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

Percentage Accurate: 79.7% → 94.1%

Time: 16.8s

Alternatives: 17

Speedup: 0.9×

• 37.8% 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: 79.7% 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: 94.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\frac{b}{z} - \mathsf{fma}\left(x, \frac{y}{z} \cdot -9, \left(a \cdot t\right) \cdot 4\right)}{c}\\ \mathbf{if}\;z \leq -1.95 \cdot 10^{-46}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-16}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x \cdot 9, y, \mathsf{fma}\left(a, -4 \cdot \left(z \cdot t\right), b\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (- (/ b z) (fma x (* (/ y z) -9.0) (* (* a t) 4.0))) c)))
   (if (<= z -1.95e-46)
     t_1
     (if (<= z 5e-16)
       (/ (fma (* x 9.0) y (fma a (* -4.0 (* z t)) b)) (* z c))
       t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = ((b / z) - fma(x, ((y / z) * -9.0), ((a * t) * 4.0))) / c;
	double tmp;
	if (z <= -1.95e-46) {
		tmp = t_1;
	} else if (z <= 5e-16) {
		tmp = fma((x * 9.0), y, fma(a, (-4.0 * (z * t)), b)) / (z * c);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(Float64(b / z) - fma(x, Float64(Float64(y / z) * -9.0), Float64(Float64(a * t) * 4.0))) / c)
	tmp = 0.0
	if (z <= -1.95e-46)
		tmp = t_1;
	elseif (z <= 5e-16)
		tmp = Float64(fma(Float64(x * 9.0), y, fma(a, Float64(-4.0 * Float64(z * t)), b)) / Float64(z * c));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(N[(b / z), $MachinePrecision] - N[(x * N[(N[(y / z), $MachinePrecision] * -9.0), $MachinePrecision] + N[(N[(a * t), $MachinePrecision] * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]}, If[LessEqual[z, -1.95e-46], t$95$1, If[LessEqual[z, 5e-16], N[(N[(N[(x * 9.0), $MachinePrecision] * y + N[(a * N[(-4.0 * N[(z * t), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.9500000000000001e-46 or 5.0000000000000004e-16 < z

   1. Initial program 65.3%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   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. lower-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. lower-*.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. lower-/.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 83.5%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-/.f64 N/A

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

      6. lift-/.f64 N/A

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

      7. associate-*r/ N/A

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

      8. *-commutative N/A

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

      9. associate-/l* N/A

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

      10. lower-fma.f64 N/A

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

      11. lift-*.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 N/A

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

      14. lower-/.f64 84.0

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

   7. Applied egg-rr 84.0%

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

   8. Taylor expanded in c around -inf

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

      1. mul-1-neg N/A

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

      2. distribute-neg-frac2 N/A

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

      3. lower-/.f64 N/A

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

   10. Simplified 95.6%

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

   if -1.9500000000000001e-46 < z < 5.0000000000000004e-16

   1. Initial program 95.8%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. associate-+l- N/A

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

      7. sub-neg N/A

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

      8. lift-*.f64 N/A

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

      9. lower-fma.f64 N/A

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

      10. neg-sub0 N/A

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

      11. associate-+l- N/A

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

      12. neg-sub0 N/A

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

      13. lift-*.f64 N/A

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

      14. *-commutative N/A

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

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

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

      16. lower-fma.f64 N/A

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

   4. Applied egg-rr 95.8%

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

4. Final simplification 95.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.95 \cdot 10^{-46}:\\ \;\;\;\;\frac{\frac{b}{z} - \mathsf{fma}\left(x, \frac{y}{z} \cdot -9, \left(a \cdot t\right) \cdot 4\right)}{c}\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-16}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x \cdot 9, y, \mathsf{fma}\left(a, -4 \cdot \left(z \cdot t\right), b\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{z} - \mathsf{fma}\left(x, \frac{y}{z} \cdot -9, \left(a \cdot t\right) \cdot 4\right)}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 52.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{z \cdot c}\\ t_2 := y \cdot \left(x \cdot 9\right)\\ \mathbf{if}\;t\_2 \leq -1.5 \cdot 10^{+28}:\\ \;\;\;\;9 \cdot \left(x \cdot t\_1\right)\\ \mathbf{elif}\;t\_2 \leq -2 \cdot 10^{-161}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;t\_2 \leq 10^{-117}:\\ \;\;\;\;a \cdot \left(t \cdot \frac{-4}{c}\right)\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+112}:\\ \;\;\;\;b \cdot \frac{1}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(9 \cdot t\_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ y (* z c))) (t_2 (* y (* x 9.0))))
   (if (<= t_2 -1.5e+28)
     (* 9.0 (* x t_1))
     (if (<= t_2 -2e-161)
       (/ (/ b c) z)
       (if (<= t_2 1e-117)
         (* a (* t (/ -4.0 c)))
         (if (<= t_2 2e+112) (* b (/ 1.0 (* z c))) (* x (* 9.0 t_1))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = y / (z * c);
	double t_2 = y * (x * 9.0);
	double tmp;
	if (t_2 <= -1.5e+28) {
		tmp = 9.0 * (x * t_1);
	} else if (t_2 <= -2e-161) {
		tmp = (b / c) / z;
	} else if (t_2 <= 1e-117) {
		tmp = a * (t * (-4.0 / c));
	} else if (t_2 <= 2e+112) {
		tmp = b * (1.0 / (z * c));
	} else {
		tmp = x * (9.0 * t_1);
	}
	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) :: tmp
    t_1 = y / (z * c)
    t_2 = y * (x * 9.0d0)
    if (t_2 <= (-1.5d+28)) then
        tmp = 9.0d0 * (x * t_1)
    else if (t_2 <= (-2d-161)) then
        tmp = (b / c) / z
    else if (t_2 <= 1d-117) then
        tmp = a * (t * ((-4.0d0) / c))
    else if (t_2 <= 2d+112) then
        tmp = b * (1.0d0 / (z * c))
    else
        tmp = x * (9.0d0 * t_1)
    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 = y / (z * c);
	double t_2 = y * (x * 9.0);
	double tmp;
	if (t_2 <= -1.5e+28) {
		tmp = 9.0 * (x * t_1);
	} else if (t_2 <= -2e-161) {
		tmp = (b / c) / z;
	} else if (t_2 <= 1e-117) {
		tmp = a * (t * (-4.0 / c));
	} else if (t_2 <= 2e+112) {
		tmp = b * (1.0 / (z * c));
	} else {
		tmp = x * (9.0 * t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = y / (z * c)
	t_2 = y * (x * 9.0)
	tmp = 0
	if t_2 <= -1.5e+28:
		tmp = 9.0 * (x * t_1)
	elif t_2 <= -2e-161:
		tmp = (b / c) / z
	elif t_2 <= 1e-117:
		tmp = a * (t * (-4.0 / c))
	elif t_2 <= 2e+112:
		tmp = b * (1.0 / (z * c))
	else:
		tmp = x * (9.0 * t_1)
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(y / Float64(z * c))
	t_2 = Float64(y * Float64(x * 9.0))
	tmp = 0.0
	if (t_2 <= -1.5e+28)
		tmp = Float64(9.0 * Float64(x * t_1));
	elseif (t_2 <= -2e-161)
		tmp = Float64(Float64(b / c) / z);
	elseif (t_2 <= 1e-117)
		tmp = Float64(a * Float64(t * Float64(-4.0 / c)));
	elseif (t_2 <= 2e+112)
		tmp = Float64(b * Float64(1.0 / Float64(z * c)));
	else
		tmp = Float64(x * Float64(9.0 * t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = y / (z * c);
	t_2 = y * (x * 9.0);
	tmp = 0.0;
	if (t_2 <= -1.5e+28)
		tmp = 9.0 * (x * t_1);
	elseif (t_2 <= -2e-161)
		tmp = (b / c) / z;
	elseif (t_2 <= 1e-117)
		tmp = a * (t * (-4.0 / c));
	elseif (t_2 <= 2e+112)
		tmp = b * (1.0 / (z * c));
	else
		tmp = x * (9.0 * t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(y / N[(z * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(x * 9.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -1.5e+28], N[(9.0 * N[(x * t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, -2e-161], N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t$95$2, 1e-117], N[(a * N[(t * N[(-4.0 / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 2e+112], N[(b * N[(1.0 / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(9.0 * t$95$1), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -1.5e28

