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

Percentage Accurate: 79.5% → 91.5%

Time: 12.2s

Alternatives: 14

Speedup: 0.9×

• 37.5% 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: 79.5% 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: 91.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ c\_s \cdot \begin{array}{l} \mathbf{if}\;c\_m \leq 5 \cdot 10^{-14}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{z} - \left(t \cdot a\right) \cdot 4}{c\_m}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{c\_m \cdot z} \cdot 9, y, \mathsf{fma}\left(-4, t \cdot \frac{a}{c\_m}, \frac{b}{c\_m \cdot z}\right)\right)\\ \end{array} \end{array} \]

FPCore

c\_m = (fabs.f64 c)
c\_s = (copysign.f64 #s(literal 1 binary64) c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
(FPCore (c_s x y z t a b c_m)
 :precision binary64
 (*
  c_s
  (if (<= c_m 5e-14)
    (/ (- (/ (fma (* y x) 9.0 b) z) (* (* t a) 4.0)) c_m)
    (fma
     (* (/ x (* c_m z)) 9.0)
     y
     (fma -4.0 (* t (/ a c_m)) (/ b (* c_m z)))))))

C

c\_m = fabs(c);
c\_s = copysign(1.0, c);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if (c_m <= 5e-14) {
		tmp = ((fma((y * x), 9.0, b) / z) - ((t * a) * 4.0)) / c_m;
	} else {
		tmp = fma(((x / (c_m * z)) * 9.0), y, fma(-4.0, (t * (a / c_m)), (b / (c_m * z))));
	}
	return c_s * tmp;
}

Julia

c\_m = abs(c)
c\_s = copysign(1.0, c)
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
function code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0
	if (c_m <= 5e-14)
		tmp = Float64(Float64(Float64(fma(Float64(y * x), 9.0, b) / z) - Float64(Float64(t * a) * 4.0)) / c_m);
	else
		tmp = fma(Float64(Float64(x / Float64(c_m * z)) * 9.0), y, fma(-4.0, Float64(t * Float64(a / c_m)), Float64(b / Float64(c_m * z))));
	end
	return Float64(c_s * tmp)
end

Wolfram

c\_m = N[Abs[c], $MachinePrecision]
c\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
code[c$95$s_, x_, y_, z_, t_, a_, b_, c$95$m_] := N[(c$95$s * If[LessEqual[c$95$m, 5e-14], N[(N[(N[(N[(N[(y * x), $MachinePrecision] * 9.0 + b), $MachinePrecision] / z), $MachinePrecision] - N[(N[(t * a), $MachinePrecision] * 4.0), $MachinePrecision]), $MachinePrecision] / c$95$m), $MachinePrecision], N[(N[(N[(x / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision] * 9.0), $MachinePrecision] * y + N[(-4.0 * N[(t * N[(a / c$95$m), $MachinePrecision]), $MachinePrecision] + N[(b / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if c < 5.0000000000000002e-14

   1. Initial program 83.3%

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

   3. Taylor expanded in 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. associate--l+ N/A

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

      2. associate-*r/ N/A

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

      3. associate-*r* N/A

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

      4. associate-*l/ N/A

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

      5. associate-*r/ N/A

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

      6. lower-fma.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. lower-*.f64 N/A

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

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

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

      12. metadata-eval N/A

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

      13. +-commutative N/A

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

      14. lower-fma.f64 N/A

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

      15. lower-/.f64 N/A

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

      16. lower-*.f64 N/A

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

      17. lower-/.f64 N/A

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

      18. lower-*.f64 78.3

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

   5. Applied rewrites 78.3%

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

   6. Taylor expanded in c around -inf

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

   8. Applied rewrites 89.5%

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

   if 5.0000000000000002e-14 < c

   1. Initial program 64.2%

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

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

      2. associate-*r/ N/A

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

      3. associate-*r* N/A

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

      4. associate-*l/ N/A

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

      5. associate-*r/ N/A

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

      6. lower-fma.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. lower-*.f64 N/A

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

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

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

      12. metadata-eval N/A

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

      13. +-commutative N/A

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

      14. lower-fma.f64 N/A

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

      15. lower-/.f64 N/A

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

      16. lower-*.f64 N/A

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

      17. lower-/.f64 N/A

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

      18. lower-*.f64 90.8

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

   5. Applied rewrites 90.8%

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

   7. Applied rewrites 96.2%

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

Alternative 2: 51.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ \begin{array}{l} t_1 := \left(\frac{x}{c\_m \cdot z} \cdot y\right) \cdot 9\\ t_2 := \left(x \cdot 9\right) \cdot y\\ c\_s \cdot \begin{array}{l} \mathbf{if}\;t\_2 \leq -4 \cdot 10^{+95}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq -2 \cdot 10^{-17}:\\ \;\;\;\;\frac{-4}{\frac{c\_m}{a \cdot t}}\\ \mathbf{elif}\;t\_2 \leq 10^{-120}:\\ \;\;\;\;\frac{\frac{b}{c\_m}}{z}\\ \mathbf{elif}\;t\_2 \leq 10^{+207}:\\ \;\;\;\;\left(-4 \cdot t\right) \cdot \frac{a}{c\_m}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \end{array} \]

FPCore

c\_m = (fabs.f64 c)
c\_s = (copysign.f64 #s(literal 1 binary64) c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
(FPCore (c_s x y z t a b c_m)
 :precision binary64
 (let* ((t_1 (* (* (/ x (* c_m z)) y) 9.0)) (t_2 (* (* x 9.0) y)))
   (*
    c_s
    (if (<= t_2 -4e+95)
      t_1
      (if (<= t_2 -2e-17)
        (/ -4.0 (/ c_m (* a t)))
        (if (<= t_2 1e-120)
          (/ (/ b c_m) z)
          (if (<= t_2 1e+207) (* (* -4.0 t) (/ a c_m)) t_1)))))))

C

c\_m = fabs(c);
c\_s = copysign(1.0, c);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double t_1 = ((x / (c_m * z)) * y) * 9.0;
	double t_2 = (x * 9.0) * y;
	double tmp;
	if (t_2 <= -4e+95) {
		tmp = t_1;
	} else if (t_2 <= -2e-17) {
		tmp = -4.0 / (c_m / (a * t));
	} else if (t_2 <= 1e-120) {
		tmp = (b / c_m) / z;
	} else if (t_2 <= 1e+207) {
		tmp = (-4.0 * t) * (a / c_m);
	} else {
		tmp = t_1;
	}
	return c_s * tmp;
}

Fortran

c\_m = abs(c)
c\_s = copysign(1.0d0, c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
real(8) function code(c_s, x, y, z, t, a, b, c_m)
    real(8), intent (in) :: c_s
    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_m
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = ((x / (c_m * z)) * y) * 9.0d0
    t_2 = (x * 9.0d0) * y
    if (t_2 <= (-4d+95)) then
        tmp = t_1
    else if (t_2 <= (-2d-17)) then
        tmp = (-4.0d0) / (c_m / (a * t))
    else if (t_2 <= 1d-120) then
        tmp = (b / c_m) / z
    else if (t_2 <= 1d+207) then
        tmp = ((-4.0d0) * t) * (a / c_m)
    else
        tmp = t_1
    end if
    code = c_s * tmp
end function

Java

c\_m = Math.abs(c);
c\_s = Math.copySign(1.0, c);
assert x < y && y < z && z < t && t < a && a < b && b < c_m;
public static double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double t_1 = ((x / (c_m * z)) * y) * 9.0;
	double t_2 = (x * 9.0) * y;
	double tmp;
	if (t_2 <= -4e+95) {
		tmp = t_1;
	} else if (t_2 <= -2e-17) {
		tmp = -4.0 / (c_m / (a * t));
	} else if (t_2 <= 1e-120) {
		tmp = (b / c_m) / z;
	} else if (t_2 <= 1e+207) {
		tmp = (-4.0 * t) * (a / c_m);
	} else {
		tmp = t_1;
	}
	return c_s * tmp;
}

