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

Percentage Accurate: 79.6% → 89.1%

Time: 16.7s

Alternatives: 16

Speedup: 0.9×

• 38.3% 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: 79.6% 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: 89.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\\\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ c\_s \cdot \begin{array}{l} \mathbf{if}\;c\_m \leq 2 \cdot 10^{-112}:\\ \;\;\;\;\frac{\mathsf{fma}\left(z, -4 \cdot \left(a \cdot t\right), \mathsf{fma}\left(x, 9 \cdot y, b\right)\right)}{z} \cdot \frac{1}{c\_m}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a, t \cdot \frac{-4}{c\_m}, \mathsf{fma}\left(x, \frac{9 \cdot y}{c\_m \cdot z}, \frac{b}{c\_m \cdot z}\right)\right)\\ \end{array} \end{array} \]

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.
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 2e-112)
    (* (/ (fma z (* -4.0 (* a t)) (fma x (* 9.0 y) b)) z) (/ 1.0 c_m))
    (fma
     a
     (* t (/ -4.0 c_m))
     (fma x (/ (* 9.0 y) (* c_m z)) (/ 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);
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 <= 2e-112) {
		tmp = (fma(z, (-4.0 * (a * t)), fma(x, (9.0 * y), b)) / z) * (1.0 / c_m);
	} else {
		tmp = fma(a, (t * (-4.0 / c_m)), fma(x, ((9.0 * y) / (c_m * z)), (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])
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 <= 2e-112)
		tmp = Float64(Float64(fma(z, Float64(-4.0 * Float64(a * t)), fma(x, Float64(9.0 * y), b)) / z) * Float64(1.0 / c_m));
	else
		tmp = fma(a, Float64(t * Float64(-4.0 / c_m)), fma(x, Float64(Float64(9.0 * y) / Float64(c_m * z)), 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.
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, 2e-112], N[(N[(N[(z * N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision] + N[(x * N[(9.0 * y), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] * N[(1.0 / c$95$m), $MachinePrecision]), $MachinePrecision], N[(a * N[(t * N[(-4.0 / c$95$m), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(9.0 * y), $MachinePrecision] / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision] + N[(b / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if c < 1.9999999999999999e-112

   1. Initial program 78.0%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/r* N/A

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

      4. lower-/.f64 N/A

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

   4. Applied rewrites 84.8%

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

      1. lift-/.f64 N/A

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

      2. clear-num N/A

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

      3. lower-/.f64 N/A

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

      4. lower-/.f64 84.8

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

      5. lift-*.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lift-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lift-*.f64 N/A

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

      11. *-commutative N/A

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

      12. associate-*l* N/A

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

      13. lower-*.f64 N/A

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

      14. lower-*.f64 84.8

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

   6. Applied rewrites 84.8%

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

      1. lift-/.f64 N/A

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

      2. div-inv N/A

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

      3. lower-*.f64 N/A

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

   8. Applied rewrites 89.1%

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

   if 1.9999999999999999e-112 < c

   1. Initial program 71.4%

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

   3. Taylor expanded in x around 0

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. associate-/l* N/A

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

      6. associate-*r* N/A

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

      7. *-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. *-commutative N/A

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

      10. associate-*l/ N/A

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

      11. associate-/l* N/A

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

      12. lower-*.f64 N/A

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

      13. lower-/.f64 N/A

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

      14. *-commutative N/A

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

      15. associate-/l* N/A

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

      16. associate-*l* N/A

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

      17. *-commutative N/A

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

   5. Applied rewrites 89.2%

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

4. Final simplification 89.2%

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

Alternative 2: 74.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\\\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ \begin{array}{l} t_1 := \mathsf{fma}\left(9, x \cdot y, b\right)\\ t_2 := y \cdot \left(x \cdot 9\right)\\ c\_s \cdot \begin{array}{l} \mathbf{if}\;t\_2 \leq -1 \cdot 10^{+144}:\\ \;\;\;\;\frac{\frac{t\_1}{z}}{c\_m}\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+14}:\\ \;\;\;\;\mathsf{fma}\left(-4, \frac{a \cdot t}{c\_m}, \frac{b}{c\_m \cdot z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t\_1}{c\_m \cdot z}\\ \end{array} \end{array} \end{array} \]

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.
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 (fma 9.0 (* x y) b)) (t_2 (* y (* x 9.0))))
   (*
    c_s
    (if (<= t_2 -1e+144)
      (/ (/ t_1 z) c_m)
      (if (<= t_2 5e+14)
        (fma -4.0 (/ (* a t) c_m) (/ b (* c_m z)))
        (/ t_1 (* 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);
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 = fma(9.0, (x * y), b);
	double t_2 = y * (x * 9.0);
	double tmp;
	if (t_2 <= -1e+144) {
		tmp = (t_1 / z) / c_m;
	} else if (t_2 <= 5e+14) {
		tmp = fma(-4.0, ((a * t) / c_m), (b / (c_m * z)));
	} else {
		tmp = t_1 / (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])
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 = fma(9.0, Float64(x * y), b)
	t_2 = Float64(y * Float64(x * 9.0))
	tmp = 0.0
	if (t_2 <= -1e+144)
		tmp = Float64(Float64(t_1 / z) / c_m);
	elseif (t_2 <= 5e+14)
		tmp = fma(-4.0, Float64(Float64(a * t) / c_m), Float64(b / Float64(c_m * z)));
	else
		tmp = Float64(t_1 / 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.
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[(9.0 * N[(x * y), $MachinePrecision] + b), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(x * 9.0), $MachinePrecision]), $MachinePrecision]}, N[(c$95$s * If[LessEqual[t$95$2, -1e+144], N[(N[(t$95$1 / z), $MachinePrecision] / c$95$m), $MachinePrecision], If[LessEqual[t$95$2, 5e+14], N[(-4.0 * N[(N[(a * t), $MachinePrecision] / c$95$m), $MachinePrecision] + N[(b / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -1.00000000000000002e144

