. Initial program 93.2%

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

   3. Taylor expanded in z around 0 93.2%

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

      1. *-commutative 93.2%

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

      2. associate-*r* 89.7%

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

      3. *-commutative 89.7%

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

      4. associate-*r* 89.7%

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

      5. associate-*l* 93.7%

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

      6. *-commutative 93.7%

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

   5. Simplified 93.7%

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

4. Final simplification 91.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+134} \lor \neg \left(z \leq 1.4 \cdot 10^{+151}\right):\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right) + 9 \cdot \left(x \cdot \frac{y}{z}\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(9 \cdot x\right) - t \cdot \left(a \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 64.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq -3.25 \cdot 10^{-83}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;a \leq 1.02 \cdot 10^{+146}:\\ \;\;\;\;\frac{b + x \cdot \left(9 \cdot y\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right) + 9 \cdot \left(x \cdot \frac{y}{z}\right)}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= a -3.25e-83)
   (* -4.0 (/ a (/ c t)))
   (if (<= a 1.02e+146)
     (/ (+ b (* x (* 9.0 y))) (* z c))
     (/ (+ (* -4.0 (* a t)) (* 9.0 (* x (/ y z)))) c))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (a <= -3.25e-83) {
		tmp = -4.0 * (a / (c / t));
	} else if (a <= 1.02e+146) {
		tmp = (b + (x * (9.0 * y))) / (z * c);
	} else {
		tmp = ((-4.0 * (a * t)) + (9.0 * (x * (y / z)))) / c;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c 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 (a <= (-3.25d-83)) then
        tmp = (-4.0d0) * (a / (c / t))
    else if (a <= 1.02d+146) then
        tmp = (b + (x * (9.0d0 * y))) / (z * c)
    else
        tmp = (((-4.0d0) * (a * t)) + (9.0d0 * (x * (y / z)))) / c
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (a <= -3.25e-83) {
		tmp = -4.0 * (a / (c / t));
	} else if (a <= 1.02e+146) {
		tmp = (b + (x * (9.0 * y))) / (z * c);
	} else {
		tmp = ((-4.0 * (a * t)) + (9.0 * (x * (y / z)))) / c;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if a <= -3.25e-83:
		tmp = -4.0 * (a / (c / t))
	elif a <= 1.02e+146:
		tmp = (b + (x * (9.0 * y))) / (z * c)
	else:
		tmp = ((-4.0 * (a * t)) + (9.0 * (x * (y / z)))) / c
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (a <= -3.25e-83)
		tmp = Float64(-4.0 * Float64(a / Float64(c / t)));
	elseif (a <= 1.02e+146)
		tmp = Float64(Float64(b + Float64(x * Float64(9.0 * y))) / Float64(z * c));
	else
		tmp = Float64(Float64(Float64(-4.0 * Float64(a * t)) + Float64(9.0 * Float64(x * Float64(y / z)))) / c);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (a <= -3.25e-83)
		tmp = -4.0 * (a / (c / t));
	elseif (a <= 1.02e+146)
		tmp = (b + (x * (9.0 * y))) / (z * c);
	else
		tmp = ((-4.0 * (a * t)) + (9.0 * (x * (y / z)))) / c;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[a, -3.25e-83], N[(-4.0 * N[(a / N[(c / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.02e+146], N[(N[(b + N[(x * N[(9.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(N[(N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision] + N[(9.0 * N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -3.25e-83

   1. Initial program 84.2%

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

   3. Taylor expanded in z around inf 46.6%

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

      1. *-commutative 46.6%

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

      2. associate-/l* 51.0%

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

   5. Simplified 51.0%

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

   if -3.25e-83 < a < 1.01999999999999997e146

   1. Initial program 83.0%

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

   3. Taylor expanded in x around inf 73.8%

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

      1. associate-*r* 73.8%

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

      2. *-commutative 73.8%

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

      3. associate-*r* 73.7%

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

   5. Simplified 73.7%

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

   if 1.01999999999999997e146 < a

   1. Initial program 76.9%

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

   3. Taylor expanded in b around 0 70.1%

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

   4. Taylor expanded in x around 0 73.0%

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

   5. Taylor expanded in c around 0 69.8%

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

      1. add0 69.8%

         \[\leadsto \frac{-4 \cdot \left(a \cdot t\right) + 9 \cdot \color{blue}{\left(\frac{x \cdot y}{z} + 0\right)}}{c} \]