Python

c\_m = math.fabs(c)
c\_s = math.copysign(1.0, c)
[x, y, z, t, a, b, c_m] = sort([x, y, z, t, a, b, c_m])
def code(c_s, x, y, z, t, a, b, c_m):
	t_1 = ((x / (c_m * z)) * y) * 9.0
	t_2 = (x * 9.0) * y
	tmp = 0
	if t_2 <= -4e+95:
		tmp = t_1
	elif t_2 <= -2e-17:
		tmp = -4.0 / (c_m / (a * t))
	elif t_2 <= 1e-120:
		tmp = (b / c_m) / z
	elif t_2 <= 1e+207:
		tmp = (-4.0 * t) * (a / c_m)
	else:
		tmp = t_1
	return c_s * tmp

Julia

c\_m = abs(c)
c\_s = copysign(1.0, c)
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
function code(c_s, x, y, z, t, a, b, c_m)
	t_1 = Float64(Float64(Float64(x / Float64(c_m * z)) * y) * 9.0)
	t_2 = Float64(Float64(x * 9.0) * y)
	tmp = 0.0
	if (t_2 <= -4e+95)
		tmp = t_1;
	elseif (t_2 <= -2e-17)
		tmp = Float64(-4.0 / Float64(c_m / Float64(a * t)));
	elseif (t_2 <= 1e-120)
		tmp = Float64(Float64(b / c_m) / z);
	elseif (t_2 <= 1e+207)
		tmp = Float64(Float64(-4.0 * t) * Float64(a / c_m));
	else
		tmp = t_1;
	end
	return Float64(c_s * tmp)
end

MATLAB

c\_m = abs(c);
c\_s = sign(c) * abs(1.0);
x, y, z, t, a, b, c_m = num2cell(sort([x, y, z, t, a, b, c_m])){:}
function tmp_2 = code(c_s, x, y, z, t, a, b, c_m)
	t_1 = ((x / (c_m * z)) * y) * 9.0;
	t_2 = (x * 9.0) * y;
	tmp = 0.0;
	if (t_2 <= -4e+95)
		tmp = t_1;
	elseif (t_2 <= -2e-17)
		tmp = -4.0 / (c_m / (a * t));
	elseif (t_2 <= 1e-120)
		tmp = (b / c_m) / z;
	elseif (t_2 <= 1e+207)
		tmp = (-4.0 * t) * (a / c_m);
	else
		tmp = t_1;
	end
	tmp_2 = c_s * tmp;
end

Wolfram

c\_m = N[Abs[c], $MachinePrecision]
c\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
code[c$95$s_, x_, y_, z_, t_, a_, b_, c$95$m_] := Block[{t$95$1 = N[(N[(N[(x / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision] * 9.0), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision]}, N[(c$95$s * If[LessEqual[t$95$2, -4e+95], t$95$1, If[LessEqual[t$95$2, -2e-17], N[(-4.0 / N[(c$95$m / N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 1e-120], N[(N[(b / c$95$m), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t$95$2, 1e+207], N[(N[(-4.0 * t), $MachinePrecision] * N[(a / c$95$m), $MachinePrecision]), $MachinePrecision], t$95$1]]]]), $MachinePrecision]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -4.00000000000000008e95 or 1e207 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 74.8%

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

   3. Taylor expanded in 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. associate--l+ N/A

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

      2. associate-*r/ N/A

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

      3. associate-*r* N/A

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

      4. associate-*l/ N/A

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

      5. associate-*r/ N/A

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

      6. lower-fma.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. lower-*.f64 N/A

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

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

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

      12. metadata-eval N/A

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

      13. +-commutative N/A

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

      14. lower-fma.f64 N/A

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

      15. lower-/.f64 N/A

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

      16. lower-*.f64 N/A

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

      17. lower-/.f64 N/A

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

      18. lower-*.f64 78.6

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

   5. Applied rewrites 78.6%

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

   6. Taylor expanded in c around -inf

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

   8. Applied rewrites 77.8%

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

   9. Taylor expanded in x around inf

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

       1. *-commutative N/A

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

       2. lower-*.f64 N/A

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

       3. associate-*l/ N/A

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

       4. lower-*.f64 N/A

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

       5. lower-/.f64 N/A

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

       6. lower-*.f64 78.5

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

   11. Applied rewrites 78.5%

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

   if -4.00000000000000008e95 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -2.00000000000000014e-17

   1. Initial program 83.7%

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

   3. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 71.4

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

   5. Applied rewrites 71.4%

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

   7. Applied rewrites 71.5%

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

   if -2.00000000000000014e-17 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 9.99999999999999979e-121

   1. Initial program 83.0%

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

   3. Taylor expanded in 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. lower-*.f64 56.6

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

   5. Applied rewrites 56.6%

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

   7. Applied rewrites 57.5%

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

   if 9.99999999999999979e-121 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 1e207

   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 z around inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 49.8

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

   5. Applied rewrites 49.8%

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

   7. Applied rewrites 55.3%

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

Alternative 3: 51.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ \begin{array}{l} t_1 := \left(\frac{x}{c\_m \cdot z} \cdot y\right) \cdot 9\\ t_2 := \left(x \cdot 9\right) \cdot y\\ c\_s \cdot \begin{array}{l} \mathbf{if}\;t\_2 \leq -4 \cdot 10^{+95}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq -2 \cdot 10^{-17}:\\ \;\;\;\;-4 \cdot \frac{a \cdot t}{c\_m}\\ \mathbf{elif}\;t\_2 \leq 10^{-120}:\\ \;\;\;\;\frac{\frac{b}{c\_m}}{z}\\ \mathbf{elif}\;t\_2 \leq 10^{+207}:\\ \;\;\;\;\left(-4 \cdot t\right) \cdot \frac{a}{c\_m}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \end{array} \]

FPCore

c\_m = (fabs.f64 c)
c\_s = (copysign.f64 #s(literal 1 binary64) c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
(FPCore (c_s x y z t a b c_m)
 :precision binary64
 (let* ((t_1 (* (* (/ x (* c_m z)) y) 9.0)) (t_2 (* (* x 9.0) y)))
   (*
    c_s
    (if (<= t_2 -4e+95)
      t_1
      (if (<= t_2 -2e-17)
        (* -4.0 (/ (* a t) c_m))
        (if (<= t_2 1e-120)
          (/ (/ b c_m) z)
          (if (<= t_2 1e+207) (* (* -4.0 t) (/ a c_m)) t_1)))))))

C

c\_m = fabs(c);
c\_s = copysign(1.0, c);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double t_1 = ((x / (c_m * z)) * y) * 9.0;
	double t_2 = (x * 9.0) * y;
	double tmp;
	if (t_2 <= -4e+95) {
		tmp = t_1;
	} else if (t_2 <= -2e-17) {
		tmp = -4.0 * ((a * t) / c_m);
	} else if (t_2 <= 1e-120) {
		tmp = (b / c_m) / z;
	} else if (t_2 <= 1e+207) {
		tmp = (-4.0 * t) * (a / c_m);
	} else {
		tmp = t_1;
	}
	return c_s * tmp;
}

Fortran

c\_m = abs(c)
c\_s = copysign(1.0d0, c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
real(8) function code(c_s, x, y, z, t, a, b, c_m)
    real(8), intent (in) :: c_s
    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_m
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = ((x / (c_m * z)) * y) * 9.0d0
    t_2 = (x * 9.0d0) * y
    if (t_2 <= (-4d+95)) then
        tmp = t_1
    else if (t_2 <= (-2d-17)) then
        tmp = (-4.0d0) * ((a * t) / c_m)
    else if (t_2 <= 1d-120) then
        tmp = (b / c_m) / z
    else if (t_2 <= 1d+207) then
        tmp = ((-4.0d0) * t) * (a / c_m)
    else
        tmp = t_1
    end if
    code = c_s * tmp
end function

Java

c\_m = Math.abs(c);
c\_s = Math.copySign(1.0, c);
assert x < y && y < z && z < t && t < a && a < b && b < c_m;
public static double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double t_1 = ((x / (c_m * z)) * y) * 9.0;
	double t_2 = (x * 9.0) * y;
	double tmp;
	if (t_2 <= -4e+95) {
		tmp = t_1;
	} else if (t_2 <= -2e-17) {
		tmp = -4.0 * ((a * t) / c_m);
	} else if (t_2 <= 1e-120) {
		tmp = (b / c_m) / z;
	} else if (t_2 <= 1e+207) {
		tmp = (-4.0 * t) * (a / c_m);
	} else {
		tmp = t_1;
	}
	return c_s * tmp;
}