   1. Initial program 59.6%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/r* N/A

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

      4. lower-/.f64 N/A

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

   4. Applied rewrites 68.5%

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

      1. lift-/.f64 N/A

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

      2. clear-num N/A

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

      3. lower-/.f64 N/A

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

      4. lower-/.f64 68.5

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

      5. lift-*.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lift-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lift-*.f64 N/A

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

      11. *-commutative N/A

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

      12. associate-*l* N/A

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

      13. lower-*.f64 N/A

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

      14. lower-*.f64 68.5

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

   6. Applied rewrites 68.5%

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

   7. Taylor expanded in z around 0

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

      1. lower-/.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-*.f64 70.5

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

   9. Applied rewrites 70.5%

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

   if -1.00000000000000002e144 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 5e14

   1. Initial program 79.7%

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

      1. lift-/.f64 N/A

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

      2. 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. lift--.f64 N/A

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

      4. associate-+l- N/A

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

      5. div-sub N/A

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

      6. sub-neg N/A

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

      7. lift-*.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. associate-*l* N/A

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

      10. *-commutative N/A

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

      11. lift-*.f64 N/A

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

      12. *-commutative N/A

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

      13. times-frac N/A

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

      14. lower-fma.f64 N/A

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

      15. lower-/.f64 N/A

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

      16. lower-*.f64 N/A

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

      17. lower-/.f64 N/A

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

   4. Applied rewrites 76.8%

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

   5. Taylor expanded in y around 0

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lower-*.f64 80.8

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

   7. Applied rewrites 80.8%

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

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

   1. Initial program 72.9%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-*.f64 69.1

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

   5. Applied rewrites 69.1%

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

4. Final simplification 77.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \left(x \cdot 9\right) \leq -1 \cdot 10^{+144}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(9, x \cdot y, b\right)}{z}}{c}\\ \mathbf{elif}\;y \cdot \left(x \cdot 9\right) \leq 5 \cdot 10^{+14}:\\ \;\;\;\;\mathsf{fma}\left(-4, \frac{a \cdot t}{c}, \frac{b}{c \cdot z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(9, x \cdot y, b\right)}{c \cdot z}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 84.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\\\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ c\_s \cdot \begin{array}{l} \mathbf{if}\;c\_m \leq 7.4 \cdot 10^{-19}:\\ \;\;\;\;\frac{\mathsf{fma}\left(z, -4 \cdot \left(a \cdot t\right), \mathsf{fma}\left(x, 9 \cdot y, b\right)\right)}{z} \cdot \frac{1}{c\_m}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(9, \frac{x \cdot y}{c\_m}, \frac{\mathsf{fma}\left(a, -4 \cdot \left(z \cdot t\right), b\right)}{c\_m}\right)}{z}\\ \end{array} \end{array} \]

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.
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 7.4e-19)
    (* (/ (fma z (* -4.0 (* a t)) (fma x (* 9.0 y) b)) z) (/ 1.0 c_m))
    (/ (fma 9.0 (/ (* x y) c_m) (/ (fma a (* -4.0 (* z t)) 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);
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 <= 7.4e-19) {
		tmp = (fma(z, (-4.0 * (a * t)), fma(x, (9.0 * y), b)) / z) * (1.0 / c_m);
	} else {
		tmp = fma(9.0, ((x * y) / c_m), (fma(a, (-4.0 * (z * t)), 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])
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 <= 7.4e-19)
		tmp = Float64(Float64(fma(z, Float64(-4.0 * Float64(a * t)), fma(x, Float64(9.0 * y), b)) / z) * Float64(1.0 / c_m));
	else
		tmp = Float64(fma(9.0, Float64(Float64(x * y) / c_m), Float64(fma(a, Float64(-4.0 * Float64(z * t)), b) / 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.
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, 7.4e-19], N[(N[(N[(z * N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision] + N[(x * N[(9.0 * y), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] * N[(1.0 / c$95$m), $MachinePrecision]), $MachinePrecision], N[(N[(9.0 * N[(N[(x * y), $MachinePrecision] / c$95$m), $MachinePrecision] + N[(N[(a * N[(-4.0 * N[(z * t), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision] / c$95$m), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if c < 7.40000000000000011e-19

   1. Initial program 79.8%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/r* N/A

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

      4. lower-/.f64 N/A

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

   4. Applied rewrites 86.1%

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

      1. lift-/.f64 N/A

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

      2. clear-num N/A

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

      3. lower-/.f64 N/A

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

      4. lower-/.f64 86.0

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

      5. lift-*.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lift-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lift-*.f64 N/A

