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

Percentage Accurate: 79.1% → 90.0%

Time: 19.0s

Alternatives: 14

Speedup: 0.7×

• 37.2% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 79.1% 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: 90.0% accurate, 0.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+41}:\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right) + \left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right)}{c}\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{+54}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(9 \cdot x\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-4, \frac{a}{\frac{c}{t}}, \mathsf{fma}\left(9, \frac{x}{c} \cdot \frac{y}{z}, \frac{b}{z \cdot c}\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= z -2e+41)
   (/ (+ (* -4.0 (* a t)) (+ (* 9.0 (/ (* x y) z)) (/ b z))) c)
   (if (<= z 6.2e+54)
     (/ (+ b (- (* y (* 9.0 x)) (* a (* t (* z 4.0))))) (* z c))
     (fma -4.0 (/ a (/ c t)) (fma 9.0 (* (/ x c) (/ y z)) (/ b (* z c)))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (z <= -2e+41) {
		tmp = ((-4.0 * (a * t)) + ((9.0 * ((x * y) / z)) + (b / z))) / c;
	} else if (z <= 6.2e+54) {
		tmp = (b + ((y * (9.0 * x)) - (a * (t * (z * 4.0))))) / (z * c);
	} else {
		tmp = fma(-4.0, (a / (c / t)), fma(9.0, ((x / c) * (y / z)), (b / (z * c))));
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (z <= -2e+41)
		tmp = Float64(Float64(Float64(-4.0 * Float64(a * t)) + Float64(Float64(9.0 * Float64(Float64(x * y) / z)) + Float64(b / z))) / c);
	elseif (z <= 6.2e+54)
		tmp = Float64(Float64(b + Float64(Float64(y * Float64(9.0 * x)) - Float64(a * Float64(t * Float64(z * 4.0))))) / Float64(z * c));
	else
		tmp = fma(-4.0, Float64(a / Float64(c / t)), fma(9.0, Float64(Float64(x / c) * Float64(y / z)), Float64(b / Float64(z * c))));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[z, -2e+41], N[(N[(N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision] + N[(N[(9.0 * N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] + N[(b / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[z, 6.2e+54], N[(N[(b + N[(N[(y * N[(9.0 * x), $MachinePrecision]), $MachinePrecision] - N[(a * N[(t * N[(z * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(-4.0 * N[(a / N[(c / t), $MachinePrecision]), $MachinePrecision] + N[(9.0 * N[(N[(x / c), $MachinePrecision] * N[(y / z), $MachinePrecision]), $MachinePrecision] + N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.00000000000000001e41

   1. Initial program 69.0%

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

      1. associate-+l- 69.0%

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

      2. *-commutative 69.0%

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

      3. associate-*r* 68.9%

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

      4. *-commutative 68.9%

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

      5. associate-+l- 68.9%

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

      6. *-commutative 68.9%

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

      7. associate-*r* 69.0%

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

      8. *-commutative 69.0%

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

      9. associate-*l* 68.9%

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

      10. associate-*l* 72.8%

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

   3. Simplified 72.8%

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

      1. clear-num 72.8%

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

      2. associate-/r/ 72.8%

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

      3. associate-/r* 72.8%

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

      4. reciprocal-define 72.8%

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

      5. associate-*r* 68.9%

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

      6. cancel-sign-sub-inv 68.9%

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

      7. fma-def 68.9%

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

      8. distribute-lft-neg-in 68.9%

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

      9. *-commutative 68.9%

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

      10. distribute-rgt-neg-in 68.9%

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

      11. *-commutative 68.9%

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

      12. distribute-rgt-neg-in 68.9%

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

      13. distribute-rgt-neg-in 68.9%

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

      14. metadata-eval 68.9%

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

   6. Applied egg-rr 68.9%

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

      1. associate-*l/ 76.2%

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

   8. Applied egg-rr 76.2%

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

   9. Taylor expanded in z around 0 89.1%

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

   if -2.00000000000000001e41 < z < 6.1999999999999999e54

   1. Initial program 95.0%

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

   if 6.1999999999999999e54 < z

   1. Initial program 54.9%

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

      1. associate-+l- 54.9%

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

      2. *-commutative 54.9%

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

      3. associate-*r* 54.9%

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

      4. *-commutative 54.9%

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

      5. associate-+l- 54.9%

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

      6. *-commutative 54.9%

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

      7. associate-*r* 54.9%

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

      8. *-commutative 54.9%

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

      9. associate-*l* 54.9%

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

      10. associate-*l* 62.7%

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

   3. Simplified 62.7%

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

   5. Taylor expanded in x around 0 80.6%

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

      1. cancel-sign-sub-inv 80.6%

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

      2. metadata-eval 80.6%

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

      3. +-commutative 80.6%

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

      4. fma-def 80.6%

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

      5. associate-/l* 86.0%

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

      6. fma-def 86.0%

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

      7. times-frac 91.7%

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

      8. *-commutative 91.7%

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

   7. Simplified 91.7%

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

4. Final simplification 93.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+41}:\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right) + \left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right)}{c}\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{+54}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(9 \cdot x\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-4, \frac{a}{\frac{c}{t}}, \mathsf{fma}\left(9, \frac{x}{c} \cdot \frac{y}{z}, \frac{b}{z \cdot c}\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 47.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \frac{x}{z} \cdot \frac{9 \cdot y}{c}\\ t_2 := -4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{if}\;t \leq -2.7 \cdot 10^{+106}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -7.3 \cdot 10^{+90}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -4000000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -9.2 \cdot 10^{-203}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;t \leq 6.8 \cdot 10^{-158}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{a \cdot t}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (/ x z) (/ (* 9.0 y) c))) (t_2 (* -4.0 (* t (/ a c)))))
   (if (<= t -2.7e+106)
     t_2
     (if (<= t -7.3e+90)
       t_1
       (if (<= t -4000000.0)
         t_2
         (if (<= t -9.2e-203)
           (/ b (* z c))
           (if (<= t 6.8e-158) t_1 (* -4.0 (/ (* a t) c)))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (x / z) * ((9.0 * y) / c);
	double t_2 = -4.0 * (t * (a / c));
	double tmp;
	if (t <= -2.7e+106) {
		tmp = t_2;
	} else if (t <= -7.3e+90) {
		tmp = t_1;
	} else if (t <= -4000000.0) {
		tmp = t_2;
	} else if (t <= -9.2e-203) {
		tmp = b / (z * c);
	} else if (t <= 6.8e-158) {
		tmp = t_1;
	} else {
		tmp = -4.0 * ((a * t) / c);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x / z) * ((9.0d0 * y) / c)
    t_2 = (-4.0d0) * (t * (a / c))
    if (t <= (-2.7d+106)) then
        tmp = t_2
    else if (t <= (-7.3d+90)) then
        tmp = t_1
    else if (t <= (-4000000.0d0)) then
        tmp = t_2
    else if (t <= (-9.2d-203)) then
        tmp = b / (z * c)
    else if (t <= 6.8d-158) then
        tmp = t_1
    else
        tmp = (-4.0d0) * ((a * t) / c)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (x / z) * ((9.0 * y) / c);
	double t_2 = -4.0 * (t * (a / c));
	double tmp;
	if (t <= -2.7e+106) {
		tmp = t_2;
	} else if (t <= -7.3e+90) {
		tmp = t_1;
	} else if (t <= -4000000.0) {
		tmp = t_2;
	} else if (t <= -9.2e-203) {
		tmp = b / (z * c);
	} else if (t <= 6.8e-158) {
		tmp = t_1;
	} else {
		tmp = -4.0 * ((a * t) / c);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	t_1 = (x / z) * ((9.0 * y) / c)
	t_2 = -4.0 * (t * (a / c))
	tmp = 0
	if t <= -2.7e+106:
		tmp = t_2
	elif t <= -7.3e+90:
		tmp = t_1
	elif t <= -4000000.0:
		tmp = t_2
	elif t <= -9.2e-203:
		tmp = b / (z * c)
	elif t <= 6.8e-158:
		tmp = t_1
	else:
		tmp = -4.0 * ((a * t) / c)
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(x / z) * Float64(Float64(9.0 * y) / c))
	t_2 = Float64(-4.0 * Float64(t * Float64(a / c)))
	tmp = 0.0
	if (t <= -2.7e+106)
		tmp = t_2;
	elseif (t <= -7.3e+90)
		tmp = t_1;
	elseif (t <= -4000000.0)
		tmp = t_2;
	elseif (t <= -9.2e-203)
		tmp = Float64(b / Float64(z * c));
	elseif (t <= 6.8e-158)
		tmp = t_1;
	else
		tmp = Float64(-4.0 * Float64(Float64(a * t) / c));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (x / z) * ((9.0 * y) / c);
	t_2 = -4.0 * (t * (a / c));
	tmp = 0.0;
	if (t <= -2.7e+106)
		tmp = t_2;
	elseif (t <= -7.3e+90)
		tmp = t_1;
	elseif (t <= -4000000.0)
		tmp = t_2;
	elseif (t <= -9.2e-203)
		tmp = b / (z * c);
	elseif (t <= 6.8e-158)
		tmp = t_1;
	else
		tmp = -4.0 * ((a * t) / c);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(x / z), $MachinePrecision] * N[(N[(9.0 * y), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.7e+106], t$95$2, If[LessEqual[t, -7.3e+90], t$95$1, If[LessEqual[t, -4000000.0], t$95$2, If[LessEqual[t, -9.2e-203], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6.8e-158], t$95$1, N[(-4.0 * N[(N[(a * t), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -2.70000000000000006e106 or -7.29999999999999995e90 < t < -4e6

   1. Initial program 79.2%

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

      1. associate-+l- 79.2%

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

      2. *-commutative 79.2%

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

      3. associate-*r* 82.6%

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

      4. *-commutative 82.6%

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

      5. associate-+l- 82.6%

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

      6. *-commutative 82.6%

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

      7. associate-*r* 79.2%

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

      8. *-commutative 79.2%

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

      9. associate-*l* 79.2%

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

      10. associate-*l* 72.0%

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

   3. Simplified 72.0%

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

   5. Taylor expanded in z around inf 52.9%

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

      1. *-commutative 52.9%

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

      2. associate-/l* 60.0%

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

      3. associate-/r/ 67.6%

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

   7. Simplified 67.6%

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

   if -2.70000000000000006e106 < t < -7.29999999999999995e90 or -9.19999999999999966e-203 < t < 6.7999999999999999e-158