Python

c\_m = math.fabs(c)
c\_s = math.copysign(1.0, c)
[x, y, z, t, a, b, c_m] = sort([x, y, z, t, a, b, c_m])
def code(c_s, x, y, z, t, a, b, c_m):
	t_1 = ((x / (c_m * z)) * y) * 9.0
	t_2 = (x * 9.0) * y
	tmp = 0
	if t_2 <= -4e+95:
		tmp = t_1
	elif t_2 <= -2e-17:
		tmp = -4.0 * ((a * t) / c_m)
	elif t_2 <= 1e-120:
		tmp = (b / c_m) / z
	elif t_2 <= 1e+207:
		tmp = (-4.0 * t) * (a / c_m)
	else:
		tmp = t_1
	return c_s * tmp

Julia

c\_m = abs(c)
c\_s = copysign(1.0, c)
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
function code(c_s, x, y, z, t, a, b, c_m)
	t_1 = Float64(Float64(Float64(x / Float64(c_m * z)) * y) * 9.0)
	t_2 = Float64(Float64(x * 9.0) * y)
	tmp = 0.0
	if (t_2 <= -4e+95)
		tmp = t_1;
	elseif (t_2 <= -2e-17)
		tmp = Float64(-4.0 * Float64(Float64(a * t) / c_m));
	elseif (t_2 <= 1e-120)
		tmp = Float64(Float64(b / c_m) / z);
	elseif (t_2 <= 1e+207)
		tmp = Float64(Float64(-4.0 * t) * Float64(a / c_m));
	else
		tmp = t_1;
	end
	return Float64(c_s * tmp)
end

MATLAB

c\_m = abs(c);
c\_s = sign(c) * abs(1.0);
x, y, z, t, a, b, c_m = num2cell(sort([x, y, z, t, a, b, c_m])){:}
function tmp_2 = code(c_s, x, y, z, t, a, b, c_m)
	t_1 = ((x / (c_m * z)) * y) * 9.0;
	t_2 = (x * 9.0) * y;
	tmp = 0.0;
	if (t_2 <= -4e+95)
		tmp = t_1;
	elseif (t_2 <= -2e-17)
		tmp = -4.0 * ((a * t) / c_m);
	elseif (t_2 <= 1e-120)
		tmp = (b / c_m) / z;
	elseif (t_2 <= 1e+207)
		tmp = (-4.0 * t) * (a / c_m);
	else
		tmp = t_1;
	end
	tmp_2 = c_s * tmp;
end

Wolfram

c\_m = N[Abs[c], $MachinePrecision]
c\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
code[c$95$s_, x_, y_, z_, t_, a_, b_, c$95$m_] := Block[{t$95$1 = N[(N[(N[(x / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision] * 9.0), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision]}, N[(c$95$s * If[LessEqual[t$95$2, -4e+95], t$95$1, If[LessEqual[t$95$2, -2e-17], N[(-4.0 * N[(N[(a * t), $MachinePrecision] / c$95$m), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 1e-120], N[(N[(b / c$95$m), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t$95$2, 1e+207], N[(N[(-4.0 * t), $MachinePrecision] * N[(a / c$95$m), $MachinePrecision]), $MachinePrecision], t$95$1]]]]), $MachinePrecision]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -4.00000000000000008e95 or 1e207 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 74.8%

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

   3. Taylor expanded in 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. associate--l+ N/A

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

      2. associate-*r/ N/A

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

      3. associate-*r* N/A

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

      4. associate-*l/ N/A

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

      5. associate-*r/ N/A

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

      6. lower-fma.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. lower-*.f64 N/A

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

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

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

      12. metadata-eval N/A

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

      13. +-commutative N/A

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

      14. lower-fma.f64 N/A

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

      15. lower-/.f64 N/A

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

      16. lower-*.f64 N/A

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

      17. lower-/.f64 N/A

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

      18. lower-*.f64 78.6

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

   5. Applied rewrites 78.6%

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

   6. Taylor expanded in c around -inf

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

   8. Applied rewrites 77.8%

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

   9. Taylor expanded in x around inf

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

       1. *-commutative N/A

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

       2. lower-*.f64 N/A

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

       3. associate-*l/ N/A

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

       4. lower-*.f64 N/A

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

       5. lower-/.f64 N/A

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

       6. lower-*.f64 78.5

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

   11. Applied rewrites 78.5%

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

   if -4.00000000000000008e95 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -2.00000000000000014e-17

   1. Initial program 83.7%

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

   3. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 71.4

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

   5. Applied rewrites 71.4%

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

   if -2.00000000000000014e-17 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 9.99999999999999979e-121

   1. Initial program 83.0%

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

   3. Taylor expanded in 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. lower-*.f64 56.6

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

   5. Applied rewrites 56.6%

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

   7. Applied rewrites 57.5%

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

   if 9.99999999999999979e-121 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 1e207

   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 z around inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 49.8

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

   5. Applied rewrites 49.8%

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

   7. Applied rewrites 55.3%

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

Alternative 4: 78.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ \begin{array}{l} t_1 := \left(x \cdot 9\right) \cdot y\\ c\_s \cdot \begin{array}{l} \mathbf{if}\;t\_1 \leq -2 \cdot 10^{-17} \lor \neg \left(t\_1 \leq 10000\right):\\ \;\;\;\;\frac{\mathsf{fma}\left(-4 \cdot t, a, \frac{x \cdot y}{z} \cdot 9\right)}{c\_m}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(t \cdot a, -4, \frac{b}{z}\right)}{c\_m}\\ \end{array} \end{array} \end{array} \]

FPCore

c\_m = (fabs.f64 c)
c\_s = (copysign.f64 #s(literal 1 binary64) c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
(FPCore (c_s x y z t a b c_m)
 :precision binary64
 (let* ((t_1 (* (* x 9.0) y)))
   (*
    c_s
    (if (or (<= t_1 -2e-17) (not (<= t_1 10000.0)))
      (/ (fma (* -4.0 t) a (* (/ (* x y) z) 9.0)) c_m)
      (/ (fma (* t a) -4.0 (/ b z)) c_m)))))

C

c\_m = fabs(c);
c\_s = copysign(1.0, c);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double t_1 = (x * 9.0) * y;
	double tmp;
	if ((t_1 <= -2e-17) || !(t_1 <= 10000.0)) {
		tmp = fma((-4.0 * t), a, (((x * y) / z) * 9.0)) / c_m;
	} else {
		tmp = fma((t * a), -4.0, (b / z)) / c_m;
	}
	return c_s * tmp;
}

Julia

c\_m = abs(c)
c\_s = copysign(1.0, c)
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
function code(c_s, x, y, z, t, a, b, c_m)
	t_1 = Float64(Float64(x * 9.0) * y)
	tmp = 0.0
	if ((t_1 <= -2e-17) || !(t_1 <= 10000.0))
		tmp = Float64(fma(Float64(-4.0 * t), a, Float64(Float64(Float64(x * y) / z) * 9.0)) / c_m);
	else
		tmp = Float64(fma(Float64(t * a), -4.0, Float64(b / z)) / c_m);
	end
	return Float64(c_s * tmp)
end

Wolfram

c\_m = N[Abs[c], $MachinePrecision]
c\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
code[c$95$s_, x_, y_, z_, t_, a_, b_, c$95$m_] := Block[{t$95$1 = N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision]}, N[(c$95$s * If[Or[LessEqual[t$95$1, -2e-17], N[Not[LessEqual[t$95$1, 10000.0]], $MachinePrecision]], N[(N[(N[(-4.0 * t), $MachinePrecision] * a + N[(N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision] * 9.0), $MachinePrecision]), $MachinePrecision] / c$95$m), $MachinePrecision], N[(N[(N[(t * a), $MachinePrecision] * -4.0 + N[(b / z), $MachinePrecision]), $MachinePrecision] / c$95$m), $MachinePrecision]]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -2.00000000000000014e-17 or 1e4 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 74.2%