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

      11. *-commutative N/A

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

      12. associate-*l* N/A

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

      13. lower-*.f64 N/A

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

      14. lower-*.f64 86.0

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

   6. Applied rewrites 86.0%

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

      1. lift-/.f64 N/A

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

      2. div-inv N/A

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

      3. lower-*.f64 N/A

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

   8. Applied rewrites 90.0%

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

   if 7.40000000000000011e-19 < c

   1. Initial program 65.9%

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

   3. Taylor expanded in z around 0

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

      1. lower-/.f64 N/A

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

   5. Applied rewrites 74.9%

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

4. Final simplification 85.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq 7.4 \cdot 10^{-19}:\\ \;\;\;\;\frac{\mathsf{fma}\left(z, -4 \cdot \left(a \cdot t\right), \mathsf{fma}\left(x, 9 \cdot y, b\right)\right)}{z} \cdot \frac{1}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(9, \frac{x \cdot y}{c}, \frac{\mathsf{fma}\left(a, -4 \cdot \left(z \cdot t\right), b\right)}{c}\right)}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 71.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\\\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ \begin{array}{l} t_1 := \mathsf{fma}\left(9, x \cdot y, b\right)\\ t_2 := y \cdot \left(x \cdot 9\right)\\ c\_s \cdot \begin{array}{l} \mathbf{if}\;t\_2 \leq -4 \cdot 10^{+96}:\\ \;\;\;\;\frac{\frac{t\_1}{z}}{c\_m}\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+14}:\\ \;\;\;\;\frac{\mathsf{fma}\left(z, -4 \cdot \left(a \cdot t\right), b\right)}{c\_m \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t\_1}{c\_m \cdot z}\\ \end{array} \end{array} \end{array} \]

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.
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 (fma 9.0 (* x y) b)) (t_2 (* y (* x 9.0))))
   (*
    c_s
    (if (<= t_2 -4e+96)
      (/ (/ t_1 z) c_m)
      (if (<= t_2 5e+14)
        (/ (fma z (* -4.0 (* a t)) b) (* c_m z))
        (/ t_1 (* 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);
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 = fma(9.0, (x * y), b);
	double t_2 = y * (x * 9.0);
	double tmp;
	if (t_2 <= -4e+96) {
		tmp = (t_1 / z) / c_m;
	} else if (t_2 <= 5e+14) {
		tmp = fma(z, (-4.0 * (a * t)), b) / (c_m * z);
	} else {
		tmp = t_1 / (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])
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 = fma(9.0, Float64(x * y), b)
	t_2 = Float64(y * Float64(x * 9.0))
	tmp = 0.0
	if (t_2 <= -4e+96)
		tmp = Float64(Float64(t_1 / z) / c_m);
	elseif (t_2 <= 5e+14)
		tmp = Float64(fma(z, Float64(-4.0 * Float64(a * t)), b) / Float64(c_m * z));
	else
		tmp = Float64(t_1 / 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.
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[(9.0 * N[(x * y), $MachinePrecision] + b), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(x * 9.0), $MachinePrecision]), $MachinePrecision]}, N[(c$95$s * If[LessEqual[t$95$2, -4e+96], N[(N[(t$95$1 / z), $MachinePrecision] / c$95$m), $MachinePrecision], If[LessEqual[t$95$2, 5e+14], N[(N[(z * N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision] / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision], N[(t$95$1 / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -4.0000000000000002e96

   1. Initial program 62.5%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/r* N/A

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

      4. lower-/.f64 N/A

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

   4. Applied rewrites 69.1%

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

      1. lift-/.f64 N/A

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

      2. clear-num N/A

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

      3. lower-/.f64 N/A

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

      4. lower-/.f64 69.1

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

      5. lift-*.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lift-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lift-*.f64 N/A

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

      11. *-commutative N/A

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

      12. associate-*l* N/A

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

      13. lower-*.f64 N/A

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

      14. lower-*.f64 69.1

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

   6. Applied rewrites 69.1%

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

   7. Taylor expanded in z around 0

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

      1. lower-/.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-*.f64 70.4

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

   9. Applied rewrites 70.4%

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

   if -4.0000000000000002e96 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 5e14

   1. Initial program 80.2%

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

   3. Taylor expanded in b around 0

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. associate-*l* N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower-*.f64 N/A

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

      11. lower-*.f64 N/A

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

      12. lower-*.f64 45.9

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

   5. Applied rewrites 45.9%

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

   6. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. associate-*r* N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-*.f64 52.1

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

   8. Applied rewrites 52.1%

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

   9. Taylor expanded in x around 0

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

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

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

       2. metadata-eval N/A

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

       3. +-commutative N/A

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

       4. *-commutative N/A

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

       5. *-commutative N/A

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

       6. *-commutative N/A

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

       7. associate-*l* N/A

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

       8. *-commutative N/A

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

       9. associate-*r* N/A

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

       10. *-commutative N/A

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

       11. lower-fma.f64 N/A

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

       12. lower-*.f64 N/A

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

       13. lower-*.f64 76.6

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

   11. Applied rewrites 76.6%

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

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

   1. Initial program 72.9%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-*.f64 69.1

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

   5. Applied rewrites 69.1%

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

4. Final simplification 73.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \left(x \cdot 9\right) \leq -4 \cdot 10^{+96}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(9, x \cdot y, b\right)}{z}}{c}\\ \mathbf{elif}\;y \cdot \left(x \cdot 9\right) \leq 5 \cdot 10^{+14}:\\ \;\;\;\;\frac{\mathsf{fma}\left(z, -4 \cdot \left(a \cdot t\right), b\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(9, x \cdot y, b\right)}{c \cdot z}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 70.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\\\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot 9\right)\\ c\_s \cdot \begin{array}{l} \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+144}:\\ \;\;\;\;\frac{\frac{9 \cdot \left(x \cdot y\right)}{z}}{c\_m}\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+14}:\\ \;\;\;\;\frac{\mathsf{fma}\left(z, -4 \cdot \left(a \cdot t\right), b\right)}{c\_m \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(9, x \cdot y, b\right)}{c\_m \cdot z}\\ \end{array} \end{array} \end{array} \]