   1. Initial program 88.4%

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

      1. associate-+l- 88.4%

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

      2. *-commutative 88.4%

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

      3. associate-*r* 79.9%

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

      4. *-commutative 79.9%

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

      5. associate-+l- 79.9%

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

      6. *-commutative 79.9%

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

      7. associate-*r* 88.4%

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

      8. *-commutative 88.4%

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

      9. associate-*l* 88.3%

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

      10. associate-*l* 88.3%

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

   3. Simplified 88.3%

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

   5. Taylor expanded in x around inf 50.9%

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

      1. associate-*r/ 51.1%

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

      2. associate-*r* 51.1%

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

      3. *-commutative 51.1%

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

      4. associate-*r* 51.0%

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

      5. *-commutative 51.0%

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

      6. times-frac 61.8%

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

   7. Simplified 61.8%

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

   if -4e6 < t < -9.19999999999999966e-203

   1. Initial program 92.2%

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

      1. associate-+l- 92.2%

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

      2. *-commutative 92.2%

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

      3. associate-*r* 88.5%

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

      4. *-commutative 88.5%

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

      5. associate-+l- 88.5%

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

      6. *-commutative 88.5%

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

      7. associate-*r* 92.2%

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

      8. *-commutative 92.2%

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

      9. associate-*l* 92.2%

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

      10. associate-*l* 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. Add Preprocessing

   5. Taylor expanded in b around inf 58.2%

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

      1. *-commutative 58.2%

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

   7. Simplified 58.2%

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

   if 6.7999999999999999e-158 < t

   1. Initial program 73.4%

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

      1. associate-+l- 73.4%

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

      2. *-commutative 73.4%

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

      3. associate-*r* 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* 73.4%

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

      8. *-commutative 73.4%

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

      9. associate-*l* 73.4%

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

      10. associate-*l* 78.4%

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

   3. Simplified 78.4%

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

   5. Taylor expanded in z around inf 49.1%

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

4. Final simplification 57.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.7 \cdot 10^{+106}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;t \leq -7.3 \cdot 10^{+90}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{9 \cdot y}{c}\\ \mathbf{elif}\;t \leq -4000000:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;t \leq -9.2 \cdot 10^{-203}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;t \leq 6.8 \cdot 10^{-158}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{9 \cdot y}{c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{a \cdot t}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 46.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := -4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{if}\;t \leq -2.7 \cdot 10^{+106}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -7.6 \cdot 10^{+90}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{9 \cdot y}{c}\\ \mathbf{elif}\;t \leq -13500:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -4.6 \cdot 10^{-193}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;t \leq 1.02 \cdot 10^{-158}:\\ \;\;\;\;\frac{9}{\frac{z}{x} \cdot \frac{c}{y}}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{a \cdot t}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* -4.0 (* t (/ a c)))))
   (if (<= t -2.7e+106)
     t_1
     (if (<= t -7.6e+90)
       (* (/ x z) (/ (* 9.0 y) c))
       (if (<= t -13500.0)
         t_1
         (if (<= t -4.6e-193)
           (/ b (* z c))
           (if (<= t 1.02e-158)
             (/ 9.0 (* (/ z x) (/ c y)))
             (* -4.0 (/ (* a t) c)))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = -4.0 * (t * (a / c));
	double tmp;
	if (t <= -2.7e+106) {
		tmp = t_1;
	} else if (t <= -7.6e+90) {
		tmp = (x / z) * ((9.0 * y) / c);
	} else if (t <= -13500.0) {
		tmp = t_1;
	} else if (t <= -4.6e-193) {
		tmp = b / (z * c);
	} else if (t <= 1.02e-158) {
		tmp = 9.0 / ((z / x) * (c / y));
	} else {
		tmp = -4.0 * ((a * t) / c);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (-4.0d0) * (t * (a / c))
    if (t <= (-2.7d+106)) then
        tmp = t_1
    else if (t <= (-7.6d+90)) then
        tmp = (x / z) * ((9.0d0 * y) / c)
    else if (t <= (-13500.0d0)) then
        tmp = t_1
    else if (t <= (-4.6d-193)) then
        tmp = b / (z * c)
    else if (t <= 1.02d-158) then
        tmp = 9.0d0 / ((z / x) * (c / y))
    else
        tmp = (-4.0d0) * ((a * t) / c)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = -4.0 * (t * (a / c));
	double tmp;
	if (t <= -2.7e+106) {
		tmp = t_1;
	} else if (t <= -7.6e+90) {
		tmp = (x / z) * ((9.0 * y) / c);
	} else if (t <= -13500.0) {
		tmp = t_1;
	} else if (t <= -4.6e-193) {
		tmp = b / (z * c);
	} else if (t <= 1.02e-158) {
		tmp = 9.0 / ((z / x) * (c / y));
	} else {
		tmp = -4.0 * ((a * t) / c);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	t_1 = -4.0 * (t * (a / c))
	tmp = 0
	if t <= -2.7e+106:
		tmp = t_1
	elif t <= -7.6e+90:
		tmp = (x / z) * ((9.0 * y) / c)
	elif t <= -13500.0:
		tmp = t_1
	elif t <= -4.6e-193:
		tmp = b / (z * c)
	elif t <= 1.02e-158:
		tmp = 9.0 / ((z / x) * (c / y))
	else:
		tmp = -4.0 * ((a * t) / c)
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(-4.0 * Float64(t * Float64(a / c)))
	tmp = 0.0
	if (t <= -2.7e+106)
		tmp = t_1;
	elseif (t <= -7.6e+90)
		tmp = Float64(Float64(x / z) * Float64(Float64(9.0 * y) / c));
	elseif (t <= -13500.0)
		tmp = t_1;
	elseif (t <= -4.6e-193)
		tmp = Float64(b / Float64(z * c));
	elseif (t <= 1.02e-158)
		tmp = Float64(9.0 / Float64(Float64(z / x) * Float64(c / y)));
	else
		tmp = Float64(-4.0 * Float64(Float64(a * t) / c));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = -4.0 * (t * (a / c));
	tmp = 0.0;
	if (t <= -2.7e+106)
		tmp = t_1;
	elseif (t <= -7.6e+90)
		tmp = (x / z) * ((9.0 * y) / c);
	elseif (t <= -13500.0)
		tmp = t_1;
	elseif (t <= -4.6e-193)
		tmp = b / (z * c);
	elseif (t <= 1.02e-158)
		tmp = 9.0 / ((z / x) * (c / y));
	else
		tmp = -4.0 * ((a * t) / c);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.7e+106], t$95$1, If[LessEqual[t, -7.6e+90], N[(N[(x / z), $MachinePrecision] * N[(N[(9.0 * y), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -13500.0], t$95$1, If[LessEqual[t, -4.6e-193], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.02e-158], N[(9.0 / N[(N[(z / x), $MachinePrecision] * N[(c / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-4.0 * N[(N[(a * t), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -2.70000000000000006e106 or -7.6000000000000002e90 < t < -13500

   1. Initial program 79.2%

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

      1. associate-+l- 79.2%

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

      2. *-commutative 79.2%

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

      3. associate-*r* 82.6%

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

      4. *-commutative 82.6%

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

      5. associate-+l- 82.6%

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

      6. *-commutative 82.6%

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

      7. associate-*r* 79.2%

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

      8. *-commutative 79.2%

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

      9. associate-*l* 79.2%

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

      10. associate-*l* 72.0%

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

   3. Simplified 72.0%

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

   5. Taylor expanded in z around inf 52.9%

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

      1. *-commutative 52.9%

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

      2. associate-/l* 60.0%

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

      3. associate-/r/ 67.6%

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

   7. Simplified 67.6%

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

   if -2.70000000000000006e106 < t < -7.6000000000000002e90

   1. Initial program 99.7%

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

      1. associate-+l- 99.7%

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

      2. *-commutative 99.7%

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

      3. associate-*r* 99.7%

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

      4. *-commutative 99.7%

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

      5. associate-+l- 99.7%

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

      6. *-commutative 99.7%

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

      7. associate-*r* 99.7%

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

      8. *-commutative 99.7%

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

      9. associate-*l* 99.7%

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

      10. associate-*l* 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around inf 61.6%