   1. Initial program 71.0%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. 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. lower-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. lower-*.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. lower-/.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 70.7%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-/.f64 N/A

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

      6. lift-/.f64 N/A

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

      7. associate-*r/ N/A

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

      8. *-commutative N/A

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

      9. associate-/l* N/A

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

      10. lower-fma.f64 N/A

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

      11. lift-*.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 N/A

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

      14. lower-/.f64 77.5

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

   7. Applied egg-rr 77.5%

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

   8. Taylor expanded in y around inf

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

      1. lower-*.f64 N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower-*.f64 55.4

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

   10. Simplified 55.4%

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

   if -1.5e28 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -2.00000000000000006e-161

   1. Initial program 90.4%

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

   3. Taylor expanded in b around inf

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 55.4

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

   5. Simplified 55.4%

      \[\leadsto \color{blue}{\frac{b}{z \cdot c}} \]
   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. lower-/.f64 N/A

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

      4. lower-/.f64 58.4

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

   7. Applied egg-rr 58.4%

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

   if -2.00000000000000006e-161 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 1.00000000000000003e-117

   1. Initial program 77.5%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. 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. lower-/.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 50.6

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

   5. Simplified 50.6%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. associate-*r/ N/A

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

      4. lift-/.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. associate-*l* N/A

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

      7. lower-*.f64 N/A

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

      8. lower-*.f64 53.1

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

   7. Applied egg-rr 53.1%

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

   if 1.00000000000000003e-117 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 1.9999999999999999e112

   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 inf

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 56.9

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

   5. Simplified 56.9%

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

      1. lift-*.f64 N/A

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

      2. clear-num N/A

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

      3. associate-/r/ N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 57.0

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

   7. Applied egg-rr 57.0%

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

   if 1.9999999999999999e112 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 76.7%

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

   3. Taylor expanded in x around 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. lower-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. lower-*.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. lower-/.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 74.1%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-/.f64 N/A

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

      6. lift-/.f64 N/A

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

      7. associate-*r/ N/A

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

      8. *-commutative N/A

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

      9. associate-/l* N/A

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

      10. lower-fma.f64 N/A

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

      11. lift-*.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 N/A

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

      14. lower-/.f64 74.2

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

   7. Applied egg-rr 74.2%

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

   8. Taylor expanded in c around -inf

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

      1. mul-1-neg N/A

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

      2. distribute-neg-frac2 N/A

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

      3. lower-/.f64 N/A

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

   10. Simplified 79.2%

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

   11. Taylor expanded in x around inf

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

       1. associate-/l* N/A

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

       2. associate-*r* N/A

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

       3. *-commutative N/A

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

       4. associate-*r* N/A

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

       5. lower-*.f64 N/A

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

       6. lower-*.f64 N/A

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

       7. lower-/.f64 N/A

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

       8. *-commutative N/A

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

       9. lower-*.f64 78.9

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

   13. Simplified 78.9%

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

4. Final simplification 59.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \left(x \cdot 9\right) \leq -1.5 \cdot 10^{+28}:\\ \;\;\;\;9 \cdot \left(x \cdot \frac{y}{z \cdot c}\right)\\ \mathbf{elif}\;y \cdot \left(x \cdot 9\right) \leq -2 \cdot 10^{-161}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;y \cdot \left(x \cdot 9\right) \leq 10^{-117}:\\ \;\;\;\;a \cdot \left(t \cdot \frac{-4}{c}\right)\\ \mathbf{elif}\;y \cdot \left(x \cdot 9\right) \leq 2 \cdot 10^{+112}:\\ \;\;\;\;b \cdot \frac{1}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(9 \cdot \frac{y}{z \cdot c}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 52.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot 9\right)\\ t_2 := 9 \cdot \left(x \cdot \frac{y}{z \cdot c}\right)\\ \mathbf{if}\;t\_1 \leq -1.5 \cdot 10^{+28}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq -2 \cdot 10^{-161}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;t\_1 \leq 10^{-117}:\\ \;\;\;\;a \cdot \left(t \cdot \frac{-4}{c}\right)\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+112}:\\ \;\;\;\;b \cdot \frac{1}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* y (* x 9.0))) (t_2 (* 9.0 (* x (/ y (* z c))))))
   (if (<= t_1 -1.5e+28)
     t_2
     (if (<= t_1 -2e-161)
       (/ (/ b c) z)
       (if (<= t_1 1e-117)
         (* a (* t (/ -4.0 c)))
         (if (<= t_1 2e+112) (* b (/ 1.0 (* z c))) t_2))))))

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 = 9.0 * (x * (y / (z * c)));
	double tmp;
	if (t_1 <= -1.5e+28) {
		tmp = t_2;
	} else if (t_1 <= -2e-161) {
		tmp = (b / c) / z;
	} else if (t_1 <= 1e-117) {
		tmp = a * (t * (-4.0 / c));
	} else if (t_1 <= 2e+112) {
		tmp = b * (1.0 / (z * c));
	} else {
		tmp = 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) :: tmp
    t_1 = y * (x * 9.0d0)
    t_2 = 9.0d0 * (x * (y / (z * c)))
    if (t_1 <= (-1.5d+28)) then
        tmp = t_2
    else if (t_1 <= (-2d-161)) then
        tmp = (b / c) / z
    else if (t_1 <= 1d-117) then
        tmp = a * (t * ((-4.0d0) / c))
    else if (t_1 <= 2d+112) then
        tmp = b * (1.0d0 / (z * c))
    else
        tmp = 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 = y * (x * 9.0);
	double t_2 = 9.0 * (x * (y / (z * c)));
	double tmp;
	if (t_1 <= -1.5e+28) {
		tmp = t_2;
	} else if (t_1 <= -2e-161) {
		tmp = (b / c) / z;
	} else if (t_1 <= 1e-117) {
		tmp = a * (t * (-4.0 / c));
	} else if (t_1 <= 2e+112) {
		tmp = b * (1.0 / (z * c));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = y * (x * 9.0)
	t_2 = 9.0 * (x * (y / (z * c)))
	tmp = 0
	if t_1 <= -1.5e+28:
		tmp = t_2
	elif t_1 <= -2e-161:
		tmp = (b / c) / z
	elif t_1 <= 1e-117:
		tmp = a * (t * (-4.0 / c))
	elif t_1 <= 2e+112:
		tmp = b * (1.0 / (z * c))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(y * Float64(x * 9.0))
	t_2 = Float64(9.0 * Float64(x * Float64(y / Float64(z * c))))
	tmp = 0.0
	if (t_1 <= -1.5e+28)
		tmp = t_2;
	elseif (t_1 <= -2e-161)
		tmp = Float64(Float64(b / c) / z);
	elseif (t_1 <= 1e-117)
		tmp = Float64(a * Float64(t * Float64(-4.0 / c)));
	elseif (t_1 <= 2e+112)
		tmp = Float64(b * Float64(1.0 / Float64(z * c)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = y * (x * 9.0);
	t_2 = 9.0 * (x * (y / (z * c)));
	tmp = 0.0;
	if (t_1 <= -1.5e+28)
		tmp = t_2;
	elseif (t_1 <= -2e-161)
		tmp = (b / c) / z;
	elseif (t_1 <= 1e-117)
		tmp = a * (t * (-4.0 / c));
	elseif (t_1 <= 2e+112)
		tmp = b * (1.0 / (z * c));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

