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

Percentage Accurate: 79.0% → 86.7%

Time: 20.3s

Alternatives: 18

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: 79.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 86.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -8.8 \cdot 10^{-76}:\\ \;\;\;\;\frac{x \cdot \left(\frac{\mathsf{fma}\left(-4, a \cdot t, \frac{b}{z}\right)}{x} - \frac{y \cdot -9}{z}\right)}{c}\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-68}:\\ \;\;\;\;\frac{\mathsf{fma}\left(9, \frac{y \cdot x}{c}, \frac{\mathsf{fma}\left(a, -4 \cdot \left(z \cdot t\right), b\right)}{c}\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a, t \cdot \frac{-4}{c}, \mathsf{fma}\left(x, \frac{y \cdot 9}{z \cdot c}, \frac{b}{z \cdot c}\right)\right)\\ \end{array} \end{array} \]

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 -8.8e-76)
   (/ (* x (- (/ (fma -4.0 (* a t) (/ b z)) x) (/ (* y -9.0) z))) c)
   (if (<= z 7.5e-68)
     (/ (fma 9.0 (/ (* y x) c) (/ (fma a (* -4.0 (* z t)) b) c)) z)
     (fma a (* t (/ -4.0 c)) (fma x (/ (* y 9.0) (* z c)) (/ b (* z c)))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (z <= -8.8e-76) {
		tmp = (x * ((fma(-4.0, (a * t), (b / z)) / x) - ((y * -9.0) / z))) / c;
	} else if (z <= 7.5e-68) {
		tmp = fma(9.0, ((y * x) / c), (fma(a, (-4.0 * (z * t)), b) / c)) / z;
	} else {
		tmp = fma(a, (t * (-4.0 / c)), fma(x, ((y * 9.0) / (z * c)), (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 <= -8.8e-76)
		tmp = Float64(Float64(x * Float64(Float64(fma(-4.0, Float64(a * t), Float64(b / z)) / x) - Float64(Float64(y * -9.0) / z))) / c);
	elseif (z <= 7.5e-68)
		tmp = Float64(fma(9.0, Float64(Float64(y * x) / c), Float64(fma(a, Float64(-4.0 * Float64(z * t)), b) / c)) / z);
	else
		tmp = fma(a, Float64(t * Float64(-4.0 / c)), fma(x, Float64(Float64(y * 9.0) / Float64(z * c)), 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, -8.8e-76], N[(N[(x * N[(N[(N[(-4.0 * N[(a * t), $MachinePrecision] + N[(b / z), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision] - N[(N[(y * -9.0), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[z, 7.5e-68], N[(N[(9.0 * N[(N[(y * x), $MachinePrecision] / c), $MachinePrecision] + N[(N[(a * N[(-4.0 * N[(z * t), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], N[(a * N[(t * N[(-4.0 / c), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(y * 9.0), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision] + N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.79999999999999997e-76

   1. Initial program 66.5%

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

      1. associate-/r* N/A

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

      2. /-lowering-/.f64 N/A

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

   4. Applied egg-rr 83.3%

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

   5. Taylor expanded in x around -inf

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

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

      3. *-lowering-*.f64 N/A

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

      4. mul-1-neg N/A

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

      5. unsub-neg N/A

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

      6. --lowering--.f64 N/A

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

      7. associate-*r/ N/A

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

      8. /-lowering-/.f64 N/A

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

      9. *-commutative N/A

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

      10. *-lowering-*.f64 N/A

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

      11. /-lowering-/.f64 N/A

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

      12. accelerator-lowering-fma.f64 N/A

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

      13. *-lowering-*.f64 N/A

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

      14. /-lowering-/.f64 N/A

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

      15. mul-1-neg N/A

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

      16. neg-sub0 N/A

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

      17. --lowering--.f64 86.1

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

   7. Simplified 86.1%

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

   if -8.79999999999999997e-76 < z < 7.50000000000000081e-68

   1. Initial program 97.7%

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

   3. Taylor expanded in z around 0

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

      1. /-lowering-/.f64 N/A

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

   5. Simplified 98.9%

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

   if 7.50000000000000081e-68 < z

   1. Initial program 66.3%

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

   3. Taylor expanded in x around 0

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

      1. cancel-sign-sub-inv N/A

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. associate-/l* N/A

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

      6. associate-*r* N/A

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

      7. *-commutative N/A

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

      8. accelerator-lowering-fma.f64 N/A

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

      9. *-commutative N/A

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

      10. associate-*l/ N/A

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

      11. associate-/l* N/A

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

      12. *-lowering-*.f64 N/A

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

      13. /-lowering-/.f64 N/A

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

      14. *-commutative N/A

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

      15. associate-/l* N/A

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

      16. associate-*l* N/A

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

      17. *-commutative N/A

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

   5. Simplified 92.8%

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

4. Final simplification 93.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.8 \cdot 10^{-76}:\\ \;\;\;\;\frac{x \cdot \left(\frac{\mathsf{fma}\left(-4, a \cdot t, \frac{b}{z}\right)}{x} - \frac{y \cdot -9}{z}\right)}{c}\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-68}:\\ \;\;\;\;\frac{\mathsf{fma}\left(9, \frac{y \cdot x}{c}, \frac{\mathsf{fma}\left(a, -4 \cdot \left(z \cdot t\right), b\right)}{c}\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a, t \cdot \frac{-4}{c}, \mathsf{fma}\left(x, \frac{y \cdot 9}{z \cdot c}, \frac{b}{z \cdot c}\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 87.1% accurate, 0.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c}\\ t_2 := \mathsf{fma}\left(a \cdot t, z \cdot -4, b\right)\\ \mathbf{if}\;t\_1 \leq -4 \cdot 10^{+81}:\\ \;\;\;\;\frac{\mathsf{fma}\left(a \cdot \left(z \cdot -4\right), t, \mathsf{fma}\left(x, y \cdot 9, b\right)\right)}{z \cdot c}\\ \mathbf{elif}\;t\_1 \leq 10^{+83}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(x, y \cdot 9, t\_2\right)}{c}}{z}\\ \mathbf{elif}\;t\_1 \leq \infty:\\ \;\;\;\;\frac{\mathsf{fma}\left(x \cdot 9, y, t\_2\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-4, a \cdot \frac{t}{c}, \frac{9 \cdot \left(y \cdot x\right)}{z \cdot c}\right)\\ \end{array} \end{array} \]

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
 (let* ((t_1 (/ (+ b (- (* y (* x 9.0)) (* a (* t (* z 4.0))))) (* z c)))
        (t_2 (fma (* a t) (* z -4.0) b)))
   (if (<= t_1 -4e+81)
     (/ (fma (* a (* z -4.0)) t (fma x (* y 9.0) b)) (* z c))
     (if (<= t_1 1e+83)
       (/ (/ (fma x (* y 9.0) t_2) c) z)
       (if (<= t_1 INFINITY)
         (/ (fma (* x 9.0) y t_2) (* z c))
         (fma -4.0 (* a (/ t c)) (/ (* 9.0 (* y x)) (* z c))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (b + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (z * c);
	double t_2 = fma((a * t), (z * -4.0), b);
	double tmp;
	if (t_1 <= -4e+81) {
		tmp = fma((a * (z * -4.0)), t, fma(x, (y * 9.0), b)) / (z * c);
	} else if (t_1 <= 1e+83) {
		tmp = (fma(x, (y * 9.0), t_2) / c) / z;
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = fma((x * 9.0), y, t_2) / (z * c);
	} else {
		tmp = fma(-4.0, (a * (t / c)), ((9.0 * (y * x)) / (z * c)));
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(b + Float64(Float64(y * Float64(x * 9.0)) - Float64(a * Float64(t * Float64(z * 4.0))))) / Float64(z * c))
	t_2 = fma(Float64(a * t), Float64(z * -4.0), b)
	tmp = 0.0
	if (t_1 <= -4e+81)
		tmp = Float64(fma(Float64(a * Float64(z * -4.0)), t, fma(x, Float64(y * 9.0), b)) / Float64(z * c));
	elseif (t_1 <= 1e+83)
		tmp = Float64(Float64(fma(x, Float64(y * 9.0), t_2) / c) / z);
	elseif (t_1 <= Inf)
		tmp = Float64(fma(Float64(x * 9.0), y, t_2) / Float64(z * c));
	else
		tmp = fma(-4.0, Float64(a * Float64(t / c)), Float64(Float64(9.0 * Float64(y * x)) / 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_] := Block[{t$95$1 = N[(N[(b + N[(N[(y * N[(x * 9.0), $MachinePrecision]), $MachinePrecision] - N[(a * N[(t * N[(z * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(a * t), $MachinePrecision] * N[(z * -4.0), $MachinePrecision] + b), $MachinePrecision]}, If[LessEqual[t$95$1, -4e+81], N[(N[(N[(a * N[(z * -4.0), $MachinePrecision]), $MachinePrecision] * t + N[(x * N[(y * 9.0), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+83], N[(N[(N[(x * N[(y * 9.0), $MachinePrecision] + t$95$2), $MachinePrecision] / c), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t$95$1, Infinity], N[(N[(N[(x * 9.0), $MachinePrecision] * y + t$95$2), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(-4.0 * N[(a * N[(t / c), $MachinePrecision]), $MachinePrecision] + N[(N[(9.0 * N[(y * x), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x #s(literal 9 binary64)) y) (*.f64 (*.f64 (*.f64 z #s(literal 4 binary64)) t) a)) b) (*.f64 z c)) < -3.99999999999999969e81

   1. Initial program 87.3%

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

      4. associate-*l* N/A

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

      5. distribute-lft-neg-in N/A

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

      6. *-commutative N/A

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

      7. associate-*r* N/A

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

      8. accelerator-lowering-fma.f64 N/A

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

      9. *-lowering-*.f64 N/A

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

      10. distribute-rgt-neg-in N/A

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

      11. *-lowering-*.f64 N/A

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

      12. metadata-eval N/A

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

      13. associate-*l* N/A

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

      14. accelerator-lowering-fma.f64 N/A

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

      15. *-lowering-*.f64 89.6

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

   4. Applied egg-rr 89.6%

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

   if -3.99999999999999969e81 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x #s(literal 9 binary64)) y) (*.f64 (*.f64 (*.f64 z #s(literal 4 binary64)) t) a)) b) (*.f64 z c)) < 1.00000000000000003e83

