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

Percentage Accurate: 78.8% → 93.3%

Time: 19.7s

Alternatives: 18

Speedup: 0.8×

• 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: 78.8% 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: 93.3% accurate, 0.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{+59} \lor \neg \left(z \leq 1.4 \cdot 10^{+37}\right):\\ \;\;\;\;\left(-4 \cdot \left(a \cdot t\right) + \left(9 \cdot \frac{1}{\frac{\frac{z}{y}}{x}} + \frac{b}{z}\right)\right) \cdot \frac{1}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b + \mathsf{fma}\left(x, 9 \cdot y, a \cdot \left(z \cdot \left(-4 \cdot t\right)\right)\right)}{c}}{z}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
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 -3.5e+59) (not (<= z 1.4e+37)))
   (* (+ (* -4.0 (* a t)) (+ (* 9.0 (/ 1.0 (/ (/ z y) x))) (/ b z))) (/ 1.0 c))
   (/ (/ (+ b (fma x (* 9.0 y) (* a (* z (* -4.0 t))))) c) z)))

C

assert(x < y && y < z && z < t && t < a && a < b && b < 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 <= -3.5e+59) || !(z <= 1.4e+37)) {
		tmp = ((-4.0 * (a * t)) + ((9.0 * (1.0 / ((z / y) / x))) + (b / z))) * (1.0 / c);
	} else {
		tmp = ((b + fma(x, (9.0 * y), (a * (z * (-4.0 * t))))) / c) / z;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
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 <= -3.5e+59) || !(z <= 1.4e+37))
		tmp = Float64(Float64(Float64(-4.0 * Float64(a * t)) + Float64(Float64(9.0 * Float64(1.0 / Float64(Float64(z / y) / x))) + Float64(b / z))) * Float64(1.0 / c));
	else
		tmp = Float64(Float64(Float64(b + fma(x, Float64(9.0 * y), Float64(a * Float64(z * Float64(-4.0 * t))))) / c) / z);
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
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, -3.5e+59], N[Not[LessEqual[z, 1.4e+37]], $MachinePrecision]], N[(N[(N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision] + N[(N[(9.0 * N[(1.0 / N[(N[(z / y), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(1.0 / c), $MachinePrecision]), $MachinePrecision], N[(N[(N[(b + N[(x * N[(9.0 * y), $MachinePrecision] + N[(a * N[(z * N[(-4.0 * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision] / z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.5e59 or 1.3999999999999999e37 < z

   1. Initial program 62.2%

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

      1. associate-+l- 62.2%

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

      2. *-commutative 62.2%

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

      3. associate-*r* 61.3%

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

      4. *-commutative 61.3%

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

      5. associate-+l- 61.3%

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

      6. *-commutative 61.3%

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

      7. associate-*r* 62.2%

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

      8. *-commutative 62.2%

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

      9. associate-*l* 62.2%

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

      10. associate-*l* 67.8%

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

   3. Simplified 67.8%

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

   5. Applied egg-rr 74.6%

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

   6. Taylor expanded in x around 0 89.1%

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

      1. clear-num 89.1%

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

      2. inv-pow 89.1%

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

   8. Applied egg-rr 89.1%

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

      1. unpow-1 89.1%

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

      2. *-commutative 89.1%

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

      3. associate-/r* 92.9%

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

   10. Simplified 92.9%

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

   if -3.5e59 < z < 1.3999999999999999e37

   1. Initial program 92.4%

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

      1. associate-+l- 92.4%

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

      2. *-commutative 92.4%

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

      3. associate-*r* 93.2%

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

      4. *-commutative 93.2%

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

      5. associate-+l- 93.2%

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

      6. *-commutative 93.2%

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

      7. associate-*r* 92.4%

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

      8. *-commutative 92.4%

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

      9. associate-*l* 92.5%

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

      10. associate-*l* 89.6%

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

   3. Simplified 89.6%

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

   5. Applied egg-rr 93.8%

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

      1. associate-*l/ 93.9%

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

      2. *-un-lft-identity 93.9%

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

   7. Applied egg-rr 93.9%

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

4. Final simplification 93.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{+59} \lor \neg \left(z \leq 1.4 \cdot 10^{+37}\right):\\ \;\;\;\;\left(-4 \cdot \left(a \cdot t\right) + \left(9 \cdot \frac{1}{\frac{\frac{z}{y}}{x}} + \frac{b}{z}\right)\right) \cdot \frac{1}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b + \mathsf{fma}\left(x, 9 \cdot y, a \cdot \left(z \cdot \left(-4 \cdot t\right)\right)\right)}{c}}{z}\\ \end{array} \]

Alternative 2: 87.0% accurate, 0.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := -4 \cdot \left(a \cdot t\right)\\ t_2 := \frac{b + \left(y \cdot \left(9 \cdot x\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c}\\ t_3 := \frac{b + \left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(a \cdot t\right)\right)}{z \cdot c}\\ \mathbf{if}\;t_2 \leq -2 \cdot 10^{-94}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t_2 \leq 0:\\ \;\;\;\;\frac{t_1 + \frac{b}{z}}{c}\\ \mathbf{elif}\;t_2 \leq \infty:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{c} \cdot \left(t_1 + \frac{9 \cdot x}{\frac{z}{y}}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
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 (* -4.0 (* a t)))
        (t_2 (/ (+ b (- (* y (* 9.0 x)) (* a (* t (* z 4.0))))) (* z c)))
        (t_3 (/ (+ b (- (* x (* 9.0 y)) (* (* z 4.0) (* a t)))) (* z c))))
   (if (<= t_2 -2e-94)
     t_3
     (if (<= t_2 0.0)
       (/ (+ t_1 (/ b z)) c)
       (if (<= t_2 INFINITY)
         t_3
         (* (/ 1.0 c) (+ t_1 (/ (* 9.0 x) (/ z y)))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < 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 = -4.0 * (a * t);
	double t_2 = (b + ((y * (9.0 * x)) - (a * (t * (z * 4.0))))) / (z * c);
	double t_3 = (b + ((x * (9.0 * y)) - ((z * 4.0) * (a * t)))) / (z * c);
	double tmp;
	if (t_2 <= -2e-94) {
		tmp = t_3;
	} else if (t_2 <= 0.0) {
		tmp = (t_1 + (b / z)) / c;
	} else if (t_2 <= ((double) INFINITY)) {
		tmp = t_3;
	} else {
		tmp = (1.0 / c) * (t_1 + ((9.0 * x) / (z / y)));
	}
	return tmp;
}

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
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 = -4.0 * (a * t);
	double t_2 = (b + ((y * (9.0 * x)) - (a * (t * (z * 4.0))))) / (z * c);
	double t_3 = (b + ((x * (9.0 * y)) - ((z * 4.0) * (a * t)))) / (z * c);
	double tmp;
	if (t_2 <= -2e-94) {
		tmp = t_3;
	} else if (t_2 <= 0.0) {
		tmp = (t_1 + (b / z)) / c;
	} else if (t_2 <= Double.POSITIVE_INFINITY) {
		tmp = t_3;
	} else {
		tmp = (1.0 / c) * (t_1 + ((9.0 * x) / (z / y)));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
[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 = -4.0 * (a * t)
	t_2 = (b + ((y * (9.0 * x)) - (a * (t * (z * 4.0))))) / (z * c)
	t_3 = (b + ((x * (9.0 * y)) - ((z * 4.0) * (a * t)))) / (z * c)
	tmp = 0
	if t_2 <= -2e-94:
		tmp = t_3
	elif t_2 <= 0.0:
		tmp = (t_1 + (b / z)) / c
	elif t_2 <= math.inf:
		tmp = t_3
	else:
		tmp = (1.0 / c) * (t_1 + ((9.0 * x) / (z / y)))
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
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(-4.0 * Float64(a * t))
	t_2 = Float64(Float64(b + Float64(Float64(y * Float64(9.0 * x)) - Float64(a * Float64(t * Float64(z * 4.0))))) / Float64(z * c))
	t_3 = Float64(Float64(b + Float64(Float64(x * Float64(9.0 * y)) - Float64(Float64(z * 4.0) * Float64(a * t)))) / Float64(z * c))
	tmp = 0.0
	if (t_2 <= -2e-94)
		tmp = t_3;
	elseif (t_2 <= 0.0)
		tmp = Float64(Float64(t_1 + Float64(b / z)) / c);
	elseif (t_2 <= Inf)
		tmp = t_3;
	else
		tmp = Float64(Float64(1.0 / c) * Float64(t_1 + Float64(Float64(9.0 * x) / Float64(z / y))));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
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 = -4.0 * (a * t);
	t_2 = (b + ((y * (9.0 * x)) - (a * (t * (z * 4.0))))) / (z * c);
	t_3 = (b + ((x * (9.0 * y)) - ((z * 4.0) * (a * t)))) / (z * c);
	tmp = 0.0;
	if (t_2 <= -2e-94)
		tmp = t_3;
	elseif (t_2 <= 0.0)
		tmp = (t_1 + (b / z)) / c;
	elseif (t_2 <= Inf)
		tmp = t_3;
	else
		tmp = (1.0 / c) * (t_1 + ((9.0 * x) / (z / 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.
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[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b + N[(N[(y * N[(9.0 * x), $MachinePrecision]), $MachinePrecision] - N[(a * N[(t * N[(z * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(b + N[(N[(x * N[(9.0 * y), $MachinePrecision]), $MachinePrecision] - N[(N[(z * 4.0), $MachinePrecision] * N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -2e-94], t$95$3, If[LessEqual[t$95$2, 0.0], N[(N[(t$95$1 + N[(b / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[t$95$2, Infinity], t$95$3, N[(N[(1.0 / c), $MachinePrecision] * N[(t$95$1 + N[(N[(9.0 * x), $MachinePrecision] / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)) b) (*.f64 z c)) < -1.9999999999999999e-94 or -0.0 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)) b) (*.f64 z c)) < +inf.0

   1. Initial program 90.8%

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

      1. associate-+l- 90.8%

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

      2. *-commutative 90.8%

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

      3. associate-*r* 90.8%

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

      4. *-commutative 90.8%

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

      5. associate-+l- 90.8%

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

      6. *-commutative 90.8%

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

      7. associate-*r* 90.8%

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

      8. *-commutative 90.8%

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

      9. associate-*l* 90.9%

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

      10. associate-*l* 92.3%

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

   3. Simplified 92.3%

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

   if -1.9999999999999999e-94 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)) b) (*.f64 z c)) < -0.0

   1. Initial program 46.2%

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

      1. associate-+l- 46.2%

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

      2. *-commutative 46.2%

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

      3. associate-*r* 45.2%

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

      4. *-commutative 45.2%

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

      5. associate-+l- 45.2%

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

      6. *-commutative 45.2%

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

      7. associate-*r* 46.2%

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

      8. *-commutative 46.2%

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

      9. associate-*l* 46.2%

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

      10. associate-*l* 46.2%

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

   3. Simplified 46.2%

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

   5. Applied egg-rr 99.3%

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

   6. Taylor expanded in x around 0 99.4%

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

   7. Taylor expanded in x around 0 81.1%

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

   if +inf.0 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)) b) (*.f64 z c))

   1. Initial program 0.0%

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

      1. associate-+l- 0.0%

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

      2. *-commutative 0.0%

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

      3. associate-*r* 1.2%

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

      4. *-commutative 1.2%

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

      5. associate-+l- 1.2%

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

      6. *-commutative 1.2%

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

      7. associate-*r* 0.0%

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

      8. *-commutative 0.0%

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

      9. associate-*l* 0.0%

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

      10. associate-*l* 1.2%

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

   3. Simplified 1.2%

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

   5. Applied egg-rr 11.7%

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

   6. Taylor expanded in x around 0 53.9%

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

   7. Taylor expanded in x around inf 49.7%

      \[\leadsto \left(-4 \cdot \left(a \cdot t\right) + \color{blue}{9 \cdot \frac{x \cdot y}{z}}\right) \cdot \frac{1}{c} \]
   8. Step-by-step derivation

      1. associate-/l* 70.6%

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

      2. associate-*r/ 70.7%

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

   9. Simplified 70.7%

      \[\leadsto \left(-4 \cdot \left(a \cdot t\right) + \color{blue}{\frac{9 \cdot x}{\frac{z}{y}}}\right) \cdot \frac{1}{c} \]
3. Recombined 3 regimes into one program.

4. Final simplification 89.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{b + \left(y \cdot \left(9 \cdot x\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c} \leq -2 \cdot 10^{-94}:\\ \;\;\;\;\frac{b + \left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(a \cdot t\right)\right)}{z \cdot c}\\ \mathbf{elif}\;\frac{b + \left(y \cdot \left(9 \cdot x\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c} \leq 0:\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right) + \frac{b}{z}}{c}\\ \mathbf{elif}\;\frac{b + \left(y \cdot \left(9 \cdot x\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c} \leq \infty:\\ \;\;\;\;\frac{b + \left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(a \cdot t\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{c} \cdot \left(-4 \cdot \left(a \cdot t\right) + \frac{9 \cdot x}{\frac{z}{y}}\right)\\ \end{array} \]

Alternative 3: 93.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+15} \lor \neg \left(z \leq 0.3\right):\\ \;\;\;\;\left(-4 \cdot \left(a \cdot t\right) + \left(9 \cdot \frac{1}{\frac{\frac{z}{y}}{x}} + \frac{b}{z}\right)\right) \cdot \frac{1}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(9 \cdot x\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
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 -1e+15) (not (<= z 0.3)))
   (* (+ (* -4.0 (* a t)) (+ (* 9.0 (/ 1.0 (/ (/ z y) x))) (/ b z))) (/ 1.0 c))
   (/ (+ b (- (* y (* 9.0 x)) (* a (* t (* z 4.0))))) (* z c))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < 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 <= -1e+15) || !(z <= 0.3)) {
		tmp = ((-4.0 * (a * t)) + ((9.0 * (1.0 / ((z / y) / x))) + (b / z))) * (1.0 / c);
	} else {
		tmp = (b + ((y * (9.0 * x)) - (a * (t * (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.
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 <= (-1d+15)) .or. (.not. (z <= 0.3d0))) then
        tmp = (((-4.0d0) * (a * t)) + ((9.0d0 * (1.0d0 / ((z / y) / x))) + (b / z))) * (1.0d0 / c)
    else
        tmp = (b + ((y * (9.0d0 * x)) - (a * (t * (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;
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 <= -1e+15) || !(z <= 0.3)) {
		tmp = ((-4.0 * (a * t)) + ((9.0 * (1.0 / ((z / y) / x))) + (b / z))) * (1.0 / c);
	} else {
		tmp = (b + ((y * (9.0 * x)) - (a * (t * (z * 4.0))))) / (z * c);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
[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 <= -1e+15) or not (z <= 0.3):
		tmp = ((-4.0 * (a * t)) + ((9.0 * (1.0 / ((z / y) / x))) + (b / z))) * (1.0 / c)
	else:
		tmp = (b + ((y * (9.0 * x)) - (a * (t * (z * 4.0))))) / (z * c)
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
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 <= -1e+15) || !(z <= 0.3))
		tmp = Float64(Float64(Float64(-4.0 * Float64(a * t)) + Float64(Float64(9.0 * Float64(1.0 / Float64(Float64(z / y) / x))) + Float64(b / z))) * Float64(1.0 / c));
	else
		tmp = Float64(Float64(b + Float64(Float64(y * Float64(9.0 * x)) - Float64(a * Float64(t * Float64(z * 4.0))))) / Float64(z * c));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
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 <= -1e+15) || ~((z <= 0.3)))
		tmp = ((-4.0 * (a * t)) + ((9.0 * (1.0 / ((z / y) / x))) + (b / z))) * (1.0 / c);
	else
		tmp = (b + ((y * (9.0 * x)) - (a * (t * (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.
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, -1e+15], N[Not[LessEqual[z, 0.3]], $MachinePrecision]], N[(N[(N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision] + N[(N[(9.0 * N[(1.0 / N[(N[(z / y), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(1.0 / c), $MachinePrecision]), $MachinePrecision], N[(N[(b + N[(N[(y * N[(9.0 * x), $MachinePrecision]), $MachinePrecision] - N[(a * N[(t * N[(z * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1e15 or 0.299999999999999989 < z