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[(9.0 * N[(x * N[(y / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1.5e+28], t$95$2, If[LessEqual[t$95$1, -2e-161], N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t$95$1, 1e-117], N[(a * N[(t * N[(-4.0 / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+112], N[(b * N[(1.0 / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -1.5e28 or 1.9999999999999999e112 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 73.5%

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

   3. Taylor expanded in x around 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. lower-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. lower-*.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. lower-/.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 72.2%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-/.f64 N/A

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

      6. lift-/.f64 N/A

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

      7. associate-*r/ N/A

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

      8. *-commutative N/A

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

      9. associate-/l* N/A

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

      10. lower-fma.f64 N/A

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

      11. lift-*.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 N/A

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

      14. lower-/.f64 76.0

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

   7. Applied egg-rr 76.0%

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

   8. Taylor expanded in y around inf

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

      1. lower-*.f64 N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower-*.f64 65.9

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

   10. Simplified 65.9%

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

   if -1.5e28 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -2.00000000000000006e-161

   1. Initial program 90.4%

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

   3. Taylor expanded in b around inf

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 55.4

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

   5. Simplified 55.4%

      \[\leadsto \color{blue}{\frac{b}{z \cdot c}} \]
   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. lower-/.f64 N/A

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

      4. lower-/.f64 58.4

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

   7. Applied egg-rr 58.4%

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

   if -2.00000000000000006e-161 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 1.00000000000000003e-117

   1. Initial program 77.5%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. 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. lower-/.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 50.6

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

   5. Simplified 50.6%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. associate-*r/ N/A

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

      4. lift-/.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. associate-*l* N/A

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

      7. lower-*.f64 N/A

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

      8. lower-*.f64 53.1

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

   7. Applied egg-rr 53.1%

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

   if 1.00000000000000003e-117 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 1.9999999999999999e112

   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 inf

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 56.9

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

   5. Simplified 56.9%

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

      1. lift-*.f64 N/A

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

      2. clear-num N/A

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

      3. associate-/r/ N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 57.0

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

   7. Applied egg-rr 57.0%

      \[\leadsto \color{blue}{\frac{1}{z \cdot c} \cdot b} \]
3. Recombined 4 regimes into one program.

4. Final simplification 59.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \left(x \cdot 9\right) \leq -1.5 \cdot 10^{+28}:\\ \;\;\;\;9 \cdot \left(x \cdot \frac{y}{z \cdot c}\right)\\ \mathbf{elif}\;y \cdot \left(x \cdot 9\right) \leq -2 \cdot 10^{-161}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;y \cdot \left(x \cdot 9\right) \leq 10^{-117}:\\ \;\;\;\;a \cdot \left(t \cdot \frac{-4}{c}\right)\\ \mathbf{elif}\;y \cdot \left(x \cdot 9\right) \leq 2 \cdot 10^{+112}:\\ \;\;\;\;b \cdot \frac{1}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;9 \cdot \left(x \cdot \frac{y}{z \cdot c}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 70.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot 9\right)\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+14}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(9, x \cdot y, b\right)}{c}}{z}\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+112}:\\ \;\;\;\;\frac{\mathsf{fma}\left(a, -4 \cdot \left(z \cdot t\right), b\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(9 \cdot \frac{y}{z \cdot c}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* y (* x 9.0))))
   (if (<= t_1 -5e+14)
     (/ (/ (fma 9.0 (* x y) b) c) z)
     (if (<= t_1 2e+112)
       (/ (fma a (* -4.0 (* z t)) b) (* z c))
       (* x (* 9.0 (/ y (* z c))))))))

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 <= -5e+14) {
		tmp = (fma(9.0, (x * y), b) / c) / z;
	} else if (t_1 <= 2e+112) {
		tmp = fma(a, (-4.0 * (z * t)), b) / (z * c);
	} else {
		tmp = x * (9.0 * (y / (z * c)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(y * Float64(x * 9.0))
	tmp = 0.0
	if (t_1 <= -5e+14)
		tmp = Float64(Float64(fma(9.0, Float64(x * y), b) / c) / z);
	elseif (t_1 <= 2e+112)
		tmp = Float64(fma(a, Float64(-4.0 * Float64(z * t)), b) / Float64(z * c));
	else
		tmp = Float64(x * Float64(9.0 * Float64(y / Float64(z * c))));
	end
	return tmp
end

Wolfram

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, -5e+14], N[(N[(N[(9.0 * N[(x * y), $MachinePrecision] + b), $MachinePrecision] / c), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t$95$1, 2e+112], 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[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -5e14

   1. Initial program 70.7%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lift--.f64 N/A

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

      7. lift-+.f64 N/A

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

      8. associate-/l/ N/A

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

      9. lower-/.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 71.1%

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

   5. Taylor expanded in a around 0

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

      1. lower-/.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-*.f64 66.5

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

   7. Simplified 66.5%

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

   if -5e14 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 1.9999999999999999e112

   1. Initial program 83.9%

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

   3. Taylor expanded in 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. lower-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. lower-*.f64 N/A

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

      10. lower-*.f64 77.3

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

   5. Simplified 77.3%

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

   if 1.9999999999999999e112 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 76.7%

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

   3. Taylor expanded in x around 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. lower-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. lower-*.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. lower-/.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 74.1%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-/.f64 N/A

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

      6. lift-/.f64 N/A

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

      7. associate-*r/ N/A

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

      8. *-commutative N/A

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

      9. associate-/l* N/A

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

      10. lower-fma.f64 N/A

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

      11. lift-*.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 N/A

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

      14. lower-/.f64 74.2

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

   7. Applied egg-rr 74.2%

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

   8. Taylor expanded in c around -inf

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

      1. mul-1-neg N/A

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

      2. distribute-neg-frac2 N/A

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

      3. lower-/.f64 N/A

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

   10. Simplified 79.2%

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

   11. Taylor expanded in x around inf

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

       1. associate-/l* N/A

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

       2. associate-*r* N/A

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

       3. *-commutative N/A

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

       4. associate-*r* N/A

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

       5. lower-*.f64 N/A

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

       6. lower-*.f64 N/A

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

       7. lower-/.f64 N/A

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

       8. *-commutative N/A

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

       9. lower-*.f64 78.9

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

   13. Simplified 78.9%

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

4. Final simplification 74.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \left(x \cdot 9\right) \leq -5 \cdot 10^{+14}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(9, x \cdot y, b\right)}{c}}{z}\\ \mathbf{elif}\;y \cdot \left(x \cdot 9\right) \leq 2 \cdot 10^{+112}:\\ \;\;\;\;\frac{\mathsf{fma}\left(a, -4 \cdot \left(z \cdot t\right), b\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(9 \cdot \frac{y}{z \cdot c}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 70.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot 9\right)\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+15}:\\ \;\;\;\;\frac{\mathsf{fma}\left(9, x \cdot y, b\right)}{z \cdot c}\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+112}:\\ \;\;\;\;\frac{\mathsf{fma}\left(a, -4 \cdot \left(z \cdot t\right), b\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(9 \cdot \frac{y}{z \cdot c}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* y (* x 9.0))))
   (if (<= t_1 -1e+15)
     (/ (fma 9.0 (* x y) b) (* z c))
     (if (<= t_1 2e+112)
       (/ (fma a (* -4.0 (* z t)) b) (* z c))
       (* x (* 9.0 (/ y (* z c))))))))