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.
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 (* y (* x 9.0))))
   (*
    c_s
    (if (<= t_1 -1e+144)
      (/ (/ (* 9.0 (* x y)) z) c_m)
      (if (<= t_1 5e+14)
        (/ (fma z (* -4.0 (* a t)) b) (* c_m z))
        (/ (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);
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 = y * (x * 9.0);
	double tmp;
	if (t_1 <= -1e+144) {
		tmp = ((9.0 * (x * y)) / z) / c_m;
	} else if (t_1 <= 5e+14) {
		tmp = fma(z, (-4.0 * (a * t)), b) / (c_m * z);
	} else {
		tmp = 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])
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(y * Float64(x * 9.0))
	tmp = 0.0
	if (t_1 <= -1e+144)
		tmp = Float64(Float64(Float64(9.0 * Float64(x * y)) / z) / c_m);
	elseif (t_1 <= 5e+14)
		tmp = Float64(fma(z, Float64(-4.0 * Float64(a * t)), b) / Float64(c_m * z));
	else
		tmp = Float64(fma(9.0, Float64(x * y), 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.
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[(y * N[(x * 9.0), $MachinePrecision]), $MachinePrecision]}, N[(c$95$s * If[LessEqual[t$95$1, -1e+144], N[(N[(N[(9.0 * N[(x * y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] / c$95$m), $MachinePrecision], If[LessEqual[t$95$1, 5e+14], N[(N[(z * N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision] / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision], N[(N[(9.0 * N[(x * y), $MachinePrecision] + b), $MachinePrecision] / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -1.00000000000000002e144

   1. Initial program 59.6%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/r* N/A

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

      4. lower-/.f64 N/A

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

   4. Applied rewrites 68.5%

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

   5. Taylor expanded in x around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 68.7

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

   7. Applied rewrites 68.7%

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

   if -1.00000000000000002e144 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 5e14

   1. Initial program 79.7%

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

   3. Taylor expanded in b around 0

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. associate-*l* N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower-*.f64 N/A

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

      11. lower-*.f64 N/A

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

      12. lower-*.f64 44.5

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

   5. Applied rewrites 44.5%

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

   6. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. associate-*r* N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-*.f64 53.2

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

   8. Applied rewrites 53.2%

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

   9. Taylor expanded in x around 0

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

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

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

       2. metadata-eval N/A

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

       3. +-commutative N/A

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

       4. *-commutative N/A

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

       5. *-commutative N/A

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

       6. *-commutative N/A

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

       7. associate-*l* N/A

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

       8. *-commutative N/A

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

       9. associate-*r* N/A

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

       10. *-commutative N/A

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

       11. lower-fma.f64 N/A

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

       12. lower-*.f64 N/A

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

       13. lower-*.f64 75.7

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

   11. Applied rewrites 75.7%

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

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

   1. Initial program 72.9%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-*.f64 69.1

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

   5. Applied rewrites 69.1%

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

4. Final simplification 73.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \left(x \cdot 9\right) \leq -1 \cdot 10^{+144}:\\ \;\;\;\;\frac{\frac{9 \cdot \left(x \cdot y\right)}{z}}{c}\\ \mathbf{elif}\;y \cdot \left(x \cdot 9\right) \leq 5 \cdot 10^{+14}:\\ \;\;\;\;\frac{\mathsf{fma}\left(z, -4 \cdot \left(a \cdot t\right), b\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(9, x \cdot y, b\right)}{c \cdot z}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 71.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\\\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ \begin{array}{l} t_1 := \frac{\mathsf{fma}\left(9, x \cdot y, b\right)}{c\_m \cdot z}\\ t_2 := y \cdot \left(x \cdot 9\right)\\ c\_s \cdot \begin{array}{l} \mathbf{if}\;t\_2 \leq -1 \cdot 10^{-29}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+14}:\\ \;\;\;\;\frac{\mathsf{fma}\left(z, -4 \cdot \left(a \cdot t\right), b\right)}{c\_m \cdot z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \end{array} \]