   1. Initial program 88.9%

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

      1. associate-/l/ N/A

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

      2. /-lowering-/.f64 N/A

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

   4. Applied egg-rr 93.6%

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

   if 1.00000000000000003e83 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x #s(literal 9 binary64)) y) (*.f64 (*.f64 (*.f64 z #s(literal 4 binary64)) t) a)) b) (*.f64 z c)) < +inf.0

   1. Initial program 87.1%

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

      1. associate-+l- N/A

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

      2. sub-neg N/A

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

      3. accelerator-lowering-fma.f64 N/A

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

      4. *-lowering-*.f64 N/A

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

      5. neg-sub0 N/A

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

      6. associate-+l- N/A

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

      7. neg-sub0 N/A

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

      8. associate-*l* N/A

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

      9. *-commutative N/A

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

      10. distribute-rgt-neg-in N/A

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

      11. accelerator-lowering-fma.f64 N/A

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

      12. *-lowering-*.f64 N/A

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

      13. distribute-rgt-neg-in N/A

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

      14. *-lowering-*.f64 N/A

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

      15. metadata-eval 88.4

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

   4. Applied egg-rr 88.4%

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

   if +inf.0 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x #s(literal 9 binary64)) y) (*.f64 (*.f64 (*.f64 z #s(literal 4 binary64)) t) a)) b) (*.f64 z c))

   1. Initial program 0.0%

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

      1. clear-num N/A

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

      2. associate-/r/ N/A

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

      3. associate-+l- N/A

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

      4. sub-neg N/A

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

      5. distribute-rgt-in N/A

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

      6. div-inv N/A

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

      7. associate-*l* N/A

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

      8. *-commutative N/A

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

      9. *-commutative N/A

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

      10. times-frac N/A

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

      11. accelerator-lowering-fma.f64 N/A

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

      12. /-lowering-/.f64 N/A

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

      13. *-lowering-*.f64 N/A

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

      14. /-lowering-/.f64 N/A

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

      15. *-lowering-*.f64 N/A

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

   4. Applied egg-rr 12.2%

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

   5. Taylor expanded in t around inf

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

      1. associate-*r/ N/A

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

      2. /-lowering-/.f64 N/A

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

      3. *-lowering-*.f64 N/A

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

      4. *-lowering-*.f64 77.8

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

   7. Simplified 77.8%

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

   8. Taylor expanded in y around 0

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

      1. associate-/l* N/A

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

      2. associate-*r* N/A

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

      3. *-commutative N/A

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

      4. associate-*r* N/A

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

      5. accelerator-lowering-fma.f64 N/A

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

      6. associate-/l* N/A

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

      7. *-lowering-*.f64 N/A

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

      8. /-lowering-/.f64 N/A

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

      9. associate-*r* N/A

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

      10. *-commutative N/A

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

      11. associate-/l* N/A

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

      12. associate-*r* N/A

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

      13. /-lowering-/.f64 N/A

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

      14. *-lowering-*.f64 N/A

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

      15. *-lowering-*.f64 N/A

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

      16. *-lowering-*.f64 80.9

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

   10. Simplified 80.9%

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

4. Final simplification 89.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c} \leq -4 \cdot 10^{+81}:\\ \;\;\;\;\frac{\mathsf{fma}\left(a \cdot \left(z \cdot -4\right), t, \mathsf{fma}\left(x, y \cdot 9, b\right)\right)}{z \cdot c}\\ \mathbf{elif}\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c} \leq 10^{+83}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(x, y \cdot 9, \mathsf{fma}\left(a \cdot t, z \cdot -4, b\right)\right)}{c}}{z}\\ \mathbf{elif}\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c} \leq \infty:\\ \;\;\;\;\frac{\mathsf{fma}\left(x \cdot 9, y, \mathsf{fma}\left(a \cdot t, z \cdot -4, b\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-4, a \cdot \frac{t}{c}, \frac{9 \cdot \left(y \cdot x\right)}{z \cdot c}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 86.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+64}:\\ \;\;\;\;\frac{\mathsf{fma}\left(a \cdot \left(z \cdot -4\right), t, \mathsf{fma}\left(x, y \cdot 9, b\right)\right)}{z \cdot c}\\ \mathbf{elif}\;t\_1 \leq \infty:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(x, y \cdot 9, \mathsf{fma}\left(a \cdot t, z \cdot -4, b\right)\right)}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-4, a \cdot \frac{t}{c}, \frac{9 \cdot \left(y \cdot x\right)}{z \cdot c}\right)\\ \end{array} \end{array} \]

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
 (let* ((t_1 (/ (+ b (- (* y (* x 9.0)) (* a (* t (* z 4.0))))) (* z c))))
   (if (<= t_1 -1e+64)
     (/ (fma (* a (* z -4.0)) t (fma x (* y 9.0) b)) (* z c))
     (if (<= t_1 INFINITY)
       (/ (/ (fma x (* y 9.0) (fma (* a t) (* z -4.0) b)) z) c)
       (fma -4.0 (* a (/ t c)) (/ (* 9.0 (* y x)) (* z c)))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (b + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (z * c);
	double tmp;
	if (t_1 <= -1e+64) {
		tmp = fma((a * (z * -4.0)), t, fma(x, (y * 9.0), b)) / (z * c);
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = (fma(x, (y * 9.0), fma((a * t), (z * -4.0), b)) / z) / c;
	} else {
		tmp = fma(-4.0, (a * (t / c)), ((9.0 * (y * x)) / (z * c)));
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(b + Float64(Float64(y * Float64(x * 9.0)) - Float64(a * Float64(t * Float64(z * 4.0))))) / Float64(z * c))
	tmp = 0.0
	if (t_1 <= -1e+64)
		tmp = Float64(fma(Float64(a * Float64(z * -4.0)), t, fma(x, Float64(y * 9.0), b)) / Float64(z * c));
	elseif (t_1 <= Inf)
		tmp = Float64(Float64(fma(x, Float64(y * 9.0), fma(Float64(a * t), Float64(z * -4.0), b)) / z) / c);
	else
		tmp = fma(-4.0, Float64(a * Float64(t / c)), Float64(Float64(9.0 * Float64(y * x)) / 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_] := Block[{t$95$1 = N[(N[(b + N[(N[(y * N[(x * 9.0), $MachinePrecision]), $MachinePrecision] - N[(a * N[(t * N[(z * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+64], N[(N[(N[(a * N[(z * -4.0), $MachinePrecision]), $MachinePrecision] * t + N[(x * N[(y * 9.0), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, Infinity], N[(N[(N[(x * N[(y * 9.0), $MachinePrecision] + N[(N[(a * t), $MachinePrecision] * N[(z * -4.0), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] / c), $MachinePrecision], N[(-4.0 * N[(a * N[(t / c), $MachinePrecision]), $MachinePrecision] + N[(N[(9.0 * N[(y * x), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x #s(literal 9 binary64)) y) (*.f64 (*.f64 (*.f64 z #s(literal 4 binary64)) t) a)) b) (*.f64 z c)) < -1.00000000000000002e64

   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. Add Preprocessing
   3. Step-by-step derivation

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

      4. associate-*l* N/A

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

      5. distribute-lft-neg-in N/A

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

      6. *-commutative N/A

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

      7. associate-*r* N/A

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

      8. accelerator-lowering-fma.f64 N/A

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

      9. *-lowering-*.f64 N/A

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

      10. distribute-rgt-neg-in N/A

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

      11. *-lowering-*.f64 N/A

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

      12. metadata-eval N/A

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

      13. associate-*l* N/A

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

      14. accelerator-lowering-fma.f64 N/A

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

      15. *-lowering-*.f64 90.2

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

   4. Applied egg-rr 90.2%

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

   if -1.00000000000000002e64 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x #s(literal 9 binary64)) y) (*.f64 (*.f64 (*.f64 z #s(literal 4 binary64)) t) a)) b) (*.f64 z c)) < +inf.0

   1. Initial program 87.5%

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

      1. associate-/r* N/A

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

      2. /-lowering-/.f64 N/A

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

   4. Applied egg-rr 89.0%

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

   if +inf.0 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x #s(literal 9 binary64)) y) (*.f64 (*.f64 (*.f64 z #s(literal 4 binary64)) t) a)) b) (*.f64 z c))

   1. Initial program 0.0%

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

      1. clear-num N/A

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

      2. associate-/r/ N/A

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

      3. associate-+l- N/A

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

      4. sub-neg N/A

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

      5. distribute-rgt-in N/A

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

      6. div-inv N/A

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

      7. associate-*l* N/A

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

      8. *-commutative N/A

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

      9. *-commutative N/A

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

      10. times-frac N/A

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

      11. accelerator-lowering-fma.f64 N/A

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

      12. /-lowering-/.f64 N/A

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

      13. *-lowering-*.f64 N/A

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

      14. /-lowering-/.f64 N/A

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

      15. *-lowering-*.f64 N/A

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

   4. Applied egg-rr 12.2%

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

   5. Taylor expanded in t around inf

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

      1. associate-*r/ N/A

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

      2. /-lowering-/.f64 N/A

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

      3. *-lowering-*.f64 N/A

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

      4. *-lowering-*.f64 77.8

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

   7. Simplified 77.8%

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

   8. Taylor expanded in y around 0

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

      1. associate-/l* N/A

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

      2. associate-*r* N/A

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

      3. *-commutative N/A

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

      4. associate-*r* N/A

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

      5. accelerator-lowering-fma.f64 N/A

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

      6. associate-/l* N/A

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

      7. *-lowering-*.f64 N/A

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

      8. /-lowering-/.f64 N/A

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

      9. associate-*r* N/A

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

      10. *-commutative N/A

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

      11. associate-/l* N/A

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

      12. associate-*r* N/A

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

      13. /-lowering-/.f64 N/A

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

      14. *-lowering-*.f64 N/A

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

      15. *-lowering-*.f64 N/A

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

      16. *-lowering-*.f64 80.9

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

   10. Simplified 80.9%

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

4. Final simplification 88.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c} \leq -1 \cdot 10^{+64}:\\ \;\;\;\;\frac{\mathsf{fma}\left(a \cdot \left(z \cdot -4\right), t, \mathsf{fma}\left(x, y \cdot 9, b\right)\right)}{z \cdot c}\\ \mathbf{elif}\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c} \leq \infty:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(x, y \cdot 9, \mathsf{fma}\left(a \cdot t, z \cdot -4, b\right)\right)}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-4, a \cdot \frac{t}{c}, \frac{9 \cdot \left(y \cdot x\right)}{z \cdot c}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 84.0% accurate, 0.5× speedup