      2. associate-/l* 76.7%

         \[\leadsto \frac{-4 \cdot \left(a \cdot t\right) + 9 \cdot \left(\color{blue}{\frac{x}{\frac{z}{y}}} + 0\right)}{c} \]

   7. Applied egg-rr 76.7%

      \[\leadsto \frac{-4 \cdot \left(a \cdot t\right) + 9 \cdot \color{blue}{\left(\frac{x}{\frac{z}{y}} + 0\right)}}{c} \]
   8. Step-by-step derivation

      1. associate-/l* 69.8%

         \[\leadsto \frac{-4 \cdot \left(a \cdot t\right) + 9 \cdot \left(\color{blue}{\frac{x \cdot y}{z}} + 0\right)}{c} \]

      2. associate-*r/ 76.7%

         \[\leadsto \frac{-4 \cdot \left(a \cdot t\right) + 9 \cdot \left(\color{blue}{x \cdot \frac{y}{z}} + 0\right)}{c} \]

      3. add0 76.7%

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

   9. Simplified 76.7%

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

4. Final simplification 66.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.25 \cdot 10^{-83}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;a \leq 1.02 \cdot 10^{+146}:\\ \;\;\;\;\frac{b + x \cdot \left(9 \cdot y\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right) + 9 \cdot \left(x \cdot \frac{y}{z}\right)}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 68.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq -5.8 \cdot 10^{-121}:\\ \;\;\;\;9 \cdot \frac{x \cdot y}{z \cdot c} + -4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{+146}:\\ \;\;\;\;\frac{b + x \cdot \left(9 \cdot y\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right) + 9 \cdot \left(x \cdot \frac{y}{z}\right)}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= a -5.8e-121)
   (+ (* 9.0 (/ (* x y) (* z c))) (* -4.0 (* t (/ a c))))
   (if (<= a 1.6e+146)
     (/ (+ b (* x (* 9.0 y))) (* z c))
     (/ (+ (* -4.0 (* a t)) (* 9.0 (* x (/ y z)))) c))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (a <= -5.8e-121) {
		tmp = (9.0 * ((x * y) / (z * c))) + (-4.0 * (t * (a / c)));
	} else if (a <= 1.6e+146) {
		tmp = (b + (x * (9.0 * y))) / (z * c);
	} else {
		tmp = ((-4.0 * (a * t)) + (9.0 * (x * (y / z)))) / c;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c 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 (a <= (-5.8d-121)) then
        tmp = (9.0d0 * ((x * y) / (z * c))) + ((-4.0d0) * (t * (a / c)))
    else if (a <= 1.6d+146) then
        tmp = (b + (x * (9.0d0 * y))) / (z * c)
    else
        tmp = (((-4.0d0) * (a * t)) + (9.0d0 * (x * (y / z)))) / c
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (a <= -5.8e-121) {
		tmp = (9.0 * ((x * y) / (z * c))) + (-4.0 * (t * (a / c)));
	} else if (a <= 1.6e+146) {
		tmp = (b + (x * (9.0 * y))) / (z * c);
	} else {
		tmp = ((-4.0 * (a * t)) + (9.0 * (x * (y / z)))) / c;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if a <= -5.8e-121:
		tmp = (9.0 * ((x * y) / (z * c))) + (-4.0 * (t * (a / c)))
	elif a <= 1.6e+146:
		tmp = (b + (x * (9.0 * y))) / (z * c)
	else:
		tmp = ((-4.0 * (a * t)) + (9.0 * (x * (y / z)))) / c
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (a <= -5.8e-121)
		tmp = Float64(Float64(9.0 * Float64(Float64(x * y) / Float64(z * c))) + Float64(-4.0 * Float64(t * Float64(a / c))));
	elseif (a <= 1.6e+146)
		tmp = Float64(Float64(b + Float64(x * Float64(9.0 * y))) / Float64(z * c));
	else
		tmp = Float64(Float64(Float64(-4.0 * Float64(a * t)) + Float64(9.0 * Float64(x * Float64(y / z)))) / c);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (a <= -5.8e-121)
		tmp = (9.0 * ((x * y) / (z * c))) + (-4.0 * (t * (a / c)));
	elseif (a <= 1.6e+146)
		tmp = (b + (x * (9.0 * y))) / (z * c);
	else
		tmp = ((-4.0 * (a * t)) + (9.0 * (x * (y / z)))) / c;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[a, -5.8e-121], N[(N[(9.0 * N[(N[(x * y), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.6e+146], N[(N[(b + N[(x * N[(9.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(N[(N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision] + N[(9.0 * N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -5.8e-121