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.
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 (/ (fma 9.0 (* x y) b) (* c_m z))) (t_2 (* y (* x 9.0))))
   (*
    c_s
    (if (<= t_2 -1e-29)
      t_1
      (if (<= t_2 5e+14) (/ (fma z (* -4.0 (* a t)) b) (* c_m z)) 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);
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 = fma(9.0, (x * y), b) / (c_m * z);
	double t_2 = y * (x * 9.0);
	double tmp;
	if (t_2 <= -1e-29) {
		tmp = t_1;
	} else if (t_2 <= 5e+14) {
		tmp = fma(z, (-4.0 * (a * t)), b) / (c_m * z);
	} 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])
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(fma(9.0, Float64(x * y), b) / Float64(c_m * z))
	t_2 = Float64(y * Float64(x * 9.0))
	tmp = 0.0
	if (t_2 <= -1e-29)
		tmp = t_1;
	elseif (t_2 <= 5e+14)
		tmp = Float64(fma(z, Float64(-4.0 * Float64(a * t)), b) / Float64(c_m * z));
	else
		tmp = t_1;
	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.
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[(9.0 * N[(x * y), $MachinePrecision] + b), $MachinePrecision] / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(x * 9.0), $MachinePrecision]), $MachinePrecision]}, N[(c$95$s * If[LessEqual[t$95$2, -1e-29], t$95$1, If[LessEqual[t$95$2, 5e+14], N[(N[(z * N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision] / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision], t$95$1]]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -9.99999999999999943e-30 or 5e14 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 71.6%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-*.f64 66.5

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

   5. Applied rewrites 66.5%

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

   if -9.99999999999999943e-30 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 5e14

   1. Initial program 79.1%

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

   3. Taylor expanded in b around 0

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. associate-*l* N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower-*.f64 N/A

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

      11. lower-*.f64 N/A

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

      12. lower-*.f64 42.8

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

   5. Applied rewrites 42.8%

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

   6. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. associate-*r* N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-*.f64 50.0

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

   8. Applied rewrites 50.0%

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

   9. Taylor expanded in x around 0

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

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

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

       2. metadata-eval N/A

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

       3. +-commutative N/A

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

       4. *-commutative N/A

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

       5. *-commutative N/A

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

       6. *-commutative N/A

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

       7. associate-*l* N/A

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

       8. *-commutative N/A

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

       9. associate-*r* N/A

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

       10. *-commutative N/A

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

       11. lower-fma.f64 N/A

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

       12. lower-*.f64 N/A

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

       13. lower-*.f64 78.7

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

   11. Applied rewrites 78.7%

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

4. Final simplification 73.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \left(x \cdot 9\right) \leq -1 \cdot 10^{-29}:\\ \;\;\;\;\frac{\mathsf{fma}\left(9, x \cdot y, b\right)}{c \cdot z}\\ \mathbf{elif}\;y \cdot \left(x \cdot 9\right) \leq 5 \cdot 10^{+14}:\\ \;\;\;\;\frac{\mathsf{fma}\left(z, -4 \cdot \left(a \cdot t\right), b\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(9, x \cdot y, b\right)}{c \cdot z}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 70.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\\\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ \begin{array}{l} t_1 := \frac{\mathsf{fma}\left(9, x \cdot y, b\right)}{c\_m \cdot z}\\ t_2 := y \cdot \left(x \cdot 9\right)\\ c\_s \cdot \begin{array}{l} \mathbf{if}\;t\_2 \leq -5 \cdot 10^{-56}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+14}:\\ \;\;\;\;\frac{\mathsf{fma}\left(a, -4 \cdot \left(z \cdot t\right), b\right)}{c\_m \cdot z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \end{array} \]

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.
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 (/ (fma 9.0 (* x y) b) (* c_m z))) (t_2 (* y (* x 9.0))))
   (*
    c_s
    (if (<= t_2 -5e-56)
      t_1
      (if (<= t_2 5e+14) (/ (fma a (* -4.0 (* z t)) b) (* c_m z)) 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);
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 = fma(9.0, (x * y), b) / (c_m * z);
	double t_2 = y * (x * 9.0);
	double tmp;
	if (t_2 <= -5e-56) {
		tmp = t_1;
	} else if (t_2 <= 5e+14) {
		tmp = fma(a, (-4.0 * (z * t)), b) / (c_m * z);
	} 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])
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(fma(9.0, Float64(x * y), b) / Float64(c_m * z))
	t_2 = Float64(y * Float64(x * 9.0))
	tmp = 0.0
	if (t_2 <= -5e-56)
		tmp = t_1;
	elseif (t_2 <= 5e+14)
		tmp = Float64(fma(a, Float64(-4.0 * Float64(z * t)), b) / Float64(c_m * z));
	else
		tmp = t_1;
	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.
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[(9.0 * N[(x * y), $MachinePrecision] + b), $MachinePrecision] / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(x * 9.0), $MachinePrecision]), $MachinePrecision]}, N[(c$95$s * If[LessEqual[t$95$2, -5e-56], t$95$1, If[LessEqual[t$95$2, 5e+14], N[(N[(a * N[(-4.0 * N[(z * t), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision] / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision], t$95$1]]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -4.99999999999999997e-56 or 5e14 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 71.9%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-*.f64 66.5

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

   5. Applied rewrites 66.5%

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

   if -4.99999999999999997e-56 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 5e14

   1. Initial program 79.1%

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

   3. Taylor expanded in x around 0

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. associate-*l* N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower-*.f64 74.8

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

   5. Applied rewrites 74.8%

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

4. Final simplification 70.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \left(x \cdot 9\right) \leq -5 \cdot 10^{-56}:\\ \;\;\;\;\frac{\mathsf{fma}\left(9, x \cdot y, b\right)}{c \cdot z}\\ \mathbf{elif}\;y \cdot \left(x \cdot 9\right) \leq 5 \cdot 10^{+14}:\\ \;\;\;\;\frac{\mathsf{fma}\left(a, -4 \cdot \left(z \cdot t\right), b\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(9, x \cdot y, b\right)}{c \cdot z}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 85.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\\\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-4, \frac{a \cdot t}{c\_m}, \frac{b}{c\_m \cdot z}\right)\\ c\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -8.2 \cdot 10^{+191}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.14 \cdot 10^{+136}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(x, 9 \cdot y, \mathsf{fma}\left(a, -4 \cdot \left(z \cdot t\right), b\right)\right)}{c\_m}}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \end{array} \]