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 <= -1e+15) {
		tmp = fma(9.0, (x * y), b) / (z * c);
	} else if (t_1 <= 2e+112) {
		tmp = fma(a, (-4.0 * (z * t)), b) / (z * c);
	} else {
		tmp = x * (9.0 * (y / (z * c)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(y * Float64(x * 9.0))
	tmp = 0.0
	if (t_1 <= -1e+15)
		tmp = Float64(fma(9.0, Float64(x * y), b) / Float64(z * c));
	elseif (t_1 <= 2e+112)
		tmp = Float64(fma(a, Float64(-4.0 * Float64(z * t)), b) / Float64(z * c));
	else
		tmp = Float64(x * Float64(9.0 * Float64(y / Float64(z * c))));
	end
	return tmp
end

Wolfram

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, -1e+15], N[(N[(9.0 * N[(x * y), $MachinePrecision] + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+112], 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[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -1e15

   1. Initial program 70.2%

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

   3. Taylor expanded in z around 0

      \[\leadsto \frac{\color{blue}{b + 9 \cdot \left(x \cdot y\right)}}{z \cdot c} \]
   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. lower-fma.f64 N/A

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

      3. lower-*.f64 62.9

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

   5. Simplified 62.9%

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

   if -1e15 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 1.9999999999999999e112

   1. Initial program 84.0%

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

   3. Taylor expanded in x around 0

      \[\leadsto \frac{\color{blue}{b - 4 \cdot \left(a \cdot \left(t \cdot z\right)\right)}}{z \cdot c} \]
   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. lower-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. lower-*.f64 N/A

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

      10. lower-*.f64 77.4

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

   5. Simplified 77.4%

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

   if 1.9999999999999999e112 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 76.7%

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

   3. Taylor expanded in x around 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. lower-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. lower-*.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. lower-/.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 74.1%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-/.f64 N/A

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

      6. lift-/.f64 N/A

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

      7. associate-*r/ N/A

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

      8. *-commutative N/A

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

      9. associate-/l* N/A

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

      10. lower-fma.f64 N/A

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

      11. lift-*.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 N/A

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

      14. lower-/.f64 74.2

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

   7. Applied egg-rr 74.2%

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

   8. Taylor expanded in c around -inf

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

      1. mul-1-neg N/A

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

      2. distribute-neg-frac2 N/A

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

      3. lower-/.f64 N/A

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

   10. Simplified 79.2%

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

   11. Taylor expanded in x around inf

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

       1. associate-/l* N/A

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

       2. associate-*r* N/A

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

       3. *-commutative N/A

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

       4. associate-*r* N/A

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

       5. lower-*.f64 N/A

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

       6. lower-*.f64 N/A

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

       7. lower-/.f64 N/A

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

       8. *-commutative N/A

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

       9. lower-*.f64 78.9

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

   13. Simplified 78.9%

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

4. Final simplification 74.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \left(x \cdot 9\right) \leq -1 \cdot 10^{+15}:\\ \;\;\;\;\frac{\mathsf{fma}\left(9, x \cdot y, b\right)}{z \cdot c}\\ \mathbf{elif}\;y \cdot \left(x \cdot 9\right) \leq 2 \cdot 10^{+112}:\\ \;\;\;\;\frac{\mathsf{fma}\left(a, -4 \cdot \left(z \cdot t\right), b\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(9 \cdot \frac{y}{z \cdot c}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 91.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\mathsf{fma}\left(t \cdot 4, a, \frac{x \cdot \left(y \cdot -9\right) - b}{z}\right)}{-c}\\ \mathbf{if}\;z \leq -1.34 \cdot 10^{-45}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-51}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x \cdot 9, y, \mathsf{fma}\left(a, -4 \cdot \left(z \cdot t\right), b\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (fma (* t 4.0) a (/ (- (* x (* y -9.0)) b) z)) (- c))))
   (if (<= z -1.34e-45)
     t_1
     (if (<= z 8e-51)
       (/ (fma (* x 9.0) y (fma a (* -4.0 (* z t)) b)) (* z c))
       t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = fma((t * 4.0), a, (((x * (y * -9.0)) - b) / z)) / -c;
	double tmp;
	if (z <= -1.34e-45) {
		tmp = t_1;
	} else if (z <= 8e-51) {
		tmp = fma((x * 9.0), y, fma(a, (-4.0 * (z * t)), b)) / (z * c);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(fma(Float64(t * 4.0), a, Float64(Float64(Float64(x * Float64(y * -9.0)) - b) / z)) / Float64(-c))
	tmp = 0.0
	if (z <= -1.34e-45)
		tmp = t_1;
	elseif (z <= 8e-51)
		tmp = Float64(fma(Float64(x * 9.0), y, fma(a, Float64(-4.0 * Float64(z * t)), b)) / Float64(z * c));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(N[(t * 4.0), $MachinePrecision] * a + N[(N[(N[(x * N[(y * -9.0), $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] / (-c)), $MachinePrecision]}, If[LessEqual[z, -1.34e-45], t$95$1, If[LessEqual[z, 8e-51], N[(N[(N[(x * 9.0), $MachinePrecision] * y + N[(a * N[(-4.0 * N[(z * t), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.34e-45 or 8.0000000000000001e-51 < z

   1. Initial program 65.9%

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

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) - 4 \cdot \frac{a \cdot t}{c}} \]
   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. lower-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. lower-*.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. lower-/.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 83.1%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-/.f64 N/A