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

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

      2. associate-*r/ N/A

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

      3. associate-*r* N/A

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

      4. associate-*l/ N/A

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

      5. associate-*r/ N/A

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

      6. lower-fma.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. lower-*.f64 N/A

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

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

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

      12. metadata-eval N/A

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

      13. +-commutative N/A

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

      14. lower-fma.f64 N/A

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

      15. lower-/.f64 N/A

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

      16. lower-*.f64 N/A

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

      17. lower-/.f64 N/A

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

      18. lower-*.f64 82.0

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

   5. Applied rewrites 82.0%

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

   6. Taylor expanded in c around -inf

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

   8. Applied rewrites 86.6%

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

   9. Taylor expanded in b around 0

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

   11. Applied rewrites 82.1%

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

   if -2.00000000000000014e-17 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 1e4

   1. Initial program 82.3%

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

   3. 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. associate--l+ N/A

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

      2. associate-*r/ N/A

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

      3. associate-*r* N/A

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

      4. associate-*l/ N/A

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

      5. associate-*r/ N/A

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

      6. lower-fma.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. lower-*.f64 N/A

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

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

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

      12. metadata-eval N/A

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

      13. +-commutative N/A

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

      14. lower-fma.f64 N/A

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

      15. lower-/.f64 N/A

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

      16. lower-*.f64 N/A

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

      17. lower-/.f64 N/A

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

      18. lower-*.f64 81.4

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

   5. Applied rewrites 81.4%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 83.5%

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

4. Final simplification 82.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x \cdot 9\right) \cdot y \leq -2 \cdot 10^{-17} \lor \neg \left(\left(x \cdot 9\right) \cdot y \leq 10000\right):\\ \;\;\;\;\frac{\mathsf{fma}\left(-4 \cdot t, a, \frac{x \cdot y}{z} \cdot 9\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(t \cdot a, -4, \frac{b}{z}\right)}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 91.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ c\_s \cdot \begin{array}{l} \mathbf{if}\;c\_m \leq 1.55 \cdot 10^{+66}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{z} - \left(t \cdot a\right) \cdot 4}{c\_m}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-4 \cdot a, \frac{t}{c\_m}, \frac{\frac{\mathsf{fma}\left(-9 \cdot x, y, -b\right)}{c\_m}}{-z}\right)\\ \end{array} \end{array} \]

FPCore

c\_m = (fabs.f64 c)
c\_s = (copysign.f64 #s(literal 1 binary64) c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
(FPCore (c_s x y z t a b c_m)
 :precision binary64
 (*
  c_s
  (if (<= c_m 1.55e+66)
    (/ (- (/ (fma (* y x) 9.0 b) z) (* (* t a) 4.0)) c_m)
    (fma (* -4.0 a) (/ t c_m) (/ (/ (fma (* -9.0 x) y (- b)) c_m) (- z))))))

C

c\_m = fabs(c);
c\_s = copysign(1.0, c);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if (c_m <= 1.55e+66) {
		tmp = ((fma((y * x), 9.0, b) / z) - ((t * a) * 4.0)) / c_m;
	} else {
		tmp = fma((-4.0 * a), (t / c_m), ((fma((-9.0 * x), y, -b) / c_m) / -z));
	}
	return c_s * tmp;
}

Julia

c\_m = abs(c)
c\_s = copysign(1.0, c)
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
function code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0
	if (c_m <= 1.55e+66)
		tmp = Float64(Float64(Float64(fma(Float64(y * x), 9.0, b) / z) - Float64(Float64(t * a) * 4.0)) / c_m);
	else
		tmp = fma(Float64(-4.0 * a), Float64(t / c_m), Float64(Float64(fma(Float64(-9.0 * x), y, Float64(-b)) / c_m) / Float64(-z)));
	end
	return Float64(c_s * tmp)
end

Wolfram

c\_m = N[Abs[c], $MachinePrecision]
c\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
code[c$95$s_, x_, y_, z_, t_, a_, b_, c$95$m_] := N[(c$95$s * If[LessEqual[c$95$m, 1.55e+66], N[(N[(N[(N[(N[(y * x), $MachinePrecision] * 9.0 + b), $MachinePrecision] / z), $MachinePrecision] - N[(N[(t * a), $MachinePrecision] * 4.0), $MachinePrecision]), $MachinePrecision] / c$95$m), $MachinePrecision], N[(N[(-4.0 * a), $MachinePrecision] * N[(t / c$95$m), $MachinePrecision] + N[(N[(N[(N[(-9.0 * x), $MachinePrecision] * y + (-b)), $MachinePrecision] / c$95$m), $MachinePrecision] / (-z)), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if c < 1.55000000000000009e66

   1. Initial program 82.4%

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

   3. Taylor expanded in x around 0

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

      1. associate--l+ N/A

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

      2. associate-*r/ N/A

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

      3. associate-*r* N/A

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

      4. associate-*l/ N/A

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

      5. associate-*r/ N/A

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

      6. lower-fma.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. lower-*.f64 N/A

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

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

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

      12. metadata-eval N/A

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

      13. +-commutative N/A

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

      14. lower-fma.f64 N/A

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

      15. lower-/.f64 N/A

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

      16. lower-*.f64 N/A

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

      17. lower-/.f64 N/A

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

      18. lower-*.f64 79.1

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

   5. Applied rewrites 79.1%

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

   6. Taylor expanded in c around -inf

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

   8. Applied rewrites 89.7%

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

   if 1.55000000000000009e66 < c

   1. Initial program 62.8%

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

   3. Taylor expanded in 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. associate--l+ N/A

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

      2. associate-*r/ N/A

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

      3. associate-*r* N/A

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

      4. associate-*l/ N/A

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

      5. associate-*r/ N/A

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

      6. lower-fma.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. lower-*.f64 N/A

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

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

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

      12. metadata-eval N/A

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

      13. +-commutative N/A

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

      14. lower-fma.f64 N/A

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

      15. lower-/.f64 N/A

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

      16. lower-*.f64 N/A

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

      17. lower-/.f64 N/A

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

      18. lower-*.f64 91.1

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

   5. Applied rewrites 91.1%

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

   6. Taylor expanded in z around -inf

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

   8. Applied rewrites 88.6%

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

Alternative 6: 91.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ c\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{+83} \lor \neg \left(z \leq 1.5 \cdot 10^{-41}\right):\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{z} - \left(t \cdot a\right) \cdot 4}{c\_m}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c\_m}\\ \end{array} \end{array} \]

FPCore

c\_m = (fabs.f64 c)
c\_s = (copysign.f64 #s(literal 1 binary64) c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
(FPCore (c_s x y z t a b c_m)
 :precision binary64
 (*
  c_s
  (if (or (<= z -1.25e+83) (not (<= z 1.5e-41)))
    (/ (- (/ (fma (* y x) 9.0 b) z) (* (* t a) 4.0)) c_m)
    (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c_m)))))

C

c\_m = fabs(c);
c\_s = copysign(1.0, c);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if ((z <= -1.25e+83) || !(z <= 1.5e-41)) {
		tmp = ((fma((y * x), 9.0, b) / z) - ((t * a) * 4.0)) / c_m;
	} else {
		tmp = ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c_m);
	}
	return c_s * tmp;
}

Julia

c\_m = abs(c)
c\_s = copysign(1.0, c)
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
function code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0
	if ((z <= -1.25e+83) || !(z <= 1.5e-41))
		tmp = Float64(Float64(Float64(fma(Float64(y * x), 9.0, b) / z) - Float64(Float64(t * a) * 4.0)) / c_m);
	else
		tmp = Float64(Float64(Float64(Float64(Float64(x * 9.0) * y) - Float64(Float64(Float64(z * 4.0) * t) * a)) + b) / Float64(z * c_m));
	end
	return Float64(c_s * tmp)
end