   1. Initial program 62.4%

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

      1. associate-+l- 62.4%

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

      2. *-commutative 62.4%

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

      3. associate-*r* 62.3%

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

      4. *-commutative 62.3%

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

      5. associate-+l- 62.3%

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

      6. *-commutative 62.3%

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

      7. associate-*r* 62.4%

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

      8. *-commutative 62.4%

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

      9. associate-*l* 62.4%

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

      10. associate-*l* 68.0%

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

   3. Simplified 68.0%

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

   5. Applied egg-rr 74.8%

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

   6. Taylor expanded in x around 0 89.0%

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

      1. clear-num 88.9%

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

      2. inv-pow 88.9%

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

   8. Applied egg-rr 88.9%

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

      1. unpow-1 88.9%

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

      2. *-commutative 88.9%

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

      3. associate-/r* 92.4%

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

   10. Simplified 92.4%

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

   if -1e15 < z < 0.299999999999999989

   1. Initial program 96.5%

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

4. Final simplification 94.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+15} \lor \neg \left(z \leq 0.3\right):\\ \;\;\;\;\left(-4 \cdot \left(a \cdot t\right) + \left(9 \cdot \frac{1}{\frac{\frac{z}{y}}{x}} + \frac{b}{z}\right)\right) \cdot \frac{1}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(9 \cdot x\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c}\\ \end{array} \]

Alternative 4: 91.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{+16} \lor \neg \left(z \leq 0.34\right):\\ \;\;\;\;\frac{1}{c} \cdot \left(-4 \cdot \left(a \cdot t\right) + \left(\frac{b}{z} + 9 \cdot \frac{y \cdot x}{z}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(9 \cdot x\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
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 -5e+16) (not (<= z 0.34)))
   (* (/ 1.0 c) (+ (* -4.0 (* a t)) (+ (/ b z) (* 9.0 (/ (* y x) z)))))
   (/ (+ b (- (* y (* 9.0 x)) (* a (* t (* z 4.0))))) (* z c))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < 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 <= -5e+16) || !(z <= 0.34)) {
		tmp = (1.0 / c) * ((-4.0 * (a * t)) + ((b / z) + (9.0 * ((y * x) / z))));
	} else {
		tmp = (b + ((y * (9.0 * x)) - (a * (t * (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.
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 <= (-5d+16)) .or. (.not. (z <= 0.34d0))) then
        tmp = (1.0d0 / c) * (((-4.0d0) * (a * t)) + ((b / z) + (9.0d0 * ((y * x) / z))))
    else
        tmp = (b + ((y * (9.0d0 * x)) - (a * (t * (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;
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 <= -5e+16) || !(z <= 0.34)) {
		tmp = (1.0 / c) * ((-4.0 * (a * t)) + ((b / z) + (9.0 * ((y * x) / z))));
	} else {
		tmp = (b + ((y * (9.0 * x)) - (a * (t * (z * 4.0))))) / (z * c);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
[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 <= -5e+16) or not (z <= 0.34):
		tmp = (1.0 / c) * ((-4.0 * (a * t)) + ((b / z) + (9.0 * ((y * x) / z))))
	else:
		tmp = (b + ((y * (9.0 * x)) - (a * (t * (z * 4.0))))) / (z * c)
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
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 <= -5e+16) || !(z <= 0.34))
		tmp = Float64(Float64(1.0 / c) * Float64(Float64(-4.0 * Float64(a * t)) + Float64(Float64(b / z) + Float64(9.0 * Float64(Float64(y * x) / z)))));
	else
		tmp = Float64(Float64(b + Float64(Float64(y * Float64(9.0 * x)) - Float64(a * Float64(t * Float64(z * 4.0))))) / Float64(z * c));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
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 <= -5e+16) || ~((z <= 0.34)))
		tmp = (1.0 / c) * ((-4.0 * (a * t)) + ((b / z) + (9.0 * ((y * x) / z))));
	else
		tmp = (b + ((y * (9.0 * x)) - (a * (t * (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.
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, -5e+16], N[Not[LessEqual[z, 0.34]], $MachinePrecision]], N[(N[(1.0 / c), $MachinePrecision] * N[(N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision] + N[(N[(b / z), $MachinePrecision] + N[(9.0 * N[(N[(y * x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b + N[(N[(y * N[(9.0 * x), $MachinePrecision]), $MachinePrecision] - N[(a * N[(t * N[(z * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5e16 or 0.340000000000000024 < z

   1. Initial program 62.4%

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

      1. associate-+l- 62.4%

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

      2. *-commutative 62.4%

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

      3. associate-*r* 62.3%

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

      4. *-commutative 62.3%

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

      5. associate-+l- 62.3%

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

      6. *-commutative 62.3%

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

      7. associate-*r* 62.4%

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

      8. *-commutative 62.4%

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

      9. associate-*l* 62.4%

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

      10. associate-*l* 68.0%

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

   3. Simplified 68.0%

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

   5. Applied egg-rr 74.8%

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

   6. Taylor expanded in x around 0 89.0%

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

   if -5e16 < z < 0.340000000000000024

   1. Initial program 96.5%

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

4. Final simplification 92.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{+16} \lor \neg \left(z \leq 0.34\right):\\ \;\;\;\;\frac{1}{c} \cdot \left(-4 \cdot \left(a \cdot t\right) + \left(\frac{b}{z} + 9 \cdot \frac{y \cdot x}{z}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(9 \cdot x\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c}\\ \end{array} \]

Alternative 5: 67.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \frac{-4 \cdot \left(a \cdot t\right) + \frac{b}{z}}{c}\\ \mathbf{if}\;x \leq -2.5 \cdot 10^{+169}:\\ \;\;\;\;\frac{1}{c} \cdot \left(9 \cdot \frac{x}{\frac{z}{y}}\right)\\ \mathbf{elif}\;x \leq -3.9 \cdot 10^{+127}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -7.5 \cdot 10^{+75}:\\ \;\;\;\;9 \cdot \left(x \cdot \frac{y}{z \cdot c}\right)\\ \mathbf{elif}\;x \leq -5.8 \cdot 10^{+43}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;x \leq 1.95 \cdot 10^{-102}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{9}{z} \cdot \frac{x}{\frac{c}{y}}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
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 (/ (+ (* -4.0 (* a t)) (/ b z)) c)))
   (if (<= x -2.5e+169)
     (* (/ 1.0 c) (* 9.0 (/ x (/ z y))))
     (if (<= x -3.9e+127)
       t_1
       (if (<= x -7.5e+75)
         (* 9.0 (* x (/ y (* z c))))
         (if (<= x -5.8e+43)
           (* -4.0 (/ a (/ c t)))
           (if (<= x 1.95e-102) t_1 (* (/ 9.0 z) (/ x (/ c y))))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < 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 = ((-4.0 * (a * t)) + (b / z)) / c;
	double tmp;
	if (x <= -2.5e+169) {
		tmp = (1.0 / c) * (9.0 * (x / (z / y)));
	} else if (x <= -3.9e+127) {
		tmp = t_1;
	} else if (x <= -7.5e+75) {
		tmp = 9.0 * (x * (y / (z * c)));
	} else if (x <= -5.8e+43) {
		tmp = -4.0 * (a / (c / t));
	} else if (x <= 1.95e-102) {
		tmp = t_1;
	} else {
		tmp = (9.0 / 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.
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) :: tmp
    t_1 = (((-4.0d0) * (a * t)) + (b / z)) / c
    if (x <= (-2.5d+169)) then
        tmp = (1.0d0 / c) * (9.0d0 * (x / (z / y)))
    else if (x <= (-3.9d+127)) then
        tmp = t_1
    else if (x <= (-7.5d+75)) then
        tmp = 9.0d0 * (x * (y / (z * c)))
    else if (x <= (-5.8d+43)) then
        tmp = (-4.0d0) * (a / (c / t))
    else if (x <= 1.95d-102) then
        tmp = t_1
    else
        tmp = (9.0d0 / z) * (x / (c / y))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
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 = ((-4.0 * (a * t)) + (b / z)) / c;
	double tmp;
	if (x <= -2.5e+169) {
		tmp = (1.0 / c) * (9.0 * (x / (z / y)));
	} else if (x <= -3.9e+127) {
		tmp = t_1;
	} else if (x <= -7.5e+75) {
		tmp = 9.0 * (x * (y / (z * c)));
	} else if (x <= -5.8e+43) {
		tmp = -4.0 * (a / (c / t));
	} else if (x <= 1.95e-102) {
		tmp = t_1;
	} else {
		tmp = (9.0 / z) * (x / (c / y));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
[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 = ((-4.0 * (a * t)) + (b / z)) / c
	tmp = 0
	if x <= -2.5e+169:
		tmp = (1.0 / c) * (9.0 * (x / (z / y)))
	elif x <= -3.9e+127:
		tmp = t_1
	elif x <= -7.5e+75:
		tmp = 9.0 * (x * (y / (z * c)))
	elif x <= -5.8e+43:
		tmp = -4.0 * (a / (c / t))
	elif x <= 1.95e-102:
		tmp = t_1
	else:
		tmp = (9.0 / z) * (x / (c / y))
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
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(Float64(Float64(-4.0 * Float64(a * t)) + Float64(b / z)) / c)
	tmp = 0.0
	if (x <= -2.5e+169)
		tmp = Float64(Float64(1.0 / c) * Float64(9.0 * Float64(x / Float64(z / y))));
	elseif (x <= -3.9e+127)
		tmp = t_1;
	elseif (x <= -7.5e+75)
		tmp = Float64(9.0 * Float64(x * Float64(y / Float64(z * c))));
	elseif (x <= -5.8e+43)
		tmp = Float64(-4.0 * Float64(a / Float64(c / t)));
	elseif (x <= 1.95e-102)
		tmp = t_1;
	else
		tmp = Float64(Float64(9.0 / z) * Float64(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])){:}
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 = ((-4.0 * (a * t)) + (b / z)) / c;
	tmp = 0.0;
	if (x <= -2.5e+169)
		tmp = (1.0 / c) * (9.0 * (x / (z / y)));
	elseif (x <= -3.9e+127)
		tmp = t_1;
	elseif (x <= -7.5e+75)
		tmp = 9.0 * (x * (y / (z * c)));
	elseif (x <= -5.8e+43)
		tmp = -4.0 * (a / (c / t));
	elseif (x <= 1.95e-102)
		tmp = t_1;
	else
		tmp = (9.0 / 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.
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[(N[(N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision] + N[(b / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]}, If[LessEqual[x, -2.5e+169], N[(N[(1.0 / c), $MachinePrecision] * N[(9.0 * N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -3.9e+127], t$95$1, If[LessEqual[x, -7.5e+75], N[(9.0 * N[(x * N[(y / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -5.8e+43], N[(-4.0 * N[(a / N[(c / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.95e-102], t$95$1, N[(N[(9.0 / z), $MachinePrecision] * N[(x / N[(c / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -2.50000000000000009e169

   1. Initial program 75.6%

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

      1. associate-+l- 75.6%

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

      2. *-commutative 75.6%

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

      3. associate-*r* 75.2%

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

      4. *-commutative 75.2%

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

      5. associate-+l- 75.2%

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

      6. *-commutative 75.2%

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

      7. associate-*r* 75.6%

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

      8. *-commutative 75.6%

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

      9. associate-*l* 75.6%

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

      10. associate-*l* 75.6%

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

   3. Simplified 75.6%

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

   5. Applied egg-rr 79.9%

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

   6. Taylor expanded in x around inf 59.2%

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

      1. associate-/l* 67.7%

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

   8. Simplified 67.7%

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

   if -2.50000000000000009e169 < x < -3.89999999999999981e127 or -5.8000000000000004e43 < x < 1.95e-102

   1. Initial program 79.6%

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

      1. associate-+l- 79.6%

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

      2. *-commutative 79.6%

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

      3. associate-*r* 80.4%

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

      4. *-commutative 80.4%

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

      5. associate-+l- 80.4%

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

      6. *-commutative 80.4%

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

      7. associate-*r* 79.6%

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

      8. *-commutative 79.6%

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

      9. associate-*l* 79.6%

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

      10. associate-*l* 82.0%

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

   3. Simplified 82.0%

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

   5. Applied egg-rr 78.2%

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

   6. Taylor expanded in x around 0 88.4%

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

   7. Taylor expanded in x around 0 78.6%

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

   if -3.89999999999999981e127 < x < -7.4999999999999995e75

   1. Initial program 100.0%

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

      1. associate-+l- 100.0%

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

      2. *-commutative 100.0%

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

      3. associate-*r* 100.0%

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

      4. *-commutative 100.0%

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

      5. associate-+l- 100.0%

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

      6. *-commutative 100.0%

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

      7. associate-*r* 100.0%

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

      8. *-commutative 100.0%

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

      9. associate-*l* 100.0%

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

      10. associate-*l* 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around inf 75.0%

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

      1. expm1-log1p-u 50.0%

         \[\leadsto 9 \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{x \cdot y}{c \cdot z}\right)\right)} \]

      2. expm1-udef 50.0%

         \[\leadsto 9 \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(\frac{x \cdot y}{c \cdot z}\right)} - 1\right)} \]

      3. times-frac 50.0%

         \[\leadsto 9 \cdot \left(e^{\mathsf{log1p}\left(\color{blue}{\frac{x}{c} \cdot \frac{y}{z}}\right)} - 1\right) \]

   6. Applied egg-rr 50.0%

      \[\leadsto 9 \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(\frac{x}{c} \cdot \frac{y}{z}\right)} - 1\right)} \]
   7. Step-by-step derivation

      1. expm1-def 50.0%

         \[\leadsto 9 \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{x}{c} \cdot \frac{y}{z}\right)\right)} \]