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

      6. lift-/.f64 N/A

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

      7. associate-*r/ N/A

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

      8. *-commutative N/A

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

      9. associate-/l* N/A

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

      10. lower-fma.f64 N/A

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

      11. lift-*.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 N/A

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

      14. lower-/.f64 84.2

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

   7. Applied egg-rr 84.2%

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

   8. Taylor expanded in c around -inf

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

      1. mul-1-neg N/A

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

      2. distribute-neg-frac2 N/A

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

      3. lower-/.f64 N/A

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

   10. Simplified 94.5%

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

       1. lift-/.f64 N/A

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

       2. lift-*.f64 N/A

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

       3. lift-*.f64 N/A

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

       4. lift-*.f64 N/A

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

       5. +-commutative N/A

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

       6. lift-/.f64 N/A

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

       7. associate--l+ N/A

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

       8. lift-*.f64 N/A

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

       9. lift-*.f64 N/A

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

       10. associate-*l* N/A

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

       11. *-commutative N/A

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

       12. lower-fma.f64 N/A

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

       13. lower-*.f64 N/A

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

       14. lift-*.f64 N/A

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

       15. lift-/.f64 N/A

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

       16. associate-*l/ N/A

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

       17. associate-*r/ N/A

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

       18. lift-/.f64 N/A

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

       19. sub-div N/A

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

   12. Applied egg-rr 88.7%

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

   if -1.34e-45 < z < 8.0000000000000001e-51

   1. Initial program 97.2%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. associate-+l- N/A

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

      7. sub-neg N/A

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

      8. lift-*.f64 N/A

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

      9. lower-fma.f64 N/A

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

      10. neg-sub0 N/A

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

      11. associate-+l- N/A

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

      12. neg-sub0 N/A

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

      13. lift-*.f64 N/A

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

      14. *-commutative N/A

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

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

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

      16. lower-fma.f64 N/A

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

   4. Applied egg-rr 97.2%

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

Alternative 7: 86.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\frac{b}{z} + t \cdot \left(a \cdot -4\right)}{c}\\ \mathbf{if}\;z \leq -1.18 \cdot 10^{+73}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{+65}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x \cdot 9, y, \mathsf{fma}\left(a, -4 \cdot \left(z \cdot t\right), b\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (+ (/ b z) (* t (* a -4.0))) c)))
   (if (<= z -1.18e+73)
     t_1
     (if (<= z 3.8e+65)
       (/ (fma (* x 9.0) y (fma a (* -4.0 (* z t)) b)) (* z c))
       t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = ((b / z) + (t * (a * -4.0))) / c;
	double tmp;
	if (z <= -1.18e+73) {
		tmp = t_1;
	} else if (z <= 3.8e+65) {
		tmp = fma((x * 9.0), y, fma(a, (-4.0 * (z * t)), b)) / (z * c);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(Float64(b / z) + Float64(t * Float64(a * -4.0))) / c)
	tmp = 0.0
	if (z <= -1.18e+73)
		tmp = t_1;
	elseif (z <= 3.8e+65)
		tmp = Float64(fma(Float64(x * 9.0), y, fma(a, Float64(-4.0 * Float64(z * t)), b)) / Float64(z * c));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(N[(b / z), $MachinePrecision] + N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]}, If[LessEqual[z, -1.18e+73], t$95$1, If[LessEqual[z, 3.8e+65], N[(N[(N[(x * 9.0), $MachinePrecision] * y + N[(a * N[(-4.0 * N[(z * t), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.18000000000000004e73 or 3.80000000000000011e65 < z

   1. Initial program 50.6%

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

   3. Taylor expanded in x around 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. lower-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. lower-*.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. lower-/.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 82.5%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-/.f64 N/A

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

      6. lift-/.f64 N/A

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

      7. associate-*r/ N/A

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

      8. *-commutative N/A

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

      9. associate-/l* N/A

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

      10. lower-fma.f64 N/A

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

      11. lift-*.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 N/A

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

      14. lower-/.f64 81.5

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

   7. Applied egg-rr 81.5%

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

   8. Taylor expanded in c around -inf

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

      1. mul-1-neg N/A

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

      2. distribute-neg-frac2 N/A

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

      3. lower-/.f64 N/A

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

   10. Simplified 93.7%

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

   11. Taylor expanded in x around 0

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

       1. associate-*r/ N/A

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

       2. lower-/.f64 N/A

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

       3. mul-1-neg N/A

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

       4. sub-neg N/A

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

       5. +-commutative N/A

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

       6. distribute-neg-in N/A

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

       7. remove-double-neg N/A

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

       8. sub-neg N/A

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

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

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

       10. metadata-eval N/A

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

       11. lower-+.f64 N/A

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

       12. lower-/.f64 N/A

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

       13. associate-*r* N/A

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

       14. *-commutative N/A

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

       15. lower-*.f64 N/A

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

       16. *-commutative N/A

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

       17. lower-*.f64 76.3

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

   13. Simplified 76.3%

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

   if -1.18000000000000004e73 < z < 3.80000000000000011e65

   1. Initial program 96.0%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. associate-+l- N/A

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

      7. sub-neg N/A

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

      8. lift-*.f64 N/A

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

      9. lower-fma.f64 N/A

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

      10. neg-sub0 N/A

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

      11. associate-+l- N/A

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

      12. neg-sub0 N/A

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

      13. lift-*.f64 N/A

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

      14. *-commutative N/A

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

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

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

      16. lower-fma.f64 N/A

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

   4. Applied egg-rr 96.0%

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

Alternative 8: 69.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a \cdot -4\right) \cdot \frac{t}{c}\\ \mathbf{if}\;z \leq -3.8 \cdot 10^{+81}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{-68}:\\ \;\;\;\;\frac{\mathsf{fma}\left(9, x \cdot y, b\right)}{z \cdot c}\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{+134}:\\ \;\;\;\;\frac{\mathsf{fma}\left(z \cdot \left(a \cdot -4\right), t, b\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* a -4.0) (/ t c))))
   (if (<= z -3.8e+81)
     t_1
     (if (<= z 1.05e-68)
       (/ (fma 9.0 (* x y) b) (* z c))
       (if (<= z 2.8e+134) (/ (fma (* z (* a -4.0)) t b) (* z c)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (a * -4.0) * (t / c);
	double tmp;
	if (z <= -3.8e+81) {
		tmp = t_1;
	} else if (z <= 1.05e-68) {
		tmp = fma(9.0, (x * y), b) / (z * c);
	} else if (z <= 2.8e+134) {
		tmp = fma((z * (a * -4.0)), t, b) / (z * c);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(a * -4.0) * Float64(t / c))
	tmp = 0.0
	if (z <= -3.8e+81)
		tmp = t_1;
	elseif (z <= 1.05e-68)
		tmp = Float64(fma(9.0, Float64(x * y), b) / Float64(z * c));
	elseif (z <= 2.8e+134)
		tmp = Float64(fma(Float64(z * Float64(a * -4.0)), t, b) / Float64(z * c));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(a * -4.0), $MachinePrecision] * N[(t / c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.8e+81], t$95$1, If[LessEqual[z, 1.05e-68], N[(N[(9.0 * N[(x * y), $MachinePrecision] + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.8e+134], N[(N[(N[(z * N[(a * -4.0), $MachinePrecision]), $MachinePrecision] * t + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.8e81 or 2.7999999999999999e134 < z

   1. Initial program 49.2%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   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. lower-/.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 60.2

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

   5. Simplified 60.2%

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

      1. associate-*r* N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 63.6

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

   7. Applied egg-rr 63.6%

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

   if -3.8e81 < z < 1.05000000000000004e-68

   1. Initial program 96.7%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. 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. lower-fma.f64 N/A

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

      3. lower-*.f64 85.2

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

   5. Simplified 85.2%

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

   if 1.05000000000000004e-68 < z < 2.7999999999999999e134

   1. Initial program 80.3%

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

   3. Taylor expanded in x around 0

      \[\leadsto \frac{\color{blue}{b - 4 \cdot \left(a \cdot \left(t \cdot z\right)\right)}}{z \cdot c} \]
   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. lower-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. lower-*.f64 N/A

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

      10. lower-*.f64 67.9

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

   5. Simplified 67.9%

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

      1. *-commutative N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-*r* N/A

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

      5. lift-*.f64 N/A

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

      6. associate-*r* N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 70.2

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

   7. Applied egg-rr 70.2%

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

4. Final simplification 76.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{+81}:\\ \;\;\;\;\left(a \cdot -4\right) \cdot \frac{t}{c}\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{-68}:\\ \;\;\;\;\frac{\mathsf{fma}\left(9, x \cdot y, b\right)}{z \cdot c}\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{+134}:\\ \;\;\;\;\frac{\mathsf{fma}\left(z \cdot \left(a \cdot -4\right), t, b\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\left(a \cdot -4\right) \cdot \frac{t}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 75.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\frac{b}{z} + t \cdot \left(a \cdot -4\right)}{c}\\ \mathbf{if}\;z \leq -2.4 \cdot 10^{+72}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.25 \cdot 10^{-83}:\\ \;\;\;\;\frac{\mathsf{fma}\left(9, x \cdot y, b\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (+ (/ b z) (* t (* a -4.0))) c)))
   (if (<= z -2.4e+72)
     t_1
     (if (<= z 2.25e-83) (/ (fma 9.0 (* x y) b) (* z c)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = ((b / z) + (t * (a * -4.0))) / c;
	double tmp;
	if (z <= -2.4e+72) {
		tmp = t_1;
	} else if (z <= 2.25e-83) {
		tmp = fma(9.0, (x * y), b) / (z * c);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(Float64(b / z) + Float64(t * Float64(a * -4.0))) / c)
	tmp = 0.0
	if (z <= -2.4e+72)
		tmp = t_1;
	elseif (z <= 2.25e-83)
		tmp = Float64(fma(9.0, Float64(x * y), b) / Float64(z * c));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(N[(b / z), $MachinePrecision] + N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]}, If[LessEqual[z, -2.4e+72], t$95$1, If[LessEqual[z, 2.25e-83], N[(N[(9.0 * N[(x * y), $MachinePrecision] + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -2.4000000000000001e72 or 2.24999999999999999e-83 < z