Math

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

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 (<= (/ (+ b (- (* y (* x 9.0)) (* a (* t (* z 4.0))))) (* z c)) INFINITY)
   (/ (fma (* x 9.0) y (fma (* a t) (* z -4.0) b)) (* z c))
   (fma -4.0 (* a (/ t c)) (/ (* 9.0 (* y x)) (* z c)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (((b + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (z * c)) <= ((double) INFINITY)) {
		tmp = fma((x * 9.0), y, fma((a * t), (z * -4.0), b)) / (z * c);
	} else {
		tmp = fma(-4.0, (a * (t / c)), ((9.0 * (y * x)) / (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 (Float64(Float64(b + Float64(Float64(y * Float64(x * 9.0)) - Float64(a * Float64(t * Float64(z * 4.0))))) / Float64(z * c)) <= Inf)
		tmp = Float64(fma(Float64(x * 9.0), y, fma(Float64(a * t), Float64(z * -4.0), b)) / Float64(z * c));
	else
		tmp = fma(-4.0, Float64(a * Float64(t / c)), Float64(Float64(9.0 * Float64(y * x)) / 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[N[(N[(b + N[(N[(y * N[(x * 9.0), $MachinePrecision]), $MachinePrecision] - N[(a * N[(t * N[(z * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], Infinity], N[(N[(N[(x * 9.0), $MachinePrecision] * y + N[(N[(a * t), $MachinePrecision] * N[(z * -4.0), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(-4.0 * N[(a * N[(t / c), $MachinePrecision]), $MachinePrecision] + N[(N[(9.0 * N[(y * x), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x #s(literal 9 binary64)) y) (*.f64 (*.f64 (*.f64 z #s(literal 4 binary64)) t) a)) b) (*.f64 z c)) < +inf.0

   1. Initial program 87.7%

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

      1. associate-+l- N/A

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

      2. sub-neg N/A

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

      3. accelerator-lowering-fma.f64 N/A

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

      4. *-lowering-*.f64 N/A

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

      5. neg-sub0 N/A

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

      6. associate-+l- N/A

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

      7. neg-sub0 N/A

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

      8. associate-*l* N/A

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

      9. *-commutative N/A

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

      10. distribute-rgt-neg-in N/A

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

      11. accelerator-lowering-fma.f64 N/A

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

      12. *-lowering-*.f64 N/A

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

      13. distribute-rgt-neg-in N/A

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

      14. *-lowering-*.f64 N/A

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

      15. metadata-eval 88.6

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

   4. Applied egg-rr 88.6%

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

   if +inf.0 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x #s(literal 9 binary64)) y) (*.f64 (*.f64 (*.f64 z #s(literal 4 binary64)) t) a)) b) (*.f64 z c))

   1. Initial program 0.0%

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

      1. clear-num N/A

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

      2. associate-/r/ N/A

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

      3. associate-+l- N/A

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

      4. sub-neg N/A

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

      5. distribute-rgt-in N/A

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

      6. div-inv N/A

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

      7. associate-*l* N/A

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

      8. *-commutative N/A

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

      9. *-commutative N/A

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

      10. times-frac N/A

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

      11. accelerator-lowering-fma.f64 N/A

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

      12. /-lowering-/.f64 N/A

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

      13. *-lowering-*.f64 N/A

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

      14. /-lowering-/.f64 N/A

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

      15. *-lowering-*.f64 N/A

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

   4. Applied egg-rr 12.2%

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

   5. Taylor expanded in t around inf

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

      1. associate-*r/ N/A

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

      2. /-lowering-/.f64 N/A

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

      3. *-lowering-*.f64 N/A

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

      4. *-lowering-*.f64 77.8

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

   7. Simplified 77.8%

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

   8. Taylor expanded in y around 0

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

      1. associate-/l* N/A

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

      2. associate-*r* N/A

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

      3. *-commutative N/A

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

      4. associate-*r* N/A

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

      5. accelerator-lowering-fma.f64 N/A

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

      6. associate-/l* N/A

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

      7. *-lowering-*.f64 N/A

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

      8. /-lowering-/.f64 N/A

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

      9. associate-*r* N/A

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

      10. *-commutative N/A

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

      11. associate-/l* N/A

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

      12. associate-*r* N/A

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

      13. /-lowering-/.f64 N/A

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

      14. *-lowering-*.f64 N/A

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

      15. *-lowering-*.f64 N/A

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

      16. *-lowering-*.f64 80.9

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

   10. Simplified 80.9%

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

4. Final simplification 87.8%

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

Alternative 5: 83.9% accurate, 0.5× speedup

Math

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

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= (/ (+ b (- (* y (* x 9.0)) (* a (* t (* z 4.0))))) (* z c)) INFINITY)
   (/ (fma (* x 9.0) y (fma (* a t) (* z -4.0) 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 + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (z * c)) <= ((double) INFINITY)) {
		tmp = fma((x * 9.0), y, fma((a * t), (z * -4.0), 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 (Float64(Float64(b + Float64(Float64(y * Float64(x * 9.0)) - Float64(a * Float64(t * Float64(z * 4.0))))) / Float64(z * c)) <= Inf)
		tmp = Float64(fma(Float64(x * 9.0), y, fma(Float64(a * t), Float64(z * -4.0), b)) / Float64(z * c));
	else
		tmp = Float64(Float64(-4.0 * Float64(a * t)) / c);
	end
	return tmp
end

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x #s(literal 9 binary64)) y) (*.f64 (*.f64 (*.f64 z #s(literal 4 binary64)) t) a)) b) (*.f64 z c)) < +inf.0

   1. Initial program 87.7%

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

      1. associate-+l- N/A

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

      2. sub-neg N/A

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

      3. accelerator-lowering-fma.f64 N/A

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

      4. *-lowering-*.f64 N/A

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

      5. neg-sub0 N/A

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

      6. associate-+l- N/A

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

      7. neg-sub0 N/A

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

      8. associate-*l* N/A

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

      9. *-commutative N/A

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

      10. distribute-rgt-neg-in N/A

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

      11. accelerator-lowering-fma.f64 N/A

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

      12. *-lowering-*.f64 N/A

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

      13. distribute-rgt-neg-in N/A

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

      14. *-lowering-*.f64 N/A

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

      15. metadata-eval 88.6

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

   4. Applied egg-rr 88.6%

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

   if +inf.0 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x #s(literal 9 binary64)) y) (*.f64 (*.f64 (*.f64 z #s(literal 4 binary64)) t) a)) b) (*.f64 z c))

   1. Initial program 0.0%

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

   3. Taylor expanded in z around inf

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

      1. associate-*r/ N/A

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

      2. /-lowering-/.f64 N/A

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

      3. *-lowering-*.f64 N/A

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

      4. *-lowering-*.f64 60.4

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

   5. Simplified 60.4%

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

4. Final simplification 85.7%

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

Alternative 6: 71.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := -4 \cdot \left(z \cdot t\right)\\ t_2 := y \cdot \left(x \cdot 9\right)\\ \mathbf{if}\;t\_2 \leq -2 \cdot 10^{+16}:\\ \;\;\;\;\frac{\mathsf{fma}\left(a, t\_1, 9 \cdot \left(y \cdot x\right)\right)}{z \cdot c}\\ \mathbf{elif}\;t\_2 \leq 10^{-21}:\\ \;\;\;\;\frac{\mathsf{fma}\left(a, t\_1, b\right)}{z \cdot c}\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+266}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y \cdot x, 9, t \cdot \left(a \cdot \left(z \cdot -4\right)\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot 9\right) \cdot \frac{\frac{x}{z}}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* -4.0 (* z t))) (t_2 (* y (* x 9.0))))
   (if (<= t_2 -2e+16)
     (/ (fma a t_1 (* 9.0 (* y x))) (* z c))
     (if (<= t_2 1e-21)
       (/ (fma a t_1 b) (* z c))
       (if (<= t_2 2e+266)
         (/ (fma (* y x) 9.0 (* t (* a (* z -4.0)))) (* z c))
         (* (* y 9.0) (/ (/ x z) c)))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = -4.0 * (z * t);
	double t_2 = y * (x * 9.0);
	double tmp;
	if (t_2 <= -2e+16) {
		tmp = fma(a, t_1, (9.0 * (y * x))) / (z * c);
	} else if (t_2 <= 1e-21) {
		tmp = fma(a, t_1, b) / (z * c);
	} else if (t_2 <= 2e+266) {
		tmp = fma((y * x), 9.0, (t * (a * (z * -4.0)))) / (z * c);
	} else {
		tmp = (y * 9.0) * ((x / z) / c);
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(-4.0 * Float64(z * t))
	t_2 = Float64(y * Float64(x * 9.0))
	tmp = 0.0
	if (t_2 <= -2e+16)
		tmp = Float64(fma(a, t_1, Float64(9.0 * Float64(y * x))) / Float64(z * c));
	elseif (t_2 <= 1e-21)
		tmp = Float64(fma(a, t_1, b) / Float64(z * c));
	elseif (t_2 <= 2e+266)
		tmp = Float64(fma(Float64(y * x), 9.0, Float64(t * Float64(a * Float64(z * -4.0)))) / Float64(z * c));
	else
		tmp = Float64(Float64(y * 9.0) * Float64(Float64(x / 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_] := Block[{t$95$1 = N[(-4.0 * N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(x * 9.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -2e+16], N[(N[(a * t$95$1 + N[(9.0 * N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 1e-21], N[(N[(a * t$95$1 + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 2e+266], N[(N[(N[(y * x), $MachinePrecision] * 9.0 + N[(t * N[(a * N[(z * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(N[(y * 9.0), $MachinePrecision] * N[(N[(x / z), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -2e16