      2. expm1-log1p 75.0%

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

      3. times-frac 75.0%

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

      4. *-commutative 75.0%

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

      5. associate-*r/ 75.0%

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

      6. *-commutative 75.0%

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

   8. Simplified 75.0%

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

   if -7.4999999999999995e75 < x < -5.8000000000000004e43

   1. Initial program 100.0%

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

      1. associate-+l- 100.0%

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

      2. *-commutative 100.0%

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

      3. associate-*r* 100.0%

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

      4. *-commutative 100.0%

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

      5. associate-+l- 100.0%

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

      6. *-commutative 100.0%

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

      7. associate-*r* 100.0%

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

      8. *-commutative 100.0%

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

      9. associate-*l* 100.0%

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

      10. associate-*l* 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in z around inf 67.0%

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

      1. *-commutative 67.0%

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

      2. associate-/l* 67.0%

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

   6. Simplified 67.0%

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

   if 1.95e-102 < x

   1. Initial program 73.1%

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

      1. associate-+l- 73.1%

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

      2. *-commutative 73.1%

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

      3. associate-*r* 71.9%

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

      4. *-commutative 71.9%

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

      5. associate-+l- 71.9%

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

      6. *-commutative 71.9%

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

      7. associate-*r* 73.1%

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

      8. *-commutative 73.1%

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

      9. associate-*l* 73.1%

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

      10. associate-*l* 73.2%

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

   3. Simplified 73.2%

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

   5. Applied egg-rr 78.8%

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

   6. Taylor expanded in x around inf 48.4%

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

      1. associate-*r/ 48.4%

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

      2. *-commutative 48.4%

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

      3. times-frac 50.0%

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

      4. associate-/l* 50.0%

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

   8. Simplified 50.0%

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

4. Final simplification 67.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.5 \cdot 10^{+169}:\\ \;\;\;\;\frac{1}{c} \cdot \left(9 \cdot \frac{x}{\frac{z}{y}}\right)\\ \mathbf{elif}\;x \leq -3.9 \cdot 10^{+127}:\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right) + \frac{b}{z}}{c}\\ \mathbf{elif}\;x \leq -7.5 \cdot 10^{+75}:\\ \;\;\;\;9 \cdot \left(x \cdot \frac{y}{z \cdot c}\right)\\ \mathbf{elif}\;x \leq -5.8 \cdot 10^{+43}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;x \leq 1.95 \cdot 10^{-102}:\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right) + \frac{b}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{9}{z} \cdot \frac{x}{\frac{c}{y}}\\ \end{array} \]

Alternative 6: 74.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \frac{b + y \cdot \left(9 \cdot x\right)}{z \cdot c}\\ t_2 := \frac{-4 \cdot \left(a \cdot t\right) + \frac{b}{z}}{c}\\ \mathbf{if}\;z \leq -4.1 \cdot 10^{-52}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-190}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-50}:\\ \;\;\;\;\frac{1}{\frac{z \cdot c}{b + \left(-4 \cdot a\right) \cdot \left(z \cdot t\right)}}\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-19}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
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 (* y (* 9.0 x))) (* z c)))
        (t_2 (/ (+ (* -4.0 (* a t)) (/ b z)) c)))
   (if (<= z -4.1e-52)
     t_2
     (if (<= z 1.7e-190)
       t_1
       (if (<= z 4e-50)
         (/ 1.0 (/ (* z c) (+ b (* (* -4.0 a) (* z t)))))
         (if (<= z 2.2e-19) t_1 t_2))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < 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 + (y * (9.0 * x))) / (z * c);
	double t_2 = ((-4.0 * (a * t)) + (b / z)) / c;
	double tmp;
	if (z <= -4.1e-52) {
		tmp = t_2;
	} else if (z <= 1.7e-190) {
		tmp = t_1;
	} else if (z <= 4e-50) {
		tmp = 1.0 / ((z * c) / (b + ((-4.0 * a) * (z * t))));
	} else if (z <= 2.2e-19) {
		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.
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 = (b + (y * (9.0d0 * x))) / (z * c)
    t_2 = (((-4.0d0) * (a * t)) + (b / z)) / c
    if (z <= (-4.1d-52)) then
        tmp = t_2
    else if (z <= 1.7d-190) then
        tmp = t_1
    else if (z <= 4d-50) then
        tmp = 1.0d0 / ((z * c) / (b + (((-4.0d0) * a) * (z * t))))
    else if (z <= 2.2d-19) 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;
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 = (b + (y * (9.0 * x))) / (z * c);
	double t_2 = ((-4.0 * (a * t)) + (b / z)) / c;
	double tmp;
	if (z <= -4.1e-52) {
		tmp = t_2;
	} else if (z <= 1.7e-190) {
		tmp = t_1;
	} else if (z <= 4e-50) {
		tmp = 1.0 / ((z * c) / (b + ((-4.0 * a) * (z * t))));
	} else if (z <= 2.2e-19) {
		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])
[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 = (b + (y * (9.0 * x))) / (z * c)
	t_2 = ((-4.0 * (a * t)) + (b / z)) / c
	tmp = 0
	if z <= -4.1e-52:
		tmp = t_2
	elif z <= 1.7e-190:
		tmp = t_1
	elif z <= 4e-50:
		tmp = 1.0 / ((z * c) / (b + ((-4.0 * a) * (z * t))))
	elif z <= 2.2e-19:
		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])
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(Float64(b + Float64(y * Float64(9.0 * x))) / Float64(z * c))
	t_2 = Float64(Float64(Float64(-4.0 * Float64(a * t)) + Float64(b / z)) / c)
	tmp = 0.0
	if (z <= -4.1e-52)
		tmp = t_2;
	elseif (z <= 1.7e-190)
		tmp = t_1;
	elseif (z <= 4e-50)
		tmp = Float64(1.0 / Float64(Float64(z * c) / Float64(b + Float64(Float64(-4.0 * a) * Float64(z * t)))));
	elseif (z <= 2.2e-19)
		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])){:}
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 = (b + (y * (9.0 * x))) / (z * c);
	t_2 = ((-4.0 * (a * t)) + (b / z)) / c;
	tmp = 0.0;
	if (z <= -4.1e-52)
		tmp = t_2;
	elseif (z <= 1.7e-190)
		tmp = t_1;
	elseif (z <= 4e-50)
		tmp = 1.0 / ((z * c) / (b + ((-4.0 * a) * (z * t))));
	elseif (z <= 2.2e-19)
		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.
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[(N[(b + N[(y * N[(9.0 * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision] + N[(b / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]}, If[LessEqual[z, -4.1e-52], t$95$2, If[LessEqual[z, 1.7e-190], t$95$1, If[LessEqual[z, 4e-50], N[(1.0 / N[(N[(z * c), $MachinePrecision] / N[(b + N[(N[(-4.0 * a), $MachinePrecision] * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.2e-19], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.09999999999999988e-52 or 2.1999999999999998e-19 < z

   1. Initial program 64.5%

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

      1. associate-+l- 64.5%

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

      2. *-commutative 64.5%

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

      3. associate-*r* 64.5%

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

      4. *-commutative 64.5%

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

      5. associate-+l- 64.5%

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

      6. *-commutative 64.5%

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

      7. associate-*r* 64.5%

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

      8. *-commutative 64.5%

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

      9. associate-*l* 64.5%

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

      10. associate-*l* 69.7%

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

   3. Simplified 69.7%

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

   5. Applied egg-rr 76.0%

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

   6. Taylor expanded in x around 0 89.2%

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

   7. Taylor expanded in x around 0 72.0%

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

   if -4.09999999999999988e-52 < z < 1.69999999999999991e-190 or 4.00000000000000003e-50 < z < 2.1999999999999998e-19

   1. Initial program 97.0%

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

      1. associate-+l- 97.0%

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

      2. *-commutative 97.0%

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

      3. associate-*r* 97.0%

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

      4. *-commutative 97.0%

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

      5. associate-+l- 97.0%

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

      6. *-commutative 97.0%

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

      7. associate-*r* 97.0%

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

      8. *-commutative 97.0%

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

      9. associate-*l* 97.1%

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

      10. associate-*l* 92.9%

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

   3. Simplified 92.9%

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

   4. Taylor expanded in x around inf 91.9%

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

      1. associate-*r* 91.9%

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

   6. Simplified 91.9%

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

   if 1.69999999999999991e-190 < z < 4.00000000000000003e-50

   1. Initial program 96.7%

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

      1. associate-+l- 96.7%

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

      2. *-commutative 96.7%

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

      3. associate-*r* 96.8%

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

      4. *-commutative 96.8%

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

      5. associate-+l- 96.8%

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

      6. *-commutative 96.8%

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

      7. associate-*r* 96.7%

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

      8. *-commutative 96.7%

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

      9. associate-*l* 96.8%

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

      10. associate-*l* 90.9%

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

   3. Simplified 90.9%

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

   4. Taylor expanded in x around 0 80.4%

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

      1. clear-num 80.5%

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

      2. inv-pow 80.5%

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

      3. *-commutative 80.5%

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

      4. *-commutative 80.5%

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

   6. Applied egg-rr 80.5%

      \[\leadsto \color{blue}{{\left(\frac{z \cdot c}{b - 4 \cdot \left(a \cdot \left(z \cdot t\right)\right)}\right)}^{-1}} \]
   7. Step-by-step derivation

      1. unpow-1 80.5%

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

      2. *-commutative 80.5%

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

      3. cancel-sign-sub-inv 80.5%

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

      4. metadata-eval 80.5%

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

      5. associate-*r* 80.5%

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

   8. Simplified 80.5%

      \[\leadsto \color{blue}{\frac{1}{\frac{c \cdot z}{b + \left(-4 \cdot a\right) \cdot \left(z \cdot t\right)}}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 78.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.1 \cdot 10^{-52}:\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right) + \frac{b}{z}}{c}\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-190}:\\ \;\;\;\;\frac{b + y \cdot \left(9 \cdot x\right)}{z \cdot c}\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-50}:\\ \;\;\;\;\frac{1}{\frac{z \cdot c}{b + \left(-4 \cdot a\right) \cdot \left(z \cdot t\right)}}\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-19}:\\ \;\;\;\;\frac{b + y \cdot \left(9 \cdot x\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right) + \frac{b}{z}}{c}\\ \end{array} \]

Alternative 7: 76.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := -4 \cdot \left(a \cdot t\right)\\ \mathbf{if}\;x \leq -1.32 \cdot 10^{+35} \lor \neg \left(x \leq 4.2 \cdot 10^{-103}\right):\\ \;\;\;\;\frac{1}{c} \cdot \left(t_1 + \frac{9 \cdot x}{\frac{z}{y}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t_1 + \frac{b}{z}}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
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 (* -4.0 (* a t))))
   (if (or (<= x -1.32e+35) (not (<= x 4.2e-103)))
     (* (/ 1.0 c) (+ t_1 (/ (* 9.0 x) (/ z y))))
     (/ (+ t_1 (/ b z)) c))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < 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 = -4.0 * (a * t);
	double tmp;
	if ((x <= -1.32e+35) || !(x <= 4.2e-103)) {
		tmp = (1.0 / c) * (t_1 + ((9.0 * x) / (z / y)));
	} else {
		tmp = (t_1 + (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.
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) :: tmp
    t_1 = (-4.0d0) * (a * t)
    if ((x <= (-1.32d+35)) .or. (.not. (x <= 4.2d-103))) then
        tmp = (1.0d0 / c) * (t_1 + ((9.0d0 * x) / (z / y)))
    else
        tmp = (t_1 + (b / z)) / c
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
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 = -4.0 * (a * t);
	double tmp;
	if ((x <= -1.32e+35) || !(x <= 4.2e-103)) {
		tmp = (1.0 / c) * (t_1 + ((9.0 * x) / (z / y)));
	} else {
		tmp = (t_1 + (b / z)) / c;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
[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 = -4.0 * (a * t)
	tmp = 0
	if (x <= -1.32e+35) or not (x <= 4.2e-103):
		tmp = (1.0 / c) * (t_1 + ((9.0 * x) / (z / y)))
	else:
		tmp = (t_1 + (b / z)) / c
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
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(-4.0 * Float64(a * t))
	tmp = 0.0
	if ((x <= -1.32e+35) || !(x <= 4.2e-103))
		tmp = Float64(Float64(1.0 / c) * Float64(t_1 + Float64(Float64(9.0 * x) / Float64(z / y))));
	else
		tmp = Float64(Float64(t_1 + Float64(b / z)) / c);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
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 = -4.0 * (a * t);
	tmp = 0.0;
	if ((x <= -1.32e+35) || ~((x <= 4.2e-103)))
		tmp = (1.0 / c) * (t_1 + ((9.0 * x) / (z / y)));
	else
		tmp = (t_1 + (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.
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[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[x, -1.32e+35], N[Not[LessEqual[x, 4.2e-103]], $MachinePrecision]], N[(N[(1.0 / c), $MachinePrecision] * N[(t$95$1 + N[(N[(9.0 * x), $MachinePrecision] / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t$95$1 + N[(b / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.31999999999999995e35 or 4.20000000000000009e-103 < x

   1. Initial program 74.2%

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

      1. associate-+l- 74.2%

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

      2. *-commutative 74.2%

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

      3. associate-*r* 73.3%

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

      4. *-commutative 73.3%

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

      5. associate-+l- 73.3%

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

      6. *-commutative 73.3%

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

      7. associate-*r* 74.2%

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

      8. *-commutative 74.2%

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

      9. associate-*l* 74.3%

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

      10. associate-*l* 74.4%

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

   3. Simplified 74.4%

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

   5. Applied egg-rr 80.4%

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

   6. Taylor expanded in x around 0 83.2%

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

   7. Taylor expanded in x around inf 71.0%

      \[\leadsto \left(-4 \cdot \left(a \cdot t\right) + \color{blue}{9 \cdot \frac{x \cdot y}{z}}\right) \cdot \frac{1}{c} \]
   8. Step-by-step derivation

      1. associate-/l* 74.7%

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

      2. associate-*r/ 74.8%

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

   9. Simplified 74.8%

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

   if -1.31999999999999995e35 < x < 4.20000000000000009e-103

   1. Initial program 80.7%

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

      1. associate-+l- 80.7%

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

      2. *-commutative 80.7%

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

      3. associate-*r* 81.6%

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

      4. *-commutative 81.6%

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

      5. associate-+l- 81.6%

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

      6. *-commutative 81.6%

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

      7. associate-*r* 80.7%

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

      8. *-commutative 80.7%

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

      9. associate-*l* 80.7%

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

      10. associate-*l* 83.2%

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

   3. Simplified 83.2%

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

   5. Applied egg-rr 77.8%

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

   6. Taylor expanded in x around 0 87.7%

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

   7. Taylor expanded in x around 0 78.1%

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

4. Final simplification 76.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.32 \cdot 10^{+35} \lor \neg \left(x \leq 4.2 \cdot 10^{-103}\right):\\ \;\;\;\;\frac{1}{c} \cdot \left(-4 \cdot \left(a \cdot t\right) + \frac{9 \cdot x}{\frac{z}{y}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right) + \frac{b}{z}}{c}\\ \end{array} \]