Wolfram

c\_m = N[Abs[c], $MachinePrecision]
c\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
code[c$95$s_, x_, y_, z_, t_, a_, b_, c$95$m_] := N[(c$95$s * If[Or[LessEqual[z, -1.25e+83], N[Not[LessEqual[z, 1.5e-41]], $MachinePrecision]], N[(N[(N[(N[(N[(y * x), $MachinePrecision] * 9.0 + b), $MachinePrecision] / z), $MachinePrecision] - N[(N[(t * a), $MachinePrecision] * 4.0), $MachinePrecision]), $MachinePrecision] / c$95$m), $MachinePrecision], 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$95$m), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if z < -1.25000000000000007e83 or 1.49999999999999994e-41 < z

   1. Initial program 58.8%

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

   3. Taylor expanded in 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. associate--l+ N/A

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

      2. associate-*r/ N/A

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

      3. associate-*r* N/A

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

      4. associate-*l/ N/A

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

      5. associate-*r/ N/A

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

      6. lower-fma.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. lower-*.f64 N/A

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

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

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

      12. metadata-eval N/A

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

      13. +-commutative N/A

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

      14. lower-fma.f64 N/A

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

      15. lower-/.f64 N/A

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

      16. lower-*.f64 N/A

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

      17. lower-/.f64 N/A

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

      18. lower-*.f64 88.5

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

   5. Applied rewrites 88.5%

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

   6. Taylor expanded in c around -inf

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

   8. Applied rewrites 91.3%

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

   if -1.25000000000000007e83 < z < 1.49999999999999994e-41

   1. Initial program 96.3%

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

4. Final simplification 93.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{+83} \lor \neg \left(z \leq 1.5 \cdot 10^{-41}\right):\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{z} - \left(t \cdot a\right) \cdot 4}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 91.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ c\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -29000000000000 \lor \neg \left(z \leq 1.5 \cdot 10^{-41}\right):\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{z} - \left(t \cdot a\right) \cdot 4}{c\_m}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y \cdot 9, x, \mathsf{fma}\left(\left(-4 \cdot z\right) \cdot a, t, b\right)\right)}{z \cdot c\_m}\\ \end{array} \end{array} \]

FPCore

c\_m = (fabs.f64 c)
c\_s = (copysign.f64 #s(literal 1 binary64) c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
(FPCore (c_s x y z t a b c_m)
 :precision binary64
 (*
  c_s
  (if (or (<= z -29000000000000.0) (not (<= z 1.5e-41)))
    (/ (- (/ (fma (* y x) 9.0 b) z) (* (* t a) 4.0)) c_m)
    (/ (fma (* y 9.0) x (fma (* (* -4.0 z) a) t b)) (* z c_m)))))

C

c\_m = fabs(c);
c\_s = copysign(1.0, c);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if ((z <= -29000000000000.0) || !(z <= 1.5e-41)) {
		tmp = ((fma((y * x), 9.0, b) / z) - ((t * a) * 4.0)) / c_m;
	} else {
		tmp = fma((y * 9.0), x, fma(((-4.0 * z) * a), t, b)) / (z * c_m);
	}
	return c_s * tmp;
}

Julia

c\_m = abs(c)
c\_s = copysign(1.0, c)
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
function code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0
	if ((z <= -29000000000000.0) || !(z <= 1.5e-41))
		tmp = Float64(Float64(Float64(fma(Float64(y * x), 9.0, b) / z) - Float64(Float64(t * a) * 4.0)) / c_m);
	else
		tmp = Float64(fma(Float64(y * 9.0), x, fma(Float64(Float64(-4.0 * z) * a), t, b)) / Float64(z * c_m));
	end
	return Float64(c_s * tmp)
end

Wolfram

c\_m = N[Abs[c], $MachinePrecision]
c\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
code[c$95$s_, x_, y_, z_, t_, a_, b_, c$95$m_] := N[(c$95$s * If[Or[LessEqual[z, -29000000000000.0], N[Not[LessEqual[z, 1.5e-41]], $MachinePrecision]], N[(N[(N[(N[(N[(y * x), $MachinePrecision] * 9.0 + b), $MachinePrecision] / z), $MachinePrecision] - N[(N[(t * a), $MachinePrecision] * 4.0), $MachinePrecision]), $MachinePrecision] / c$95$m), $MachinePrecision], N[(N[(N[(y * 9.0), $MachinePrecision] * x + N[(N[(N[(-4.0 * z), $MachinePrecision] * a), $MachinePrecision] * t + b), $MachinePrecision]), $MachinePrecision] / N[(z * c$95$m), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if z < -2.9e13 or 1.49999999999999994e-41 < z

   1. Initial program 61.3%

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

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

      2. associate-*r/ N/A

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

      3. associate-*r* N/A

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

      4. associate-*l/ N/A

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

      5. associate-*r/ N/A

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

      6. lower-fma.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. lower-*.f64 N/A

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

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

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

      12. metadata-eval N/A

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

      13. +-commutative N/A

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

      14. lower-fma.f64 N/A

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

      15. lower-/.f64 N/A

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

      16. lower-*.f64 N/A

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

      17. lower-/.f64 N/A

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

      18. lower-*.f64 88.4

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

   5. Applied rewrites 88.4%

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

   6. Taylor expanded in c around -inf

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

   8. Applied rewrites 91.8%

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

   if -2.9e13 < z < 1.49999999999999994e-41

   1. Initial program 96.1%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. associate-+l- N/A

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

      4. sub-neg N/A

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

      5. lift-*.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. associate-*l* N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. neg-sub0 N/A

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

      13. associate-+l- N/A

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

      14. neg-sub0 N/A

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

   4. Applied rewrites 95.3%

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

4. Final simplification 93.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -29000000000000 \lor \neg \left(z \leq 1.5 \cdot 10^{-41}\right):\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{z} - \left(t \cdot a\right) \cdot 4}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y \cdot 9, x, \mathsf{fma}\left(\left(-4 \cdot z\right) \cdot a, t, b\right)\right)}{z \cdot c}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 85.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ c\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{+91}:\\ \;\;\;\;\frac{\mathsf{fma}\left(t \cdot a, -4, \frac{b}{z}\right)}{c\_m}\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{+149}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y \cdot 9, x, \mathsf{fma}\left(\left(-4 \cdot z\right) \cdot a, t, b\right)\right)}{z \cdot c\_m}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(-4 \cdot t, a, \frac{x \cdot y}{z} \cdot 9\right)}{c\_m}\\ \end{array} \end{array} \]

FPCore

c\_m = (fabs.f64 c)
c\_s = (copysign.f64 #s(literal 1 binary64) c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
(FPCore (c_s x y z t a b c_m)
 :precision binary64
 (*
  c_s
  (if (<= z -3.2e+91)
    (/ (fma (* t a) -4.0 (/ b z)) c_m)
    (if (<= z 4.6e+149)
      (/ (fma (* y 9.0) x (fma (* (* -4.0 z) a) t b)) (* z c_m))
      (/ (fma (* -4.0 t) a (* (/ (* x y) z) 9.0)) c_m)))))

C

c\_m = fabs(c);
c\_s = copysign(1.0, c);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if (z <= -3.2e+91) {
		tmp = fma((t * a), -4.0, (b / z)) / c_m;
	} else if (z <= 4.6e+149) {
		tmp = fma((y * 9.0), x, fma(((-4.0 * z) * a), t, b)) / (z * c_m);
	} else {
		tmp = fma((-4.0 * t), a, (((x * y) / z) * 9.0)) / c_m;
	}
	return c_s * tmp;
}

Julia

c\_m = abs(c)
c\_s = copysign(1.0, c)
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
function code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0
	if (z <= -3.2e+91)
		tmp = Float64(fma(Float64(t * a), -4.0, Float64(b / z)) / c_m);
	elseif (z <= 4.6e+149)
		tmp = Float64(fma(Float64(y * 9.0), x, fma(Float64(Float64(-4.0 * z) * a), t, b)) / Float64(z * c_m));
	else
		tmp = Float64(fma(Float64(-4.0 * t), a, Float64(Float64(Float64(x * y) / z) * 9.0)) / c_m);
	end
	return Float64(c_s * tmp)
end