   1. Initial program 74.5%

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

   3. Taylor expanded in b around 0

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

      1. cancel-sign-sub-inv N/A

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. associate-*l* N/A

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

      6. *-commutative N/A

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

      7. accelerator-lowering-fma.f64 N/A

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

      8. *-commutative N/A

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

      9. *-lowering-*.f64 N/A

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

      10. *-lowering-*.f64 N/A

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

      11. *-lowering-*.f64 N/A

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

      12. *-lowering-*.f64 67.1

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

   5. Simplified 67.1%

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

   if -2e16 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 9.99999999999999908e-22

   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. Add Preprocessing

   3. Taylor expanded in x around 0

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

      1. cancel-sign-sub-inv N/A

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. associate-*l* N/A

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

      6. *-commutative N/A

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

      7. accelerator-lowering-fma.f64 N/A

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

      8. *-commutative N/A

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

      9. *-lowering-*.f64 N/A

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

      10. *-lowering-*.f64 76.9

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

   5. Simplified 76.9%

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

   if 9.99999999999999908e-22 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 2.0000000000000001e266

   1. Initial program 88.3%

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

   3. Taylor expanded in b around 0

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

      1. cancel-sign-sub-inv N/A

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. associate-*l* N/A

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

      6. *-commutative N/A

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

      7. accelerator-lowering-fma.f64 N/A

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

      8. *-commutative N/A

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

      9. *-lowering-*.f64 N/A

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

      10. *-lowering-*.f64 N/A

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

      11. *-lowering-*.f64 N/A

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

      12. *-lowering-*.f64 77.0

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

   5. Simplified 77.0%

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-*l* N/A

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

      4. associate-*r* N/A

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

      5. *-commutative N/A

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

      6. accelerator-lowering-fma.f64 N/A

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

      7. *-lowering-*.f64 N/A

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

      8. associate-*l* N/A

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

      9. *-lowering-*.f64 N/A

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

      10. *-lowering-*.f64 N/A

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

      11. *-lowering-*.f64 78.8

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

   7. Applied egg-rr 78.8%

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

   if 2.0000000000000001e266 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 58.2%

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

   3. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 N/A

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

      2. *-lowering-*.f64 58.3

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

   5. Simplified 58.3%

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

      1. *-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. frac-times N/A

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

      5. metadata-eval N/A

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

      6. distribute-lft-neg-in N/A

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

      7. *-commutative N/A

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

      8. associate-*l/ N/A

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

      9. associate-/l* N/A

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

      10. *-lowering-*.f64 N/A

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

      11. distribute-rgt-neg-in N/A

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

      12. metadata-eval N/A

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

      13. *-lowering-*.f64 N/A

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

      14. /-lowering-/.f64 N/A

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

      15. /-lowering-/.f64 91.4

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

   7. Applied egg-rr 91.4%

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

4. Final simplification 76.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \left(x \cdot 9\right) \leq -2 \cdot 10^{+16}:\\ \;\;\;\;\frac{\mathsf{fma}\left(a, -4 \cdot \left(z \cdot t\right), 9 \cdot \left(y \cdot x\right)\right)}{z \cdot c}\\ \mathbf{elif}\;y \cdot \left(x \cdot 9\right) \leq 10^{-21}:\\ \;\;\;\;\frac{\mathsf{fma}\left(a, -4 \cdot \left(z \cdot t\right), b\right)}{z \cdot c}\\ \mathbf{elif}\;y \cdot \left(x \cdot 9\right) \leq 2 \cdot 10^{+266}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y \cdot x, 9, t \cdot \left(a \cdot \left(z \cdot -4\right)\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot 9\right) \cdot \frac{\frac{x}{z}}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 72.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := -4 \cdot \left(z \cdot t\right)\\ t_2 := 9 \cdot \left(y \cdot x\right)\\ t_3 := y \cdot \left(x \cdot 9\right)\\ \mathbf{if}\;t\_3 \leq -2 \cdot 10^{+16}:\\ \;\;\;\;\frac{\mathsf{fma}\left(a, t\_1, t\_2\right)}{z \cdot c}\\ \mathbf{elif}\;t\_3 \leq 10^{+39}:\\ \;\;\;\;\frac{\mathsf{fma}\left(a, t\_1, b\right)}{z \cdot c}\\ \mathbf{elif}\;t\_3 \leq 2 \cdot 10^{+266}:\\ \;\;\;\;\frac{\mathsf{fma}\left(-4, a \cdot \left(z \cdot t\right), t\_2\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot 9\right) \cdot \frac{\frac{x}{z}}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* -4.0 (* z t))) (t_2 (* 9.0 (* y x))) (t_3 (* y (* x 9.0))))
   (if (<= t_3 -2e+16)
     (/ (fma a t_1 t_2) (* z c))
     (if (<= t_3 1e+39)
       (/ (fma a t_1 b) (* z c))
       (if (<= t_3 2e+266)
         (/ (fma -4.0 (* a (* z t)) t_2) (* z c))
         (* (* y 9.0) (/ (/ x z) c)))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = -4.0 * (z * t);
	double t_2 = 9.0 * (y * x);
	double t_3 = y * (x * 9.0);
	double tmp;
	if (t_3 <= -2e+16) {
		tmp = fma(a, t_1, t_2) / (z * c);
	} else if (t_3 <= 1e+39) {
		tmp = fma(a, t_1, b) / (z * c);
	} else if (t_3 <= 2e+266) {
		tmp = fma(-4.0, (a * (z * t)), t_2) / (z * c);
	} else {
		tmp = (y * 9.0) * ((x / z) / c);
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(-4.0 * Float64(z * t))
	t_2 = Float64(9.0 * Float64(y * x))
	t_3 = Float64(y * Float64(x * 9.0))
	tmp = 0.0
	if (t_3 <= -2e+16)
		tmp = Float64(fma(a, t_1, t_2) / Float64(z * c));
	elseif (t_3 <= 1e+39)
		tmp = Float64(fma(a, t_1, b) / Float64(z * c));
	elseif (t_3 <= 2e+266)
		tmp = Float64(fma(-4.0, Float64(a * Float64(z * t)), t_2) / Float64(z * c));
	else
		tmp = Float64(Float64(y * 9.0) * Float64(Float64(x / 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_] := Block[{t$95$1 = N[(-4.0 * N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(9.0 * N[(y * x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(y * N[(x * 9.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$3, -2e+16], N[(N[(a * t$95$1 + t$95$2), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, 1e+39], N[(N[(a * t$95$1 + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, 2e+266], N[(N[(-4.0 * N[(a * N[(z * t), $MachinePrecision]), $MachinePrecision] + t$95$2), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(N[(y * 9.0), $MachinePrecision] * N[(N[(x / z), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -2e16

   1. Initial program 74.5%

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

   3. Taylor expanded in b around 0

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

      1. cancel-sign-sub-inv N/A

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. associate-*l* N/A

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

      6. *-commutative N/A

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

      7. accelerator-lowering-fma.f64 N/A

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

      8. *-commutative N/A

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

      9. *-lowering-*.f64 N/A

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

      10. *-lowering-*.f64 N/A

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

      11. *-lowering-*.f64 N/A

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

      12. *-lowering-*.f64 67.1

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

   5. Simplified 67.1%

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

   if -2e16 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 9.9999999999999994e38

   1. Initial program 81.9%

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

   3. Taylor expanded in x around 0

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

      1. cancel-sign-sub-inv N/A

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. associate-*l* N/A

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

      6. *-commutative N/A

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

      7. accelerator-lowering-fma.f64 N/A

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

      8. *-commutative N/A

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

      9. *-lowering-*.f64 N/A

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

      10. *-lowering-*.f64 75.8

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

   5. Simplified 75.8%

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

   if 9.9999999999999994e38 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 2.0000000000000001e266

   1. Initial program 87.6%

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

      1. associate-/r* N/A

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

      2. /-lowering-/.f64 N/A

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

   4. Applied egg-rr 83.1%

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

   5. Taylor expanded in b around 0

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

      1. /-lowering-/.f64 N/A

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

      2. accelerator-lowering-fma.f64 N/A

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

      3. *-lowering-*.f64 N/A

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

      4. *-lowering-*.f64 N/A

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

      5. *-lowering-*.f64 N/A

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

      6. *-lowering-*.f64 N/A

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

      7. *-commutative N/A

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

      8. *-lowering-*.f64 80.6

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

   7. Simplified 80.6%

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

   if 2.0000000000000001e266 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 58.2%