Alternative 8: 74.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \frac{b + y \cdot \left(9 \cdot x\right)}{z \cdot c}\\ t_2 := \frac{-4 \cdot \left(a \cdot t\right) + \frac{b}{z}}{c}\\ \mathbf{if}\;z \leq -1.42 \cdot 10^{-52}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-192}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-44}:\\ \;\;\;\;\frac{b - 4 \cdot \left(a \cdot \left(z \cdot t\right)\right)}{z \cdot c}\\ \mathbf{elif}\;z \leq 9 \cdot 10^{-21}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
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 (* y (* 9.0 x))) (* z c)))
        (t_2 (/ (+ (* -4.0 (* a t)) (/ b z)) c)))
   (if (<= z -1.42e-52)
     t_2
     (if (<= z 8e-192)
       t_1
       (if (<= z 1.8e-44)
         (/ (- b (* 4.0 (* a (* z t)))) (* z c))
         (if (<= z 9e-21) t_1 t_2))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < 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 + (y * (9.0 * x))) / (z * c);
	double t_2 = ((-4.0 * (a * t)) + (b / z)) / c;
	double tmp;
	if (z <= -1.42e-52) {
		tmp = t_2;
	} else if (z <= 8e-192) {
		tmp = t_1;
	} else if (z <= 1.8e-44) {
		tmp = (b - (4.0 * (a * (z * t)))) / (z * c);
	} else if (z <= 9e-21) {
		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.
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 = (b + (y * (9.0d0 * x))) / (z * c)
    t_2 = (((-4.0d0) * (a * t)) + (b / z)) / c
    if (z <= (-1.42d-52)) then
        tmp = t_2
    else if (z <= 8d-192) then
        tmp = t_1
    else if (z <= 1.8d-44) then
        tmp = (b - (4.0d0 * (a * (z * t)))) / (z * c)
    else if (z <= 9d-21) 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;
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 = (b + (y * (9.0 * x))) / (z * c);
	double t_2 = ((-4.0 * (a * t)) + (b / z)) / c;
	double tmp;
	if (z <= -1.42e-52) {
		tmp = t_2;
	} else if (z <= 8e-192) {
		tmp = t_1;
	} else if (z <= 1.8e-44) {
		tmp = (b - (4.0 * (a * (z * t)))) / (z * c);
	} else if (z <= 9e-21) {
		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])
[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 = (b + (y * (9.0 * x))) / (z * c)
	t_2 = ((-4.0 * (a * t)) + (b / z)) / c
	tmp = 0
	if z <= -1.42e-52:
		tmp = t_2
	elif z <= 8e-192:
		tmp = t_1
	elif z <= 1.8e-44:
		tmp = (b - (4.0 * (a * (z * t)))) / (z * c)
	elif z <= 9e-21:
		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])
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(Float64(b + Float64(y * Float64(9.0 * x))) / Float64(z * c))
	t_2 = Float64(Float64(Float64(-4.0 * Float64(a * t)) + Float64(b / z)) / c)
	tmp = 0.0
	if (z <= -1.42e-52)
		tmp = t_2;
	elseif (z <= 8e-192)
		tmp = t_1;
	elseif (z <= 1.8e-44)
		tmp = Float64(Float64(b - Float64(4.0 * Float64(a * Float64(z * t)))) / Float64(z * c));
	elseif (z <= 9e-21)
		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])){:}
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 = (b + (y * (9.0 * x))) / (z * c);
	t_2 = ((-4.0 * (a * t)) + (b / z)) / c;
	tmp = 0.0;
	if (z <= -1.42e-52)
		tmp = t_2;
	elseif (z <= 8e-192)
		tmp = t_1;
	elseif (z <= 1.8e-44)
		tmp = (b - (4.0 * (a * (z * t)))) / (z * c);
	elseif (z <= 9e-21)
		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.
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[(N[(b + N[(y * N[(9.0 * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision] + N[(b / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]}, If[LessEqual[z, -1.42e-52], t$95$2, If[LessEqual[z, 8e-192], t$95$1, If[LessEqual[z, 1.8e-44], N[(N[(b - N[(4.0 * N[(a * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9e-21], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.4200000000000001e-52 or 8.99999999999999936e-21 < z

   1. Initial program 64.5%

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

      1. associate-+l- 64.5%

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

      2. *-commutative 64.5%

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

      3. associate-*r* 64.5%

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

      4. *-commutative 64.5%

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

      5. associate-+l- 64.5%

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

      6. *-commutative 64.5%

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

      7. associate-*r* 64.5%

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

      8. *-commutative 64.5%

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

      9. associate-*l* 64.5%

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

      10. associate-*l* 69.7%

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

   3. Simplified 69.7%

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

   5. Applied egg-rr 76.0%

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

   6. Taylor expanded in x around 0 89.2%

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

   7. Taylor expanded in x around 0 72.0%

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

   if -1.4200000000000001e-52 < z < 8.0000000000000008e-192 or 1.7999999999999999e-44 < z < 8.99999999999999936e-21

   1. Initial program 97.0%

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

      1. associate-+l- 97.0%

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

      2. *-commutative 97.0%

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

      3. associate-*r* 97.0%

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

      4. *-commutative 97.0%

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

      5. associate-+l- 97.0%

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

      6. *-commutative 97.0%

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

      7. associate-*r* 97.0%

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

      8. *-commutative 97.0%

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

      9. associate-*l* 97.1%

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

      10. associate-*l* 92.9%

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

   3. Simplified 92.9%

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

   4. Taylor expanded in x around inf 91.9%

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

      1. associate-*r* 91.9%

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

   6. Simplified 91.9%

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

   if 8.0000000000000008e-192 < z < 1.7999999999999999e-44

   1. Initial program 96.7%

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

      1. associate-+l- 96.7%

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

      2. *-commutative 96.7%

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

      3. associate-*r* 96.8%

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

      4. *-commutative 96.8%

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

      5. associate-+l- 96.8%

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

      6. *-commutative 96.8%

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

      7. associate-*r* 96.7%

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

      8. *-commutative 96.7%

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

      9. associate-*l* 96.8%

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

      10. associate-*l* 90.9%

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

   3. Simplified 90.9%

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

   4. Taylor expanded in x around 0 80.4%

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

4. Final simplification 78.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.42 \cdot 10^{-52}:\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right) + \frac{b}{z}}{c}\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-192}:\\ \;\;\;\;\frac{b + y \cdot \left(9 \cdot x\right)}{z \cdot c}\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-44}:\\ \;\;\;\;\frac{b - 4 \cdot \left(a \cdot \left(z \cdot t\right)\right)}{z \cdot c}\\ \mathbf{elif}\;z \leq 9 \cdot 10^{-21}:\\ \;\;\;\;\frac{b + y \cdot \left(9 \cdot x\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right) + \frac{b}{z}}{c}\\ \end{array} \]

Alternative 9: 74.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := -4 \cdot \left(a \cdot t\right)\\ \mathbf{if}\;x \leq -5.9 \cdot 10^{+35} \lor \neg \left(x \leq 4.5 \cdot 10^{-104}\right):\\ \;\;\;\;\frac{t_1 + 9 \cdot \frac{y \cdot x}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{t_1 + \frac{b}{z}}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
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 (* -4.0 (* a t))))
   (if (or (<= x -5.9e+35) (not (<= x 4.5e-104)))
     (/ (+ t_1 (* 9.0 (/ (* y x) z))) c)
     (/ (+ t_1 (/ b z)) c))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < 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 = -4.0 * (a * t);
	double tmp;
	if ((x <= -5.9e+35) || !(x <= 4.5e-104)) {
		tmp = (t_1 + (9.0 * ((y * x) / z))) / c;
	} else {
		tmp = (t_1 + (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.
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) :: tmp
    t_1 = (-4.0d0) * (a * t)
    if ((x <= (-5.9d+35)) .or. (.not. (x <= 4.5d-104))) then
        tmp = (t_1 + (9.0d0 * ((y * x) / z))) / c
    else
        tmp = (t_1 + (b / z)) / c
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
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 = -4.0 * (a * t);
	double tmp;
	if ((x <= -5.9e+35) || !(x <= 4.5e-104)) {
		tmp = (t_1 + (9.0 * ((y * x) / z))) / c;
	} else {
		tmp = (t_1 + (b / z)) / c;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
[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 = -4.0 * (a * t)
	tmp = 0
	if (x <= -5.9e+35) or not (x <= 4.5e-104):
		tmp = (t_1 + (9.0 * ((y * x) / z))) / c
	else:
		tmp = (t_1 + (b / z)) / c
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
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(-4.0 * Float64(a * t))
	tmp = 0.0
	if ((x <= -5.9e+35) || !(x <= 4.5e-104))
		tmp = Float64(Float64(t_1 + Float64(9.0 * Float64(Float64(y * x) / z))) / c);
	else
		tmp = Float64(Float64(t_1 + Float64(b / z)) / c);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
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 = -4.0 * (a * t);
	tmp = 0.0;
	if ((x <= -5.9e+35) || ~((x <= 4.5e-104)))
		tmp = (t_1 + (9.0 * ((y * x) / z))) / c;
	else
		tmp = (t_1 + (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.
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[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[x, -5.9e+35], N[Not[LessEqual[x, 4.5e-104]], $MachinePrecision]], N[(N[(t$95$1 + N[(9.0 * N[(N[(y * x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], N[(N[(t$95$1 + N[(b / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -5.89999999999999985e35 or 4.4999999999999997e-104 < x

   1. Initial program 74.2%

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

      1. associate-+l- 74.2%

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

      2. *-commutative 74.2%

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

      3. associate-*r* 73.3%

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

      4. *-commutative 73.3%

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

      5. associate-+l- 73.3%

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

      6. *-commutative 73.3%

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

      7. associate-*r* 74.2%

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

      8. *-commutative 74.2%

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

      9. associate-*l* 74.3%

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

      10. associate-*l* 74.4%

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

   3. Simplified 74.4%

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

   5. Applied egg-rr 80.4%

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

   6. Taylor expanded in x around 0 83.2%

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

   7. Taylor expanded in b around 0 71.0%

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

   if -5.89999999999999985e35 < x < 4.4999999999999997e-104

   1. Initial program 80.7%

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

      1. associate-+l- 80.7%

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

      2. *-commutative 80.7%

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

      3. associate-*r* 81.6%

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

      4. *-commutative 81.6%

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

      5. associate-+l- 81.6%

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

      6. *-commutative 81.6%

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

      7. associate-*r* 80.7%

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

      8. *-commutative 80.7%

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

      9. associate-*l* 80.7%

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

      10. associate-*l* 83.2%

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

   3. Simplified 83.2%

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

   5. Applied egg-rr 77.8%

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

   6. Taylor expanded in x around 0 87.7%

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

   7. Taylor expanded in x around 0 78.1%

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

4. Final simplification 74.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.9 \cdot 10^{+35} \lor \neg \left(x \leq 4.5 \cdot 10^{-104}\right):\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right) + 9 \cdot \frac{y \cdot x}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right) + \frac{b}{z}}{c}\\ \end{array} \]

Alternative 10: 50.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := -4 \cdot \frac{t}{\frac{c}{a}}\\ \mathbf{if}\;z \leq -1.35 \cdot 10^{+155}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -6.2 \cdot 10^{+92}:\\ \;\;\;\;\frac{b \cdot \frac{1}{c}}{z}\\ \mathbf{elif}\;z \leq -1.12 \cdot 10^{-35}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.45 \cdot 10^{-279}:\\ \;\;\;\;9 \cdot \left(x \cdot \frac{y}{z \cdot c}\right)\\ \mathbf{elif}\;z \leq 2.06 \cdot 10^{-20}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
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 (* -4.0 (/ t (/ c a)))))
   (if (<= z -1.35e+155)
     t_1
     (if (<= z -6.2e+92)
       (/ (* b (/ 1.0 c)) z)
       (if (<= z -1.12e-35)
         t_1
         (if (<= z -1.45e-279)
           (* 9.0 (* x (/ y (* z c))))
           (if (<= z 2.06e-20) (/ b (* z c)) t_1)))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < 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 = -4.0 * (t / (c / a));
	double tmp;
	if (z <= -1.35e+155) {
		tmp = t_1;
	} else if (z <= -6.2e+92) {
		tmp = (b * (1.0 / c)) / z;
	} else if (z <= -1.12e-35) {
		tmp = t_1;
	} else if (z <= -1.45e-279) {
		tmp = 9.0 * (x * (y / (z * c)));
	} else if (z <= 2.06e-20) {
		tmp = b / (z * c);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
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) :: tmp
    t_1 = (-4.0d0) * (t / (c / a))
    if (z <= (-1.35d+155)) then
        tmp = t_1
    else if (z <= (-6.2d+92)) then
        tmp = (b * (1.0d0 / c)) / z
    else if (z <= (-1.12d-35)) then
        tmp = t_1
    else if (z <= (-1.45d-279)) then
        tmp = 9.0d0 * (x * (y / (z * c)))
    else if (z <= 2.06d-20) then
        tmp = b / (z * c)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
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 = -4.0 * (t / (c / a));
	double tmp;
	if (z <= -1.35e+155) {
		tmp = t_1;
	} else if (z <= -6.2e+92) {
		tmp = (b * (1.0 / c)) / z;
	} else if (z <= -1.12e-35) {
		tmp = t_1;
	} else if (z <= -1.45e-279) {
		tmp = 9.0 * (x * (y / (z * c)));
	} else if (z <= 2.06e-20) {
		tmp = b / (z * c);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
[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 = -4.0 * (t / (c / a))
	tmp = 0
	if z <= -1.35e+155:
		tmp = t_1
	elif z <= -6.2e+92:
		tmp = (b * (1.0 / c)) / z
	elif z <= -1.12e-35:
		tmp = t_1
	elif z <= -1.45e-279:
		tmp = 9.0 * (x * (y / (z * c)))
	elif z <= 2.06e-20:
		tmp = b / (z * c)
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
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(-4.0 * Float64(t / Float64(c / a)))
	tmp = 0.0
	if (z <= -1.35e+155)
		tmp = t_1;
	elseif (z <= -6.2e+92)
		tmp = Float64(Float64(b * Float64(1.0 / c)) / z);
	elseif (z <= -1.12e-35)
		tmp = t_1;
	elseif (z <= -1.45e-279)
		tmp = Float64(9.0 * Float64(x * Float64(y / Float64(z * c))));
	elseif (z <= 2.06e-20)
		tmp = Float64(b / Float64(z * c));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
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 = -4.0 * (t / (c / a));
	tmp = 0.0;
	if (z <= -1.35e+155)
		tmp = t_1;
	elseif (z <= -6.2e+92)
		tmp = (b * (1.0 / c)) / z;
	elseif (z <= -1.12e-35)
		tmp = t_1;
	elseif (z <= -1.45e-279)
		tmp = 9.0 * (x * (y / (z * c)));
	elseif (z <= 2.06e-20)
		tmp = b / (z * c);
	else
		tmp = t_1;
	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.
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[(-4.0 * N[(t / N[(c / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.35e+155], t$95$1, If[LessEqual[z, -6.2e+92], N[(N[(b * N[(1.0 / c), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, -1.12e-35], t$95$1, If[LessEqual[z, -1.45e-279], N[(9.0 * N[(x * N[(y / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.06e-20], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.34999999999999997e155 or -6.2000000000000004e92 < z < -1.12e-35 or 2.06000000000000008e-20 < z