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

      1. associate-*r/ 61.9%

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

      2. associate-*r* 61.9%

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

      3. *-commutative 61.9%

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

      4. associate-*r* 61.9%

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

      5. *-commutative 61.9%

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

      6. times-frac 80.4%

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

   7. Simplified 80.4%

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

   if -13500 < t < -4.60000000000000017e-193

   1. Initial program 91.8%

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

      1. associate-+l- 91.8%

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

      2. *-commutative 91.8%

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

      3. associate-*r* 89.7%

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

      4. *-commutative 89.7%

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

      5. associate-+l- 89.7%

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

      6. *-commutative 89.7%

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

      7. associate-*r* 91.8%

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

      8. *-commutative 91.8%

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

      9. associate-*l* 91.8%

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

      10. associate-*l* 91.9%

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

   3. Simplified 91.9%

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

   5. Taylor expanded in b around inf 57.7%

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

      1. *-commutative 57.7%

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

   7. Simplified 57.7%

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

   if -4.60000000000000017e-193 < t < 1.0199999999999999e-158

   1. Initial program 88.0%

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

      1. associate-+l- 88.0%

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

      2. *-commutative 88.0%

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

      3. associate-*r* 77.5%

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

      4. *-commutative 77.5%

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

      5. associate-+l- 77.5%

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

      6. *-commutative 77.5%

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

      7. associate-*r* 88.0%

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

      8. *-commutative 88.0%

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

      9. associate-*l* 87.9%

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

      10. associate-*l* 87.9%

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

   3. Simplified 87.9%

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

   5. Taylor expanded in x around inf 47.3%

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

      1. associate-*r/ 47.5%

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

      2. associate-*r* 47.4%

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

      3. *-commutative 47.4%

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

      4. associate-*r* 47.4%

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

      5. *-commutative 47.4%

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

      6. times-frac 56.9%

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

   7. Simplified 56.9%

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

      1. clear-num 56.9%

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

      2. associate-/l* 56.8%

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

      3. frac-times 56.9%

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

      4. metadata-eval 56.9%

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

   9. Applied egg-rr 56.9%

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

   if 1.0199999999999999e-158 < t

   1. Initial program 73.4%

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

      1. associate-+l- 73.4%

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

      2. *-commutative 73.4%

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

      3. associate-*r* 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* 73.4%

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

      8. *-commutative 73.4%

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

      9. associate-*l* 73.4%

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

      10. associate-*l* 78.4%

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

   3. Simplified 78.4%

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

   5. Taylor expanded in z around inf 49.1%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 56.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.7 \cdot 10^{+106}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;t \leq -7.6 \cdot 10^{+90}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{9 \cdot y}{c}\\ \mathbf{elif}\;t \leq -13500:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;t \leq -4.6 \cdot 10^{-193}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;t \leq 1.02 \cdot 10^{-158}:\\ \;\;\;\;\frac{9}{\frac{z}{x} \cdot \frac{c}{y}}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{a \cdot t}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 85.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \frac{-4 \cdot \left(a \cdot t\right) + \left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right)}{c}\\ \mathbf{if}\;z \leq -8 \cdot 10^{-137}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-239}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \mathbf{elif}\;z \leq 2.05 \cdot 10^{-122}:\\ \;\;\;\;\frac{b - 4 \cdot \left(a \cdot \left(z \cdot t\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (+ (* -4.0 (* a t)) (+ (* 9.0 (/ (* x y) z)) (/ b z))) c)))
   (if (<= z -8e-137)
     t_1
     (if (<= z 1.1e-239)
       (/ (+ b (* 9.0 (* x y))) (* z c))
       (if (<= z 2.05e-122) (/ (- b (* 4.0 (* a (* z t)))) (* z c)) t_1)))))

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)) + ((9.0 * ((x * y) / z)) + (b / z))) / c;
	double tmp;
	if (z <= -8e-137) {
		tmp = t_1;
	} else if (z <= 1.1e-239) {
		tmp = (b + (9.0 * (x * y))) / (z * c);
	} else if (z <= 2.05e-122) {
		tmp = (b - (4.0 * (a * (z * t)))) / (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.
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)) + ((9.0d0 * ((x * y) / z)) + (b / z))) / c
    if (z <= (-8d-137)) then
        tmp = t_1
    else if (z <= 1.1d-239) then
        tmp = (b + (9.0d0 * (x * y))) / (z * c)
    else if (z <= 2.05d-122) then
        tmp = (b - (4.0d0 * (a * (z * t)))) / (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;
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)) + ((9.0 * ((x * y) / z)) + (b / z))) / c;
	double tmp;
	if (z <= -8e-137) {
		tmp = t_1;
	} else if (z <= 1.1e-239) {
		tmp = (b + (9.0 * (x * y))) / (z * c);
	} else if (z <= 2.05e-122) {
		tmp = (b - (4.0 * (a * (z * t)))) / (z * c);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	t_1 = ((-4.0 * (a * t)) + ((9.0 * ((x * y) / z)) + (b / z))) / c
	tmp = 0
	if z <= -8e-137:
		tmp = t_1
	elif z <= 1.1e-239:
		tmp = (b + (9.0 * (x * y))) / (z * c)
	elif z <= 2.05e-122:
		tmp = (b - (4.0 * (a * (z * t)))) / (z * c)
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(Float64(-4.0 * Float64(a * t)) + Float64(Float64(9.0 * Float64(Float64(x * y) / z)) + Float64(b / z))) / c)
	tmp = 0.0
	if (z <= -8e-137)
		tmp = t_1;
	elseif (z <= 1.1e-239)
		tmp = Float64(Float64(b + Float64(9.0 * Float64(x * y))) / Float64(z * c));
	elseif (z <= 2.05e-122)
		tmp = Float64(Float64(b - Float64(4.0 * Float64(a * Float64(z * t)))) / 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])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = ((-4.0 * (a * t)) + ((9.0 * ((x * y) / z)) + (b / z))) / c;
	tmp = 0.0;
	if (z <= -8e-137)
		tmp = t_1;
	elseif (z <= 1.1e-239)
		tmp = (b + (9.0 * (x * y))) / (z * c);
	elseif (z <= 2.05e-122)
		tmp = (b - (4.0 * (a * (z * t)))) / (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.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision] + N[(N[(9.0 * N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] + N[(b / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]}, If[LessEqual[z, -8e-137], t$95$1, If[LessEqual[z, 1.1e-239], N[(N[(b + N[(9.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.05e-122], N[(N[(b - N[(4.0 * N[(a * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.99999999999999982e-137 or 2.05e-122 < z

   1. Initial program 76.4%

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

      1. associate-+l- 76.4%

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

      2. *-commutative 76.4%

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

      3. associate-*r* 76.4%

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

      4. *-commutative 76.4%

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

      5. associate-+l- 76.4%

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

      6. *-commutative 76.4%

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

      7. associate-*r* 76.4%

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

      8. *-commutative 76.4%

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

      9. associate-*l* 76.4%

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

      10. associate-*l* 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%

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

      1. clear-num 79.3%

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

      2. associate-/r/ 79.5%

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

      3. associate-/r* 79.5%

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

      4. reciprocal-define 79.5%

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

      5. associate-*r* 76.3%

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

      6. cancel-sign-sub-inv 76.3%

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

      7. fma-def 76.3%

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

      8. distribute-lft-neg-in 76.3%

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

      9. *-commutative 76.3%

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

      10. distribute-rgt-neg-in 76.3%

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

      11. *-commutative 76.3%

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

      12. distribute-rgt-neg-in 76.3%

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

      13. distribute-rgt-neg-in 76.3%

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

      14. metadata-eval 76.3%

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

   6. Applied egg-rr 76.3%

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

      1. associate-*l/ 78.2%

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

   8. Applied egg-rr 78.2%

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

   9. Taylor expanded in z around 0 88.0%

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

   if -7.99999999999999982e-137 < z < 1.09999999999999991e-239

   1. Initial program 95.7%

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

      1. associate-+l- 95.7%

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

      2. *-commutative 95.7%

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

      3. associate-*r* 99.7%

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

      4. *-commutative 99.7%

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

      5. associate-+l- 99.7%

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

      6. *-commutative 99.7%

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

      7. associate-*r* 95.7%

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

      8. *-commutative 95.7%

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

      9. associate-*l* 95.7%

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

      10. associate-*l* 93.2%

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

   3. Simplified 93.2%

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

   5. Taylor expanded in z around 0 87.0%

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

      1. *-commutative 87.0%

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

   7. Simplified 87.0%

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

   if 1.09999999999999991e-239 < z < 2.05e-122

   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* 95.8%

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

      4. *-commutative 95.8%

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

      5. associate-+l- 95.8%

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

      6. *-commutative 95.8%

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

      7. associate-*r* 96.9%

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

      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* 81.8%

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

   3. Simplified 81.8%

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

   5. Taylor expanded in x around 0 89.1%

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

4. Final simplification 87.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{-137}:\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right) + \left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right)}{c}\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-239}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \mathbf{elif}\;z \leq 2.05 \cdot 10^{-122}:\\ \;\;\;\;\frac{b - 4 \cdot \left(a \cdot \left(z \cdot t\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right) + \left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right)}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 73.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \frac{\frac{b}{z} - \left(a \cdot t\right) \cdot 4}{c}\\ \mathbf{if}\;z \leq -2.6 \cdot 10^{+41}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-182}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-98} \lor \neg \left(z \leq 6.5 \cdot 10^{-56}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{9 \cdot y}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (- (/ b z) (* (* a t) 4.0)) c)))
   (if (<= z -2.6e+41)
     t_1
     (if (<= z 2.2e-182)
       (/ (+ b (* 9.0 (* x y))) (* z c))
       (if (or (<= z 5.8e-98) (not (<= z 6.5e-56)))
         t_1
         (* (/ x z) (/ (* 9.0 y) c)))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = ((b / z) - ((a * t) * 4.0)) / c;
	double tmp;
	if (z <= -2.6e+41) {
		tmp = t_1;
	} else if (z <= 2.2e-182) {
		tmp = (b + (9.0 * (x * y))) / (z * c);
	} else if ((z <= 5.8e-98) || !(z <= 6.5e-56)) {
		tmp = t_1;
	} else {
		tmp = (x / z) * ((9.0 * y) / c);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((b / z) - ((a * t) * 4.0d0)) / c
    if (z <= (-2.6d+41)) then
        tmp = t_1
    else if (z <= 2.2d-182) then
        tmp = (b + (9.0d0 * (x * y))) / (z * c)
    else if ((z <= 5.8d-98) .or. (.not. (z <= 6.5d-56))) then
        tmp = t_1
    else
        tmp = (x / z) * ((9.0d0 * y) / c)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = ((b / z) - ((a * t) * 4.0)) / c;
	double tmp;
	if (z <= -2.6e+41) {
		tmp = t_1;
	} else if (z <= 2.2e-182) {
		tmp = (b + (9.0 * (x * y))) / (z * c);
	} else if ((z <= 5.8e-98) || !(z <= 6.5e-56)) {
		tmp = t_1;
	} else {
		tmp = (x / z) * ((9.0 * y) / c);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	t_1 = ((b / z) - ((a * t) * 4.0)) / c
	tmp = 0
	if z <= -2.6e+41:
		tmp = t_1
	elif z <= 2.2e-182:
		tmp = (b + (9.0 * (x * y))) / (z * c)
	elif (z <= 5.8e-98) or not (z <= 6.5e-56):
		tmp = t_1
	else:
		tmp = (x / z) * ((9.0 * y) / c)
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(Float64(b / z) - Float64(Float64(a * t) * 4.0)) / c)
	tmp = 0.0
	if (z <= -2.6e+41)
		tmp = t_1;
	elseif (z <= 2.2e-182)
		tmp = Float64(Float64(b + Float64(9.0 * Float64(x * y))) / Float64(z * c));
	elseif ((z <= 5.8e-98) || !(z <= 6.5e-56))
		tmp = t_1;
	else
		tmp = Float64(Float64(x / z) * Float64(Float64(9.0 * y) / c));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = ((b / z) - ((a * t) * 4.0)) / c;
	tmp = 0.0;
	if (z <= -2.6e+41)
		tmp = t_1;
	elseif (z <= 2.2e-182)
		tmp = (b + (9.0 * (x * y))) / (z * c);
	elseif ((z <= 5.8e-98) || ~((z <= 6.5e-56)))
		tmp = t_1;
	else
		tmp = (x / z) * ((9.0 * y) / c);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(N[(b / z), $MachinePrecision] - N[(N[(a * t), $MachinePrecision] * 4.0), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]}, If[LessEqual[z, -2.6e+41], t$95$1, If[LessEqual[z, 2.2e-182], N[(N[(b + N[(9.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, 5.8e-98], N[Not[LessEqual[z, 6.5e-56]], $MachinePrecision]], t$95$1, N[(N[(x / z), $MachinePrecision] * N[(N[(9.0 * y), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.6000000000000001e41 or 2.2e-182 < z < 5.8e-98 or 6.4999999999999997e-56 < z