   1. Initial program 61.1%

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

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\left(9 \cdot \frac{x \cdot y}{c \cdot z} + \frac{b}{c \cdot z}\right) - 4 \cdot \frac{a \cdot t}{c}} \]
   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. lower-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. lower-*.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. lower-/.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 84.4%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-/.f64 N/A

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

      6. lift-/.f64 N/A

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

      7. associate-*r/ N/A

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

      8. *-commutative N/A

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

      9. associate-/l* N/A

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

      10. lower-fma.f64 N/A

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

      11. lift-*.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 N/A

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

      14. lower-/.f64 85.2

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

   7. Applied egg-rr 85.2%

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

   8. Taylor expanded in c around -inf

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

      1. mul-1-neg N/A

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

      2. distribute-neg-frac2 N/A

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

      3. lower-/.f64 N/A

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

   10. Simplified 93.1%

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

   11. Taylor expanded in x around 0

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

       1. associate-*r/ N/A

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

       2. lower-/.f64 N/A

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

       3. mul-1-neg N/A

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

       4. sub-neg N/A

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

       5. +-commutative N/A

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

       6. distribute-neg-in N/A

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

       7. remove-double-neg N/A

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

       8. sub-neg N/A

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

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

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

       10. metadata-eval N/A

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

       11. lower-+.f64 N/A

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

       12. lower-/.f64 N/A

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

       13. associate-*r* N/A

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

       14. *-commutative N/A

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

       15. lower-*.f64 N/A

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

       16. *-commutative N/A

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

       17. lower-*.f64 75.8

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

   13. Simplified 75.8%

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

   if -2.4000000000000001e72 < z < 2.24999999999999999e-83

   1. Initial program 97.3%

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

   3. Taylor expanded in z around 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. lower-fma.f64 N/A

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

      3. lower-*.f64 85.0

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

   5. Simplified 85.0%

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

Alternative 10: 49.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -3.7 \cdot 10^{+86}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{elif}\;b \leq 10^{-166}:\\ \;\;\;\;\left(a \cdot -4\right) \cdot \frac{t}{c}\\ \mathbf{elif}\;b \leq 0.000185:\\ \;\;\;\;\frac{9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= b -3.7e+86)
   (/ (/ b z) c)
   (if (<= b 1e-166)
     (* (* a -4.0) (/ t c))
     (if (<= b 0.000185) (/ (* 9.0 (* x y)) (* z c)) (/ (/ b c) z)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (b <= -3.7e+86) {
		tmp = (b / z) / c;
	} else if (b <= 1e-166) {
		tmp = (a * -4.0) * (t / c);
	} else if (b <= 0.000185) {
		tmp = (9.0 * (x * y)) / (z * c);
	} else {
		tmp = (b / c) / z;
	}
	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) :: tmp
    if (b <= (-3.7d+86)) then
        tmp = (b / z) / c
    else if (b <= 1d-166) then
        tmp = (a * (-4.0d0)) * (t / c)
    else if (b <= 0.000185d0) then
        tmp = (9.0d0 * (x * y)) / (z * c)
    else
        tmp = (b / c) / z
    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 tmp;
	if (b <= -3.7e+86) {
		tmp = (b / z) / c;
	} else if (b <= 1e-166) {
		tmp = (a * -4.0) * (t / c);
	} else if (b <= 0.000185) {
		tmp = (9.0 * (x * y)) / (z * c);
	} else {
		tmp = (b / c) / z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if b <= -3.7e+86:
		tmp = (b / z) / c
	elif b <= 1e-166:
		tmp = (a * -4.0) * (t / c)
	elif b <= 0.000185:
		tmp = (9.0 * (x * y)) / (z * c)
	else:
		tmp = (b / c) / z
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (b <= -3.7e+86)
		tmp = Float64(Float64(b / z) / c);
	elseif (b <= 1e-166)
		tmp = Float64(Float64(a * -4.0) * Float64(t / c));
	elseif (b <= 0.000185)
		tmp = Float64(Float64(9.0 * Float64(x * y)) / Float64(z * c));
	else
		tmp = Float64(Float64(b / c) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (b <= -3.7e+86)
		tmp = (b / z) / c;
	elseif (b <= 1e-166)
		tmp = (a * -4.0) * (t / c);
	elseif (b <= 0.000185)
		tmp = (9.0 * (x * y)) / (z * c);
	else
		tmp = (b / c) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[b, -3.7e+86], N[(N[(b / z), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[b, 1e-166], N[(N[(a * -4.0), $MachinePrecision] * N[(t / c), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 0.000185], N[(N[(9.0 * N[(x * y), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if b < -3.69999999999999992e86

   1. Initial program 72.2%

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

   3. Taylor expanded in b around inf

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 58.8

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

   5. Simplified 58.8%

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

      1. associate-/r* N/A

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

      2. lower-/.f64 N/A

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

      3. lower-/.f64 64.1

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

   7. Applied egg-rr 64.1%

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

   if -3.69999999999999992e86 < b < 1.00000000000000004e-166

   1. Initial program 79.0%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. 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. lower-/.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 53.7

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

   5. Simplified 53.7%

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

      1. associate-*r* N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 53.8

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

   7. Applied egg-rr 53.8%

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

   if 1.00000000000000004e-166 < b < 1.85e-4

   1. Initial program 79.3%

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

   3. 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. lower-*.f64 N/A

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

      2. lower-*.f64 65.1

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

   5. Simplified 65.1%

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

   if 1.85e-4 < b

   1. Initial program 85.4%

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

   3. Taylor expanded in b around inf

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 59.9

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

   5. Simplified 59.9%

      \[\leadsto \color{blue}{\frac{b}{z \cdot c}} \]
   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. lower-/.f64 N/A

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

      4. lower-/.f64 60.0

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

   7. Applied egg-rr 60.0%

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

Alternative 11: 69.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.4 \cdot 10^{+87}:\\ \;\;\;\;\left(a \cdot -4\right) \cdot \frac{t}{c}\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{+70}:\\ \;\;\;\;\frac{\mathsf{fma}\left(9, x \cdot y, b\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(a \cdot \frac{-4}{c}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= z -7.4e+87)
   (* (* a -4.0) (/ t c))
   (if (<= z 5.5e+70) (/ (fma 9.0 (* x y) b) (* z c)) (* t (* a (/ -4.0 c))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (z <= -7.4e+87) {
		tmp = (a * -4.0) * (t / c);
	} else if (z <= 5.5e+70) {
		tmp = fma(9.0, (x * y), b) / (z * c);
	} else {
		tmp = t * (a * (-4.0 / c));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (z <= -7.4e+87)
		tmp = Float64(Float64(a * -4.0) * Float64(t / c));
	elseif (z <= 5.5e+70)
		tmp = Float64(fma(9.0, Float64(x * y), b) / Float64(z * c));
	else
		tmp = Float64(t * Float64(a * Float64(-4.0 / c)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[z, -7.4e+87], N[(N[(a * -4.0), $MachinePrecision] * N[(t / c), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.5e+70], N[(N[(9.0 * N[(x * y), $MachinePrecision] + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(t * N[(a * N[(-4.0 / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.40000000000000005e87