   1. Initial program 64.2%

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

      1. associate-+l- 64.2%

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

      2. *-commutative 64.2%

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

      3. associate-*r* 64.9%

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

      4. *-commutative 64.9%

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

      5. associate-+l- 64.9%

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

      6. *-commutative 64.9%

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

      7. associate-*r* 64.2%

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

      8. *-commutative 64.2%

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

      9. associate-*l* 64.1%

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

      10. associate-*l* 69.6%

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

   3. Simplified 69.6%

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

   5. Applied egg-rr 74.3%

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

   6. Taylor expanded in x around 0 88.6%

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

      1. clear-num 88.5%

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

      2. inv-pow 88.5%

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

   8. Applied egg-rr 88.5%

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

      1. unpow-1 88.5%

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

      2. *-commutative 88.5%

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

      3. associate-/r* 91.6%

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

   10. Simplified 91.6%

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

   11. Taylor expanded in a around inf 54.5%

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

       1. *-commutative 54.5%

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

       2. associate-/l* 60.2%

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

   13. Simplified 60.2%

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

   if -1.34999999999999997e155 < z < -6.2000000000000004e92

   1. Initial program 63.7%

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

      1. associate-+l- 63.7%

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

      2. *-commutative 63.7%

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

      3. associate-*r* 59.3%

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

      4. *-commutative 59.3%

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

      5. associate-+l- 59.3%

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

      6. *-commutative 59.3%

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

      7. associate-*r* 63.7%

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

      8. *-commutative 63.7%

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

      9. associate-*l* 63.7%

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

      10. associate-*l* 67.9%

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

   3. Simplified 67.9%

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

   5. Applied egg-rr 83.3%

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

   6. Taylor expanded in b around inf 36.4%

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

      1. associate-*l/ 44.6%

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

   8. Applied egg-rr 44.6%

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

   if -1.12e-35 < z < -1.45e-279

   1. Initial program 97.2%

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

      1. associate-+l- 97.2%

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

      2. *-commutative 97.2%

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

      3. associate-*r* 97.2%

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

      4. *-commutative 97.2%

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

      5. associate-+l- 97.2%

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

      6. *-commutative 97.2%

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

      7. associate-*r* 97.2%

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

      8. *-commutative 97.2%

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

      9. associate-*l* 97.3%

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

      10. associate-*l* 94.7%

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

   3. Simplified 94.7%

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

   4. Taylor expanded in x around inf 69.1%

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

      1. expm1-log1p-u 34.0%

         \[\leadsto 9 \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{x \cdot y}{c \cdot z}\right)\right)} \]

      2. expm1-udef 32.6%

         \[\leadsto 9 \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(\frac{x \cdot y}{c \cdot z}\right)} - 1\right)} \]

      3. times-frac 23.8%

         \[\leadsto 9 \cdot \left(e^{\mathsf{log1p}\left(\color{blue}{\frac{x}{c} \cdot \frac{y}{z}}\right)} - 1\right) \]

   6. Applied egg-rr 23.8%

      \[\leadsto 9 \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(\frac{x}{c} \cdot \frac{y}{z}\right)} - 1\right)} \]
   7. Step-by-step derivation

      1. expm1-def 23.8%

         \[\leadsto 9 \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{x}{c} \cdot \frac{y}{z}\right)\right)} \]

      2. expm1-log1p 55.5%

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

      3. times-frac 69.1%

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

      4. *-commutative 69.1%

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

      5. associate-*r/ 59.5%

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

      6. *-commutative 59.5%

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

   8. Simplified 59.5%

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

   if -1.45e-279 < z < 2.06000000000000008e-20

   1. Initial program 96.9%

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

      1. associate-+l- 96.9%

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

      2. *-commutative 96.9%

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

      3. associate-*r* 96.9%

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

      4. *-commutative 96.9%

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

      5. associate-+l- 96.9%

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

      6. *-commutative 96.9%

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

      7. associate-*r* 96.9%

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

      8. *-commutative 96.9%

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

      9. associate-*l* 96.9%

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

      10. associate-*l* 91.1%

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

   3. Simplified 91.1%

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

   4. Taylor expanded in b around inf 61.8%

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

      1. *-commutative 61.8%

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

   6. Simplified 61.8%

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

4. Final simplification 59.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{+155}:\\ \;\;\;\;-4 \cdot \frac{t}{\frac{c}{a}}\\ \mathbf{elif}\;z \leq -6.2 \cdot 10^{+92}:\\ \;\;\;\;\frac{b \cdot \frac{1}{c}}{z}\\ \mathbf{elif}\;z \leq -1.12 \cdot 10^{-35}:\\ \;\;\;\;-4 \cdot \frac{t}{\frac{c}{a}}\\ \mathbf{elif}\;z \leq -1.45 \cdot 10^{-279}:\\ \;\;\;\;9 \cdot \left(x \cdot \frac{y}{z \cdot c}\right)\\ \mathbf{elif}\;z \leq 2.06 \cdot 10^{-20}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{t}{\frac{c}{a}}\\ \end{array} \]

Alternative 11: 49.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := -4 \cdot \frac{t}{\frac{c}{a}}\\ \mathbf{if}\;z \leq -9 \cdot 10^{+139}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -6.2 \cdot 10^{+45}:\\ \;\;\;\;9 \cdot \left(\frac{y}{c} \cdot \frac{x}{z}\right)\\ \mathbf{elif}\;z \leq -2.7 \cdot 10^{-34}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.75 \cdot 10^{-279}:\\ \;\;\;\;9 \cdot \left(x \cdot \frac{y}{z \cdot c}\right)\\ \mathbf{elif}\;z \leq 1.32 \cdot 10^{-21}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
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 (* -4.0 (/ t (/ c a)))))
   (if (<= z -9e+139)
     t_1
     (if (<= z -6.2e+45)
       (* 9.0 (* (/ y c) (/ x z)))
       (if (<= z -2.7e-34)
         t_1
         (if (<= z -2.75e-279)
           (* 9.0 (* x (/ y (* z c))))
           (if (<= z 1.32e-21) (/ b (* z c)) t_1)))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < 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 = -4.0 * (t / (c / a));
	double tmp;
	if (z <= -9e+139) {
		tmp = t_1;
	} else if (z <= -6.2e+45) {
		tmp = 9.0 * ((y / c) * (x / z));
	} else if (z <= -2.7e-34) {
		tmp = t_1;
	} else if (z <= -2.75e-279) {
		tmp = 9.0 * (x * (y / (z * c)));
	} else if (z <= 1.32e-21) {
		tmp = b / (z * c);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
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) :: tmp
    t_1 = (-4.0d0) * (t / (c / a))
    if (z <= (-9d+139)) then
        tmp = t_1
    else if (z <= (-6.2d+45)) then
        tmp = 9.0d0 * ((y / c) * (x / z))
    else if (z <= (-2.7d-34)) then
        tmp = t_1
    else if (z <= (-2.75d-279)) then
        tmp = 9.0d0 * (x * (y / (z * c)))
    else if (z <= 1.32d-21) then
        tmp = b / (z * c)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
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 = -4.0 * (t / (c / a));
	double tmp;
	if (z <= -9e+139) {
		tmp = t_1;
	} else if (z <= -6.2e+45) {
		tmp = 9.0 * ((y / c) * (x / z));
	} else if (z <= -2.7e-34) {
		tmp = t_1;
	} else if (z <= -2.75e-279) {
		tmp = 9.0 * (x * (y / (z * c)));
	} else if (z <= 1.32e-21) {
		tmp = b / (z * c);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
[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 = -4.0 * (t / (c / a))
	tmp = 0
	if z <= -9e+139:
		tmp = t_1
	elif z <= -6.2e+45:
		tmp = 9.0 * ((y / c) * (x / z))
	elif z <= -2.7e-34:
		tmp = t_1
	elif z <= -2.75e-279:
		tmp = 9.0 * (x * (y / (z * c)))
	elif z <= 1.32e-21:
		tmp = b / (z * c)
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
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(-4.0 * Float64(t / Float64(c / a)))
	tmp = 0.0
	if (z <= -9e+139)
		tmp = t_1;
	elseif (z <= -6.2e+45)
		tmp = Float64(9.0 * Float64(Float64(y / c) * Float64(x / z)));
	elseif (z <= -2.7e-34)
		tmp = t_1;
	elseif (z <= -2.75e-279)
		tmp = Float64(9.0 * Float64(x * Float64(y / Float64(z * c))));
	elseif (z <= 1.32e-21)
		tmp = Float64(b / Float64(z * c));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
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 = -4.0 * (t / (c / a));
	tmp = 0.0;
	if (z <= -9e+139)
		tmp = t_1;
	elseif (z <= -6.2e+45)
		tmp = 9.0 * ((y / c) * (x / z));
	elseif (z <= -2.7e-34)
		tmp = t_1;
	elseif (z <= -2.75e-279)
		tmp = 9.0 * (x * (y / (z * c)));
	elseif (z <= 1.32e-21)
		tmp = b / (z * c);
	else
		tmp = t_1;
	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.
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[(-4.0 * N[(t / N[(c / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -9e+139], t$95$1, If[LessEqual[z, -6.2e+45], N[(9.0 * N[(N[(y / c), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.7e-34], t$95$1, If[LessEqual[z, -2.75e-279], N[(9.0 * N[(x * N[(y / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.32e-21], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -8.9999999999999999e139 or -6.19999999999999975e45 < z < -2.70000000000000017e-34 or 1.32e-21 < z

   1. Initial program 61.3%

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

      1. associate-+l- 61.3%

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

      2. *-commutative 61.3%

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

      3. associate-*r* 62.8%

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

      4. *-commutative 62.8%

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

      5. associate-+l- 62.8%

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

      6. *-commutative 62.8%

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

      7. associate-*r* 61.3%

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

      8. *-commutative 61.3%

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

      9. associate-*l* 61.4%

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

      10. associate-*l* 67.7%

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

   3. Simplified 67.7%

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

   5. Applied egg-rr 73.8%

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

   6. Taylor expanded in x around 0 88.4%

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

      1. clear-num 88.4%

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

      2. inv-pow 88.4%

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

   8. Applied egg-rr 88.4%

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

      1. unpow-1 88.4%

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

      2. *-commutative 88.4%

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

      3. associate-/r* 91.5%

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

   10. Simplified 91.5%

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

   11. Taylor expanded in a around inf 54.4%

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

       1. *-commutative 54.4%

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

       2. associate-/l* 59.5%

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

   13. Simplified 59.5%

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

   if -8.9999999999999999e139 < z < -6.19999999999999975e45

   1. Initial program 77.4%

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

      1. associate-+l- 77.4%

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

      2. *-commutative 77.4%

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

      3. associate-*r* 69.6%

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

      4. *-commutative 69.6%

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

      5. associate-+l- 69.6%

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

      6. *-commutative 69.6%

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

      7. associate-*r* 77.4%

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

      8. *-commutative 77.4%

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

      9. associate-*l* 77.2%

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

      10. associate-*l* 77.4%

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

   3. Simplified 77.4%

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

   4. Taylor expanded in x around inf 39.8%

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

      1. *-commutative 39.8%

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

      2. times-frac 48.3%

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

   6. Applied egg-rr 48.3%

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

   if -2.70000000000000017e-34 < z < -2.7500000000000001e-279

   1. Initial program 97.2%

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

      1. associate-+l- 97.2%

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

      2. *-commutative 97.2%

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

      3. associate-*r* 97.2%

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

      4. *-commutative 97.2%

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

      5. associate-+l- 97.2%

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

      6. *-commutative 97.2%

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

      7. associate-*r* 97.2%

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

      8. *-commutative 97.2%

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

      9. associate-*l* 97.3%

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

      10. associate-*l* 94.7%

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

   3. Simplified 94.7%

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

   4. Taylor expanded in x around inf 69.1%

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

      1. expm1-log1p-u 34.0%

         \[\leadsto 9 \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{x \cdot y}{c \cdot z}\right)\right)} \]

      2. expm1-udef 32.6%

         \[\leadsto 9 \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(\frac{x \cdot y}{c \cdot z}\right)} - 1\right)} \]

      3. times-frac 23.8%

         \[\leadsto 9 \cdot \left(e^{\mathsf{log1p}\left(\color{blue}{\frac{x}{c} \cdot \frac{y}{z}}\right)} - 1\right) \]

   6. Applied egg-rr 23.8%

      \[\leadsto 9 \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(\frac{x}{c} \cdot \frac{y}{z}\right)} - 1\right)} \]
   7. Step-by-step derivation

      1. expm1-def 23.8%

         \[\leadsto 9 \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{x}{c} \cdot \frac{y}{z}\right)\right)} \]

      2. expm1-log1p 55.5%

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

      3. times-frac 69.1%

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

      4. *-commutative 69.1%

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

      5. associate-*r/ 59.5%

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

      6. *-commutative 59.5%

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

   8. Simplified 59.5%

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

   if -2.7500000000000001e-279 < z < 1.32e-21

   1. Initial program 96.9%

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

      1. associate-+l- 96.9%

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

      2. *-commutative 96.9%

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

      3. associate-*r* 96.9%

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

      4. *-commutative 96.9%

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

      5. associate-+l- 96.9%

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

      6. *-commutative 96.9%

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

      7. associate-*r* 96.9%

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

      8. *-commutative 96.9%

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

      9. associate-*l* 96.9%

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

      10. associate-*l* 91.1%

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

   3. Simplified 91.1%

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

   4. Taylor expanded in b around inf 61.8%

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

      1. *-commutative 61.8%

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

   6. Simplified 61.8%

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

4. Final simplification 58.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{+139}:\\ \;\;\;\;-4 \cdot \frac{t}{\frac{c}{a}}\\ \mathbf{elif}\;z \leq -6.2 \cdot 10^{+45}:\\ \;\;\;\;9 \cdot \left(\frac{y}{c} \cdot \frac{x}{z}\right)\\ \mathbf{elif}\;z \leq -2.7 \cdot 10^{-34}:\\ \;\;\;\;-4 \cdot \frac{t}{\frac{c}{a}}\\ \mathbf{elif}\;z \leq -2.75 \cdot 10^{-279}:\\ \;\;\;\;9 \cdot \left(x \cdot \frac{y}{z \cdot c}\right)\\ \mathbf{elif}\;z \leq 1.32 \cdot 10^{-21}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{t}{\frac{c}{a}}\\ \end{array} \]