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.
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 (fma -4.0 (/ (* a t) c_m) (/ b (* c_m z)))))
   (*
    c_s
    (if (<= z -8.2e+191)
      t_1
      (if (<= z 1.14e+136)
        (/ (/ (fma x (* 9.0 y) (fma a (* -4.0 (* z t)) b)) c_m) z)
        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);
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 = fma(-4.0, ((a * t) / c_m), (b / (c_m * z)));
	double tmp;
	if (z <= -8.2e+191) {
		tmp = t_1;
	} else if (z <= 1.14e+136) {
		tmp = (fma(x, (9.0 * y), fma(a, (-4.0 * (z * t)), b)) / c_m) / z;
	} 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])
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 = fma(-4.0, Float64(Float64(a * t) / c_m), Float64(b / Float64(c_m * z)))
	tmp = 0.0
	if (z <= -8.2e+191)
		tmp = t_1;
	elseif (z <= 1.14e+136)
		tmp = Float64(Float64(fma(x, Float64(9.0 * y), fma(a, Float64(-4.0 * Float64(z * t)), b)) / c_m) / z);
	else
		tmp = t_1;
	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.
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[(-4.0 * N[(N[(a * t), $MachinePrecision] / c$95$m), $MachinePrecision] + N[(b / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, N[(c$95$s * If[LessEqual[z, -8.2e+191], t$95$1, If[LessEqual[z, 1.14e+136], N[(N[(N[(x * N[(9.0 * y), $MachinePrecision] + N[(a * N[(-4.0 * N[(z * t), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] / c$95$m), $MachinePrecision] / z), $MachinePrecision], t$95$1]]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -8.1999999999999998e191 or 1.14e136 < z

   1. Initial program 45.6%

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

      1. lift-/.f64 N/A

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

      2. 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. lift--.f64 N/A

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

      4. associate-+l- N/A

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

      5. div-sub N/A

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

      6. sub-neg N/A

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

      7. lift-*.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. associate-*l* N/A

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

      10. *-commutative N/A

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

      11. lift-*.f64 N/A

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

      12. *-commutative N/A

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

      13. times-frac N/A

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

      14. lower-fma.f64 N/A

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

      15. lower-/.f64 N/A

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

      16. lower-*.f64 N/A

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

      17. lower-/.f64 N/A

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

   4. Applied rewrites 52.6%

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

   5. Taylor expanded in y around 0

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lower-*.f64 76.7

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

   7. Applied rewrites 76.7%

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

   if -8.1999999999999998e191 < z < 1.14e136

   1. Initial program 84.6%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l/ N/A

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

      4. lower-/.f64 N/A

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

   4. Applied rewrites 88.8%

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

Alternative 9: 85.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\\\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-4, \frac{a \cdot t}{c\_m}, \frac{b}{c\_m \cdot z}\right)\\ c\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+177}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 4.3 \cdot 10^{+168}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x \cdot 9, y, \mathsf{fma}\left(a, -4 \cdot \left(z \cdot t\right), b\right)\right)}{c\_m \cdot z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \end{array} \]

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.
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 (fma -4.0 (/ (* a t) c_m) (/ b (* c_m z)))))
   (*
    c_s
    (if (<= z -4.5e+177)
      t_1
      (if (<= z 4.3e+168)
        (/ (fma (* x 9.0) y (fma a (* -4.0 (* z t)) b)) (* c_m z))
        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);
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 = fma(-4.0, ((a * t) / c_m), (b / (c_m * z)));
	double tmp;
	if (z <= -4.5e+177) {
		tmp = t_1;
	} else if (z <= 4.3e+168) {
		tmp = fma((x * 9.0), y, fma(a, (-4.0 * (z * t)), b)) / (c_m * z);
	} 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])
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 = fma(-4.0, Float64(Float64(a * t) / c_m), Float64(b / Float64(c_m * z)))
	tmp = 0.0
	if (z <= -4.5e+177)
		tmp = t_1;
	elseif (z <= 4.3e+168)
		tmp = Float64(fma(Float64(x * 9.0), y, fma(a, Float64(-4.0 * Float64(z * t)), b)) / Float64(c_m * z));
	else
		tmp = t_1;
	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.
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[(-4.0 * N[(N[(a * t), $MachinePrecision] / c$95$m), $MachinePrecision] + N[(b / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, N[(c$95$s * If[LessEqual[z, -4.5e+177], t$95$1, If[LessEqual[z, 4.3e+168], N[(N[(N[(x * 9.0), $MachinePrecision] * y + N[(a * N[(-4.0 * N[(z * t), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision], t$95$1]]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.4999999999999997e177 or 4.2999999999999998e168 < z

   1. Initial program 39.2%

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

      1. lift-/.f64 N/A

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

      2. 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. lift--.f64 N/A

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

      4. associate-+l- N/A

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

      5. div-sub N/A

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

      6. sub-neg N/A

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

      7. lift-*.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. associate-*l* N/A