   1. Initial program 72.3%

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

      1. associate-+l- 72.3%

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

      2. *-commutative 72.3%

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

      3. associate-*r* 72.2%

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

      4. *-commutative 72.2%

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

      5. associate-+l- 72.2%

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

      6. *-commutative 72.2%

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

      7. associate-*r* 72.3%

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

      8. *-commutative 72.3%

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

      9. associate-*l* 72.3%

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

      10. associate-*l* 75.1%

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

   3. Simplified 75.1%

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

   5. Taylor expanded in x around 0 60.0%

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

      1. div-sub 58.1%

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

      2. *-commutative 58.1%

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

      3. *-commutative 58.1%

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

      4. times-frac 59.6%

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

      5. *-commutative 59.6%

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

   7. Applied egg-rr 59.6%

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

      1. expm1-log1p-u 40.1%

         \[\leadsto \frac{b}{z \cdot c} - \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{4}{z} \cdot \frac{a \cdot \left(z \cdot t\right)}{c}\right)\right)} \]

      2. expm1-udef 36.3%

         \[\leadsto \frac{b}{z \cdot c} - \color{blue}{\left(e^{\mathsf{log1p}\left(\frac{4}{z} \cdot \frac{a \cdot \left(z \cdot t\right)}{c}\right)} - 1\right)} \]

      3. associate-*l/ 36.3%

         \[\leadsto \frac{b}{z \cdot c} - \left(e^{\mathsf{log1p}\left(\color{blue}{\frac{4 \cdot \frac{a \cdot \left(z \cdot t\right)}{c}}{z}}\right)} - 1\right) \]

      4. *-un-lft-identity 36.3%

         \[\leadsto \frac{b}{z \cdot c} - \left(e^{\mathsf{log1p}\left(\frac{4 \cdot \frac{a \cdot \left(z \cdot t\right)}{c}}{\color{blue}{1 \cdot z}}\right)} - 1\right) \]

      5. times-frac 36.3%

         \[\leadsto \frac{b}{z \cdot c} - \left(e^{\mathsf{log1p}\left(\color{blue}{\frac{4}{1} \cdot \frac{\frac{a \cdot \left(z \cdot t\right)}{c}}{z}}\right)} - 1\right) \]

      6. metadata-eval 36.3%

         \[\leadsto \frac{b}{z \cdot c} - \left(e^{\mathsf{log1p}\left(\color{blue}{4} \cdot \frac{\frac{a \cdot \left(z \cdot t\right)}{c}}{z}\right)} - 1\right) \]

      7. associate-/l* 36.3%

         \[\leadsto \frac{b}{z \cdot c} - \left(e^{\mathsf{log1p}\left(4 \cdot \frac{\color{blue}{\frac{a}{\frac{c}{z \cdot t}}}}{z}\right)} - 1\right) \]

   9. Applied egg-rr 36.3%

      \[\leadsto \frac{b}{z \cdot c} - \color{blue}{\left(e^{\mathsf{log1p}\left(4 \cdot \frac{\frac{a}{\frac{c}{z \cdot t}}}{z}\right)} - 1\right)} \]
   10. Step-by-step derivation

       1. expm1-def 41.4%

          \[\leadsto \frac{b}{z \cdot c} - \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(4 \cdot \frac{\frac{a}{\frac{c}{z \cdot t}}}{z}\right)\right)} \]

       2. expm1-log1p 60.9%

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

       3. associate-*r/ 60.9%

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

       4. *-commutative 60.9%

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

       5. associate-*r/ 60.9%

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

       6. associate-/r/ 60.8%

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

       7. *-commutative 60.8%

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

       8. associate-*l* 63.2%

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

   11. Simplified 63.2%

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

   12. Taylor expanded in c around 0 72.2%

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

   if -2.6000000000000001e41 < z < 2.2e-182

   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* 98.7%

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

      4. *-commutative 98.7%

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

      5. associate-+l- 98.7%

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

      6. *-commutative 98.7%

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

      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* 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. Add Preprocessing

   5. Taylor expanded in z around 0 85.5%

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

      1. *-commutative 85.5%

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

   7. Simplified 85.5%

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

   if 5.8e-98 < z < 6.4999999999999997e-56

   1. Initial program 79.0%

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

      1. associate-+l- 79.0%

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

      2. *-commutative 79.0%

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

      3. associate-*r* 79.0%

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

      4. *-commutative 79.0%

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

      5. associate-+l- 79.0%

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

      6. *-commutative 79.0%

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

      7. associate-*r* 79.0%

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

      8. *-commutative 79.0%

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

      9. associate-*l* 78.9%

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

      10. associate-*l* 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%

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

   5. Taylor expanded in x around inf 57.8%

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

      1. associate-*r/ 58.0%

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

      2. associate-*r* 58.0%

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

      3. *-commutative 58.0%

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

      4. associate-*r* 57.8%

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

      5. *-commutative 57.8%

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

      6. times-frac 78.1%

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

   7. Simplified 78.1%

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

4. Final simplification 77.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{+41}:\\ \;\;\;\;\frac{\frac{b}{z} - \left(a \cdot t\right) \cdot 4}{c}\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-182}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-98} \lor \neg \left(z \leq 6.5 \cdot 10^{-56}\right):\\ \;\;\;\;\frac{\frac{b}{z} - \left(a \cdot t\right) \cdot 4}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{9 \cdot y}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 89.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{+47} \lor \neg \left(z \leq 2.2 \cdot 10^{+76}\right):\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right) + \left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + \left(x \cdot \left(9 \cdot y\right) - \left(a \cdot t\right) \cdot \left(z \cdot 4\right)\right)}{z \cdot c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= z -5e+47) (not (<= z 2.2e+76)))
   (/ (+ (* -4.0 (* a t)) (+ (* 9.0 (/ (* x y) z)) (/ b z))) c)
   (/ (+ b (- (* x (* 9.0 y)) (* (* a t) (* z 4.0)))) (* z c))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((z <= -5e+47) || !(z <= 2.2e+76)) {
		tmp = ((-4.0 * (a * t)) + ((9.0 * ((x * y) / z)) + (b / z))) / c;
	} else {
		tmp = (b + ((x * (9.0 * y)) - ((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.
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+47)) .or. (.not. (z <= 2.2d+76))) then
        tmp = (((-4.0d0) * (a * t)) + ((9.0d0 * ((x * y) / z)) + (b / z))) / c
    else
        tmp = (b + ((x * (9.0d0 * y)) - ((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;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((z <= -5e+47) || !(z <= 2.2e+76)) {
		tmp = ((-4.0 * (a * t)) + ((9.0 * ((x * y) / z)) + (b / z))) / c;
	} else {
		tmp = (b + ((x * (9.0 * y)) - ((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])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if (z <= -5e+47) or not (z <= 2.2e+76):
		tmp = ((-4.0 * (a * t)) + ((9.0 * ((x * y) / z)) + (b / z))) / c
	else:
		tmp = (b + ((x * (9.0 * y)) - ((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])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((z <= -5e+47) || !(z <= 2.2e+76))
		tmp = Float64(Float64(Float64(-4.0 * Float64(a * t)) + Float64(Float64(9.0 * Float64(Float64(x * y) / z)) + Float64(b / z))) / c);
	else
		tmp = Float64(Float64(b + Float64(Float64(x * Float64(9.0 * y)) - Float64(Float64(a * 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])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((z <= -5e+47) || ~((z <= 2.2e+76)))
		tmp = ((-4.0 * (a * t)) + ((9.0 * ((x * y) / z)) + (b / z))) / c;
	else
		tmp = (b + ((x * (9.0 * y)) - ((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.
code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[z, -5e+47], N[Not[LessEqual[z, 2.2e+76]], $MachinePrecision]], N[(N[(N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision] + N[(N[(9.0 * N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] + N[(b / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], N[(N[(b + N[(N[(x * N[(9.0 * y), $MachinePrecision]), $MachinePrecision] - N[(N[(a * t), $MachinePrecision] * N[(z * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.00000000000000022e47 or 2.2e76 < z