Alternative 12: 49.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := -4 \cdot \frac{t}{\frac{c}{a}}\\ \mathbf{if}\;z \leq -1.35 \cdot 10^{+155}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.06 \cdot 10^{+46}:\\ \;\;\;\;9 \cdot \left(\frac{y}{z} \cdot \frac{x}{c}\right)\\ \mathbf{elif}\;z \leq -7.4 \cdot 10^{-32}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.9 \cdot 10^{-279}:\\ \;\;\;\;9 \cdot \left(x \cdot \frac{y}{z \cdot c}\right)\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-21}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
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 (* -4.0 (/ t (/ c a)))))
   (if (<= z -1.35e+155)
     t_1
     (if (<= z -1.06e+46)
       (* 9.0 (* (/ y z) (/ x c)))
       (if (<= z -7.4e-32)
         t_1
         (if (<= z -2.9e-279)
           (* 9.0 (* x (/ y (* z c))))
           (if (<= z 2.8e-21) (/ b (* z c)) t_1)))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < 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 = -4.0 * (t / (c / a));
	double tmp;
	if (z <= -1.35e+155) {
		tmp = t_1;
	} else if (z <= -1.06e+46) {
		tmp = 9.0 * ((y / z) * (x / c));
	} else if (z <= -7.4e-32) {
		tmp = t_1;
	} else if (z <= -2.9e-279) {
		tmp = 9.0 * (x * (y / (z * c)));
	} else if (z <= 2.8e-21) {
		tmp = b / (z * c);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
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) :: tmp
    t_1 = (-4.0d0) * (t / (c / a))
    if (z <= (-1.35d+155)) then
        tmp = t_1
    else if (z <= (-1.06d+46)) then
        tmp = 9.0d0 * ((y / z) * (x / c))
    else if (z <= (-7.4d-32)) then
        tmp = t_1
    else if (z <= (-2.9d-279)) then
        tmp = 9.0d0 * (x * (y / (z * c)))
    else if (z <= 2.8d-21) then
        tmp = b / (z * c)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
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 = -4.0 * (t / (c / a));
	double tmp;
	if (z <= -1.35e+155) {
		tmp = t_1;
	} else if (z <= -1.06e+46) {
		tmp = 9.0 * ((y / z) * (x / c));
	} else if (z <= -7.4e-32) {
		tmp = t_1;
	} else if (z <= -2.9e-279) {
		tmp = 9.0 * (x * (y / (z * c)));
	} else if (z <= 2.8e-21) {
		tmp = b / (z * c);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
[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 = -4.0 * (t / (c / a))
	tmp = 0
	if z <= -1.35e+155:
		tmp = t_1
	elif z <= -1.06e+46:
		tmp = 9.0 * ((y / z) * (x / c))
	elif z <= -7.4e-32:
		tmp = t_1
	elif z <= -2.9e-279:
		tmp = 9.0 * (x * (y / (z * c)))
	elif z <= 2.8e-21:
		tmp = b / (z * c)
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
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(-4.0 * Float64(t / Float64(c / a)))
	tmp = 0.0
	if (z <= -1.35e+155)
		tmp = t_1;
	elseif (z <= -1.06e+46)
		tmp = Float64(9.0 * Float64(Float64(y / z) * Float64(x / c)));
	elseif (z <= -7.4e-32)
		tmp = t_1;
	elseif (z <= -2.9e-279)
		tmp = Float64(9.0 * Float64(x * Float64(y / Float64(z * c))));
	elseif (z <= 2.8e-21)
		tmp = Float64(b / Float64(z * c));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
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 = -4.0 * (t / (c / a));
	tmp = 0.0;
	if (z <= -1.35e+155)
		tmp = t_1;
	elseif (z <= -1.06e+46)
		tmp = 9.0 * ((y / z) * (x / c));
	elseif (z <= -7.4e-32)
		tmp = t_1;
	elseif (z <= -2.9e-279)
		tmp = 9.0 * (x * (y / (z * c)));
	elseif (z <= 2.8e-21)
		tmp = b / (z * c);
	else
		tmp = t_1;
	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.
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[(-4.0 * N[(t / N[(c / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.35e+155], t$95$1, If[LessEqual[z, -1.06e+46], N[(9.0 * N[(N[(y / z), $MachinePrecision] * N[(x / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -7.4e-32], t$95$1, If[LessEqual[z, -2.9e-279], N[(9.0 * N[(x * N[(y / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.8e-21], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.34999999999999997e155 or -1.05999999999999998e46 < z < -7.4e-32 or 2.80000000000000004e-21 < z

   1. Initial program 62.5%

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

      1. associate-+l- 62.5%

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

      2. *-commutative 62.5%

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

      3. associate-*r* 63.2%

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

      4. *-commutative 63.2%

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

      5. associate-+l- 63.2%

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

      6. *-commutative 63.2%

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

      7. associate-*r* 62.5%

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

      8. *-commutative 62.5%

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

      9. associate-*l* 62.5%

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

      10. associate-*l* 68.5%

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

   3. Simplified 68.5%

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

   5. Applied egg-rr 73.5%

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

   6. Taylor expanded in x around 0 88.4%

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

      1. clear-num 88.3%

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

      2. inv-pow 88.3%

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

   8. Applied egg-rr 88.3%

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

      1. unpow-1 88.3%

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

      2. *-commutative 88.3%

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

      3. associate-/r* 91.7%

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

   10. Simplified 91.7%

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

   11. Taylor expanded in a around inf 55.9%

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

       1. *-commutative 55.9%

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

       2. associate-/l* 61.3%

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

   13. Simplified 61.3%

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

   if -1.34999999999999997e155 < z < -1.05999999999999998e46

   1. Initial program 69.4%

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

      1. associate-+l- 69.4%

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

      2. *-commutative 69.4%

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

      3. associate-*r* 66.5%

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

      4. *-commutative 66.5%

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

      5. associate-+l- 66.5%

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

      6. *-commutative 66.5%

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

      7. associate-*r* 69.4%

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

      8. *-commutative 69.4%

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

      9. associate-*l* 69.3%

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

      10. associate-*l* 72.3%

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

   3. Simplified 72.3%

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

   4. Taylor expanded in x around inf 36.0%

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

      1. *-commutative 36.0%

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

      2. *-commutative 36.0%

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

      3. times-frac 49.2%

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

   6. Applied egg-rr 49.2%

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

   if -7.4e-32 < z < -2.9e-279

   1. Initial program 97.2%

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

      1. associate-+l- 97.2%

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

      2. *-commutative 97.2%

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

      3. associate-*r* 97.2%

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

      4. *-commutative 97.2%

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

      5. associate-+l- 97.2%

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

      6. *-commutative 97.2%

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

      7. associate-*r* 97.2%

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

      8. *-commutative 97.2%

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

      9. associate-*l* 97.3%

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

      10. associate-*l* 94.7%

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

   3. Simplified 94.7%

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

   4. Taylor expanded in x around inf 69.1%

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

      1. expm1-log1p-u 34.0%

         \[\leadsto 9 \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{x \cdot y}{c \cdot z}\right)\right)} \]

      2. expm1-udef 32.6%

         \[\leadsto 9 \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(\frac{x \cdot y}{c \cdot z}\right)} - 1\right)} \]

      3. times-frac 23.8%

         \[\leadsto 9 \cdot \left(e^{\mathsf{log1p}\left(\color{blue}{\frac{x}{c} \cdot \frac{y}{z}}\right)} - 1\right) \]

   6. Applied egg-rr 23.8%

      \[\leadsto 9 \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(\frac{x}{c} \cdot \frac{y}{z}\right)} - 1\right)} \]
   7. Step-by-step derivation

      1. expm1-def 23.8%

         \[\leadsto 9 \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{x}{c} \cdot \frac{y}{z}\right)\right)} \]

      2. expm1-log1p 55.5%

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

      3. times-frac 69.1%

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

      4. *-commutative 69.1%

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

      5. associate-*r/ 59.5%

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

      6. *-commutative 59.5%

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

   8. Simplified 59.5%

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

   if -2.9e-279 < z < 2.80000000000000004e-21

   1. Initial program 96.9%

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

      1. associate-+l- 96.9%

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

      2. *-commutative 96.9%

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

      3. associate-*r* 96.9%

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

      4. *-commutative 96.9%

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

      5. associate-+l- 96.9%

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

      6. *-commutative 96.9%

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

      7. associate-*r* 96.9%

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

      8. *-commutative 96.9%

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

      9. associate-*l* 96.9%

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

      10. associate-*l* 91.1%

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

   3. Simplified 91.1%

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

   4. Taylor expanded in b around inf 61.8%

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

      1. *-commutative 61.8%

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

   6. Simplified 61.8%

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

4. Final simplification 59.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{+155}:\\ \;\;\;\;-4 \cdot \frac{t}{\frac{c}{a}}\\ \mathbf{elif}\;z \leq -1.06 \cdot 10^{+46}:\\ \;\;\;\;9 \cdot \left(\frac{y}{z} \cdot \frac{x}{c}\right)\\ \mathbf{elif}\;z \leq -7.4 \cdot 10^{-32}:\\ \;\;\;\;-4 \cdot \frac{t}{\frac{c}{a}}\\ \mathbf{elif}\;z \leq -2.9 \cdot 10^{-279}:\\ \;\;\;\;9 \cdot \left(x \cdot \frac{y}{z \cdot c}\right)\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-21}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{t}{\frac{c}{a}}\\ \end{array} \]

Alternative 13: 49.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := -4 \cdot \frac{t}{\frac{c}{a}}\\ \mathbf{if}\;z \leq -1.35 \cdot 10^{+155}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{+44}:\\ \;\;\;\;9 \cdot \left(\frac{y}{z} \cdot \frac{x}{c}\right)\\ \mathbf{elif}\;z \leq -1.55 \cdot 10^{-41}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.5 \cdot 10^{-279}:\\ \;\;\;\;9 \cdot \frac{y \cdot x}{z \cdot c}\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-18}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
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 (* -4.0 (/ t (/ c a)))))
   (if (<= z -1.35e+155)
     t_1
     (if (<= z -2.5e+44)
       (* 9.0 (* (/ y z) (/ x c)))
       (if (<= z -1.55e-41)
         t_1
         (if (<= z -1.5e-279)
           (* 9.0 (/ (* y x) (* z c)))
           (if (<= z 1.7e-18) (/ b (* z c)) t_1)))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < 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 = -4.0 * (t / (c / a));
	double tmp;
	if (z <= -1.35e+155) {
		tmp = t_1;
	} else if (z <= -2.5e+44) {
		tmp = 9.0 * ((y / z) * (x / c));
	} else if (z <= -1.55e-41) {
		tmp = t_1;
	} else if (z <= -1.5e-279) {
		tmp = 9.0 * ((y * x) / (z * c));
	} else if (z <= 1.7e-18) {
		tmp = b / (z * c);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
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) :: tmp
    t_1 = (-4.0d0) * (t / (c / a))
    if (z <= (-1.35d+155)) then
        tmp = t_1
    else if (z <= (-2.5d+44)) then
        tmp = 9.0d0 * ((y / z) * (x / c))
    else if (z <= (-1.55d-41)) then
        tmp = t_1
    else if (z <= (-1.5d-279)) then
        tmp = 9.0d0 * ((y * x) / (z * c))
    else if (z <= 1.7d-18) then
        tmp = b / (z * c)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
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 = -4.0 * (t / (c / a));
	double tmp;
	if (z <= -1.35e+155) {
		tmp = t_1;
	} else if (z <= -2.5e+44) {
		tmp = 9.0 * ((y / z) * (x / c));
	} else if (z <= -1.55e-41) {
		tmp = t_1;
	} else if (z <= -1.5e-279) {
		tmp = 9.0 * ((y * x) / (z * c));
	} else if (z <= 1.7e-18) {
		tmp = b / (z * c);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
[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 = -4.0 * (t / (c / a))
	tmp = 0
	if z <= -1.35e+155:
		tmp = t_1
	elif z <= -2.5e+44:
		tmp = 9.0 * ((y / z) * (x / c))
	elif z <= -1.55e-41:
		tmp = t_1
	elif z <= -1.5e-279:
		tmp = 9.0 * ((y * x) / (z * c))
	elif z <= 1.7e-18:
		tmp = b / (z * c)
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
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(-4.0 * Float64(t / Float64(c / a)))
	tmp = 0.0
	if (z <= -1.35e+155)
		tmp = t_1;
	elseif (z <= -2.5e+44)
		tmp = Float64(9.0 * Float64(Float64(y / z) * Float64(x / c)));
	elseif (z <= -1.55e-41)
		tmp = t_1;
	elseif (z <= -1.5e-279)
		tmp = Float64(9.0 * Float64(Float64(y * x) / Float64(z * c)));
	elseif (z <= 1.7e-18)
		tmp = Float64(b / Float64(z * c));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
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 = -4.0 * (t / (c / a));
	tmp = 0.0;
	if (z <= -1.35e+155)
		tmp = t_1;
	elseif (z <= -2.5e+44)
		tmp = 9.0 * ((y / z) * (x / c));
	elseif (z <= -1.55e-41)
		tmp = t_1;
	elseif (z <= -1.5e-279)
		tmp = 9.0 * ((y * x) / (z * c));
	elseif (z <= 1.7e-18)
		tmp = b / (z * c);
	else
		tmp = t_1;
	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.
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[(-4.0 * N[(t / N[(c / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.35e+155], t$95$1, If[LessEqual[z, -2.5e+44], N[(9.0 * N[(N[(y / z), $MachinePrecision] * N[(x / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.55e-41], t$95$1, If[LessEqual[z, -1.5e-279], N[(9.0 * N[(N[(y * x), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.7e-18], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.34999999999999997e155 or -2.4999999999999998e44 < z < -1.55e-41 or 1.70000000000000001e-18 < z