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

      10. *-commutative N/A

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

      11. lift-*.f64 N/A

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

      12. *-commutative N/A

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

      13. times-frac N/A

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

      14. lower-fma.f64 N/A

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

      15. lower-/.f64 N/A

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

      16. lower-*.f64 N/A

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

      17. lower-/.f64 N/A

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

   4. Applied rewrites 51.8%

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

   5. Taylor expanded in y around 0

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lower-*.f64 75.6

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

   7. Applied rewrites 75.6%

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

   if -4.4999999999999997e177 < z < 4.2999999999999998e168

   1. Initial program 85.8%

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

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

      7. neg-sub0 N/A

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

      8. associate-+l- N/A

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

      9. neg-sub0 N/A

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

      10. lift-*.f64 N/A

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

      11. *-commutative N/A

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

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

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

      13. lower-fma.f64 N/A

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

      14. lift-*.f64 N/A

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

      15. lift-*.f64 N/A

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

      16. *-commutative N/A

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

      17. associate-*l* N/A

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

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

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

      19. lower-*.f64 N/A

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

      20. metadata-eval N/A

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

      21. lower-*.f64 85.8

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

   4. Applied rewrites 85.8%

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

4. Final simplification 83.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+177}:\\ \;\;\;\;\mathsf{fma}\left(-4, \frac{a \cdot t}{c}, \frac{b}{c \cdot z}\right)\\ \mathbf{elif}\;z \leq 4.3 \cdot 10^{+168}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x \cdot 9, y, \mathsf{fma}\left(a, -4 \cdot \left(z \cdot t\right), b\right)\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-4, \frac{a \cdot t}{c}, \frac{b}{c \cdot z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 50.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\\\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ \begin{array}{l} t_1 := \frac{-4 \cdot \left(a \cdot t\right)}{c\_m}\\ c\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -1660000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.08 \cdot 10^{-47}:\\ \;\;\;\;b \cdot \frac{\frac{1}{c\_m}}{z}\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{+88}:\\ \;\;\;\;\frac{9 \cdot \left(x \cdot y\right)}{c\_m \cdot z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \end{array} \]

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.
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 (/ (* -4.0 (* a t)) c_m)))
   (*
    c_s
    (if (<= z -1660000.0)
      t_1
      (if (<= z 1.08e-47)
        (* b (/ (/ 1.0 c_m) z))
        (if (<= z 4.2e+88) (/ (* 9.0 (* x y)) (* c_m z)) 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);
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 = (-4.0 * (a * t)) / c_m;
	double tmp;
	if (z <= -1660000.0) {
		tmp = t_1;
	} else if (z <= 1.08e-47) {
		tmp = b * ((1.0 / c_m) / z);
	} else if (z <= 4.2e+88) {
		tmp = (9.0 * (x * y)) / (c_m * z);
	} 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.
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) :: tmp
    t_1 = ((-4.0d0) * (a * t)) / c_m
    if (z <= (-1660000.0d0)) then
        tmp = t_1
    else if (z <= 1.08d-47) then
        tmp = b * ((1.0d0 / c_m) / z)
    else if (z <= 4.2d+88) then
        tmp = (9.0d0 * (x * y)) / (c_m * z)
    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;
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 = (-4.0 * (a * t)) / c_m;
	double tmp;
	if (z <= -1660000.0) {
		tmp = t_1;
	} else if (z <= 1.08e-47) {
		tmp = b * ((1.0 / c_m) / z);
	} else if (z <= 4.2e+88) {
		tmp = (9.0 * (x * y)) / (c_m * z);
	} 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])
[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 = (-4.0 * (a * t)) / c_m
	tmp = 0
	if z <= -1660000.0:
		tmp = t_1
	elif z <= 1.08e-47:
		tmp = b * ((1.0 / c_m) / z)
	elif z <= 4.2e+88:
		tmp = (9.0 * (x * y)) / (c_m * z)
	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])
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(-4.0 * Float64(a * t)) / c_m)
	tmp = 0.0
	if (z <= -1660000.0)
		tmp = t_1;
	elseif (z <= 1.08e-47)
		tmp = Float64(b * Float64(Float64(1.0 / c_m) / z));
	elseif (z <= 4.2e+88)
		tmp = Float64(Float64(9.0 * Float64(x * y)) / Float64(c_m * z));
	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])){:}
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 = (-4.0 * (a * t)) / c_m;
	tmp = 0.0;
	if (z <= -1660000.0)
		tmp = t_1;
	elseif (z <= 1.08e-47)
		tmp = b * ((1.0 / c_m) / z);
	elseif (z <= 4.2e+88)
		tmp = (9.0 * (x * y)) / (c_m * z);
	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.
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[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision] / c$95$m), $MachinePrecision]}, N[(c$95$s * If[LessEqual[z, -1660000.0], t$95$1, If[LessEqual[z, 1.08e-47], N[(b * N[(N[(1.0 / c$95$m), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.2e+88], N[(N[(9.0 * N[(x * y), $MachinePrecision]), $MachinePrecision] / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]), $MachinePrecision]]