   1. Initial program 47.0%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   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. lower-/.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 58.4

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

   5. Simplified 58.4%

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

      1. associate-*r* N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 58.2

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

   7. Applied egg-rr 58.2%

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

   if -7.40000000000000005e87 < z < 5.49999999999999986e70

   1. Initial program 95.0%

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

   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. lower-fma.f64 N/A

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

      3. lower-*.f64 80.3

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

   5. Simplified 80.3%

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

   if 5.49999999999999986e70 < z

   1. Initial program 52.9%

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

   3. Taylor expanded in z around inf

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 57.1

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

   5. Simplified 57.1%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. associate-*r/ N/A

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

      4. lift-/.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

      7. associate-*l* N/A

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

      8. lower-*.f64 N/A

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

      9. lower-*.f64 58.0

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

   7. Applied egg-rr 58.0%

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

Alternative 12: 49.3% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -3.85 \cdot 10^{+80}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{elif}\;b \leq 1.42 \cdot 10^{+31}:\\ \;\;\;\;\left(a \cdot -4\right) \cdot \frac{t}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= b -3.85e+80)
   (/ (/ b z) c)
   (if (<= b 1.42e+31) (* (* a -4.0) (/ t c)) (/ (/ b c) z))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (b <= -3.85e+80) {
		tmp = (b / z) / c;
	} else if (b <= 1.42e+31) {
		tmp = (a * -4.0) * (t / c);
	} else {
		tmp = (b / c) / z;
	}
	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) :: tmp
    if (b <= (-3.85d+80)) then
        tmp = (b / z) / c
    else if (b <= 1.42d+31) then
        tmp = (a * (-4.0d0)) * (t / c)
    else
        tmp = (b / c) / z
    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 tmp;
	if (b <= -3.85e+80) {
		tmp = (b / z) / c;
	} else if (b <= 1.42e+31) {
		tmp = (a * -4.0) * (t / c);
	} else {
		tmp = (b / c) / z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if b <= -3.85e+80:
		tmp = (b / z) / c
	elif b <= 1.42e+31:
		tmp = (a * -4.0) * (t / c)
	else:
		tmp = (b / c) / z
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (b <= -3.85e+80)
		tmp = Float64(Float64(b / z) / c);
	elseif (b <= 1.42e+31)
		tmp = Float64(Float64(a * -4.0) * Float64(t / c));
	else
		tmp = Float64(Float64(b / c) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (b <= -3.85e+80)
		tmp = (b / z) / c;
	elseif (b <= 1.42e+31)
		tmp = (a * -4.0) * (t / c);
	else
		tmp = (b / c) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[b, -3.85e+80], N[(N[(b / z), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[b, 1.42e+31], N[(N[(a * -4.0), $MachinePrecision] * N[(t / c), $MachinePrecision]), $MachinePrecision], N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -3.84999999999999998e80

   1. Initial program 72.2%

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

   3. Taylor expanded in b around inf

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 58.8

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

   5. Simplified 58.8%

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

      1. associate-/r* N/A

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

      2. lower-/.f64 N/A

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

      3. lower-/.f64 64.1

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

   7. Applied egg-rr 64.1%

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

   if -3.84999999999999998e80 < b < 1.41999999999999997e31

   1. Initial program 79.8%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   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. lower-/.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 47.4

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

   5. Simplified 47.4%

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

      1. associate-*r* N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 47.5

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

   7. Applied egg-rr 47.5%

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

   if 1.41999999999999997e31 < b

   1. Initial program 84.7%

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

   3. Taylor expanded in b around inf

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 64.5

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

   5. Simplified 64.5%

      \[\leadsto \color{blue}{\frac{b}{z \cdot c}} \]
   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. lower-/.f64 N/A

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

      4. lower-/.f64 64.6

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

   7. Applied egg-rr 64.6%

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

Alternative 13: 50.6% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\frac{b}{c}}{z}\\ \mathbf{if}\;b \leq -6.5 \cdot 10^{+77}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1.45 \cdot 10^{+31}:\\ \;\;\;\;\left(a \cdot -4\right) \cdot \frac{t}{c}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (/ b c) z)))
   (if (<= b -6.5e+77) t_1 (if (<= b 1.45e+31) (* (* a -4.0) (/ t c)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (b / c) / z;
	double tmp;
	if (b <= -6.5e+77) {
		tmp = t_1;
	} else if (b <= 1.45e+31) {
		tmp = (a * -4.0) * (t / c);
	} else {
		tmp = t_1;
	}
	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) :: tmp
    t_1 = (b / c) / z
    if (b <= (-6.5d+77)) then
        tmp = t_1
    else if (b <= 1.45d+31) then
        tmp = (a * (-4.0d0)) * (t / c)
    else
        tmp = t_1
    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 tmp;
	if (b <= -6.5e+77) {
		tmp = t_1;
	} else if (b <= 1.45e+31) {
		tmp = (a * -4.0) * (t / c);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = (b / c) / z
	tmp = 0
	if b <= -6.5e+77:
		tmp = t_1
	elif b <= 1.45e+31:
		tmp = (a * -4.0) * (t / c)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(b / c) / z)
	tmp = 0.0
	if (b <= -6.5e+77)
		tmp = t_1;
	elseif (b <= 1.45e+31)
		tmp = Float64(Float64(a * -4.0) * Float64(t / c));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (b / c) / z;
	tmp = 0.0;
	if (b <= -6.5e+77)
		tmp = t_1;
	elseif (b <= 1.45e+31)
		tmp = (a * -4.0) * (t / c);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision]}, If[LessEqual[b, -6.5e+77], t$95$1, If[LessEqual[b, 1.45e+31], N[(N[(a * -4.0), $MachinePrecision] * N[(t / c), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -6.5e77 or 1.45e31 < b

   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

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 61.8

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

   5. Simplified 61.8%

      \[\leadsto \color{blue}{\frac{b}{z \cdot c}} \]
   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. lower-/.f64 N/A

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

      4. lower-/.f64 63.6

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

   7. Applied egg-rr 63.6%

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

   if -6.5e77 < b < 1.45e31

   1. Initial program 79.8%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   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. lower-/.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 47.4