   1. Initial program 62.5%

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

      1. associate-+l- 62.5%

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

      2. *-commutative 62.5%

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

      3. associate-*r* 63.2%

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

      4. *-commutative 63.2%

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

      5. associate-+l- 63.2%

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

      6. *-commutative 63.2%

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

      7. associate-*r* 62.5%

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

      8. *-commutative 62.5%

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

      9. associate-*l* 62.5%

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

      10. associate-*l* 68.5%

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

   3. Simplified 68.5%

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

   5. Applied egg-rr 73.5%

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

   6. Taylor expanded in x around 0 88.4%

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

      1. clear-num 88.3%

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

      2. inv-pow 88.3%

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

   8. Applied egg-rr 88.3%

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

      1. unpow-1 88.3%

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

      2. *-commutative 88.3%

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

      3. associate-/r* 91.7%

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

   10. Simplified 91.7%

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

   11. Taylor expanded in a around inf 55.9%

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

       1. *-commutative 55.9%

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

       2. associate-/l* 61.3%

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

   13. Simplified 61.3%

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

   if -1.34999999999999997e155 < z < -2.4999999999999998e44

   1. Initial program 69.4%

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

      1. associate-+l- 69.4%

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

      2. *-commutative 69.4%

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

      3. associate-*r* 66.5%

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

      4. *-commutative 66.5%

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

      5. associate-+l- 66.5%

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

      6. *-commutative 66.5%

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

      7. associate-*r* 69.4%

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

      8. *-commutative 69.4%

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

      9. associate-*l* 69.3%

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

      10. associate-*l* 72.3%

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

   3. Simplified 72.3%

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

   4. Taylor expanded in x around inf 36.0%

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

      1. *-commutative 36.0%

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

      2. *-commutative 36.0%

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

      3. times-frac 49.2%

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

   6. Applied egg-rr 49.2%

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

   if -1.55e-41 < z < -1.5e-279

   1. Initial program 97.2%

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

      1. associate-+l- 97.2%

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

      2. *-commutative 97.2%

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

      3. associate-*r* 97.2%

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

      4. *-commutative 97.2%

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

      5. associate-+l- 97.2%

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

      6. *-commutative 97.2%

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

      7. associate-*r* 97.2%

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

      8. *-commutative 97.2%

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

      9. associate-*l* 97.3%

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

      10. associate-*l* 94.7%

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

   3. Simplified 94.7%

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

   4. Taylor expanded in x around inf 69.1%

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

   if -1.5e-279 < z < 1.70000000000000001e-18

   1. Initial program 96.9%

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

      1. associate-+l- 96.9%

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

      2. *-commutative 96.9%

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

      3. associate-*r* 96.9%

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

      4. *-commutative 96.9%

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

      5. associate-+l- 96.9%

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

      6. *-commutative 96.9%

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

      7. associate-*r* 96.9%

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

      8. *-commutative 96.9%

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

      9. associate-*l* 96.9%

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

      10. associate-*l* 91.1%

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

   3. Simplified 91.1%

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

   4. Taylor expanded in b around inf 61.8%

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

      1. *-commutative 61.8%

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

   6. Simplified 61.8%

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

4. Final simplification 60.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{+155}:\\ \;\;\;\;-4 \cdot \frac{t}{\frac{c}{a}}\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{+44}:\\ \;\;\;\;9 \cdot \left(\frac{y}{z} \cdot \frac{x}{c}\right)\\ \mathbf{elif}\;z \leq -1.55 \cdot 10^{-41}:\\ \;\;\;\;-4 \cdot \frac{t}{\frac{c}{a}}\\ \mathbf{elif}\;z \leq -1.5 \cdot 10^{-279}:\\ \;\;\;\;9 \cdot \frac{y \cdot x}{z \cdot c}\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-18}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{t}{\frac{c}{a}}\\ \end{array} \]

Alternative 14: 50.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;b \leq -1.86 \cdot 10^{+53} \lor \neg \left(b \leq 0.000232 \lor \neg \left(b \leq 4 \cdot 10^{+22}\right) \land b \leq 6.7 \cdot 10^{+140}\right):\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{t}{\frac{c}{a}}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
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 (<= b -1.86e+53)
         (not (or (<= b 0.000232) (and (not (<= b 4e+22)) (<= b 6.7e+140)))))
   (/ (/ b c) z)
   (* -4.0 (/ t (/ c a)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < 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 <= -1.86e+53) || !((b <= 0.000232) || (!(b <= 4e+22) && (b <= 6.7e+140)))) {
		tmp = (b / c) / z;
	} else {
		tmp = -4.0 * (t / (c / a));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
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 <= (-1.86d+53)) .or. (.not. (b <= 0.000232d0) .or. (.not. (b <= 4d+22)) .and. (b <= 6.7d+140))) then
        tmp = (b / c) / z
    else
        tmp = (-4.0d0) * (t / (c / a))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
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 <= -1.86e+53) || !((b <= 0.000232) || (!(b <= 4e+22) && (b <= 6.7e+140)))) {
		tmp = (b / c) / z;
	} else {
		tmp = -4.0 * (t / (c / a));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
[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 <= -1.86e+53) or not ((b <= 0.000232) or (not (b <= 4e+22) and (b <= 6.7e+140))):
		tmp = (b / c) / z
	else:
		tmp = -4.0 * (t / (c / a))
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
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 <= -1.86e+53) || !((b <= 0.000232) || (!(b <= 4e+22) && (b <= 6.7e+140))))
		tmp = Float64(Float64(b / c) / z);
	else
		tmp = Float64(-4.0 * Float64(t / Float64(c / a)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
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 <= -1.86e+53) || ~(((b <= 0.000232) || (~((b <= 4e+22)) && (b <= 6.7e+140)))))
		tmp = (b / c) / z;
	else
		tmp = -4.0 * (t / (c / a));
	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.
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[b, -1.86e+53], N[Not[Or[LessEqual[b, 0.000232], And[N[Not[LessEqual[b, 4e+22]], $MachinePrecision], LessEqual[b, 6.7e+140]]]], $MachinePrecision]], N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision], N[(-4.0 * N[(t / N[(c / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.85999999999999999e53 or 2.32e-4 < b < 4e22 or 6.7e140 < b

   1. Initial program 78.3%

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

      1. associate-+l- 78.3%

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

      2. *-commutative 78.3%

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

      3. associate-*r* 76.5%

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

      4. *-commutative 76.5%

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

      5. associate-+l- 76.5%

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

      6. *-commutative 76.5%

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

      7. associate-*r* 78.3%

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

      8. *-commutative 78.3%

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

      9. associate-*l* 78.3%

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

      10. associate-*l* 77.6%

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

   3. Simplified 77.6%

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

   5. Applied egg-rr 78.6%

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

   6. Taylor expanded in b around inf 58.4%

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

      1. div-inv 58.4%

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

      2. associate-/l/ 58.5%

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

      3. associate-/r* 63.5%

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

   8. Applied egg-rr 63.5%

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

   if -1.85999999999999999e53 < b < 2.32e-4 or 4e22 < b < 6.7e140

   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. Step-by-step derivation

      1. associate-+l- 76.9%

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

      2. *-commutative 76.9%

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

      3. associate-*r* 78.0%

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

      4. *-commutative 78.0%

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

      5. associate-+l- 78.0%

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

      6. *-commutative 78.0%

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

      7. associate-*r* 76.9%

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

      8. *-commutative 76.9%

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

      9. associate-*l* 76.9%

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

      10. associate-*l* 79.5%

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

   3. Simplified 79.5%

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

   5. Applied egg-rr 79.5%

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

   6. Taylor expanded in x around 0 88.7%

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

      1. clear-num 88.7%

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

      2. inv-pow 88.7%

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

   8. Applied egg-rr 88.7%

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

      1. unpow-1 88.7%

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

      2. *-commutative 88.7%

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

      3. associate-/r* 86.3%

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

   10. Simplified 86.3%

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

   11. Taylor expanded in a around inf 48.2%

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

       1. *-commutative 48.2%

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

       2. associate-/l* 52.9%

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

   13. Simplified 52.9%

       \[\leadsto \color{blue}{-4 \cdot \frac{t}{\frac{c}{a}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 57.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.86 \cdot 10^{+53} \lor \neg \left(b \leq 0.000232 \lor \neg \left(b \leq 4 \cdot 10^{+22}\right) \land b \leq 6.7 \cdot 10^{+140}\right):\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{t}{\frac{c}{a}}\\ \end{array} \]

Alternative 15: 50.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := -4 \cdot \frac{t}{\frac{c}{a}}\\ t_2 := \frac{\frac{b}{c}}{z}\\ \mathbf{if}\;b \leq -1.05 \cdot 10^{+52}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 0.00029:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 5 \cdot 10^{+22}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 3.3 \cdot 10^{+140}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{b \cdot \frac{1}{c}}{z}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
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 (* -4.0 (/ t (/ c a)))) (t_2 (/ (/ b c) z)))
   (if (<= b -1.05e+52)
     t_2
     (if (<= b 0.00029)
       t_1
       (if (<= b 5e+22) t_2 (if (<= b 3.3e+140) t_1 (/ (* b (/ 1.0 c)) z)))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < 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 = -4.0 * (t / (c / a));
	double t_2 = (b / c) / z;
	double tmp;
	if (b <= -1.05e+52) {
		tmp = t_2;
	} else if (b <= 0.00029) {
		tmp = t_1;
	} else if (b <= 5e+22) {
		tmp = t_2;
	} else if (b <= 3.3e+140) {
		tmp = t_1;
	} else {
		tmp = (b * (1.0 / c)) / z;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
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 = (-4.0d0) * (t / (c / a))
    t_2 = (b / c) / z
    if (b <= (-1.05d+52)) then
        tmp = t_2
    else if (b <= 0.00029d0) then
        tmp = t_1
    else if (b <= 5d+22) then
        tmp = t_2
    else if (b <= 3.3d+140) then
        tmp = t_1
    else
        tmp = (b * (1.0d0 / c)) / z
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
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 = -4.0 * (t / (c / a));
	double t_2 = (b / c) / z;
	double tmp;
	if (b <= -1.05e+52) {
		tmp = t_2;
	} else if (b <= 0.00029) {
		tmp = t_1;
	} else if (b <= 5e+22) {
		tmp = t_2;
	} else if (b <= 3.3e+140) {
		tmp = t_1;
	} else {
		tmp = (b * (1.0 / c)) / z;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
[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 = -4.0 * (t / (c / a))
	t_2 = (b / c) / z
	tmp = 0
	if b <= -1.05e+52:
		tmp = t_2
	elif b <= 0.00029:
		tmp = t_1
	elif b <= 5e+22:
		tmp = t_2
	elif b <= 3.3e+140:
		tmp = t_1
	else:
		tmp = (b * (1.0 / c)) / z
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
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(-4.0 * Float64(t / Float64(c / a)))
	t_2 = Float64(Float64(b / c) / z)
	tmp = 0.0
	if (b <= -1.05e+52)
		tmp = t_2;
	elseif (b <= 0.00029)
		tmp = t_1;
	elseif (b <= 5e+22)
		tmp = t_2;
	elseif (b <= 3.3e+140)
		tmp = t_1;
	else
		tmp = Float64(Float64(b * Float64(1.0 / c)) / z);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
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 = -4.0 * (t / (c / a));
	t_2 = (b / c) / z;
	tmp = 0.0;
	if (b <= -1.05e+52)
		tmp = t_2;
	elseif (b <= 0.00029)
		tmp = t_1;
	elseif (b <= 5e+22)
		tmp = t_2;
	elseif (b <= 3.3e+140)
		tmp = t_1;
	else
		tmp = (b * (1.0 / 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.
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[(-4.0 * N[(t / N[(c / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision]}, If[LessEqual[b, -1.05e+52], t$95$2, If[LessEqual[b, 0.00029], t$95$1, If[LessEqual[b, 5e+22], t$95$2, If[LessEqual[b, 3.3e+140], t$95$1, N[(N[(b * N[(1.0 / c), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.05e52 or 2.9e-4 < b < 4.9999999999999996e22

   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. Step-by-step derivation

      1. associate-+l- 76.9%

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

      2. *-commutative 76.9%

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

      3. associate-*r* 75.3%

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

      4. *-commutative 75.3%

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

      5. associate-+l- 75.3%

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

      6. *-commutative 75.3%

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

      7. associate-*r* 76.9%

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

      8. *-commutative 76.9%

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

      9. associate-*l* 76.9%

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

      10. associate-*l* 77.2%

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

   3. Simplified 77.2%

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

   5. Applied egg-rr 75.7%

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

   6. Taylor expanded in b around inf 53.3%

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

      1. div-inv 53.3%

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

      2. associate-/l/ 51.9%

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

      3. associate-/r* 56.8%

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

   8. Applied egg-rr 56.8%

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

   if -1.05e52 < b < 2.9e-4 or 4.9999999999999996e22 < b < 3.3000000000000002e140

   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. Step-by-step derivation

      1. associate-+l- 76.9%

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

      2. *-commutative 76.9%

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

      3. associate-*r* 78.0%

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

      4. *-commutative 78.0%

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

      5. associate-+l- 78.0%

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

      6. *-commutative 78.0%

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

      7. associate-*r* 76.9%

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

      8. *-commutative 76.9%

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

      9. associate-*l* 76.9%

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

      10. associate-*l* 79.5%

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

   3. Simplified 79.5%

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

   5. Applied egg-rr 79.5%

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

   6. Taylor expanded in x around 0 88.7%

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

      1. clear-num 88.7%

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

      2. inv-pow 88.7%

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

   8. Applied egg-rr 88.7%

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

      1. unpow-1 88.7%

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

      2. *-commutative 88.7%

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

      3. associate-/r* 86.3%

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

   10. Simplified 86.3%

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

   11. Taylor expanded in a around inf 48.2%

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

       1. *-commutative 48.2%

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

       2. associate-/l* 52.9%

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

   13. Simplified 52.9%

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

   if 3.3000000000000002e140 < b

   1. Initial program 80.5%

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

      1. associate-+l- 80.5%

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

      2. *-commutative 80.5%

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

      3. associate-*r* 78.2%

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

      4. *-commutative 78.2%

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

      5. associate-+l- 78.2%

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

      6. *-commutative 78.2%

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

      7. associate-*r* 80.5%

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

      8. *-commutative 80.5%

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

      9. associate-*l* 80.5%

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

      10. associate-*l* 78.2%

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

   3. Simplified 78.2%

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

   5. Applied egg-rr 82.9%

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

   6. Taylor expanded in b around inf 66.2%

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

      1. associate-*l/ 73.6%

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

   8. Applied egg-rr 73.6%

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

4. Final simplification 57.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.05 \cdot 10^{+52}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;b \leq 0.00029:\\ \;\;\;\;-4 \cdot \frac{t}{\frac{c}{a}}\\ \mathbf{elif}\;b \leq 5 \cdot 10^{+22}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;b \leq 3.3 \cdot 10^{+140}:\\ \;\;\;\;-4 \cdot \frac{t}{\frac{c}{a}}\\ \mathbf{else}:\\ \;\;\;\;\frac{b \cdot \frac{1}{c}}{z}\\ \end{array} \]

Alternative 16: 75.9% accurate, 1.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -7.8 \cdot 10^{-53} \lor \neg \left(z \leq 3 \cdot 10^{-19}\right):\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right) + \frac{b}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + y \cdot \left(9 \cdot x\right)}{z \cdot c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
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 -7.8e-53) (not (<= z 3e-19)))
   (/ (+ (* -4.0 (* a t)) (/ b z)) c)
   (/ (+ b (* y (* 9.0 x))) (* z c))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < 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-53) || !(z <= 3e-19)) {
		tmp = ((-4.0 * (a * t)) + (b / z)) / c;
	} else {
		tmp = (b + (y * (9.0 * x))) / (z * c);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
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-53)) .or. (.not. (z <= 3d-19))) then
        tmp = (((-4.0d0) * (a * t)) + (b / z)) / c
    else
        tmp = (b + (y * (9.0d0 * x))) / (z * c)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
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-53) || !(z <= 3e-19)) {
		tmp = ((-4.0 * (a * t)) + (b / z)) / c;
	} else {
		tmp = (b + (y * (9.0 * x))) / (z * c);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
[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-53) or not (z <= 3e-19):
		tmp = ((-4.0 * (a * t)) + (b / z)) / c
	else:
		tmp = (b + (y * (9.0 * x))) / (z * c)
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
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-53) || !(z <= 3e-19))
		tmp = Float64(Float64(Float64(-4.0 * Float64(a * t)) + Float64(b / z)) / c);
	else
		tmp = Float64(Float64(b + Float64(y * Float64(9.0 * x))) / Float64(z * c));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
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-53) || ~((z <= 3e-19)))
		tmp = ((-4.0 * (a * t)) + (b / z)) / c;
	else
		tmp = (b + (y * (9.0 * x))) / (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.
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, -7.8e-53], N[Not[LessEqual[z, 3e-19]], $MachinePrecision]], N[(N[(N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision] + N[(b / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], N[(N[(b + N[(y * N[(9.0 * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -7.8000000000000004e-53 or 2.99999999999999993e-19 < z