   1. Initial program 85.4%

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

   3. Taylor expanded in b around 0 60.6%

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

   4. Taylor expanded in x around 0 58.5%

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

      1. add0 58.5%

         \[\leadsto -4 \cdot \color{blue}{\left(\frac{a \cdot t}{c} + 0\right)} + 9 \cdot \frac{x \cdot y}{c \cdot z} \]

      2. associate-/l* 61.4%

         \[\leadsto -4 \cdot \left(\color{blue}{\frac{a}{\frac{c}{t}}} + 0\right) + 9 \cdot \frac{x \cdot y}{c \cdot z} \]

   6. Applied egg-rr 61.4%

      \[\leadsto -4 \cdot \color{blue}{\left(\frac{a}{\frac{c}{t}} + 0\right)} + 9 \cdot \frac{x \cdot y}{c \cdot z} \]
   7. Step-by-step derivation

      1. associate-/r/ 62.7%

         \[\leadsto -4 \cdot \left(\color{blue}{\frac{a}{c} \cdot t} + 0\right) + 9 \cdot \frac{x \cdot y}{c \cdot z} \]

      2. add0 62.7%

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

   8. Simplified 62.7%

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

   if -5.8e-121 < a < 1.6e146

   1. Initial program 82.1%

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

   3. Taylor expanded in x around inf 73.1%

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

      1. associate-*r* 73.1%

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

      2. *-commutative 73.1%

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

      3. associate-*r* 73.1%

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

   5. Simplified 73.1%

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

   if 1.6e146 < a

   1. Initial program 76.9%

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

   3. Taylor expanded in b around 0 70.1%

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

   4. Taylor expanded in x around 0 73.0%

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

   5. Taylor expanded in c around 0 69.8%

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

      1. add0 69.8%

         \[\leadsto \frac{-4 \cdot \left(a \cdot t\right) + 9 \cdot \color{blue}{\left(\frac{x \cdot y}{z} + 0\right)}}{c} \]

      2. associate-/l* 76.7%

         \[\leadsto \frac{-4 \cdot \left(a \cdot t\right) + 9 \cdot \left(\color{blue}{\frac{x}{\frac{z}{y}}} + 0\right)}{c} \]

   7. Applied egg-rr 76.7%

      \[\leadsto \frac{-4 \cdot \left(a \cdot t\right) + 9 \cdot \color{blue}{\left(\frac{x}{\frac{z}{y}} + 0\right)}}{c} \]
   8. Step-by-step derivation

      1. associate-/l* 69.8%

         \[\leadsto \frac{-4 \cdot \left(a \cdot t\right) + 9 \cdot \left(\color{blue}{\frac{x \cdot y}{z}} + 0\right)}{c} \]

      2. associate-*r/ 76.7%

         \[\leadsto \frac{-4 \cdot \left(a \cdot t\right) + 9 \cdot \left(\color{blue}{x \cdot \frac{y}{z}} + 0\right)}{c} \]