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

   5. Simplified 47.4%

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

      1. associate-*r* N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 47.5

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

   7. Applied egg-rr 47.5%

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

Alternative 14: 49.5% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.5 \cdot 10^{+22}:\\ \;\;\;\;a \cdot \left(t \cdot \frac{-4}{c}\right)\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{-86}:\\ \;\;\;\;b \cdot \frac{1}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\left(a \cdot -4\right) \cdot \frac{t}{c}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= t -1.5e+22)
   (* a (* t (/ -4.0 c)))
   (if (<= t 9.5e-86) (* b (/ 1.0 (* z c))) (* (* a -4.0) (/ t c)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (t <= -1.5e+22) {
		tmp = a * (t * (-4.0 / c));
	} else if (t <= 9.5e-86) {
		tmp = b * (1.0 / (z * c));
	} else {
		tmp = (a * -4.0) * (t / c);
	}
	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) :: tmp
    if (t <= (-1.5d+22)) then
        tmp = a * (t * ((-4.0d0) / c))
    else if (t <= 9.5d-86) then
        tmp = b * (1.0d0 / (z * c))
    else
        tmp = (a * (-4.0d0)) * (t / c)
    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 tmp;
	if (t <= -1.5e+22) {
		tmp = a * (t * (-4.0 / c));
	} else if (t <= 9.5e-86) {
		tmp = b * (1.0 / (z * c));
	} else {
		tmp = (a * -4.0) * (t / c);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if t <= -1.5e+22:
		tmp = a * (t * (-4.0 / c))
	elif t <= 9.5e-86:
		tmp = b * (1.0 / (z * c))
	else:
		tmp = (a * -4.0) * (t / c)
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (t <= -1.5e+22)
		tmp = Float64(a * Float64(t * Float64(-4.0 / c)));
	elseif (t <= 9.5e-86)
		tmp = Float64(b * Float64(1.0 / Float64(z * c)));
	else
		tmp = Float64(Float64(a * -4.0) * Float64(t / c));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (t <= -1.5e+22)
		tmp = a * (t * (-4.0 / c));
	elseif (t <= 9.5e-86)
		tmp = b * (1.0 / (z * c));
	else
		tmp = (a * -4.0) * (t / c);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[t, -1.5e+22], N[(a * N[(t * N[(-4.0 / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 9.5e-86], N[(b * N[(1.0 / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * -4.0), $MachinePrecision] * N[(t / c), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.5e22

   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 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. lower-/.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 50.5

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

   5. Simplified 50.5%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. associate-*r/ N/A

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

      4. lift-/.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. associate-*l* N/A

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

      7. lower-*.f64 N/A

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

      8. lower-*.f64 62.2

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

   7. Applied egg-rr 62.2%

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

   if -1.5e22 < t < 9.4999999999999996e-86

   1. Initial program 89.3%

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

   3. Taylor expanded in b around inf

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 43.1

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

   5. Simplified 43.1%

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

      1. lift-*.f64 N/A

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

      2. clear-num N/A

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

      3. associate-/r/ N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 44.7

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

   7. Applied egg-rr 44.7%

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

   if 9.4999999999999996e-86 < t

   1. Initial program 67.1%

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

   3. Taylor expanded in 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. lower-/.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 50.0

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

   5. Simplified 50.0%

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

      1. associate-*r* N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 51.5

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

   7. Applied egg-rr 51.5%

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

4. Final simplification 50.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.5 \cdot 10^{+22}:\\ \;\;\;\;a \cdot \left(t \cdot \frac{-4}{c}\right)\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{-86}:\\ \;\;\;\;b \cdot \frac{1}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\left(a \cdot -4\right) \cdot \frac{t}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 49.6% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{b}{z \cdot c}\\ \mathbf{if}\;b \leq -1.46 \cdot 10^{+78}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1.72 \cdot 10^{+31}:\\ \;\;\;\;\left(a \cdot -4\right) \cdot \frac{t}{c}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ b (* z c))))
   (if (<= b -1.46e+78) t_1 (if (<= b 1.72e+31) (* (* a -4.0) (/ t c)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = b / (z * c);
	double tmp;
	if (b <= -1.46e+78) {
		tmp = t_1;
	} else if (b <= 1.72e+31) {
		tmp = (a * -4.0) * (t / c);
	} else {
		tmp = t_1;
	}
	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) :: tmp
    t_1 = b / (z * c)
    if (b <= (-1.46d+78)) then
        tmp = t_1
    else if (b <= 1.72d+31) then
        tmp = (a * (-4.0d0)) * (t / c)
    else
        tmp = t_1
    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 / (z * c);
	double tmp;
	if (b <= -1.46e+78) {
		tmp = t_1;
	} else if (b <= 1.72e+31) {
		tmp = (a * -4.0) * (t / c);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = b / (z * c)
	tmp = 0
	if b <= -1.46e+78:
		tmp = t_1
	elif b <= 1.72e+31:
		tmp = (a * -4.0) * (t / c)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(b / Float64(z * c))
	tmp = 0.0
	if (b <= -1.46e+78)
		tmp = t_1;
	elseif (b <= 1.72e+31)
		tmp = Float64(Float64(a * -4.0) * Float64(t / c));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = b / (z * c);
	tmp = 0.0;
	if (b <= -1.46e+78)
		tmp = t_1;
	elseif (b <= 1.72e+31)
		tmp = (a * -4.0) * (t / c);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.46e+78], t$95$1, If[LessEqual[b, 1.72e+31], N[(N[(a * -4.0), $MachinePrecision] * N[(t / c), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -1.46000000000000005e78 or 1.72e31 < b

   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

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 61.8

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

   5. Simplified 61.8%

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

   if -1.46000000000000005e78 < b < 1.72e31

   1. Initial program 79.8%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   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. lower-/.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 47.4

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

   5. Simplified 47.4%

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

      1. associate-*r* N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 47.5

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

   7. Applied egg-rr 47.5%

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

Alternative 16: 49.6% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{b}{z \cdot c}\\ \mathbf{if}\;b \leq -4.5 \cdot 10^{+78}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1.3 \cdot 10^{+31}:\\ \;\;\;\;a \cdot \left(t \cdot \frac{-4}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ b (* z c))))
   (if (<= b -4.5e+78) t_1 (if (<= b 1.3e+31) (* a (* t (/ -4.0 c))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = b / (z * c);
	double tmp;
	if (b <= -4.5e+78) {
		tmp = t_1;
	} else if (b <= 1.3e+31) {
		tmp = a * (t * (-4.0 / c));
	} else {
		tmp = t_1;
	}
	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) :: tmp
    t_1 = b / (z * c)
    if (b <= (-4.5d+78)) then
        tmp = t_1
    else if (b <= 1.3d+31) then
        tmp = a * (t * ((-4.0d0) / c))
    else
        tmp = t_1
    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 / (z * c);
	double tmp;
	if (b <= -4.5e+78) {
		tmp = t_1;
	} else if (b <= 1.3e+31) {
		tmp = a * (t * (-4.0 / c));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = b / (z * c)
	tmp = 0
	if b <= -4.5e+78:
		tmp = t_1
	elif b <= 1.3e+31:
		tmp = a * (t * (-4.0 / c))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(b / Float64(z * c))
	tmp = 0.0
	if (b <= -4.5e+78)
		tmp = t_1;
	elseif (b <= 1.3e+31)
		tmp = Float64(a * Float64(t * Float64(-4.0 / c)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = b / (z * c);
	tmp = 0.0;
	if (b <= -4.5e+78)
		tmp = t_1;
	elseif (b <= 1.3e+31)
		tmp = a * (t * (-4.0 / c));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -4.5e+78], t$95$1, If[LessEqual[b, 1.3e+31], N[(a * N[(t * N[(-4.0 / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -4.4999999999999999e78 or 1.3e31 < b

   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

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 61.8

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

   5. Simplified 61.8%

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

   if -4.4999999999999999e78 < b < 1.3e31

   1. Initial program 79.8%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   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. lower-/.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 47.4

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

   5. Simplified 47.4%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. associate-*r/ N/A

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

      4. lift-/.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. associate-*l* N/A

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

      7. lower-*.f64 N/A

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

      8. lower-*.f64 47.5

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

   7. Applied egg-rr 47.5%

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

Alternative 17: 35.0% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \frac{b}{z \cdot c} \end{array} \]

FPCore

(FPCore (x y z t a b c) :precision binary64 (/ b (* z c)))

C

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision]

Derivation

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. Taylor expanded in b around inf

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

   1. lower-/.f64 N/A

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

   2. *-commutative N/A

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

   3. lower-*.f64 36.2

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

5. Simplified 36.2%

   \[\leadsto \color{blue}{\frac{b}{z \cdot c}} \]
6. Add Preprocessing

Developer Target 1: 80.7% 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 2024207 
(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)))