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

   3. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 N/A

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

      2. *-lowering-*.f64 58.3

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

   5. Simplified 58.3%

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

      1. *-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. frac-times N/A

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

      5. metadata-eval N/A

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

      6. distribute-lft-neg-in N/A

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

      7. *-commutative N/A

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

      8. associate-*l/ N/A

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

      9. associate-/l* N/A

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

      10. *-lowering-*.f64 N/A

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

      11. distribute-rgt-neg-in N/A

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

      12. metadata-eval N/A

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

      13. *-lowering-*.f64 N/A

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

      14. /-lowering-/.f64 N/A

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

      15. /-lowering-/.f64 91.4

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

   7. Applied egg-rr 91.4%

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

4. Final simplification 75.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \left(x \cdot 9\right) \leq -2 \cdot 10^{+16}:\\ \;\;\;\;\frac{\mathsf{fma}\left(a, -4 \cdot \left(z \cdot t\right), 9 \cdot \left(y \cdot x\right)\right)}{z \cdot c}\\ \mathbf{elif}\;y \cdot \left(x \cdot 9\right) \leq 10^{+39}:\\ \;\;\;\;\frac{\mathsf{fma}\left(a, -4 \cdot \left(z \cdot t\right), b\right)}{z \cdot c}\\ \mathbf{elif}\;y \cdot \left(x \cdot 9\right) \leq 2 \cdot 10^{+266}:\\ \;\;\;\;\frac{\mathsf{fma}\left(-4, a \cdot \left(z \cdot t\right), 9 \cdot \left(y \cdot x\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot 9\right) \cdot \frac{\frac{x}{z}}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 72.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot 9\right)\\ t_2 := \frac{\mathsf{fma}\left(-4, a \cdot \left(z \cdot t\right), 9 \cdot \left(y \cdot x\right)\right)}{z \cdot c}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+16}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 10^{+39}:\\ \;\;\;\;\frac{\mathsf{fma}\left(a, -4 \cdot \left(z \cdot t\right), b\right)}{z \cdot c}\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+266}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot 9\right) \cdot \frac{\frac{x}{z}}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* y (* x 9.0)))
        (t_2 (/ (fma -4.0 (* a (* z t)) (* 9.0 (* y x))) (* z c))))
   (if (<= t_1 -2e+16)
     t_2
     (if (<= t_1 1e+39)
       (/ (fma a (* -4.0 (* z t)) b) (* z c))
       (if (<= t_1 2e+266) t_2 (* (* y 9.0) (/ (/ x z) c)))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = y * (x * 9.0);
	double t_2 = fma(-4.0, (a * (z * t)), (9.0 * (y * x))) / (z * c);
	double tmp;
	if (t_1 <= -2e+16) {
		tmp = t_2;
	} else if (t_1 <= 1e+39) {
		tmp = fma(a, (-4.0 * (z * t)), b) / (z * c);
	} else if (t_1 <= 2e+266) {
		tmp = t_2;
	} else {
		tmp = (y * 9.0) * ((x / z) / c);
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(y * Float64(x * 9.0))
	t_2 = Float64(fma(-4.0, Float64(a * Float64(z * t)), Float64(9.0 * Float64(y * x))) / Float64(z * c))
	tmp = 0.0
	if (t_1 <= -2e+16)
		tmp = t_2;
	elseif (t_1 <= 1e+39)
		tmp = Float64(fma(a, Float64(-4.0 * Float64(z * t)), b) / Float64(z * c));
	elseif (t_1 <= 2e+266)
		tmp = t_2;
	else
		tmp = Float64(Float64(y * 9.0) * Float64(Float64(x / 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_] := Block[{t$95$1 = N[(y * N[(x * 9.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(-4.0 * N[(a * N[(z * t), $MachinePrecision]), $MachinePrecision] + N[(9.0 * N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+16], t$95$2, If[LessEqual[t$95$1, 1e+39], N[(N[(a * N[(-4.0 * N[(z * t), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+266], t$95$2, N[(N[(y * 9.0), $MachinePrecision] * N[(N[(x / z), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -2e16 or 9.9999999999999994e38 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 2.0000000000000001e266

   1. Initial program 79.4%

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

      1. associate-/r* N/A

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

      2. /-lowering-/.f64 N/A

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

   4. Applied egg-rr 83.5%

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

   5. Taylor expanded in b around 0

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

      1. /-lowering-/.f64 N/A

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

      2. accelerator-lowering-fma.f64 N/A

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

      3. *-lowering-*.f64 N/A

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

      4. *-lowering-*.f64 N/A

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

      5. *-lowering-*.f64 N/A

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

      6. *-lowering-*.f64 N/A

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

      7. *-commutative N/A

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

      8. *-lowering-*.f64 72.1

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

   7. Simplified 72.1%

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

   if -2e16 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 9.9999999999999994e38

   1. Initial program 81.9%

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

   3. Taylor expanded in x around 0

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

      1. cancel-sign-sub-inv N/A

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. associate-*l* N/A

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

      6. *-commutative N/A

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

      7. accelerator-lowering-fma.f64 N/A

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

      8. *-commutative N/A

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

      9. *-lowering-*.f64 N/A

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

      10. *-lowering-*.f64 75.8

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

   5. Simplified 75.8%

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

   if 2.0000000000000001e266 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 58.2%

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

   3. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 N/A

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

      2. *-lowering-*.f64 58.3

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

   5. Simplified 58.3%

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

      1. *-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. frac-times N/A

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

      5. metadata-eval N/A

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

      6. distribute-lft-neg-in N/A

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

      7. *-commutative N/A

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

      8. associate-*l/ N/A

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

      9. associate-/l* N/A

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

      10. *-lowering-*.f64 N/A

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

      11. distribute-rgt-neg-in N/A

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

      12. metadata-eval N/A

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

      13. *-lowering-*.f64 N/A

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

      14. /-lowering-/.f64 N/A

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

      15. /-lowering-/.f64 91.4

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

   7. Applied egg-rr 91.4%

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

4. Final simplification 75.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \left(x \cdot 9\right) \leq -2 \cdot 10^{+16}:\\ \;\;\;\;\frac{\mathsf{fma}\left(-4, a \cdot \left(z \cdot t\right), 9 \cdot \left(y \cdot x\right)\right)}{z \cdot c}\\ \mathbf{elif}\;y \cdot \left(x \cdot 9\right) \leq 10^{+39}:\\ \;\;\;\;\frac{\mathsf{fma}\left(a, -4 \cdot \left(z \cdot t\right), b\right)}{z \cdot c}\\ \mathbf{elif}\;y \cdot \left(x \cdot 9\right) \leq 2 \cdot 10^{+266}:\\ \;\;\;\;\frac{\mathsf{fma}\left(-4, a \cdot \left(z \cdot t\right), 9 \cdot \left(y \cdot x\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot 9\right) \cdot \frac{\frac{x}{z}}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 53.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot 9\right)\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+16}:\\ \;\;\;\;\left(y \cdot 9\right) \cdot \frac{x}{z \cdot c}\\ \mathbf{elif}\;t\_1 \leq -2 \cdot 10^{-323}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;t\_1 \leq 4 \cdot 10^{+58}:\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot 9\right) \cdot \frac{y}{z \cdot c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* y (* x 9.0))))
   (if (<= t_1 -2e+16)
     (* (* y 9.0) (/ x (* z c)))
     (if (<= t_1 -2e-323)
       (/ (/ b c) z)
       (if (<= t_1 4e+58)
         (/ (* -4.0 (* a t)) c)
         (* (* x 9.0) (/ y (* z c))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = y * (x * 9.0);
	double tmp;
	if (t_1 <= -2e+16) {
		tmp = (y * 9.0) * (x / (z * c));
	} else if (t_1 <= -2e-323) {
		tmp = (b / c) / z;
	} else if (t_1 <= 4e+58) {
		tmp = (-4.0 * (a * t)) / c;
	} else {
		tmp = (x * 9.0) * (y / (z * c));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (x * 9.0d0)
    if (t_1 <= (-2d+16)) then
        tmp = (y * 9.0d0) * (x / (z * c))
    else if (t_1 <= (-2d-323)) then
        tmp = (b / c) / z
    else if (t_1 <= 4d+58) then
        tmp = ((-4.0d0) * (a * t)) / c
    else
        tmp = (x * 9.0d0) * (y / (z * c))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = y * (x * 9.0);
	double tmp;
	if (t_1 <= -2e+16) {
		tmp = (y * 9.0) * (x / (z * c));
	} else if (t_1 <= -2e-323) {
		tmp = (b / c) / z;
	} else if (t_1 <= 4e+58) {
		tmp = (-4.0 * (a * t)) / c;
	} else {
		tmp = (x * 9.0) * (y / (z * c));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	t_1 = y * (x * 9.0)
	tmp = 0
	if t_1 <= -2e+16:
		tmp = (y * 9.0) * (x / (z * c))
	elif t_1 <= -2e-323:
		tmp = (b / c) / z
	elif t_1 <= 4e+58:
		tmp = (-4.0 * (a * t)) / c
	else:
		tmp = (x * 9.0) * (y / (z * c))
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(y * Float64(x * 9.0))
	tmp = 0.0
	if (t_1 <= -2e+16)
		tmp = Float64(Float64(y * 9.0) * Float64(x / Float64(z * c)));
	elseif (t_1 <= -2e-323)
		tmp = Float64(Float64(b / c) / z);
	elseif (t_1 <= 4e+58)
		tmp = Float64(Float64(-4.0 * Float64(a * t)) / c);
	else
		tmp = Float64(Float64(x * 9.0) * Float64(y / Float64(z * c)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = y * (x * 9.0);
	tmp = 0.0;
	if (t_1 <= -2e+16)
		tmp = (y * 9.0) * (x / (z * c));
	elseif (t_1 <= -2e-323)
		tmp = (b / c) / z;
	elseif (t_1 <= 4e+58)
		tmp = (-4.0 * (a * t)) / c;
	else
		tmp = (x * 9.0) * (y / (z * c));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(y * N[(x * 9.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+16], N[(N[(y * 9.0), $MachinePrecision] * N[(x / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -2e-323], N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t$95$1, 4e+58], N[(N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], N[(N[(x * 9.0), $MachinePrecision] * N[(y / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -2e16