      3. add0 76.7%

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

   9. Simplified 76.7%

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

4. Final simplification 69.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.8 \cdot 10^{-121}:\\ \;\;\;\;9 \cdot \frac{x \cdot y}{z \cdot c} + -4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{+146}:\\ \;\;\;\;\frac{b + x \cdot \left(9 \cdot y\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right) + 9 \cdot \left(x \cdot \frac{y}{z}\right)}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 66.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -2 \cdot 10^{-25}:\\ \;\;\;\;\frac{b + x \cdot \left(9 \cdot y\right)}{z \cdot c}\\ \mathbf{elif}\;x \leq 3.1 \cdot 10^{+93}:\\ \;\;\;\;\frac{b - 4 \cdot \left(a \cdot \left(z \cdot t\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;9 \cdot \frac{1}{\frac{z}{x} \cdot \frac{c}{y}}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= x -2e-25)
   (/ (+ b (* x (* 9.0 y))) (* z c))
   (if (<= x 3.1e+93)
     (/ (- b (* 4.0 (* a (* z t)))) (* z c))
     (* 9.0 (/ 1.0 (* (/ z x) (/ c y)))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (x <= -2e-25) {
		tmp = (b + (x * (9.0 * y))) / (z * c);
	} else if (x <= 3.1e+93) {
		tmp = (b - (4.0 * (a * (z * t)))) / (z * c);
	} else {
		tmp = 9.0 * (1.0 / ((z / x) * (c / y)));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c 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 (x <= (-2d-25)) then
        tmp = (b + (x * (9.0d0 * y))) / (z * c)
    else if (x <= 3.1d+93) then
        tmp = (b - (4.0d0 * (a * (z * t)))) / (z * c)
    else
        tmp = 9.0d0 * (1.0d0 / ((z / x) * (c / y)))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (x <= -2e-25) {
		tmp = (b + (x * (9.0 * y))) / (z * c);
	} else if (x <= 3.1e+93) {
		tmp = (b - (4.0 * (a * (z * t)))) / (z * c);
	} else {
		tmp = 9.0 * (1.0 / ((z / x) * (c / y)));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if x <= -2e-25:
		tmp = (b + (x * (9.0 * y))) / (z * c)
	elif x <= 3.1e+93:
		tmp = (b - (4.0 * (a * (z * t)))) / (z * c)
	else:
		tmp = 9.0 * (1.0 / ((z / x) * (c / y)))
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (x <= -2e-25)
		tmp = Float64(Float64(b + Float64(x * Float64(9.0 * y))) / Float64(z * c));
	elseif (x <= 3.1e+93)
		tmp = Float64(Float64(b - Float64(4.0 * Float64(a * Float64(z * t)))) / Float64(z * c));
	else
		tmp = Float64(9.0 * Float64(1.0 / Float64(Float64(z / x) * Float64(c / y))));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (x <= -2e-25)
		tmp = (b + (x * (9.0 * y))) / (z * c);
	elseif (x <= 3.1e+93)
		tmp = (b - (4.0 * (a * (z * t)))) / (z * c);
	else
		tmp = 9.0 * (1.0 / ((z / x) * (c / y)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[x, -2e-25], N[(N[(b + N[(x * N[(9.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.1e+93], N[(N[(b - N[(4.0 * N[(a * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(9.0 * N[(1.0 / N[(N[(z / x), $MachinePrecision] * N[(c / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.00000000000000008e-25

   1. Initial program 79.7%

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

   3. Taylor expanded in x around inf 73.7%

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

      1. associate-*r* 73.7%

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

      2. *-commutative 73.7%

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

      3. associate-*r* 73.7%

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

   5. Simplified 73.7%

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

   if -2.00000000000000008e-25 < x < 3.10000000000000019e93

   1. Initial program 86.9%

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

   3. Taylor expanded in x around 0 73.4%

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

   if 3.10000000000000019e93 < x

   1. Initial program 74.6%

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

   3. Taylor expanded in x around inf 58.5%

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

      1. clear-num 58.5%

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

      2. inv-pow 58.5%

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

      3. *-commutative 58.5%

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

   5. Applied egg-rr 58.5%

      \[\leadsto 9 \cdot \color{blue}{{\left(\frac{z \cdot c}{x \cdot y}\right)}^{-1}} \]
   6. Step-by-step derivation