   1. Initial program 61.2%

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

      1. associate-+l- 61.2%

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

      2. *-commutative 61.2%

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

      3. associate-*r* 61.1%

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

      4. *-commutative 61.1%

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

      5. associate-+l- 61.1%

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

      6. *-commutative 61.1%

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

      7. associate-*r* 61.2%

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

      8. *-commutative 61.2%

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

      9. associate-*l* 61.1%

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

      10. associate-*l* 67.2%

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

   3. Simplified 67.2%

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

      1. clear-num 67.2%

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

      2. associate-/r/ 67.2%

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

      3. associate-/r* 67.2%

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

      4. reciprocal-define 67.2%

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

      5. associate-*r* 61.2%

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

      6. cancel-sign-sub-inv 61.2%

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

      7. fma-def 61.2%

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

      8. distribute-lft-neg-in 61.2%

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

      9. *-commutative 61.2%

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

      10. distribute-rgt-neg-in 61.2%

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

      11. *-commutative 61.2%

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

      12. distribute-rgt-neg-in 61.2%

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

      13. distribute-rgt-neg-in 61.2%

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

      14. metadata-eval 61.2%

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

   6. Applied egg-rr 61.2%

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

      1. associate-*l/ 68.5%

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

   8. Applied egg-rr 68.5%

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

   9. Taylor expanded in z around 0 87.2%

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

   if -5.00000000000000022e47 < z < 2.2e76

   1. Initial program 94.5%

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

      1. associate-+l- 94.5%

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

      2. *-commutative 94.5%

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

      3. associate-*r* 95.5%

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

      4. *-commutative 95.5%

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

      5. associate-+l- 95.5%

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

      6. *-commutative 95.5%

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

      7. associate-*r* 94.5%

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

      8. *-commutative 94.5%

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

      9. associate-*l* 94.6%

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

      10. associate-*l* 91.4%

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

   3. Simplified 91.4%

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

4. Final simplification 89.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{+47} \lor \neg \left(z \leq 2.2 \cdot 10^{+76}\right):\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right) + \left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + \left(x \cdot \left(9 \cdot y\right) - \left(a \cdot t\right) \cdot \left(z \cdot 4\right)\right)}{z \cdot c}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 91.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{+42} \lor \neg \left(z \leq 1.45 \cdot 10^{-9}\right):\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right) + \left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(9 \cdot x\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= z -4e+42) (not (<= z 1.45e-9)))
   (/ (+ (* -4.0 (* a t)) (+ (* 9.0 (/ (* x y) z)) (/ b z))) 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);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((z <= -4e+42) || !(z <= 1.45e-9)) {
		tmp = ((-4.0 * (a * t)) + ((9.0 * ((x * y) / z)) + (b / z))) / 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.
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 <= (-4d+42)) .or. (.not. (z <= 1.45d-9))) then
        tmp = (((-4.0d0) * (a * t)) + ((9.0d0 * ((x * y) / z)) + (b / z))) / 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;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((z <= -4e+42) || !(z <= 1.45e-9)) {
		tmp = ((-4.0 * (a * t)) + ((9.0 * ((x * y) / z)) + (b / z))) / 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])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if (z <= -4e+42) or not (z <= 1.45e-9):
		tmp = ((-4.0 * (a * t)) + ((9.0 * ((x * y) / z)) + (b / z))) / 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])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((z <= -4e+42) || !(z <= 1.45e-9))
		tmp = Float64(Float64(Float64(-4.0 * Float64(a * t)) + Float64(Float64(9.0 * Float64(Float64(x * y) / z)) + Float64(b / z))) / 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])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((z <= -4e+42) || ~((z <= 1.45e-9)))
		tmp = ((-4.0 * (a * t)) + ((9.0 * ((x * y) / z)) + (b / z))) / 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.
code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[z, -4e+42], N[Not[LessEqual[z, 1.45e-9]], $MachinePrecision]], N[(N[(N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision] + N[(N[(9.0 * N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] + N[(b / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $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 < -4.00000000000000018e42 or 1.44999999999999996e-9 < z

   1. Initial program 66.4%

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

      1. associate-+l- 66.4%

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

      2. *-commutative 66.4%

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

      3. associate-*r* 66.3%

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

      4. *-commutative 66.3%

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

      5. associate-+l- 66.3%

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

      6. *-commutative 66.3%

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

      7. associate-*r* 66.4%

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

      8. *-commutative 66.4%

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

      9. associate-*l* 66.4%

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

      10. associate-*l* 72.2%

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

   3. Simplified 72.2%

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

      1. clear-num 72.1%

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

      2. associate-/r/ 72.2%

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

      3. associate-/r* 72.2%

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

      4. reciprocal-define 72.2%

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

      5. associate-*r* 66.4%

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

      6. cancel-sign-sub-inv 66.4%

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

      7. fma-def 66.4%

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

      8. distribute-lft-neg-in 66.4%

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

      9. *-commutative 66.4%

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

      10. distribute-rgt-neg-in 66.4%

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

      11. *-commutative 66.4%

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

      12. distribute-rgt-neg-in 66.4%

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

      13. distribute-rgt-neg-in 66.4%

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

      14. metadata-eval 66.4%

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

   6. Applied egg-rr 66.4%

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

      1. associate-*l/ 72.4%

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

   8. Applied egg-rr 72.4%

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

   9. Taylor expanded in z around 0 88.6%

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

   if -4.00000000000000018e42 < z < 1.44999999999999996e-9

   1. Initial program 95.1%

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

4. Final simplification 92.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{+42} \lor \neg \left(z \leq 1.45 \cdot 10^{-9}\right):\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right) + \left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(9 \cdot x\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 72.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{+41}:\\ \;\;\;\;\frac{\frac{b}{z} - \left(a \cdot t\right) \cdot 4}{c}\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-239}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+45}:\\ \;\;\;\;\frac{b - 4 \cdot \left(a \cdot \left(z \cdot t\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{z \cdot c} - 4 \cdot \frac{a}{\frac{c}{t}}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= z -2.1e+41)
   (/ (- (/ b z) (* (* a t) 4.0)) c)
   (if (<= z 1.45e-239)
     (/ (+ b (* 9.0 (* x y))) (* z c))
     (if (<= z 1.5e+45)
       (/ (- b (* 4.0 (* a (* z t)))) (* z c))
       (- (/ b (* z c)) (* 4.0 (/ a (/ c t))))))))

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 <= -2.1e+41) {
		tmp = ((b / z) - ((a * t) * 4.0)) / c;
	} else if (z <= 1.45e-239) {
		tmp = (b + (9.0 * (x * y))) / (z * c);
	} else if (z <= 1.5e+45) {
		tmp = (b - (4.0 * (a * (z * t)))) / (z * c);
	} else {
		tmp = (b / (z * c)) - (4.0 * (a / (c / t)));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (z <= (-2.1d+41)) then
        tmp = ((b / z) - ((a * t) * 4.0d0)) / c
    else if (z <= 1.45d-239) then
        tmp = (b + (9.0d0 * (x * y))) / (z * c)
    else if (z <= 1.5d+45) then
        tmp = (b - (4.0d0 * (a * (z * t)))) / (z * c)
    else
        tmp = (b / (z * c)) - (4.0d0 * (a / (c / t)))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (z <= -2.1e+41) {
		tmp = ((b / z) - ((a * t) * 4.0)) / c;
	} else if (z <= 1.45e-239) {
		tmp = (b + (9.0 * (x * y))) / (z * c);
	} else if (z <= 1.5e+45) {
		tmp = (b - (4.0 * (a * (z * t)))) / (z * c);
	} else {
		tmp = (b / (z * c)) - (4.0 * (a / (c / t)));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if z <= -2.1e+41:
		tmp = ((b / z) - ((a * t) * 4.0)) / c
	elif z <= 1.45e-239:
		tmp = (b + (9.0 * (x * y))) / (z * c)
	elif z <= 1.5e+45:
		tmp = (b - (4.0 * (a * (z * t)))) / (z * c)
	else:
		tmp = (b / (z * c)) - (4.0 * (a / (c / t)))
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (z <= -2.1e+41)
		tmp = Float64(Float64(Float64(b / z) - Float64(Float64(a * t) * 4.0)) / c);
	elseif (z <= 1.45e-239)
		tmp = Float64(Float64(b + Float64(9.0 * Float64(x * y))) / Float64(z * c));
	elseif (z <= 1.5e+45)
		tmp = Float64(Float64(b - Float64(4.0 * Float64(a * Float64(z * t)))) / Float64(z * c));
	else
		tmp = Float64(Float64(b / Float64(z * c)) - Float64(4.0 * Float64(a / Float64(c / t))));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (z <= -2.1e+41)
		tmp = ((b / z) - ((a * t) * 4.0)) / c;
	elseif (z <= 1.45e-239)
		tmp = (b + (9.0 * (x * y))) / (z * c);
	elseif (z <= 1.5e+45)
		tmp = (b - (4.0 * (a * (z * t)))) / (z * c);
	else
		tmp = (b / (z * c)) - (4.0 * (a / (c / t)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[z, -2.1e+41], N[(N[(N[(b / z), $MachinePrecision] - N[(N[(a * t), $MachinePrecision] * 4.0), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[z, 1.45e-239], N[(N[(b + N[(9.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.5e+45], N[(N[(b - N[(4.0 * N[(a * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision] - N[(4.0 * N[(a / N[(c / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.1e41

   1. Initial program 69.0%

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

      1. associate-+l- 69.0%

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

      2. *-commutative 69.0%

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

      3. associate-*r* 68.9%

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

      4. *-commutative 68.9%

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

      5. associate-+l- 68.9%

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

      6. *-commutative 68.9%

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

      7. associate-*r* 69.0%

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

      8. *-commutative 69.0%

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

      9. associate-*l* 68.9%

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

      10. associate-*l* 72.8%

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

   3. Simplified 72.8%

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

   5. Taylor expanded in x around 0 60.2%

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

      1. div-sub 58.3%

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

      2. *-commutative 58.3%

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

      3. *-commutative 58.3%

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

      4. times-frac 56.7%

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

      5. *-commutative 56.7%

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

   7. Applied egg-rr 56.7%

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

      1. expm1-log1p-u 41.0%

         \[\leadsto \frac{b}{z \cdot c} - \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{4}{z} \cdot \frac{a \cdot \left(z \cdot t\right)}{c}\right)\right)} \]

      2. expm1-udef 32.0%

         \[\leadsto \frac{b}{z \cdot c} - \color{blue}{\left(e^{\mathsf{log1p}\left(\frac{4}{z} \cdot \frac{a \cdot \left(z \cdot t\right)}{c}\right)} - 1\right)} \]

      3. associate-*l/ 32.0%

         \[\leadsto \frac{b}{z \cdot c} - \left(e^{\mathsf{log1p}\left(\color{blue}{\frac{4 \cdot \frac{a \cdot \left(z \cdot t\right)}{c}}{z}}\right)} - 1\right) \]

      4. *-un-lft-identity 32.0%

         \[\leadsto \frac{b}{z \cdot c} - \left(e^{\mathsf{log1p}\left(\frac{4 \cdot \frac{a \cdot \left(z \cdot t\right)}{c}}{\color{blue}{1 \cdot z}}\right)} - 1\right) \]

      5. times-frac 32.0%

         \[\leadsto \frac{b}{z \cdot c} - \left(e^{\mathsf{log1p}\left(\color{blue}{\frac{4}{1} \cdot \frac{\frac{a \cdot \left(z \cdot t\right)}{c}}{z}}\right)} - 1\right) \]