   1. Initial program 74.5%

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

   3. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 N/A

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

      2. *-lowering-*.f64 58.7

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

   5. Simplified 58.7%

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

      1. *-commutative N/A

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

      2. associate-*l* N/A

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

      3. metadata-eval N/A

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

      4. distribute-rgt-neg-in N/A

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

      5. *-commutative N/A

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

      6. associate-/l* N/A

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

      7. *-lowering-*.f64 N/A

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

      8. distribute-rgt-neg-in N/A

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

      9. metadata-eval N/A

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

      10. *-lowering-*.f64 N/A

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

      11. /-lowering-/.f64 N/A

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

      12. *-lowering-*.f64 58.8

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

   7. Applied egg-rr 58.8%

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

   if -2e16 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -1.97626e-323

   1. Initial program 83.8%

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

   3. Taylor expanded in b around inf

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

   5. Simplified 56.4%

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

      1. *-commutative N/A

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

      2. associate-/r* N/A

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

      3. /-lowering-/.f64 N/A

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

      4. /-lowering-/.f64 58.8

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

   7. Applied egg-rr 58.8%

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

   if -1.97626e-323 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 3.99999999999999978e58

   1. Initial program 81.4%

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

   3. Taylor expanded in z around inf

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

      1. associate-*r/ N/A

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

      2. /-lowering-/.f64 N/A

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

      3. *-lowering-*.f64 N/A

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

      4. *-lowering-*.f64 51.6

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

   5. Simplified 51.6%

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

   if 3.99999999999999978e58 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 75.7%

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

   3. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 N/A

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

      2. *-lowering-*.f64 64.0

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

   5. Simplified 64.0%

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

      1. associate-*r* N/A

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

      2. associate-/l* N/A

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

      3. *-lowering-*.f64 N/A

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

      4. *-commutative N/A

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

      5. *-lowering-*.f64 N/A

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

      6. /-lowering-/.f64 N/A

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

      7. *-lowering-*.f64 74.2

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

   7. Applied egg-rr 74.2%

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

4. Final simplification 59.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \left(x \cdot 9\right) \leq -2 \cdot 10^{+16}:\\ \;\;\;\;\left(y \cdot 9\right) \cdot \frac{x}{z \cdot c}\\ \mathbf{elif}\;y \cdot \left(x \cdot 9\right) \leq -2 \cdot 10^{-323}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;y \cdot \left(x \cdot 9\right) \leq 4 \cdot 10^{+58}:\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot 9\right) \cdot \frac{y}{z \cdot c}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 86.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;c \leq 5 \cdot 10^{-15}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(x, y \cdot 9, \mathsf{fma}\left(a \cdot t, z \cdot -4, b\right)\right)}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a, t \cdot \frac{-4}{c}, \mathsf{fma}\left(x, \frac{y \cdot 9}{z \cdot c}, \frac{b}{z \cdot c}\right)\right)\\ \end{array} \end{array} \]

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 (<= c 5e-15)
   (/ (/ (fma x (* y 9.0) (fma (* a t) (* z -4.0) b)) z) c)
   (fma a (* t (/ -4.0 c)) (fma x (/ (* y 9.0) (* z c)) (/ b (* z c))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (c <= 5e-15) {
		tmp = (fma(x, (y * 9.0), fma((a * t), (z * -4.0), b)) / z) / c;
	} else {
		tmp = fma(a, (t * (-4.0 / c)), fma(x, ((y * 9.0) / (z * c)), (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 (c <= 5e-15)
		tmp = Float64(Float64(fma(x, Float64(y * 9.0), fma(Float64(a * t), Float64(z * -4.0), b)) / z) / c);
	else
		tmp = fma(a, Float64(t * Float64(-4.0 / c)), fma(x, Float64(Float64(y * 9.0) / Float64(z * c)), 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[c, 5e-15], N[(N[(N[(x * N[(y * 9.0), $MachinePrecision] + N[(N[(a * t), $MachinePrecision] * N[(z * -4.0), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] / c), $MachinePrecision], N[(a * N[(t * N[(-4.0 / c), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(y * 9.0), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision] + N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < 4.99999999999999999e-15

   1. Initial program 79.7%

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

      1. associate-/r* N/A

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

      2. /-lowering-/.f64 N/A

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

   4. Applied egg-rr 83.6%

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

   if 4.99999999999999999e-15 < c

   1. Initial program 75.4%

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

   3. Taylor expanded in x around 0

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

      1. cancel-sign-sub-inv N/A

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. associate-/l* N/A

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

      6. associate-*r* N/A

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

      7. *-commutative N/A

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

      8. accelerator-lowering-fma.f64 N/A

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

      9. *-commutative N/A

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

      10. associate-*l/ N/A

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

      11. associate-/l* N/A

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

      12. *-lowering-*.f64 N/A

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

      13. /-lowering-/.f64 N/A

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

      14. *-commutative N/A

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

      15. associate-/l* N/A

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

      16. associate-*l* N/A

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

      17. *-commutative N/A

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

   5. Simplified 96.3%

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

4. Final simplification 86.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq 5 \cdot 10^{-15}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(x, y \cdot 9, \mathsf{fma}\left(a \cdot t, z \cdot -4, b\right)\right)}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a, t \cdot \frac{-4}{c}, \mathsf{fma}\left(x, \frac{y \cdot 9}{z \cdot c}, \frac{b}{z \cdot c}\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 69.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot 9\right)\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+16}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(x, y \cdot 9, b\right)}{z}}{c}\\ \mathbf{elif}\;t\_1 \leq 10^{+83}:\\ \;\;\;\;\frac{\mathsf{fma}\left(a, -4 \cdot \left(z \cdot t\right), b\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(9 \cdot \frac{y}{\mathsf{fma}\left(c, z, 0\right)}\right)\\ \end{array} \end{array} \]

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
 (let* ((t_1 (* y (* x 9.0))))
   (if (<= t_1 -2e+16)
     (/ (/ (fma x (* y 9.0) b) z) c)
     (if (<= t_1 1e+83)
       (/ (fma a (* -4.0 (* z t)) b) (* z c))
       (* x (* 9.0 (/ y (fma c z 0.0))))))))

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 = y * (x * 9.0);
	double tmp;
	if (t_1 <= -2e+16) {
		tmp = (fma(x, (y * 9.0), b) / z) / c;
	} else if (t_1 <= 1e+83) {
		tmp = fma(a, (-4.0 * (z * t)), b) / (z * c);
	} else {
		tmp = x * (9.0 * (y / fma(c, z, 0.0)));
	}
	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(y * Float64(x * 9.0))
	tmp = 0.0
	if (t_1 <= -2e+16)
		tmp = Float64(Float64(fma(x, Float64(y * 9.0), b) / z) / c);
	elseif (t_1 <= 1e+83)
		tmp = Float64(fma(a, Float64(-4.0 * Float64(z * t)), b) / Float64(z * c));
	else
		tmp = Float64(x * Float64(9.0 * Float64(y / fma(c, z, 0.0))));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(y * N[(x * 9.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+16], N[(N[(N[(x * N[(y * 9.0), $MachinePrecision] + b), $MachinePrecision] / z), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[t$95$1, 1e+83], N[(N[(a * N[(-4.0 * N[(z * t), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(x * N[(9.0 * N[(y / N[(c * z + 0.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -2e16

   1. Initial program 74.5%

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

      1. associate-/r* N/A

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

      2. /-lowering-/.f64 N/A

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

   4. Applied egg-rr 83.8%

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

   5. Taylor expanded in t around 0

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

   7. Simplified 67.7%

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

   if -2e16 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 1.00000000000000003e83

   1. Initial program 82.1%

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

   3. Taylor expanded in x around 0

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

      1. cancel-sign-sub-inv N/A

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. associate-*l* N/A

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

      6. *-commutative N/A

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

      7. accelerator-lowering-fma.f64 N/A

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

      8. *-commutative N/A

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

      9. *-lowering-*.f64 N/A

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

      10. *-lowering-*.f64 74.4

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

   5. Simplified 74.4%

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

   if 1.00000000000000003e83 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 75.2%

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

   3. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 N/A

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

      2. *-lowering-*.f64 66.1

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

   5. Simplified 66.1%

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

      1. *-commutative N/A

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

      2. associate-*l* N/A

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

      3. metadata-eval N/A

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

      4. distribute-rgt-neg-in N/A

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

      5. *-commutative N/A

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

      6. associate-/l* N/A

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

      7. *-lowering-*.f64 N/A

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

      8. distribute-rgt-neg-in N/A

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

      9. metadata-eval N/A

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

      10. *-lowering-*.f64 N/A

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

      11. /-lowering-/.f64 N/A

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

      12. *-lowering-*.f64 77.3

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

   7. Applied egg-rr 77.3%

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

      5. *-lowering-*.f64 N/A

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

      6. *-commutative N/A

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

      7. *-rgt-identity N/A

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

      8. times-frac N/A

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

      9. metadata-eval N/A

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

      10. *-lowering-*.f64 N/A

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

      11. /-lowering-/.f64 N/A

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

      12. +-rgt-identity N/A

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

      13. *-commutative N/A

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

      14. accelerator-lowering-fma.f64 77.3

          \[\leadsto x \cdot \left(\frac{y}{\color{blue}{\mathsf{fma}\left(c, z, 0\right)}} \cdot 9\right) \]

   9. Applied egg-rr 77.3%

      \[\leadsto \color{blue}{x \cdot \left(\frac{y}{\mathsf{fma}\left(c, z, 0\right)} \cdot 9\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 73.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \left(x \cdot 9\right) \leq -2 \cdot 10^{+16}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(x, y \cdot 9, b\right)}{z}}{c}\\ \mathbf{elif}\;y \cdot \left(x \cdot 9\right) \leq 10^{+83}:\\ \;\;\;\;\frac{\mathsf{fma}\left(a, -4 \cdot \left(z \cdot t\right), b\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(9 \cdot \frac{y}{\mathsf{fma}\left(c, z, 0\right)}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 69.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot 9\right)\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+16}:\\ \;\;\;\;\frac{\mathsf{fma}\left(9, y \cdot x, b\right)}{z \cdot c}\\ \mathbf{elif}\;t\_1 \leq 10^{+83}:\\ \;\;\;\;\frac{\mathsf{fma}\left(a, -4 \cdot \left(z \cdot t\right), b\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(9 \cdot \frac{y}{\mathsf{fma}\left(c, z, 0\right)}\right)\\ \end{array} \end{array} \]