      1. unpow-1 58.5%

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

      2. times-frac 65.1%

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

   7. Simplified 65.1%

      \[\leadsto 9 \cdot \color{blue}{\frac{1}{\frac{z}{x} \cdot \frac{c}{y}}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 72.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2 \cdot 10^{-25}:\\ \;\;\;\;\frac{b + x \cdot \left(9 \cdot y\right)}{z \cdot c}\\ \mathbf{elif}\;x \leq 3.1 \cdot 10^{+93}:\\ \;\;\;\;\frac{b - 4 \cdot \left(a \cdot \left(z \cdot t\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;9 \cdot \frac{1}{\frac{z}{x} \cdot \frac{c}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 67.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -7.8 \cdot 10^{+33}:\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right)}{c}\\ \mathbf{elif}\;z \leq 1.52 \cdot 10^{+153}:\\ \;\;\;\;\frac{b + x \cdot \left(9 \cdot y\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{a \cdot t}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= z -7.8e+33)
   (/ (* -4.0 (* a t)) c)
   (if (<= z 1.52e+153)
     (/ (+ b (* x (* 9.0 y))) (* z c))
     (* -4.0 (/ (* a t) c)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (z <= -7.8e+33) {
		tmp = (-4.0 * (a * t)) / c;
	} else if (z <= 1.52e+153) {
		tmp = (b + (x * (9.0 * y))) / (z * c);
	} else {
		tmp = -4.0 * ((a * t) / c);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c 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 <= (-7.8d+33)) then
        tmp = ((-4.0d0) * (a * t)) / c
    else if (z <= 1.52d+153) then
        tmp = (b + (x * (9.0d0 * y))) / (z * c)
    else
        tmp = (-4.0d0) * ((a * t) / c)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (z <= -7.8e+33) {
		tmp = (-4.0 * (a * t)) / c;
	} else if (z <= 1.52e+153) {
		tmp = (b + (x * (9.0 * y))) / (z * c);
	} else {
		tmp = -4.0 * ((a * t) / c);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if z <= -7.8e+33:
		tmp = (-4.0 * (a * t)) / c
	elif z <= 1.52e+153:
		tmp = (b + (x * (9.0 * y))) / (z * c)
	else:
		tmp = -4.0 * ((a * t) / c)
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (z <= -7.8e+33)
		tmp = Float64(Float64(-4.0 * Float64(a * t)) / c);
	elseif (z <= 1.52e+153)
		tmp = Float64(Float64(b + Float64(x * Float64(9.0 * y))) / Float64(z * c));
	else
		tmp = Float64(-4.0 * Float64(Float64(a * t) / c));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (z <= -7.8e+33)
		tmp = (-4.0 * (a * t)) / c;
	elseif (z <= 1.52e+153)
		tmp = (b + (x * (9.0 * y))) / (z * c);
	else
		tmp = -4.0 * ((a * t) / c);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[z, -7.8e+33], N[(N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[z, 1.52e+153], N[(N[(b + N[(x * N[(9.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(-4.0 * N[(N[(a * t), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.8000000000000004e33

   1. Initial program 67.3%

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

   3. Taylor expanded in b around 0 56.0%

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

   4. Taylor expanded in x around 0 75.0%

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

   5. Taylor expanded in c around 0 75.2%

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

   6. Taylor expanded in a around inf 65.6%

      \[\leadsto \frac{\color{blue}{-4 \cdot \left(a \cdot t\right)}}{c} \]
   7. Step-by-step derivation