      6. metadata-eval 32.0%

         \[\leadsto \frac{b}{z \cdot c} - \left(e^{\mathsf{log1p}\left(\color{blue}{4} \cdot \frac{\frac{a \cdot \left(z \cdot t\right)}{c}}{z}\right)} - 1\right) \]

      7. associate-/l* 35.1%

         \[\leadsto \frac{b}{z \cdot c} - \left(e^{\mathsf{log1p}\left(4 \cdot \frac{\color{blue}{\frac{a}{\frac{c}{z \cdot t}}}}{z}\right)} - 1\right) \]

   9. Applied egg-rr 35.1%

      \[\leadsto \frac{b}{z \cdot c} - \color{blue}{\left(e^{\mathsf{log1p}\left(4 \cdot \frac{\frac{a}{\frac{c}{z \cdot t}}}{z}\right)} - 1\right)} \]
   10. Step-by-step derivation

       1. expm1-def 44.2%

          \[\leadsto \frac{b}{z \cdot c} - \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(4 \cdot \frac{\frac{a}{\frac{c}{z \cdot t}}}{z}\right)\right)} \]

       2. expm1-log1p 60.3%

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

       3. associate-*r/ 60.3%

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

       4. *-commutative 60.3%

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

       5. associate-*r/ 60.2%

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

       6. associate-/r/ 62.0%

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

       7. *-commutative 62.0%

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

       8. associate-*l* 67.1%

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

   11. Simplified 67.1%

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

   12. Taylor expanded in c around 0 72.5%

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

   if -2.1e41 < z < 1.4500000000000001e-239

   1. Initial program 96.5%

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

      1. associate-+l- 96.5%

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

      2. *-commutative 96.5%

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

      3. associate-*r* 98.6%

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

      4. *-commutative 98.6%

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

      5. associate-+l- 98.6%

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

      6. *-commutative 98.6%

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

      7. associate-*r* 96.5%

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

      8. *-commutative 96.5%

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

      9. associate-*l* 96.5%

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

      10. associate-*l* 95.2%

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

   3. Simplified 95.2%

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

   5. Taylor expanded in z around 0 87.1%

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

      1. *-commutative 87.1%

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

   7. Simplified 87.1%

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

   if 1.4500000000000001e-239 < z < 1.50000000000000005e45

   1. Initial program 93.0%

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

      1. associate-+l- 93.0%

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

      2. *-commutative 93.0%

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

      3. associate-*r* 92.7%

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

      4. *-commutative 92.7%

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

      5. associate-+l- 92.7%

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

      6. *-commutative 92.7%

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

      7. associate-*r* 93.0%

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

      8. *-commutative 93.0%

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

      9. associate-*l* 93.0%

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

      10. associate-*l* 87.4%

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

   3. Simplified 87.4%

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

   5. Taylor expanded in x around 0 72.1%

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

   if 1.50000000000000005e45 < z

   1. Initial program 55.8%

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

      1. associate-+l- 55.8%

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

      2. *-commutative 55.8%

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

      3. associate-*r* 55.7%

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

      4. *-commutative 55.7%

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

      5. associate-+l- 55.7%

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

      6. *-commutative 55.7%

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

      7. associate-*r* 55.8%

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

      8. *-commutative 55.8%

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

      9. associate-*l* 55.8%

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

      10. associate-*l* 63.4%

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

   3. Simplified 63.4%

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

   5. Taylor expanded in x around 0 44.4%

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

      1. div-sub 44.4%

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

      2. *-commutative 44.4%

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

      3. *-commutative 44.4%

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

      4. times-frac 47.2%

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

      5. *-commutative 47.2%

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

   7. Applied egg-rr 47.2%

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

   8. Taylor expanded in z around 0 73.5%

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

      1. *-commutative 73.5%

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

      2. associate-/l* 78.9%

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

   10. Simplified 78.9%

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

4. Final simplification 78.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{+41}:\\ \;\;\;\;\frac{\frac{b}{z} - \left(a \cdot t\right) \cdot 4}{c}\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-239}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+45}:\\ \;\;\;\;\frac{b - 4 \cdot \left(a \cdot \left(z \cdot t\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{z \cdot c} - 4 \cdot \frac{a}{\frac{c}{t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 65.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -5.4 \cdot 10^{+218}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{9 \cdot y}{c}\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{+50}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{+150}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= z -5.4e+218)
   (* (/ x z) (/ (* 9.0 y) c))
   (if (<= z -5.5e+50)
     (* -4.0 (/ a (/ c t)))
     (if (<= z 7.8e+150)
       (/ (+ b (* 9.0 (* x y))) (* z c))
       (* -4.0 (* t (/ a c)))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (z <= -5.4e+218) {
		tmp = (x / z) * ((9.0 * y) / c);
	} else if (z <= -5.5e+50) {
		tmp = -4.0 * (a / (c / t));
	} else if (z <= 7.8e+150) {
		tmp = (b + (9.0 * (x * y))) / (z * c);
	} else {
		tmp = -4.0 * (t * (a / c));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (z <= (-5.4d+218)) then
        tmp = (x / z) * ((9.0d0 * y) / c)
    else if (z <= (-5.5d+50)) then
        tmp = (-4.0d0) * (a / (c / t))
    else if (z <= 7.8d+150) then
        tmp = (b + (9.0d0 * (x * y))) / (z * c)
    else
        tmp = (-4.0d0) * (t * (a / c))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (z <= -5.4e+218) {
		tmp = (x / z) * ((9.0 * y) / c);
	} else if (z <= -5.5e+50) {
		tmp = -4.0 * (a / (c / t));
	} else if (z <= 7.8e+150) {
		tmp = (b + (9.0 * (x * y))) / (z * c);
	} else {
		tmp = -4.0 * (t * (a / c));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if z <= -5.4e+218:
		tmp = (x / z) * ((9.0 * y) / c)
	elif z <= -5.5e+50:
		tmp = -4.0 * (a / (c / t))
	elif z <= 7.8e+150:
		tmp = (b + (9.0 * (x * y))) / (z * c)
	else:
		tmp = -4.0 * (t * (a / c))
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (z <= -5.4e+218)
		tmp = Float64(Float64(x / z) * Float64(Float64(9.0 * y) / c));
	elseif (z <= -5.5e+50)
		tmp = Float64(-4.0 * Float64(a / Float64(c / t)));
	elseif (z <= 7.8e+150)
		tmp = Float64(Float64(b + Float64(9.0 * Float64(x * y))) / Float64(z * c));
	else
		tmp = Float64(-4.0 * Float64(t * Float64(a / c)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (z <= -5.4e+218)
		tmp = (x / z) * ((9.0 * y) / c);
	elseif (z <= -5.5e+50)
		tmp = -4.0 * (a / (c / t));
	elseif (z <= 7.8e+150)
		tmp = (b + (9.0 * (x * y))) / (z * c);
	else
		tmp = -4.0 * (t * (a / c));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[z, -5.4e+218], N[(N[(x / z), $MachinePrecision] * N[(N[(9.0 * y), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -5.5e+50], N[(-4.0 * N[(a / N[(c / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.8e+150], N[(N[(b + N[(9.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -5.40000000000000025e218