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
 (let* ((t_1 (* y (* x 9.0))))
   (if (<= t_1 -2e+16)
     (/ (fma 9.0 (* y x) b) (* z c))
     (if (<= t_1 1e+83)
       (/ (fma a (* -4.0 (* z t)) b) (* z c))
       (* x (* 9.0 (/ y (fma c z 0.0))))))))

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 = y * (x * 9.0);
	double tmp;
	if (t_1 <= -2e+16) {
		tmp = fma(9.0, (y * x), b) / (z * c);
	} else if (t_1 <= 1e+83) {
		tmp = fma(a, (-4.0 * (z * t)), b) / (z * c);
	} else {
		tmp = x * (9.0 * (y / fma(c, z, 0.0)));
	}
	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(y * Float64(x * 9.0))
	tmp = 0.0
	if (t_1 <= -2e+16)
		tmp = Float64(fma(9.0, Float64(y * x), b) / Float64(z * c));
	elseif (t_1 <= 1e+83)
		tmp = Float64(fma(a, Float64(-4.0 * Float64(z * t)), b) / Float64(z * c));
	else
		tmp = Float64(x * Float64(9.0 * Float64(y / fma(c, z, 0.0))));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(y * N[(x * 9.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+16], N[(N[(9.0 * N[(y * x), $MachinePrecision] + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+83], N[(N[(a * N[(-4.0 * N[(z * t), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(x * N[(9.0 * N[(y / N[(c * z + 0.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -2e16

   1. Initial program 74.5%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. accelerator-lowering-fma.f64 N/A

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

      3. *-lowering-*.f64 66.2

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

   5. Simplified 66.2%

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

   if -2e16 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 1.00000000000000003e83

   1. Initial program 82.1%

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

   3. Taylor expanded in x around 0

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

      1. cancel-sign-sub-inv N/A

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. associate-*l* N/A

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

      6. *-commutative N/A

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

      7. accelerator-lowering-fma.f64 N/A

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

      8. *-commutative N/A

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

      9. *-lowering-*.f64 N/A

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

      10. *-lowering-*.f64 74.4

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

   5. Simplified 74.4%

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

   if 1.00000000000000003e83 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 75.2%

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

   3. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 N/A

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

      2. *-lowering-*.f64 66.1

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

   5. Simplified 66.1%

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

      1. *-commutative N/A

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

      2. associate-*l* N/A

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

      3. metadata-eval N/A

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

      4. distribute-rgt-neg-in N/A

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

      5. *-commutative N/A

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

      6. associate-/l* N/A

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

      7. *-lowering-*.f64 N/A

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

      8. distribute-rgt-neg-in N/A

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

      9. metadata-eval N/A

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

      10. *-lowering-*.f64 N/A

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

      11. /-lowering-/.f64 N/A

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

      12. *-lowering-*.f64 77.3

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

   7. Applied egg-rr 77.3%

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

      5. *-lowering-*.f64 N/A

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

      6. *-commutative N/A

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

      7. *-rgt-identity N/A

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

      8. times-frac N/A

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

      9. metadata-eval N/A

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

      10. *-lowering-*.f64 N/A

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

      11. /-lowering-/.f64 N/A

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

      12. +-rgt-identity N/A

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

      13. *-commutative N/A

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

      14. accelerator-lowering-fma.f64 77.3

          \[\leadsto x \cdot \left(\frac{y}{\color{blue}{\mathsf{fma}\left(c, z, 0\right)}} \cdot 9\right) \]

   9. Applied egg-rr 77.3%

      \[\leadsto \color{blue}{x \cdot \left(\frac{y}{\mathsf{fma}\left(c, z, 0\right)} \cdot 9\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 72.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \left(x \cdot 9\right) \leq -2 \cdot 10^{+16}:\\ \;\;\;\;\frac{\mathsf{fma}\left(9, y \cdot x, b\right)}{z \cdot c}\\ \mathbf{elif}\;y \cdot \left(x \cdot 9\right) \leq 10^{+83}:\\ \;\;\;\;\frac{\mathsf{fma}\left(a, -4 \cdot \left(z \cdot t\right), b\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(9 \cdot \frac{y}{\mathsf{fma}\left(c, z, 0\right)}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 54.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot 9\right)\\ t_2 := \left(x \cdot 9\right) \cdot \frac{y}{z \cdot c}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+98}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 4 \cdot 10^{+58}:\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* y (* x 9.0))) (t_2 (* (* x 9.0) (/ y (* z c)))))
   (if (<= t_1 -5e+98) t_2 (if (<= t_1 4e+58) (/ (* -4.0 (* a t)) c) t_2))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = y * (x * 9.0);
	double t_2 = (x * 9.0) * (y / (z * c));
	double tmp;
	if (t_1 <= -5e+98) {
		tmp = t_2;
	} else if (t_1 <= 4e+58) {
		tmp = (-4.0 * (a * t)) / c;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y * (x * 9.0d0)
    t_2 = (x * 9.0d0) * (y / (z * c))
    if (t_1 <= (-5d+98)) then
        tmp = t_2
    else if (t_1 <= 4d+58) then
        tmp = ((-4.0d0) * (a * t)) / c
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = y * (x * 9.0);
	double t_2 = (x * 9.0) * (y / (z * c));
	double tmp;
	if (t_1 <= -5e+98) {
		tmp = t_2;
	} else if (t_1 <= 4e+58) {
		tmp = (-4.0 * (a * t)) / c;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	t_1 = y * (x * 9.0)
	t_2 = (x * 9.0) * (y / (z * c))
	tmp = 0
	if t_1 <= -5e+98:
		tmp = t_2
	elif t_1 <= 4e+58:
		tmp = (-4.0 * (a * t)) / c
	else:
		tmp = t_2
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(y * Float64(x * 9.0))
	t_2 = Float64(Float64(x * 9.0) * Float64(y / Float64(z * c)))
	tmp = 0.0
	if (t_1 <= -5e+98)
		tmp = t_2;
	elseif (t_1 <= 4e+58)
		tmp = Float64(Float64(-4.0 * Float64(a * t)) / c);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = y * (x * 9.0);
	t_2 = (x * 9.0) * (y / (z * c));
	tmp = 0.0;
	if (t_1 <= -5e+98)
		tmp = t_2;
	elseif (t_1 <= 4e+58)
		tmp = (-4.0 * (a * t)) / c;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(y * N[(x * 9.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * 9.0), $MachinePrecision] * N[(y / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+98], t$95$2, If[LessEqual[t$95$1, 4e+58], N[(N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -4.9999999999999998e98 or 3.99999999999999978e58 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 76.5%

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

   3. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 N/A

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

      2. *-lowering-*.f64 65.2

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

   5. Simplified 65.2%

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

      1. associate-*r* N/A

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

      2. associate-/l* N/A

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

      3. *-lowering-*.f64 N/A

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

      4. *-commutative N/A

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

      5. *-lowering-*.f64 N/A

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

      6. /-lowering-/.f64 N/A

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

      7. *-lowering-*.f64 72.8

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

   7. Applied egg-rr 72.8%

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

   if -4.9999999999999998e98 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 3.99999999999999978e58

   1. Initial program 80.2%

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

   3. Taylor expanded in z around inf

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

      1. associate-*r/ N/A

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

      2. /-lowering-/.f64 N/A

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

      3. *-lowering-*.f64 N/A

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

      4. *-lowering-*.f64 48.2

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

   5. Simplified 48.2%

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

4. Final simplification 57.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \left(x \cdot 9\right) \leq -5 \cdot 10^{+98}:\\ \;\;\;\;\left(x \cdot 9\right) \cdot \frac{y}{z \cdot c}\\ \mathbf{elif}\;y \cdot \left(x \cdot 9\right) \leq 4 \cdot 10^{+58}:\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot 9\right) \cdot \frac{y}{z \cdot c}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 60.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \frac{-4 \cdot \left(a \cdot t\right)}{c}\\ \mathbf{if}\;a \leq -9.5 \cdot 10^{-126}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 4.5 \cdot 10^{+107}:\\ \;\;\;\;\frac{\mathsf{fma}\left(9, y \cdot x, b\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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)) c)))
   (if (<= a -9.5e-126)
     t_1
     (if (<= a 4.5e+107) (/ (fma 9.0 (* y x) b) (* 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)) / c;
	double tmp;
	if (a <= -9.5e-126) {
		tmp = t_1;
	} else if (a <= 4.5e+107) {
		tmp = fma(9.0, (y * x), b) / (z * c);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(-4.0 * Float64(a * t)) / c)
	tmp = 0.0
	if (a <= -9.5e-126)
		tmp = t_1;
	elseif (a <= 4.5e+107)
		tmp = Float64(fma(9.0, Float64(y * x), b) / Float64(z * c));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]}, If[LessEqual[a, -9.5e-126], t$95$1, If[LessEqual[a, 4.5e+107], N[(N[(9.0 * N[(y * x), $MachinePrecision] + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -9.5000000000000003e-126 or 4.5e107 < a

   1. Initial program 75.8%

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

   3. Taylor expanded in z around inf

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

      1. associate-*r/ N/A

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

      2. /-lowering-/.f64 N/A

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

      3. *-lowering-*.f64 N/A

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

      4. *-lowering-*.f64 48.3

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

   5. Simplified 48.3%

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

   if -9.5000000000000003e-126 < a < 4.5e107

   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. Add Preprocessing

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. accelerator-lowering-fma.f64 N/A