Wolfram

c\_m = N[Abs[c], $MachinePrecision]
c\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
code[c$95$s_, x_, y_, z_, t_, a_, b_, c$95$m_] := N[(c$95$s * If[LessEqual[z, -3.2e+91], N[(N[(N[(t * a), $MachinePrecision] * -4.0 + N[(b / z), $MachinePrecision]), $MachinePrecision] / c$95$m), $MachinePrecision], If[LessEqual[z, 4.6e+149], N[(N[(N[(y * 9.0), $MachinePrecision] * x + N[(N[(N[(-4.0 * z), $MachinePrecision] * a), $MachinePrecision] * t + b), $MachinePrecision]), $MachinePrecision] / N[(z * c$95$m), $MachinePrecision]), $MachinePrecision], N[(N[(N[(-4.0 * t), $MachinePrecision] * a + N[(N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision] * 9.0), $MachinePrecision]), $MachinePrecision] / c$95$m), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if z < -3.19999999999999989e91

   1. Initial program 44.7%

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

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

      2. associate-*r/ N/A

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

      3. associate-*r* N/A

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

      4. associate-*l/ N/A

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

      5. associate-*r/ N/A

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

      6. lower-fma.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. lower-*.f64 N/A

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

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

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

      12. metadata-eval N/A

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

      13. +-commutative N/A

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

      14. lower-fma.f64 N/A

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

      15. lower-/.f64 N/A

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

      16. lower-*.f64 N/A

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

      17. lower-/.f64 N/A

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

      18. lower-*.f64 89.5

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

   5. Applied rewrites 89.5%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 83.2%

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

   if -3.19999999999999989e91 < z < 4.5999999999999997e149

   1. Initial program 92.8%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. associate-+l- N/A

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

      4. sub-neg N/A

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

      5. lift-*.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. associate-*l* N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. neg-sub0 N/A

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

      13. associate-+l- N/A

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

      14. neg-sub0 N/A

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

   4. Applied rewrites 92.9%

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

   if 4.5999999999999997e149 < z

   1. Initial program 45.9%

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

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

      2. associate-*r/ N/A

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

      3. associate-*r* N/A

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

      4. associate-*l/ N/A

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

      5. associate-*r/ N/A

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

      6. lower-fma.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. lower-*.f64 N/A

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

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

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

      12. metadata-eval N/A

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

      13. +-commutative N/A

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

      14. lower-fma.f64 N/A

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

      15. lower-/.f64 N/A

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

      16. lower-*.f64 N/A

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

      17. lower-/.f64 N/A

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

      18. lower-*.f64 87.8

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

   5. Applied rewrites 87.8%

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

   6. Taylor expanded in c around -inf

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

   8. Applied rewrites 96.8%

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

   9. Taylor expanded in b around 0

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

   11. Applied rewrites 87.2%

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

Alternative 9: 75.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ c\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{-64} \lor \neg \left(z \leq 0.16\right):\\ \;\;\;\;\frac{\mathsf{fma}\left(t \cdot a, -4, \frac{b}{z}\right)}{c\_m}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{z \cdot c\_m}\\ \end{array} \end{array} \]

FPCore

c\_m = (fabs.f64 c)
c\_s = (copysign.f64 #s(literal 1 binary64) c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
(FPCore (c_s x y z t a b c_m)
 :precision binary64
 (*
  c_s
  (if (or (<= z -4.8e-64) (not (<= z 0.16)))
    (/ (fma (* t a) -4.0 (/ b z)) c_m)
    (/ (fma (* y x) 9.0 b) (* z c_m)))))

C

c\_m = fabs(c);
c\_s = copysign(1.0, c);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if ((z <= -4.8e-64) || !(z <= 0.16)) {
		tmp = fma((t * a), -4.0, (b / z)) / c_m;
	} else {
		tmp = fma((y * x), 9.0, b) / (z * c_m);
	}
	return c_s * tmp;
}

Julia

c\_m = abs(c)
c\_s = copysign(1.0, c)
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
function code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0
	if ((z <= -4.8e-64) || !(z <= 0.16))
		tmp = Float64(fma(Float64(t * a), -4.0, Float64(b / z)) / c_m);
	else
		tmp = Float64(fma(Float64(y * x), 9.0, b) / Float64(z * c_m));
	end
	return Float64(c_s * tmp)
end

Wolfram

c\_m = N[Abs[c], $MachinePrecision]
c\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
code[c$95$s_, x_, y_, z_, t_, a_, b_, c$95$m_] := N[(c$95$s * If[Or[LessEqual[z, -4.8e-64], N[Not[LessEqual[z, 0.16]], $MachinePrecision]], N[(N[(N[(t * a), $MachinePrecision] * -4.0 + N[(b / z), $MachinePrecision]), $MachinePrecision] / c$95$m), $MachinePrecision], N[(N[(N[(y * x), $MachinePrecision] * 9.0 + b), $MachinePrecision] / N[(z * c$95$m), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if z < -4.79999999999999997e-64 or 0.160000000000000003 < z

   1. Initial program 63.9%

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

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

      2. associate-*r/ N/A

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

      3. associate-*r* N/A

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

      4. associate-*l/ N/A

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

      5. associate-*r/ N/A

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

      6. lower-fma.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. lower-*.f64 N/A

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

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

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

      12. metadata-eval N/A

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

      13. +-commutative N/A

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

      14. lower-fma.f64 N/A

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

      15. lower-/.f64 N/A

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

      16. lower-*.f64 N/A

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

      17. lower-/.f64 N/A

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

      18. lower-*.f64 90.7

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

   5. Applied rewrites 90.7%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 80.1%

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

   if -4.79999999999999997e-64 < z < 0.160000000000000003

   1. Initial program 93.7%

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

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

      3. lower-fma.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 81.7

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

   5. Applied rewrites 81.7%

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

4. Final simplification 80.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{-64} \lor \neg \left(z \leq 0.16\right):\\ \;\;\;\;\frac{\mathsf{fma}\left(t \cdot a, -4, \frac{b}{z}\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{z \cdot c}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 68.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ c\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -2.25 \cdot 10^{+92}:\\ \;\;\;\;\left(-4 \cdot t\right) \cdot \frac{a}{c\_m}\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{+119}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y \cdot x, 9, b\right)}{z \cdot c\_m}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{a \cdot t}{c\_m}\\ \end{array} \end{array} \]

FPCore

c\_m = (fabs.f64 c)
c\_s = (copysign.f64 #s(literal 1 binary64) c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
(FPCore (c_s x y z t a b c_m)
 :precision binary64
 (*
  c_s
  (if (<= z -2.25e+92)
    (* (* -4.0 t) (/ a c_m))
    (if (<= z 1.45e+119)
      (/ (fma (* y x) 9.0 b) (* z c_m))
      (* -4.0 (/ (* a t) c_m))))))

C

c\_m = fabs(c);
c\_s = copysign(1.0, c);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if (z <= -2.25e+92) {
		tmp = (-4.0 * t) * (a / c_m);
	} else if (z <= 1.45e+119) {
		tmp = fma((y * x), 9.0, b) / (z * c_m);
	} else {
		tmp = -4.0 * ((a * t) / c_m);
	}
	return c_s * tmp;
}

Julia

c\_m = abs(c)
c\_s = copysign(1.0, c)
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
function code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0
	if (z <= -2.25e+92)
		tmp = Float64(Float64(-4.0 * t) * Float64(a / c_m));
	elseif (z <= 1.45e+119)
		tmp = Float64(fma(Float64(y * x), 9.0, b) / Float64(z * c_m));
	else
		tmp = Float64(-4.0 * Float64(Float64(a * t) / c_m));
	end
	return Float64(c_s * tmp)
end

Wolfram

c\_m = N[Abs[c], $MachinePrecision]
c\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
code[c$95$s_, x_, y_, z_, t_, a_, b_, c$95$m_] := N[(c$95$s * If[LessEqual[z, -2.25e+92], N[(N[(-4.0 * t), $MachinePrecision] * N[(a / c$95$m), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.45e+119], N[(N[(N[(y * x), $MachinePrecision] * 9.0 + b), $MachinePrecision] / N[(z * c$95$m), $MachinePrecision]), $MachinePrecision], N[(-4.0 * N[(N[(a * t), $MachinePrecision] / c$95$m), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if z < -2.25e92