   1. Initial program 46.3%

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

      1. associate-+l- 46.3%

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

      2. *-commutative 46.3%

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

      3. associate-*r* 51.6%

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

      4. *-commutative 51.6%

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

      5. associate-+l- 51.6%

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

      6. *-commutative 51.6%

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

      7. associate-*r* 46.3%

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

      8. *-commutative 46.3%

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

      9. associate-*l* 46.3%

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

      10. associate-*l* 52.3%

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

   3. Simplified 52.3%

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

   5. Taylor expanded in x around inf 25.5%

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

      1. associate-*r/ 25.4%

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

      2. associate-*r* 25.4%

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

      3. *-commutative 25.4%

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

      4. associate-*r* 25.4%

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

      5. *-commutative 25.4%

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

      6. times-frac 60.2%

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

   7. Simplified 60.2%

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

   if -5.40000000000000025e218 < z < -5.4999999999999998e50

   1. Initial program 82.3%

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

      1. associate-+l- 82.3%

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

      2. *-commutative 82.3%

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

      3. associate-*r* 79.4%

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

      4. *-commutative 79.4%

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

      5. associate-+l- 79.4%

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

      6. *-commutative 79.4%

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

      7. associate-*r* 82.3%

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

      8. *-commutative 82.3%

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

      9. associate-*l* 82.2%

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

      10. associate-*l* 85.2%

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

   3. Simplified 85.2%

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

   5. Taylor expanded in z around inf 67.8%

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

      1. *-commutative 67.8%

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

      2. associate-/l* 62.2%

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

   7. Simplified 62.2%

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

   if -5.4999999999999998e50 < z < 7.79999999999999981e150

   1. Initial program 91.8%

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

      1. associate-+l- 91.8%

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

      2. *-commutative 91.8%

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

      3. associate-*r* 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* 91.8%

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

      8. *-commutative 91.8%

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

      9. associate-*l* 91.8%

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

      10. associate-*l* 90.1%

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

   3. Simplified 90.1%

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

   5. Taylor expanded in z around 0 75.3%

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

      1. *-commutative 75.3%

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

   7. Simplified 75.3%

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

   if 7.79999999999999981e150 < z

   1. Initial program 44.2%

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

      1. associate-+l- 44.2%

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

      2. *-commutative 44.2%

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

      3. associate-*r* 40.6%

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

      4. *-commutative 40.6%

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

      5. associate-+l- 40.6%

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

      6. *-commutative 40.6%

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

      7. associate-*r* 44.2%

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

      8. *-commutative 44.2%

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

      9. associate-*l* 44.2%

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

      10. associate-*l* 50.6%

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

   3. Simplified 50.6%

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

   5. Taylor expanded in z around inf 71.3%

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

      1. *-commutative 71.3%

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

      2. associate-/l* 77.3%

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

      3. associate-/r/ 70.9%

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

   7. Simplified 70.9%

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

4. Final simplification 72.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.4 \cdot 10^{+218}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{9 \cdot y}{c}\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{+50}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{+150}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 47.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -360000000:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;t \leq -9 \cdot 10^{-199}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;t \leq 8 \cdot 10^{-158}:\\ \;\;\;\;9 \cdot \frac{x \cdot y}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{a \cdot t}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= t -360000000.0)
   (* -4.0 (* t (/ a c)))
   (if (<= t -9e-199)
     (/ b (* z c))
     (if (<= t 8e-158) (* 9.0 (/ (* x y) (* z c))) (* -4.0 (/ (* a t) c))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (t <= -360000000.0) {
		tmp = -4.0 * (t * (a / c));
	} else if (t <= -9e-199) {
		tmp = b / (z * c);
	} else if (t <= 8e-158) {
		tmp = 9.0 * ((x * y) / (z * c));
	} else {
		tmp = -4.0 * ((a * t) / c);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (t <= (-360000000.0d0)) then
        tmp = (-4.0d0) * (t * (a / c))
    else if (t <= (-9d-199)) then
        tmp = b / (z * c)
    else if (t <= 8d-158) then
        tmp = 9.0d0 * ((x * y) / (z * c))
    else
        tmp = (-4.0d0) * ((a * t) / c)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (t <= -360000000.0) {
		tmp = -4.0 * (t * (a / c));
	} else if (t <= -9e-199) {
		tmp = b / (z * c);
	} else if (t <= 8e-158) {
		tmp = 9.0 * ((x * y) / (z * c));
	} else {
		tmp = -4.0 * ((a * t) / c);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if t <= -360000000.0:
		tmp = -4.0 * (t * (a / c))
	elif t <= -9e-199:
		tmp = b / (z * c)
	elif t <= 8e-158:
		tmp = 9.0 * ((x * y) / (z * c))
	else:
		tmp = -4.0 * ((a * t) / c)
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (t <= -360000000.0)
		tmp = Float64(-4.0 * Float64(t * Float64(a / c)));
	elseif (t <= -9e-199)
		tmp = Float64(b / Float64(z * c));
	elseif (t <= 8e-158)
		tmp = Float64(9.0 * Float64(Float64(x * y) / Float64(z * c)));
	else
		tmp = Float64(-4.0 * Float64(Float64(a * t) / c));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (t <= -360000000.0)
		tmp = -4.0 * (t * (a / c));
	elseif (t <= -9e-199)
		tmp = b / (z * c);
	elseif (t <= 8e-158)
		tmp = 9.0 * ((x * y) / (z * c));
	else
		tmp = -4.0 * ((a * t) / c);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[t, -360000000.0], N[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -9e-199], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 8e-158], N[(9.0 * N[(N[(x * y), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-4.0 * N[(N[(a * t), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -3.6e8

   1. Initial program 81.1%

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

      1. associate-+l- 81.1%

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

      2. *-commutative 81.1%

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

      3. associate-*r* 84.1%

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

      4. *-commutative 84.1%

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

      5. associate-+l- 84.1%

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

      6. *-commutative 84.1%

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

      7. associate-*r* 81.1%

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

      8. *-commutative 81.1%

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

      9. associate-*l* 81.1%

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

      10. associate-*l* 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%

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

   5. Taylor expanded in z around inf 48.5%

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

      1. *-commutative 48.5%

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

      2. associate-/l* 56.7%

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

      3. associate-/r/ 61.9%

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

   7. Simplified 61.9%

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

   if -3.6e8 < t < -8.99999999999999995e-199

   1. Initial program 91.9%

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

      1. associate-+l- 91.9%

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

      2. *-commutative 91.9%

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

      3. associate-*r* 90.0%

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

      4. *-commutative 90.0%

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

      5. associate-+l- 90.0%

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

      6. *-commutative 90.0%

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

      7. associate-*r* 91.9%

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

      8. *-commutative 91.9%

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

      9. associate-*l* 91.9%

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

      10. associate-*l* 92.0%

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

   3. Simplified 92.0%

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

   5. Taylor expanded in b around inf 58.5%

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

      1. *-commutative 58.5%

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

   7. Simplified 58.5%

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

   if -8.99999999999999995e-199 < t < 8.00000000000000052e-158

   1. Initial program 87.8%

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

      1. associate-+l- 87.8%

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

      2. *-commutative 87.8%

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

      3. associate-*r* 77.0%

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

      4. *-commutative 77.0%

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

      5. associate-+l- 77.0%

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

      6. *-commutative 77.0%

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

      7. associate-*r* 87.8%

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

      8. *-commutative 87.8%

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

      9. associate-*l* 87.7%

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

      10. associate-*l* 87.7%

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

   3. Simplified 87.7%

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

   5. Taylor expanded in x around inf 48.1%

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

   if 8.00000000000000052e-158 < t

   1. Initial program 73.4%

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

      1. associate-+l- 73.4%

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

      2. *-commutative 73.4%

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

      3. associate-*r* 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* 73.4%

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

      8. *-commutative 73.4%

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

      9. associate-*l* 73.4%

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

      10. associate-*l* 78.4%

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

   3. Simplified 78.4%

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

   5. Taylor expanded in z around inf 49.1%

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

4. Final simplification 53.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -360000000:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;t \leq -9 \cdot 10^{-199}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;t \leq 8 \cdot 10^{-158}:\\ \;\;\;\;9 \cdot \frac{x \cdot y}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{a \cdot t}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 72.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{+43}:\\ \;\;\;\;\frac{\frac{b}{z} - \left(a \cdot t\right) \cdot 4}{c}\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-211}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{z \cdot c} + -4 \cdot \frac{a \cdot t}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= z -1.3e+43)
   (/ (- (/ b z) (* (* a t) 4.0)) c)
   (if (<= z 5.2e-211)
     (/ (+ b (* 9.0 (* x y))) (* z c))
     (+ (/ b (* z c)) (* -4.0 (/ (* a t) c))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (z <= -1.3e+43) {
		tmp = ((b / z) - ((a * t) * 4.0)) / c;
	} else if (z <= 5.2e-211) {
		tmp = (b + (9.0 * (x * y))) / (z * c);
	} else {
		tmp = (b / (z * c)) + (-4.0 * ((a * t) / c));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (z <= (-1.3d+43)) then
        tmp = ((b / z) - ((a * t) * 4.0d0)) / c
    else if (z <= 5.2d-211) then
        tmp = (b + (9.0d0 * (x * y))) / (z * c)
    else
        tmp = (b / (z * c)) + ((-4.0d0) * ((a * t) / c))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (z <= -1.3e+43) {
		tmp = ((b / z) - ((a * t) * 4.0)) / c;
	} else if (z <= 5.2e-211) {
		tmp = (b + (9.0 * (x * y))) / (z * c);
	} else {
		tmp = (b / (z * c)) + (-4.0 * ((a * t) / c));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if z <= -1.3e+43:
		tmp = ((b / z) - ((a * t) * 4.0)) / c
	elif z <= 5.2e-211:
		tmp = (b + (9.0 * (x * y))) / (z * c)
	else:
		tmp = (b / (z * c)) + (-4.0 * ((a * t) / c))
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (z <= -1.3e+43)
		tmp = Float64(Float64(Float64(b / z) - Float64(Float64(a * t) * 4.0)) / c);
	elseif (z <= 5.2e-211)
		tmp = Float64(Float64(b + Float64(9.0 * Float64(x * y))) / Float64(z * c));
	else
		tmp = Float64(Float64(b / Float64(z * c)) + Float64(-4.0 * Float64(Float64(a * t) / c)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (z <= -1.3e+43)
		tmp = ((b / z) - ((a * t) * 4.0)) / c;
	elseif (z <= 5.2e-211)
		tmp = (b + (9.0 * (x * y))) / (z * c);
	else
		tmp = (b / (z * c)) + (-4.0 * ((a * t) / c));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[z, -1.3e+43], N[(N[(N[(b / z), $MachinePrecision] - N[(N[(a * t), $MachinePrecision] * 4.0), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[z, 5.2e-211], N[(N[(b + N[(9.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision] + N[(-4.0 * N[(N[(a * t), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.3000000000000001e43

   1. Initial program 69.0%

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

      1. associate-+l- 69.0%

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

      2. *-commutative 69.0%

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

      3. associate-*r* 68.9%

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

      4. *-commutative 68.9%

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

      5. associate-+l- 68.9%

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

      6. *-commutative 68.9%

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

      7. associate-*r* 69.0%

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

      8. *-commutative 69.0%

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

      9. associate-*l* 68.9%

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

      10. associate-*l* 72.8%

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

   3. Simplified 72.8%

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

   5. Taylor expanded in x around 0 60.2%

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

      1. div-sub 58.3%

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

      2. *-commutative 58.3%

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

      3. *-commutative 58.3%

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

      4. times-frac 56.7%

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

      5. *-commutative 56.7%

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

   7. Applied egg-rr 56.7%

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

      1. expm1-log1p-u 41.0%

         \[\leadsto \frac{b}{z \cdot c} - \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{4}{z} \cdot \frac{a \cdot \left(z \cdot t\right)}{c}\right)\right)} \]

      2. expm1-udef 32.0%

         \[\leadsto \frac{b}{z \cdot c} - \color{blue}{\left(e^{\mathsf{log1p}\left(\frac{4}{z} \cdot \frac{a \cdot \left(z \cdot t\right)}{c}\right)} - 1\right)} \]

      3. associate-*l/ 32.0%

         \[\leadsto \frac{b}{z \cdot c} - \left(e^{\mathsf{log1p}\left(\color{blue}{\frac{4 \cdot \frac{a \cdot \left(z \cdot t\right)}{c}}{z}}\right)} - 1\right) \]

      4. *-un-lft-identity 32.0%

         \[\leadsto \frac{b}{z \cdot c} - \left(e^{\mathsf{log1p}\left(\frac{4 \cdot \frac{a \cdot \left(z \cdot t\right)}{c}}{\color{blue}{1 \cdot z}}\right)} - 1\right) \]

      5. times-frac 32.0%

         \[\leadsto \frac{b}{z \cdot c} - \left(e^{\mathsf{log1p}\left(\color{blue}{\frac{4}{1} \cdot \frac{\frac{a \cdot \left(z \cdot t\right)}{c}}{z}}\right)} - 1\right) \]