   1. Initial program 64.5%

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

      1. associate-+l- 64.5%

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

      2. *-commutative 64.5%

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

      3. associate-*r* 64.5%

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

      4. *-commutative 64.5%

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

      5. associate-+l- 64.5%

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

      6. *-commutative 64.5%

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

      7. associate-*r* 64.5%

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

      8. *-commutative 64.5%

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

      9. associate-*l* 64.5%

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

      10. associate-*l* 69.7%

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

   3. Simplified 69.7%

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

   5. Applied egg-rr 76.0%

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

   6. Taylor expanded in x around 0 89.2%

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

   7. Taylor expanded in x around 0 72.0%

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

   if -7.8000000000000004e-53 < z < 2.99999999999999993e-19

   1. Initial program 96.9%

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

      1. associate-+l- 96.9%

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

      2. *-commutative 96.9%

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

      3. associate-*r* 96.9%

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

      4. *-commutative 96.9%

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

      5. associate-+l- 96.9%

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

      6. *-commutative 96.9%

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

      7. associate-*r* 96.9%

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

      8. *-commutative 96.9%

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

      9. associate-*l* 97.0%

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

      10. associate-*l* 92.3%

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

   3. Simplified 92.3%

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

   4. Taylor expanded in x around inf 84.5%

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

      1. associate-*r* 84.4%

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

   6. Simplified 84.4%

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

4. Final simplification 76.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.8 \cdot 10^{-53} \lor \neg \left(z \leq 3 \cdot 10^{-19}\right):\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right) + \frac{b}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + y \cdot \left(9 \cdot x\right)}{z \cdot c}\\ \end{array} \]

Alternative 17: 35.3% accurate, 2.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;c \leq 6.2 \cdot 10^{-89}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
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 (<= c 6.2e-89) (/ b (* z c)) (/ (/ b c) z)))

C

assert(x < y && y < z && z < t && t < a && a < b && b < 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 (c <= 6.2e-89) {
		tmp = b / (z * c);
	} else {
		tmp = (b / c) / z;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
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 (c <= 6.2d-89) then
        tmp = b / (z * c)
    else
        tmp = (b / c) / z
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
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 (c <= 6.2e-89) {
		tmp = b / (z * c);
	} else {
		tmp = (b / c) / z;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
[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 c <= 6.2e-89:
		tmp = b / (z * c)
	else:
		tmp = (b / c) / z
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
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 (c <= 6.2e-89)
		tmp = Float64(b / Float64(z * c));
	else
		tmp = Float64(Float64(b / c) / z);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
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 (c <= 6.2e-89)
		tmp = b / (z * c);
	else
		tmp = (b / 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.
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[c, 6.2e-89], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < 6.19999999999999993e-89

   1. Initial program 81.0%

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

      1. associate-+l- 81.0%

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

      2. *-commutative 81.0%

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

      3. associate-*r* 81.6%

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

      4. *-commutative 81.6%

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

      5. associate-+l- 81.6%

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

      6. *-commutative 81.6%

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

      7. associate-*r* 81.0%

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

      8. *-commutative 81.0%

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

      9. associate-*l* 81.0%

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

      10. associate-*l* 82.8%

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

   3. Simplified 82.8%

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

   4. Taylor expanded in b around inf 34.9%

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

      1. *-commutative 34.9%

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

   6. Simplified 34.9%

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

   if 6.19999999999999993e-89 < c

   1. Initial program 69.7%

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

      1. associate-+l- 69.7%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 69.7%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 68.2%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 68.2%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 68.2%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. *-commutative 68.2%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

      7. associate-*r* 69.7%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 69.7%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      9. associate-*l* 69.8%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      10. associate-*l* 69.9%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 69.9%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]

   5. Applied egg-rr 75.9%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(x, 9 \cdot y, a \cdot \left(z \cdot \left(t \cdot -4\right)\right)\right) + b}{z} \cdot \frac{1}{c}} \]

   6. Taylor expanded in b around inf 34.9%

      \[\leadsto \color{blue}{\frac{b}{z}} \cdot \frac{1}{c} \]
   7. Step-by-step derivation

      1. div-inv 34.9%

         \[\leadsto \color{blue}{\frac{\frac{b}{z}}{c}} \]

      2. associate-/l/ 31.4%

         \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]

      3. associate-/r* 36.3%

         \[\leadsto \color{blue}{\frac{\frac{b}{c}}{z}} \]

   8. Applied egg-rr 36.3%

      \[\leadsto \color{blue}{\frac{\frac{b}{c}}{z}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 35.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq 6.2 \cdot 10^{-89}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \end{array} \]

Alternative 18: 34.8% accurate, 3.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\\\ [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \frac{b}{z \cdot c} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
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);
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.
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;
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])
[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])
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])){:}
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.
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 77.5%

   \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
2. Step-by-step derivation

   1. associate-+l- 77.5%

      \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

   2. *-commutative 77.5%

      \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

   3. associate-*r* 77.4%

      \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

   4. *-commutative 77.4%

      \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

   5. associate-+l- 77.4%

      \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

   6. *-commutative 77.4%

      \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

   7. associate-*r* 77.5%

      \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

   8. *-commutative 77.5%

      \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

   9. associate-*l* 77.5%

      \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

   10. associate-*l* 78.7%

       \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

3. Simplified 78.7%

   \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]

4. Taylor expanded in b around inf 33.8%

   \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
5. Step-by-step derivation

   1. *-commutative 33.8%

      \[\leadsto \frac{b}{\color{blue}{z \cdot c}} \]

6. Simplified 33.8%

   \[\leadsto \color{blue}{\frac{b}{z \cdot c}} \]

7. Final simplification 33.8%

   \[\leadsto \frac{b}{z \cdot c} \]

Developer target: 80.1% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{b}{c \cdot z}\\ t_2 := 4 \cdot \frac{a \cdot t}{c}\\ t_3 := \left(x \cdot 9\right) \cdot y\\ t_4 := \left(t_3 - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b\\ t_5 := \frac{t_4}{z \cdot c}\\ t_6 := \frac{\left(t_3 - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}\\ \mathbf{if}\;t_5 < -1.100156740804105 \cdot 10^{-171}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;t_5 < 0:\\ \;\;\;\;\frac{\frac{t_4}{z}}{c}\\ \mathbf{elif}\;t_5 < 1.1708877911747488 \cdot 10^{-53}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;t_5 < 2.876823679546137 \cdot 10^{+130}:\\ \;\;\;\;\left(\left(9 \cdot \frac{y}{c}\right) \cdot \frac{x}{z} + t_1\right) - t_2\\ \mathbf{elif}\;t_5 < 1.3838515042456319 \cdot 10^{+158}:\\ \;\;\;\;t_6\\ \mathbf{else}:\\ \;\;\;\;\left(9 \cdot \left(\frac{y}{c \cdot z} \cdot x\right) + t_1\right) - t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ b (* c z)))
        (t_2 (* 4.0 (/ (* a t) c)))
        (t_3 (* (* x 9.0) y))
        (t_4 (+ (- t_3 (* (* (* z 4.0) t) a)) b))
        (t_5 (/ t_4 (* z c)))
        (t_6 (/ (+ (- t_3 (* (* z 4.0) (* t a))) b) (* z c))))
   (if (< t_5 -1.100156740804105e-171)
     t_6
     (if (< t_5 0.0)
       (/ (/ t_4 z) c)
       (if (< t_5 1.1708877911747488e-53)
         t_6
         (if (< t_5 2.876823679546137e+130)
           (- (+ (* (* 9.0 (/ y c)) (/ x z)) t_1) t_2)
           (if (< t_5 1.3838515042456319e+158)
             t_6
             (- (+ (* 9.0 (* (/ y (* c z)) x)) t_1) t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = b / (c * z);
	double t_2 = 4.0 * ((a * t) / c);
	double t_3 = (x * 9.0) * y;
	double t_4 = (t_3 - (((z * 4.0) * t) * a)) + b;
	double t_5 = t_4 / (z * c);
	double t_6 = ((t_3 - ((z * 4.0) * (t * a))) + b) / (z * c);
	double tmp;
	if (t_5 < -1.100156740804105e-171) {
		tmp = t_6;
	} else if (t_5 < 0.0) {
		tmp = (t_4 / z) / c;
	} else if (t_5 < 1.1708877911747488e-53) {
		tmp = t_6;
	} else if (t_5 < 2.876823679546137e+130) {
		tmp = (((9.0 * (y / c)) * (x / z)) + t_1) - t_2;
	} else if (t_5 < 1.3838515042456319e+158) {
		tmp = t_6;
	} else {
		tmp = ((9.0 * ((y / (c * z)) * x)) + t_1) - t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: tmp
    t_1 = b / (c * z)
    t_2 = 4.0d0 * ((a * t) / c)
    t_3 = (x * 9.0d0) * y
    t_4 = (t_3 - (((z * 4.0d0) * t) * a)) + b
    t_5 = t_4 / (z * c)
    t_6 = ((t_3 - ((z * 4.0d0) * (t * a))) + b) / (z * c)
    if (t_5 < (-1.100156740804105d-171)) then
        tmp = t_6
    else if (t_5 < 0.0d0) then
        tmp = (t_4 / z) / c
    else if (t_5 < 1.1708877911747488d-53) then
        tmp = t_6
    else if (t_5 < 2.876823679546137d+130) then
        tmp = (((9.0d0 * (y / c)) * (x / z)) + t_1) - t_2
    else if (t_5 < 1.3838515042456319d+158) then
        tmp = t_6
    else
        tmp = ((9.0d0 * ((y / (c * z)) * x)) + t_1) - t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = b / (c * z);
	double t_2 = 4.0 * ((a * t) / c);
	double t_3 = (x * 9.0) * y;
	double t_4 = (t_3 - (((z * 4.0) * t) * a)) + b;
	double t_5 = t_4 / (z * c);
	double t_6 = ((t_3 - ((z * 4.0) * (t * a))) + b) / (z * c);
	double tmp;
	if (t_5 < -1.100156740804105e-171) {
		tmp = t_6;
	} else if (t_5 < 0.0) {
		tmp = (t_4 / z) / c;
	} else if (t_5 < 1.1708877911747488e-53) {
		tmp = t_6;
	} else if (t_5 < 2.876823679546137e+130) {
		tmp = (((9.0 * (y / c)) * (x / z)) + t_1) - t_2;
	} else if (t_5 < 1.3838515042456319e+158) {
		tmp = t_6;
	} else {
		tmp = ((9.0 * ((y / (c * z)) * x)) + t_1) - t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = b / (c * z)
	t_2 = 4.0 * ((a * t) / c)
	t_3 = (x * 9.0) * y
	t_4 = (t_3 - (((z * 4.0) * t) * a)) + b
	t_5 = t_4 / (z * c)
	t_6 = ((t_3 - ((z * 4.0) * (t * a))) + b) / (z * c)
	tmp = 0
	if t_5 < -1.100156740804105e-171:
		tmp = t_6
	elif t_5 < 0.0:
		tmp = (t_4 / z) / c
	elif t_5 < 1.1708877911747488e-53:
		tmp = t_6
	elif t_5 < 2.876823679546137e+130:
		tmp = (((9.0 * (y / c)) * (x / z)) + t_1) - t_2
	elif t_5 < 1.3838515042456319e+158:
		tmp = t_6
	else:
		tmp = ((9.0 * ((y / (c * z)) * x)) + t_1) - t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(b / Float64(c * z))
	t_2 = Float64(4.0 * Float64(Float64(a * t) / c))
	t_3 = Float64(Float64(x * 9.0) * y)
	t_4 = Float64(Float64(t_3 - Float64(Float64(Float64(z * 4.0) * t) * a)) + b)
	t_5 = Float64(t_4 / Float64(z * c))
	t_6 = Float64(Float64(Float64(t_3 - Float64(Float64(z * 4.0) * Float64(t * a))) + b) / Float64(z * c))
	tmp = 0.0
	if (t_5 < -1.100156740804105e-171)
		tmp = t_6;
	elseif (t_5 < 0.0)
		tmp = Float64(Float64(t_4 / z) / c);
	elseif (t_5 < 1.1708877911747488e-53)
		tmp = t_6;
	elseif (t_5 < 2.876823679546137e+130)
		tmp = Float64(Float64(Float64(Float64(9.0 * Float64(y / c)) * Float64(x / z)) + t_1) - t_2);
	elseif (t_5 < 1.3838515042456319e+158)
		tmp = t_6;
	else
		tmp = Float64(Float64(Float64(9.0 * Float64(Float64(y / Float64(c * z)) * x)) + t_1) - t_2);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = b / (c * z);
	t_2 = 4.0 * ((a * t) / c);
	t_3 = (x * 9.0) * y;
	t_4 = (t_3 - (((z * 4.0) * t) * a)) + b;
	t_5 = t_4 / (z * c);
	t_6 = ((t_3 - ((z * 4.0) * (t * a))) + b) / (z * c);
	tmp = 0.0;
	if (t_5 < -1.100156740804105e-171)
		tmp = t_6;
	elseif (t_5 < 0.0)
		tmp = (t_4 / z) / c;
	elseif (t_5 < 1.1708877911747488e-53)
		tmp = t_6;
	elseif (t_5 < 2.876823679546137e+130)
		tmp = (((9.0 * (y / c)) * (x / z)) + t_1) - t_2;
	elseif (t_5 < 1.3838515042456319e+158)
		tmp = t_6;
	else
		tmp = ((9.0 * ((y / (c * z)) * x)) + t_1) - t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(b / N[(c * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(4.0 * N[(N[(a * t), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision]}, Block[{t$95$4 = N[(N[(t$95$3 - N[(N[(N[(z * 4.0), $MachinePrecision] * t), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]}, Block[{t$95$5 = N[(t$95$4 / N[(z * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(N[(N[(t$95$3 - N[(N[(z * 4.0), $MachinePrecision] * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]}, If[Less[t$95$5, -1.100156740804105e-171], t$95$6, If[Less[t$95$5, 0.0], N[(N[(t$95$4 / z), $MachinePrecision] / c), $MachinePrecision], If[Less[t$95$5, 1.1708877911747488e-53], t$95$6, If[Less[t$95$5, 2.876823679546137e+130], N[(N[(N[(N[(9.0 * N[(y / c), $MachinePrecision]), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision] - t$95$2), $MachinePrecision], If[Less[t$95$5, 1.3838515042456319e+158], t$95$6, N[(N[(N[(9.0 * N[(N[(y / N[(c * z), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision] - t$95$2), $MachinePrecision]]]]]]]]]]]]

Reproduce

herbie shell --seed 2023322 
(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)))