   1. Initial program 44.7%

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

   3. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 73.1

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

   5. Applied rewrites 73.1%

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

   7. Applied rewrites 79.3%

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

   if -2.25e92 < z < 1.45000000000000004e119

   1. Initial program 93.1%

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

   3. Taylor expanded in z around 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. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 76.1

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

   5. Applied rewrites 76.1%

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

   if 1.45000000000000004e119 < z

   1. Initial program 52.0%

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

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 70.4

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

   5. Applied rewrites 70.4%

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

Alternative 11: 50.4% accurate, 1.4× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ c\_s \cdot \begin{array}{l} \mathbf{if}\;b \leq -2.05 \cdot 10^{+75}:\\ \;\;\;\;\frac{b}{c\_m \cdot z}\\ \mathbf{elif}\;b \leq 1.05 \cdot 10^{-17}:\\ \;\;\;\;\left(-4 \cdot t\right) \cdot \frac{a}{c\_m}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{c\_m}}{z}\\ \end{array} \end{array} \]

FPCore

c\_m = (fabs.f64 c)
c\_s = (copysign.f64 #s(literal 1 binary64) c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
(FPCore (c_s x y z t a b c_m)
 :precision binary64
 (*
  c_s
  (if (<= b -2.05e+75)
    (/ b (* c_m z))
    (if (<= b 1.05e-17) (* (* -4.0 t) (/ a c_m)) (/ (/ b c_m) z)))))

C

c\_m = fabs(c);
c\_s = copysign(1.0, c);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if (b <= -2.05e+75) {
		tmp = b / (c_m * z);
	} else if (b <= 1.05e-17) {
		tmp = (-4.0 * t) * (a / c_m);
	} else {
		tmp = (b / c_m) / z;
	}
	return c_s * tmp;
}

Fortran

c\_m = abs(c)
c\_s = copysign(1.0d0, c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
real(8) function code(c_s, x, y, z, t, a, b, c_m)
    real(8), intent (in) :: c_s
    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_m
    real(8) :: tmp
    if (b <= (-2.05d+75)) then
        tmp = b / (c_m * z)
    else if (b <= 1.05d-17) then
        tmp = ((-4.0d0) * t) * (a / c_m)
    else
        tmp = (b / c_m) / z
    end if
    code = c_s * tmp
end function

Java

c\_m = Math.abs(c);
c\_s = Math.copySign(1.0, c);
assert x < y && y < z && z < t && t < a && a < b && b < c_m;
public static double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if (b <= -2.05e+75) {
		tmp = b / (c_m * z);
	} else if (b <= 1.05e-17) {
		tmp = (-4.0 * t) * (a / c_m);
	} else {
		tmp = (b / c_m) / z;
	}
	return c_s * tmp;
}

Python

c\_m = math.fabs(c)
c\_s = math.copysign(1.0, c)
[x, y, z, t, a, b, c_m] = sort([x, y, z, t, a, b, c_m])
def code(c_s, x, y, z, t, a, b, c_m):
	tmp = 0
	if b <= -2.05e+75:
		tmp = b / (c_m * z)
	elif b <= 1.05e-17:
		tmp = (-4.0 * t) * (a / c_m)
	else:
		tmp = (b / c_m) / z
	return c_s * tmp

Julia

c\_m = abs(c)
c\_s = copysign(1.0, c)
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
function code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0
	if (b <= -2.05e+75)
		tmp = Float64(b / Float64(c_m * z));
	elseif (b <= 1.05e-17)
		tmp = Float64(Float64(-4.0 * t) * Float64(a / c_m));
	else
		tmp = Float64(Float64(b / c_m) / z);
	end
	return Float64(c_s * tmp)
end

MATLAB

c\_m = abs(c);
c\_s = sign(c) * abs(1.0);
x, y, z, t, a, b, c_m = num2cell(sort([x, y, z, t, a, b, c_m])){:}
function tmp_2 = code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0;
	if (b <= -2.05e+75)
		tmp = b / (c_m * z);
	elseif (b <= 1.05e-17)
		tmp = (-4.0 * t) * (a / c_m);
	else
		tmp = (b / c_m) / z;
	end
	tmp_2 = c_s * tmp;
end

Wolfram

c\_m = N[Abs[c], $MachinePrecision]
c\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
code[c$95$s_, x_, y_, z_, t_, a_, b_, c$95$m_] := N[(c$95$s * If[LessEqual[b, -2.05e+75], N[(b / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.05e-17], N[(N[(-4.0 * t), $MachinePrecision] * N[(a / c$95$m), $MachinePrecision]), $MachinePrecision], N[(N[(b / c$95$m), $MachinePrecision] / z), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if b < -2.0499999999999999e75

   1. Initial program 82.1%

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

   3. Taylor expanded in 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. lower-*.f64 68.1

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

   5. Applied rewrites 68.1%

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

   if -2.0499999999999999e75 < b < 1.04999999999999996e-17

   1. Initial program 74.1%

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

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 54.2

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

   5. Applied rewrites 54.2%

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

   7. Applied rewrites 56.0%

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

   if 1.04999999999999996e-17 < b

   1. Initial program 82.6%

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

   3. Taylor expanded in b around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 50.3

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

   5. Applied rewrites 50.3%

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

   7. Applied rewrites 53.0%

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

Alternative 12: 49.9% accurate, 1.4× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ c\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -3100000 \lor \neg \left(z \leq 5 \cdot 10^{+24}\right):\\ \;\;\;\;-4 \cdot \frac{a \cdot t}{c\_m}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{c\_m \cdot z}\\ \end{array} \end{array} \]

FPCore

c\_m = (fabs.f64 c)
c\_s = (copysign.f64 #s(literal 1 binary64) c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
(FPCore (c_s x y z t a b c_m)
 :precision binary64
 (*
  c_s
  (if (or (<= z -3100000.0) (not (<= z 5e+24)))
    (* -4.0 (/ (* a t) c_m))
    (/ b (* c_m z)))))

C

c\_m = fabs(c);
c\_s = copysign(1.0, c);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if ((z <= -3100000.0) || !(z <= 5e+24)) {
		tmp = -4.0 * ((a * t) / c_m);
	} else {
		tmp = b / (c_m * z);
	}
	return c_s * tmp;
}

Fortran

c\_m = abs(c)
c\_s = copysign(1.0d0, c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
real(8) function code(c_s, x, y, z, t, a, b, c_m)
    real(8), intent (in) :: c_s
    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_m
    real(8) :: tmp
    if ((z <= (-3100000.0d0)) .or. (.not. (z <= 5d+24))) then
        tmp = (-4.0d0) * ((a * t) / c_m)
    else
        tmp = b / (c_m * z)
    end if
    code = c_s * tmp
end function

Java

c\_m = Math.abs(c);
c\_s = Math.copySign(1.0, c);
assert x < y && y < z && z < t && t < a && a < b && b < c_m;
public static double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if ((z <= -3100000.0) || !(z <= 5e+24)) {
		tmp = -4.0 * ((a * t) / c_m);
	} else {
		tmp = b / (c_m * z);
	}
	return c_s * tmp;
}

Python

c\_m = math.fabs(c)
c\_s = math.copysign(1.0, c)
[x, y, z, t, a, b, c_m] = sort([x, y, z, t, a, b, c_m])
def code(c_s, x, y, z, t, a, b, c_m):
	tmp = 0
	if (z <= -3100000.0) or not (z <= 5e+24):
		tmp = -4.0 * ((a * t) / c_m)
	else:
		tmp = b / (c_m * z)
	return c_s * tmp

Julia

c\_m = abs(c)
c\_s = copysign(1.0, c)
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
function code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0
	if ((z <= -3100000.0) || !(z <= 5e+24))
		tmp = Float64(-4.0 * Float64(Float64(a * t) / c_m));
	else
		tmp = Float64(b / Float64(c_m * z));
	end
	return Float64(c_s * tmp)
end