      6. metadata-eval 32.0%

         \[\leadsto \frac{b}{z \cdot c} - \left(e^{\mathsf{log1p}\left(\color{blue}{4} \cdot \frac{\frac{a \cdot \left(z \cdot t\right)}{c}}{z}\right)} - 1\right) \]

      7. associate-/l* 35.1%

         \[\leadsto \frac{b}{z \cdot c} - \left(e^{\mathsf{log1p}\left(4 \cdot \frac{\color{blue}{\frac{a}{\frac{c}{z \cdot t}}}}{z}\right)} - 1\right) \]

   9. Applied egg-rr 35.1%

      \[\leadsto \frac{b}{z \cdot c} - \color{blue}{\left(e^{\mathsf{log1p}\left(4 \cdot \frac{\frac{a}{\frac{c}{z \cdot t}}}{z}\right)} - 1\right)} \]
   10. Step-by-step derivation

       1. expm1-def 44.2%

          \[\leadsto \frac{b}{z \cdot c} - \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(4 \cdot \frac{\frac{a}{\frac{c}{z \cdot t}}}{z}\right)\right)} \]

       2. expm1-log1p 60.3%

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

       3. associate-*r/ 60.3%

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

       4. *-commutative 60.3%

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

       5. associate-*r/ 60.2%

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

       6. associate-/r/ 62.0%

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

       7. *-commutative 62.0%

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

       8. associate-*l* 67.1%

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

   11. Simplified 67.1%

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

   12. Taylor expanded in c around 0 72.5%

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

   if -1.3000000000000001e43 < z < 5.2e-211

   1. Initial program 96.6%

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

      1. associate-+l- 96.6%

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

      2. *-commutative 96.6%

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

      3. associate-*r* 98.7%

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

      4. *-commutative 98.7%

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

      5. associate-+l- 98.7%

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

      6. *-commutative 98.7%

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

      7. associate-*r* 96.6%

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

      8. *-commutative 96.6%

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

      9. associate-*l* 96.6%

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

      10. associate-*l* 94.3%

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

   3. Simplified 94.3%

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

   5. Taylor expanded in z around 0 86.6%

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

      1. *-commutative 86.6%

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

   7. Simplified 86.6%

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

   if 5.2e-211 < z

   1. Initial program 76.1%

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

      1. associate-+l- 76.1%

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

      2. *-commutative 76.1%

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

      3. associate-*r* 75.9%

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

      4. *-commutative 75.9%

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

      5. associate-+l- 75.9%

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

      6. *-commutative 75.9%

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

      7. associate-*r* 76.1%

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

      8. *-commutative 76.1%

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

      9. associate-*l* 76.1%

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

      10. associate-*l* 77.1%

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

   3. Simplified 77.1%

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

   5. Taylor expanded in x around 0 58.7%

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

   6. Taylor expanded in b around 0 69.9%

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

4. Final simplification 76.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{+43}:\\ \;\;\;\;\frac{\frac{b}{z} - \left(a \cdot t\right) \cdot 4}{c}\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-211}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{z \cdot c} + -4 \cdot \frac{a \cdot t}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 47.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;b \leq -8.5 \cdot 10^{+212} \lor \neg \left(b \leq 112000000\right):\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{a \cdot t}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= b -8.5e+212) (not (<= b 112000000.0)))
   (/ b (* z c))
   (* -4.0 (/ (* a t) c))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((b <= -8.5e+212) || !(b <= 112000000.0)) {
		tmp = b / (z * c);
	} else {
		tmp = -4.0 * ((a * t) / c);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if ((b <= (-8.5d+212)) .or. (.not. (b <= 112000000.0d0))) then
        tmp = b / (z * c)
    else
        tmp = (-4.0d0) * ((a * t) / c)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((b <= -8.5e+212) || !(b <= 112000000.0)) {
		tmp = b / (z * c);
	} else {
		tmp = -4.0 * ((a * t) / c);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if (b <= -8.5e+212) or not (b <= 112000000.0):
		tmp = b / (z * c)
	else:
		tmp = -4.0 * ((a * t) / c)
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((b <= -8.5e+212) || !(b <= 112000000.0))
		tmp = Float64(b / Float64(z * c));
	else
		tmp = Float64(-4.0 * Float64(Float64(a * t) / c));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((b <= -8.5e+212) || ~((b <= 112000000.0)))
		tmp = b / (z * c);
	else
		tmp = -4.0 * ((a * t) / c);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[b, -8.5e+212], N[Not[LessEqual[b, 112000000.0]], $MachinePrecision]], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(-4.0 * N[(N[(a * t), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -8.49999999999999979e212 or 1.12e8 < b

   1. Initial program 89.6%

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

      1. associate-+l- 89.6%

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

      2. *-commutative 89.6%

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

      3. associate-*r* 91.0%

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

      4. *-commutative 91.0%

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

      5. associate-+l- 91.0%

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

      6. *-commutative 91.0%

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

      7. associate-*r* 89.6%

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

      8. *-commutative 89.6%

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

      9. associate-*l* 89.5%

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

      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%

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

   5. Taylor expanded in b around inf 73.7%

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

      1. *-commutative 73.7%

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

   7. Simplified 73.7%

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

   if -8.49999999999999979e212 < b < 1.12e8

   1. Initial program 79.0%

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

      1. associate-+l- 79.0%

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

      2. *-commutative 79.0%

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

      3. associate-*r* 79.3%

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

      4. *-commutative 79.3%

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

      5. associate-+l- 79.3%

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

      6. *-commutative 79.3%

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

      7. associate-*r* 79.0%

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

      8. *-commutative 79.0%

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

      9. associate-*l* 79.0%

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

      10. associate-*l* 79.6%

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

   3. Simplified 79.6%

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

   5. Taylor expanded in z around inf 48.9%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 55.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -8.5 \cdot 10^{+212} \lor \neg \left(b \leq 112000000\right):\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{a \cdot t}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 47.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -13500000:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{-170}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{a \cdot t}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= t -13500000.0)
   (* -4.0 (* t (/ a c)))
   (if (<= t 9.5e-170) (/ b (* z c)) (* -4.0 (/ (* a t) c)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (t <= -13500000.0) {
		tmp = -4.0 * (t * (a / c));
	} else if (t <= 9.5e-170) {
		tmp = b / (z * c);
	} else {
		tmp = -4.0 * ((a * t) / c);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (t <= (-13500000.0d0)) then
        tmp = (-4.0d0) * (t * (a / c))
    else if (t <= 9.5d-170) then
        tmp = b / (z * c)
    else
        tmp = (-4.0d0) * ((a * t) / c)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (t <= -13500000.0) {
		tmp = -4.0 * (t * (a / c));
	} else if (t <= 9.5e-170) {
		tmp = b / (z * c);
	} else {
		tmp = -4.0 * ((a * t) / c);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if t <= -13500000.0:
		tmp = -4.0 * (t * (a / c))
	elif t <= 9.5e-170:
		tmp = b / (z * c)
	else:
		tmp = -4.0 * ((a * t) / c)
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (t <= -13500000.0)
		tmp = Float64(-4.0 * Float64(t * Float64(a / c)));
	elseif (t <= 9.5e-170)
		tmp = Float64(b / Float64(z * c));
	else
		tmp = Float64(-4.0 * Float64(Float64(a * t) / c));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (t <= -13500000.0)
		tmp = -4.0 * (t * (a / c));
	elseif (t <= 9.5e-170)
		tmp = b / (z * c);
	else
		tmp = -4.0 * ((a * t) / c);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[t, -13500000.0], N[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 9.5e-170], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(-4.0 * N[(N[(a * t), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.35e7

   1. Initial program 81.1%

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

      1. associate-+l- 81.1%

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

      2. *-commutative 81.1%

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

      3. associate-*r* 84.1%

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

      4. *-commutative 84.1%

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

      5. associate-+l- 84.1%

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

      6. *-commutative 84.1%

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

      7. associate-*r* 81.1%

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

      8. *-commutative 81.1%

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

      9. associate-*l* 81.1%

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

      10. associate-*l* 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%

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

   5. Taylor expanded in z around inf 48.5%

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

      1. *-commutative 48.5%

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

      2. associate-/l* 56.7%

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

      3. associate-/r/ 61.9%

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

   7. Simplified 61.9%

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

   if -1.35e7 < t < 9.5000000000000001e-170

   1. Initial program 90.5%

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

      1. associate-+l- 90.5%

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

      2. *-commutative 90.5%

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

      3. associate-*r* 83.8%

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

      4. *-commutative 83.8%

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

      5. associate-+l- 83.8%

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

      6. *-commutative 83.8%

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

      7. associate-*r* 90.5%

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

      8. *-commutative 90.5%

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

      9. associate-*l* 90.4%

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

      10. associate-*l* 90.5%

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

   3. Simplified 90.5%

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

   5. Taylor expanded in b around inf 55.5%

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

      1. *-commutative 55.5%

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

   7. Simplified 55.5%

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

   if 9.5000000000000001e-170 < t

   1. Initial program 72.9%

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

      1. associate-+l- 72.9%

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

      2. *-commutative 72.9%

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

      3. associate-*r* 79.9%

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

      4. *-commutative 79.9%

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

      5. associate-+l- 79.9%

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

      6. *-commutative 79.9%

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

      7. associate-*r* 72.9%

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

      8. *-commutative 72.9%

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

      9. associate-*l* 72.9%

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

      10. associate-*l* 77.8%

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

   3. Simplified 77.8%

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

   5. Taylor expanded in z around inf 49.8%

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

4. Final simplification 54.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -13500000:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{-170}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{a \cdot t}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 35.1% accurate, 3.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 81.8%

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

   1. associate-+l- 81.8%

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

   2. *-commutative 81.8%

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

   3. associate-*r* 82.4%

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

   4. *-commutative 82.4%

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

   5. associate-+l- 82.4%

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

   6. *-commutative 82.4%

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

   7. associate-*r* 81.8%

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

   8. *-commutative 81.8%

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

   9. associate-*l* 81.8%

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

   10. associate-*l* 82.2%

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

3. Simplified 82.2%

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

5. Taylor expanded in b around inf 39.7%

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

   1. *-commutative 39.7%

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

7. Simplified 39.7%

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

8. Final simplification 39.7%

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

Developer target: 81.1% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024024 
(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)))