      1. *-commutative 65.6%

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

   8. Simplified 65.6%

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

   if -7.8000000000000004e33 < z < 1.52e153

   1. Initial program 94.2%

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

   3. Taylor expanded in x around inf 80.4%

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

      1. associate-*r* 80.4%

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

      2. *-commutative 80.4%

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

      3. associate-*r* 80.3%

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

   5. Simplified 80.3%

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

   if 1.52e153 < z

   1. Initial program 46.7%

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

   3. Taylor expanded in z around inf 58.1%

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

4. Final simplification 74.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.8 \cdot 10^{+33}:\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right)}{c}\\ \mathbf{elif}\;z \leq 1.52 \cdot 10^{+153}:\\ \;\;\;\;\frac{b + x \cdot \left(9 \cdot y\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{a \cdot t}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 48.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq -8.5 \cdot 10^{-120} \lor \neg \left(a \leq 1.05 \cdot 10^{+129}\right):\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= a -8.5e-120) (not (<= a 1.05e+129)))
   (* -4.0 (* t (/ a c)))
   (/ b (* z c))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((a <= -8.5e-120) || !(a <= 1.05e+129)) {
		tmp = -4.0 * (t * (a / c));
	} else {
		tmp = b / (z * c);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c 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 ((a <= (-8.5d-120)) .or. (.not. (a <= 1.05d+129))) then
        tmp = (-4.0d0) * (t * (a / c))
    else
        tmp = b / (z * c)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((a <= -8.5e-120) || !(a <= 1.05e+129)) {
		tmp = -4.0 * (t * (a / c));
	} else {
		tmp = b / (z * c);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if (a <= -8.5e-120) or not (a <= 1.05e+129):
		tmp = -4.0 * (t * (a / c))
	else:
		tmp = b / (z * c)
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((a <= -8.5e-120) || !(a <= 1.05e+129))
		tmp = Float64(-4.0 * Float64(t * Float64(a / c)));
	else
		tmp = Float64(b / Float64(z * c));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((a <= -8.5e-120) || ~((a <= 1.05e+129)))
		tmp = -4.0 * (t * (a / c));
	else
		tmp = b / (z * c);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[a, -8.5e-120], N[Not[LessEqual[a, 1.05e+129]], $MachinePrecision]], N[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -8.50000000000000059e-120 or 1.04999999999999998e129 < a

   1. Initial program 83.9%

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

   3. Taylor expanded in b around 0 63.3%

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

   4. Taylor expanded in x around 0 61.6%

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

   5. Taylor expanded in c around 0 64.9%

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

   6. Taylor expanded in a around inf 45.0%

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

      1. associate-*l/ 50.5%

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

      2. *-commutative 50.5%

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

   8. Simplified 50.5%

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

   if -8.50000000000000059e-120 < a < 1.04999999999999998e129

   1. Initial program 81.6%

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

   3. Taylor expanded in b around inf 42.9%

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

      1. *-commutative 42.9%

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

   5. Simplified 42.9%

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

4. Final simplification 46.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -8.5 \cdot 10^{-120} \lor \neg \left(a \leq 1.05 \cdot 10^{+129}\right):\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 48.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq -8 \cdot 10^{-120}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;a \leq 5.3 \cdot 10^{+129}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= a -8e-120)
   (* -4.0 (/ a (/ c t)))
   (if (<= a 5.3e+129) (/ b (* z c)) (* -4.0 (* t (/ a c))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (a <= -8e-120) {
		tmp = -4.0 * (a / (c / t));
	} else if (a <= 5.3e+129) {
		tmp = b / (z * c);
	} else {
		tmp = -4.0 * (t * (a / c));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c 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 (a <= (-8d-120)) then
        tmp = (-4.0d0) * (a / (c / t))
    else if (a <= 5.3d+129) then
        tmp = b / (z * c)
    else
        tmp = (-4.0d0) * (t * (a / c))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (a <= -8e-120) {
		tmp = -4.0 * (a / (c / t));
	} else if (a <= 5.3e+129) {
		tmp = b / (z * c);
	} else {
		tmp = -4.0 * (t * (a / c));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if a <= -8e-120:
		tmp = -4.0 * (a / (c / t))
	elif a <= 5.3e+129:
		tmp = b / (z * c)
	else:
		tmp = -4.0 * (t * (a / c))
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (a <= -8e-120)
		tmp = Float64(-4.0 * Float64(a / Float64(c / t)));
	elseif (a <= 5.3e+129)
		tmp = Float64(b / Float64(z * c));
	else
		tmp = Float64(-4.0 * Float64(t * Float64(a / c)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (a <= -8e-120)
		tmp = -4.0 * (a / (c / t));
	elseif (a <= 5.3e+129)
		tmp = b / (z * c);
	else
		tmp = -4.0 * (t * (a / c));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[a, -8e-120], N[(-4.0 * N[(a / N[(c / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 5.3e+129], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -7.99999999999999983e-120