MATLAB

c\_m = abs(c);
c\_s = sign(c) * abs(1.0);
x, y, z, t, a, b, c_m = num2cell(sort([x, y, z, t, a, b, c_m])){:}
function tmp_2 = code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0;
	if ((z <= -3100000.0) || ~((z <= 5e+24)))
		tmp = -4.0 * ((a * t) / c_m);
	else
		tmp = b / (c_m * z);
	end
	tmp_2 = c_s * tmp;
end

Wolfram

c\_m = N[Abs[c], $MachinePrecision]
c\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
code[c$95$s_, x_, y_, z_, t_, a_, b_, c$95$m_] := N[(c$95$s * If[Or[LessEqual[z, -3100000.0], N[Not[LessEqual[z, 5e+24]], $MachinePrecision]], N[(-4.0 * N[(N[(a * t), $MachinePrecision] / c$95$m), $MachinePrecision]), $MachinePrecision], N[(b / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if z < -3.1e6 or 5.00000000000000045e24 < z

   1. Initial program 57.7%

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

   3. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 63.8

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

   5. Applied rewrites 63.8%

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

   if -3.1e6 < z < 5.00000000000000045e24

   1. Initial program 94.6%

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

   3. Taylor expanded in b around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 51.7

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

   5. Applied rewrites 51.7%

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

4. Final simplification 57.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3100000 \lor \neg \left(z \leq 5 \cdot 10^{+24}\right):\\ \;\;\;\;-4 \cdot \frac{a \cdot t}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 50.1% accurate, 1.4× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ c\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -3100000:\\ \;\;\;\;\left(-4 \cdot t\right) \cdot \frac{a}{c\_m}\\ \mathbf{elif}\;z \leq 5 \cdot 10^{+24}:\\ \;\;\;\;\frac{b}{c\_m \cdot z}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{a \cdot t}{c\_m}\\ \end{array} \end{array} \]

FPCore

c\_m = (fabs.f64 c)
c\_s = (copysign.f64 #s(literal 1 binary64) c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
(FPCore (c_s x y z t a b c_m)
 :precision binary64
 (*
  c_s
  (if (<= z -3100000.0)
    (* (* -4.0 t) (/ a c_m))
    (if (<= z 5e+24) (/ b (* c_m z)) (* -4.0 (/ (* a t) c_m))))))

C

c\_m = fabs(c);
c\_s = copysign(1.0, c);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if (z <= -3100000.0) {
		tmp = (-4.0 * t) * (a / c_m);
	} else if (z <= 5e+24) {
		tmp = b / (c_m * z);
	} else {
		tmp = -4.0 * ((a * t) / c_m);
	}
	return c_s * tmp;
}

Fortran

c\_m = abs(c)
c\_s = copysign(1.0d0, c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
real(8) function code(c_s, x, y, z, t, a, b, c_m)
    real(8), intent (in) :: c_s
    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_m
    real(8) :: tmp
    if (z <= (-3100000.0d0)) then
        tmp = ((-4.0d0) * t) * (a / c_m)
    else if (z <= 5d+24) then
        tmp = b / (c_m * z)
    else
        tmp = (-4.0d0) * ((a * t) / c_m)
    end if
    code = c_s * tmp
end function

Java

c\_m = Math.abs(c);
c\_s = Math.copySign(1.0, c);
assert x < y && y < z && z < t && t < a && a < b && b < c_m;
public static double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if (z <= -3100000.0) {
		tmp = (-4.0 * t) * (a / c_m);
	} else if (z <= 5e+24) {
		tmp = b / (c_m * z);
	} else {
		tmp = -4.0 * ((a * t) / c_m);
	}
	return c_s * tmp;
}

Python

c\_m = math.fabs(c)
c\_s = math.copysign(1.0, c)
[x, y, z, t, a, b, c_m] = sort([x, y, z, t, a, b, c_m])
def code(c_s, x, y, z, t, a, b, c_m):
	tmp = 0
	if z <= -3100000.0:
		tmp = (-4.0 * t) * (a / c_m)
	elif z <= 5e+24:
		tmp = b / (c_m * z)
	else:
		tmp = -4.0 * ((a * t) / c_m)
	return c_s * tmp

Julia

c\_m = abs(c)
c\_s = copysign(1.0, c)
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
function code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0
	if (z <= -3100000.0)
		tmp = Float64(Float64(-4.0 * t) * Float64(a / c_m));
	elseif (z <= 5e+24)
		tmp = Float64(b / Float64(c_m * z));
	else
		tmp = Float64(-4.0 * Float64(Float64(a * t) / c_m));
	end
	return Float64(c_s * tmp)
end

MATLAB

c\_m = abs(c);
c\_s = sign(c) * abs(1.0);
x, y, z, t, a, b, c_m = num2cell(sort([x, y, z, t, a, b, c_m])){:}
function tmp_2 = code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0;
	if (z <= -3100000.0)
		tmp = (-4.0 * t) * (a / c_m);
	elseif (z <= 5e+24)
		tmp = b / (c_m * z);
	else
		tmp = -4.0 * ((a * t) / c_m);
	end
	tmp_2 = c_s * tmp;
end

Wolfram

c\_m = N[Abs[c], $MachinePrecision]
c\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
code[c$95$s_, x_, y_, z_, t_, a_, b_, c$95$m_] := N[(c$95$s * If[LessEqual[z, -3100000.0], N[(N[(-4.0 * t), $MachinePrecision] * N[(a / c$95$m), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5e+24], N[(b / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision], N[(-4.0 * N[(N[(a * t), $MachinePrecision] / c$95$m), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if z < -3.1e6

   1. Initial program 55.0%

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

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 66.0

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

   5. Applied rewrites 66.0%

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

   7. Applied rewrites 70.8%

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

   if -3.1e6 < z < 5.00000000000000045e24

   1. Initial program 94.6%

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

   3. Taylor expanded in b around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 51.7

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

   5. Applied rewrites 51.7%

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

   if 5.00000000000000045e24 < z

   1. Initial program 60.6%

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

   3. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 61.4

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

   5. Applied rewrites 61.4%

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

Alternative 14: 34.6% accurate, 2.8× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ c\_s \cdot \frac{b}{c\_m \cdot z} \end{array} \]

FPCore

c\_m = (fabs.f64 c)
c\_s = (copysign.f64 #s(literal 1 binary64) c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
(FPCore (c_s x y z t a b c_m) :precision binary64 (* c_s (/ b (* c_m z))))

C

c\_m = fabs(c);
c\_s = copysign(1.0, c);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	return c_s * (b / (c_m * z));
}

Fortran

c\_m = abs(c)
c\_s = copysign(1.0d0, c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
real(8) function code(c_s, x, y, z, t, a, b, c_m)
    real(8), intent (in) :: c_s
    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_m
    code = c_s * (b / (c_m * z))
end function

Java

c\_m = Math.abs(c);
c\_s = Math.copySign(1.0, c);
assert x < y && y < z && z < t && t < a && a < b && b < c_m;
public static double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	return c_s * (b / (c_m * z));
}

Python

c\_m = math.fabs(c)
c\_s = math.copysign(1.0, c)
[x, y, z, t, a, b, c_m] = sort([x, y, z, t, a, b, c_m])
def code(c_s, x, y, z, t, a, b, c_m):
	return c_s * (b / (c_m * z))

Julia

c\_m = abs(c)
c\_s = copysign(1.0, c)
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
function code(c_s, x, y, z, t, a, b, c_m)
	return Float64(c_s * Float64(b / Float64(c_m * z)))
end

MATLAB

c\_m = abs(c);
c\_s = sign(c) * abs(1.0);
x, y, z, t, a, b, c_m = num2cell(sort([x, y, z, t, a, b, c_m])){:}
function tmp = code(c_s, x, y, z, t, a, b, c_m)
	tmp = c_s * (b / (c_m * z));
end

Wolfram

c\_m = N[Abs[c], $MachinePrecision]
c\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
code[c$95$s_, x_, y_, z_, t_, a_, b_, c$95$m_] := N[(c$95$s * N[(b / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 78.1%

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

3. Taylor expanded in 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. lower-*.f64 36.8

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

5. Applied rewrites 36.8%

   \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
6. Add Preprocessing

Developer Target 1: 80.2% 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 2024324 
(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)))