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

      3. *-lowering-*.f64 69.9

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

   5. Simplified 69.9%

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

4. Final simplification 58.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -9.5 \cdot 10^{-126}:\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right)}{c}\\ \mathbf{elif}\;a \leq 4.5 \cdot 10^{+107}:\\ \;\;\;\;\frac{\mathsf{fma}\left(9, y \cdot x, b\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right)}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 45.1% accurate, 1.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \frac{-4 \cdot \left(a \cdot t\right)}{c}\\ \mathbf{if}\;a \leq -2.2 \cdot 10^{-185}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 6 \cdot 10^{-26}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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)) c)))
   (if (<= a -2.2e-185) t_1 (if (<= a 6e-26) (/ (/ b c) z) 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)) / c;
	double tmp;
	if (a <= -2.2e-185) {
		tmp = t_1;
	} else if (a <= 6e-26) {
		tmp = (b / c) / z;
	} 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)) / c
    if (a <= (-2.2d-185)) then
        tmp = t_1
    else if (a <= 6d-26) then
        tmp = (b / c) / z
    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)) / c;
	double tmp;
	if (a <= -2.2e-185) {
		tmp = t_1;
	} else if (a <= 6e-26) {
		tmp = (b / c) / z;
	} 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)) / c
	tmp = 0
	if a <= -2.2e-185:
		tmp = t_1
	elif a <= 6e-26:
		tmp = (b / c) / z
	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(-4.0 * Float64(a * t)) / c)
	tmp = 0.0
	if (a <= -2.2e-185)
		tmp = t_1;
	elseif (a <= 6e-26)
		tmp = Float64(Float64(b / c) / z);
	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)) / c;
	tmp = 0.0;
	if (a <= -2.2e-185)
		tmp = t_1;
	elseif (a <= 6e-26)
		tmp = (b / c) / z;
	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[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]}, If[LessEqual[a, -2.2e-185], t$95$1, If[LessEqual[a, 6e-26], N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -2.2e-185 or 6.00000000000000023e-26 < a

   1. Initial program 75.3%

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

   3. Taylor expanded in z around inf

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

      1. associate-*r/ N/A

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

      2. /-lowering-/.f64 N/A

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

      3. *-lowering-*.f64 N/A

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

      4. *-lowering-*.f64 47.4

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

   5. Simplified 47.4%

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

   if -2.2e-185 < a < 6.00000000000000023e-26

   1. Initial program 85.8%

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

   3. Taylor expanded in b around inf

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

   5. Simplified 47.8%

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

      1. *-commutative N/A

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

      2. associate-/r* N/A

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

      3. /-lowering-/.f64 N/A

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

      4. /-lowering-/.f64 45.7

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

   7. Applied egg-rr 45.7%

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

Alternative 16: 45.3% accurate, 1.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \frac{-4 \cdot \left(a \cdot t\right)}{c}\\ \mathbf{if}\;a \leq -2.2 \cdot 10^{-185}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 4.8 \cdot 10^{-27}:\\ \;\;\;\;b \cdot \frac{1}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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)) c)))
   (if (<= a -2.2e-185) t_1 (if (<= a 4.8e-27) (* b (/ 1.0 (* 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)) / c;
	double tmp;
	if (a <= -2.2e-185) {
		tmp = t_1;
	} else if (a <= 4.8e-27) {
		tmp = b * (1.0 / (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)) / c
    if (a <= (-2.2d-185)) then
        tmp = t_1
    else if (a <= 4.8d-27) then
        tmp = b * (1.0d0 / (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)) / c;
	double tmp;
	if (a <= -2.2e-185) {
		tmp = t_1;
	} else if (a <= 4.8e-27) {
		tmp = b * (1.0 / (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)) / c
	tmp = 0
	if a <= -2.2e-185:
		tmp = t_1
	elif a <= 4.8e-27:
		tmp = b * (1.0 / (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(-4.0 * Float64(a * t)) / c)
	tmp = 0.0
	if (a <= -2.2e-185)
		tmp = t_1;
	elseif (a <= 4.8e-27)
		tmp = Float64(b * Float64(1.0 / 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)) / c;
	tmp = 0.0;
	if (a <= -2.2e-185)
		tmp = t_1;
	elseif (a <= 4.8e-27)
		tmp = b * (1.0 / (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[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]}, If[LessEqual[a, -2.2e-185], t$95$1, If[LessEqual[a, 4.8e-27], N[(b * N[(1.0 / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -2.2e-185 or 4.80000000000000004e-27 < a

   1. Initial program 75.3%

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

   3. Taylor expanded in z around inf

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

      1. associate-*r/ N/A

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

      2. /-lowering-/.f64 N/A

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

      3. *-lowering-*.f64 N/A

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

      4. *-lowering-*.f64 47.4

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

   5. Simplified 47.4%

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

   if -2.2e-185 < a < 4.80000000000000004e-27

   1. Initial program 85.8%

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

   3. Taylor expanded in b around inf

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

   5. Simplified 47.8%

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

      1. clear-num N/A

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

      2. associate-/r/ N/A

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

      3. *-lowering-*.f64 N/A

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

      4. /-lowering-/.f64 N/A

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

      5. *-lowering-*.f64 47.7

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

   7. Applied egg-rr 47.7%

      \[\leadsto \color{blue}{\frac{1}{z \cdot c} \cdot b} \]
3. Recombined 2 regimes into one program.

4. Final simplification 47.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.2 \cdot 10^{-185}:\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right)}{c}\\ \mathbf{elif}\;a \leq 4.8 \cdot 10^{-27}:\\ \;\;\;\;b \cdot \frac{1}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right)}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 34.0% accurate, 2.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{-252}:\\ \;\;\;\;\frac{b}{\mathsf{fma}\left(c, z, 0\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= z -1.9e-252) (/ b (fma c z 0.0)) (/ 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 <= -1.9e-252) {
		tmp = b / fma(c, z, 0.0);
	} else {
		tmp = b / (z * c);
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (z <= -1.9e-252)
		tmp = Float64(b / fma(c, z, 0.0));
	else
		tmp = 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, -1.9e-252], N[(b / N[(c * z + 0.0), $MachinePrecision]), $MachinePrecision], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.9e-252

   1. Initial program 77.6%

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

   3. Taylor expanded in b around inf

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

   5. Simplified 22.0%

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

      1. remove-double-neg N/A

         \[\leadsto \frac{b}{\color{blue}{\mathsf{neg}\left(\left(\mathsf{neg}\left(z \cdot c\right)\right)\right)}} \]

      2. neg-lowering-neg.f64 N/A

         \[\leadsto \frac{b}{\color{blue}{\mathsf{neg}\left(\left(\mathsf{neg}\left(z \cdot c\right)\right)\right)}} \]

      3. neg-sub0 N/A

         \[\leadsto \frac{b}{\mathsf{neg}\left(\color{blue}{\left(0 - z \cdot c\right)}\right)} \]

      4. --lowering--.f64 N/A

         \[\leadsto \frac{b}{\mathsf{neg}\left(\color{blue}{\left(0 - z \cdot c\right)}\right)} \]

      5. *-lowering-*.f64 22.9

         \[\leadsto \frac{b}{-\left(0 - \color{blue}{z \cdot c}\right)} \]

   7. Applied egg-rr 22.9%

      \[\leadsto \frac{b}{\color{blue}{-\left(0 - z \cdot c\right)}} \]
   8. Step-by-step derivation

      1. sub0-neg N/A

         \[\leadsto \frac{b}{\mathsf{neg}\left(\color{blue}{\left(\mathsf{neg}\left(z \cdot c\right)\right)}\right)} \]

      2. remove-double-neg N/A

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

      3. +-rgt-identity N/A

         \[\leadsto \frac{b}{\color{blue}{z \cdot c + 0}} \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \frac{b}{\color{blue}{z \cdot c + 0}} \]

      5. +-rgt-identity N/A

         \[\leadsto \frac{b}{\color{blue}{\left(z \cdot c + 0\right)} + 0} \]

      6. *-commutative N/A

         \[\leadsto \frac{b}{\left(\color{blue}{c \cdot z} + 0\right) + 0} \]

      7. accelerator-lowering-fma.f64 26.7

         \[\leadsto \frac{b}{\color{blue}{\mathsf{fma}\left(c, z, 0\right)} + 0} \]

   9. Applied egg-rr 26.7%

      \[\leadsto \frac{b}{\color{blue}{\mathsf{fma}\left(c, z, 0\right) + 0}} \]

   if -1.9e-252 < z

   1. Initial program 79.6%

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

   3. Taylor expanded in b around inf

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

   5. Simplified 37.5%

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

4. Final simplification 31.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{-252}:\\ \;\;\;\;\frac{b}{\mathsf{fma}\left(c, z, 0\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 34.0% accurate, 2.8× 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 78.8%

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

3. Taylor expanded in b around inf

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

5. Simplified 31.1%

   \[\leadsto \frac{\color{blue}{b}}{z \cdot c} \]
6. Add Preprocessing

Developer Target 1: 79.9% 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 2024196 
(FPCore (x y z t a b c)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, J"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< (/ (+ (- (* (* x 9) y) (* (* (* z 4) t) a)) b) (* z c)) -220031348160821/200000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (/ (+ (- (* (* x 9) y) (* (* z 4) (* t a))) b) (* z c)) (if (< (/ (+ (- (* (* x 9) y) (* (* (* z 4) t) a)) b) (* z c)) 0) (/ (/ (+ (- (* (* x 9) y) (* (* (* z 4) t) a)) b) z) c) (if (< (/ (+ (- (* (* x 9) y) (* (* (* z 4) t) a)) b) (* z c)) 365902434742109/31250000000000000000000000000000000000000000000000000000000000000000) (/ (+ (- (* (* x 9) y) (* (* z 4) (* t a))) b) (* z c)) (if (< (/ (+ (- (* (* x 9) y) (* (* (* z 4) t) a)) b) (* z c)) 28768236795461370000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (- (+ (* (* 9 (/ y c)) (/ x z)) (/ b (* c z))) (* 4 (/ (* a t) c))) (if (< (/ (+ (- (* (* x 9) y) (* (* (* z 4) t) a)) b) (* z c)) 138385150424563190000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (/ (+ (- (* (* x 9) y) (* (* z 4) (* t a))) b) (* z c)) (- (+ (* 9 (* (/ y (* c z)) x)) (/ b (* c z))) (* 4 (/ (* a t) c)))))))))

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