   1. Initial program 85.4%

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

   3. Taylor expanded in z around inf 44.4%

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

      1. *-commutative 44.4%

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

      2. associate-/l* 48.5%

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

   5. Simplified 48.5%

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

   if -7.99999999999999983e-120 < a < 5.2999999999999999e129

   1. Initial program 81.6%

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

   3. Taylor expanded in b around inf 42.9%

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

      1. *-commutative 42.9%

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

   5. Simplified 42.9%

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

   if 5.2999999999999999e129 < a

   1. Initial program 79.7%

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

   3. Taylor expanded in b around 0 71.0%

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

   4. Taylor expanded in x around 0 70.6%

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

   5. Taylor expanded in c around 0 67.7%

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

   6. Taylor expanded in a around inf 46.6%

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

      1. associate-*l/ 49.7%

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

      2. *-commutative 49.7%

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

   8. Simplified 49.7%

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

4. Final simplification 45.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -8 \cdot 10^{-120}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;a \leq 5.3 \cdot 10^{+129}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 35.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;b \leq -3.65 \cdot 10^{+146}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= b -3.65e+146) (/ (/ b c) z) (/ b (* z c))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (b <= -3.65e+146) {
		tmp = (b / c) / z;
	} else {
		tmp = b / (z * c);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c 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 <= (-3.65d+146)) then
        tmp = (b / c) / z
    else
        tmp = b / (z * c)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (b <= -3.65e+146) {
		tmp = (b / c) / z;
	} else {
		tmp = b / (z * c);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if b <= -3.65e+146:
		tmp = (b / c) / z
	else:
		tmp = b / (z * c)
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (b <= -3.65e+146)
		tmp = Float64(Float64(b / c) / z);
	else
		tmp = Float64(b / Float64(z * c));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (b <= -3.65e+146)
		tmp = (b / c) / z;
	else
		tmp = b / (z * c);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[b, -3.65e+146], N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -3.65000000000000017e146

   1. Initial program 79.3%

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

      1. add0 79.3%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a + 0\right)}\right) + b}{z \cdot c} \]

      2. associate-*l* 79.1%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)} + 0\right)\right) + b}{z \cdot c} \]

   4. Applied egg-rr 79.1%

      \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot \left(t \cdot a\right) + 0\right)}\right) + b}{z \cdot c} \]

   5. Taylor expanded in b around inf 54.3%

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

      1. associate-/r* 66.7%

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

   7. Simplified 66.7%

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

   if -3.65000000000000017e146 < b

   1. Initial program 83.3%

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

   3. Taylor expanded in b around inf 38.3%

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

      1. *-commutative 38.3%

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

   5. Simplified 38.3%

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

4. Final simplification 42.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.65 \cdot 10^{+146}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 35.2% accurate, 3.8× speedup

Math

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

FPCore

NOTE: x, y, z, t, a, b, and c 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(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	return b / (z * c);
}

Fortran

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

Python

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

Julia

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

MATLAB

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

Wolfram

NOTE: x, y, z, t, a, b, and c 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 82.7%

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

3. Taylor expanded in b around inf 40.7%

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

   1. *-commutative 40.7%

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

5. Simplified 40.7%

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

6. Final simplification 40.7%

   \[\leadsto \frac{b}{z \cdot c} \]
7. Add Preprocessing

Developer target: 80.5% accurate, 0.1× 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 2024034 
(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)))