Derivation

1. Split input into 3 regimes

2. if z < -1.66e6 or 4.2e88 < z

   1. Initial program 57.3%

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

   3. Taylor expanded in z around inf

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 57.8

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

   5. Applied rewrites 57.8%

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

   if -1.66e6 < z < 1.08000000000000005e-47

   1. Initial program 92.1%

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

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

      3. lower-*.f64 52.5

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

   5. Applied rewrites 52.5%

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

   7. Applied rewrites 53.2%

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

   9. Applied rewrites 53.2%

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

   if 1.08000000000000005e-47 < z < 4.2e88

   1. Initial program 80.5%

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

   3. Taylor expanded in x around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 49.4

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

   5. Applied rewrites 49.4%

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

4. Final simplification 54.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1660000:\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right)}{c}\\ \mathbf{elif}\;z \leq 1.08 \cdot 10^{-47}:\\ \;\;\;\;b \cdot \frac{\frac{1}{c}}{z}\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{+88}:\\ \;\;\;\;\frac{9 \cdot \left(x \cdot y\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right)}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 50.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\\\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ \begin{array}{l} t_1 := \frac{-4 \cdot \left(a \cdot t\right)}{c\_m}\\ c\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -1660000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.08 \cdot 10^{-47}:\\ \;\;\;\;b \cdot \frac{1}{c\_m \cdot z}\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{+88}:\\ \;\;\;\;\frac{9 \cdot \left(x \cdot y\right)}{c\_m \cdot z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \end{array} \]

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.
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 (/ (* -4.0 (* a t)) c_m)))
   (*
    c_s
    (if (<= z -1660000.0)
      t_1
      (if (<= z 1.08e-47)
        (* b (/ 1.0 (* c_m z)))
        (if (<= z 4.2e+88) (/ (* 9.0 (* x y)) (* c_m z)) 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);
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 = (-4.0 * (a * t)) / c_m;
	double tmp;
	if (z <= -1660000.0) {
		tmp = t_1;
	} else if (z <= 1.08e-47) {
		tmp = b * (1.0 / (c_m * z));
	} else if (z <= 4.2e+88) {
		tmp = (9.0 * (x * y)) / (c_m * z);
	} 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.
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) :: tmp
    t_1 = ((-4.0d0) * (a * t)) / c_m
    if (z <= (-1660000.0d0)) then
        tmp = t_1
    else if (z <= 1.08d-47) then
        tmp = b * (1.0d0 / (c_m * z))
    else if (z <= 4.2d+88) then
        tmp = (9.0d0 * (x * y)) / (c_m * z)
    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;
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 = (-4.0 * (a * t)) / c_m;
	double tmp;
	if (z <= -1660000.0) {
		tmp = t_1;
	} else if (z <= 1.08e-47) {
		tmp = b * (1.0 / (c_m * z));
	} else if (z <= 4.2e+88) {
		tmp = (9.0 * (x * y)) / (c_m * z);
	} 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])
[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 = (-4.0 * (a * t)) / c_m
	tmp = 0
	if z <= -1660000.0:
		tmp = t_1
	elif z <= 1.08e-47:
		tmp = b * (1.0 / (c_m * z))
	elif z <= 4.2e+88:
		tmp = (9.0 * (x * y)) / (c_m * z)
	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])
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(-4.0 * Float64(a * t)) / c_m)
	tmp = 0.0
	if (z <= -1660000.0)
		tmp = t_1;
	elseif (z <= 1.08e-47)
		tmp = Float64(b * Float64(1.0 / Float64(c_m * z)));
	elseif (z <= 4.2e+88)
		tmp = Float64(Float64(9.0 * Float64(x * y)) / Float64(c_m * z));
	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])){:}
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 = (-4.0 * (a * t)) / c_m;
	tmp = 0.0;
	if (z <= -1660000.0)
		tmp = t_1;
	elseif (z <= 1.08e-47)
		tmp = b * (1.0 / (c_m * z));
	elseif (z <= 4.2e+88)
		tmp = (9.0 * (x * y)) / (c_m * z);
	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.
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[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision] / c$95$m), $MachinePrecision]}, N[(c$95$s * If[LessEqual[z, -1660000.0], t$95$1, If[LessEqual[z, 1.08e-47], N[(b * N[(1.0 / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.2e+88], N[(N[(9.0 * N[(x * y), $MachinePrecision]), $MachinePrecision] / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]), $MachinePrecision]]

Derivation

1. Split input into 3 regimes

2. if z < -1.66e6 or 4.2e88 < z

   1. Initial program 57.3%

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

   3. Taylor expanded in z around inf

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 57.8

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

   5. Applied rewrites 57.8%

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

   if -1.66e6 < z < 1.08000000000000005e-47

   1. Initial program 92.1%

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

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

      3. lower-*.f64 52.5

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

   5. Applied rewrites 52.5%

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

   7. Applied rewrites 53.2%

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

   if 1.08000000000000005e-47 < z < 4.2e88

   1. Initial program 80.5%

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

   3. Taylor expanded in x around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 49.4

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

   5. Applied rewrites 49.4%

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

4. Final simplification 54.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1660000:\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right)}{c}\\ \mathbf{elif}\;z \leq 1.08 \cdot 10^{-47}:\\ \;\;\;\;b \cdot \frac{1}{c \cdot z}\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{+88}:\\ \;\;\;\;\frac{9 \cdot \left(x \cdot y\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right)}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 68.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\\\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ \begin{array}{l} t_1 := -4 \cdot \left(a \cdot t\right)\\ c\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{+53}:\\ \;\;\;\;\frac{1}{\frac{c\_m}{t\_1}}\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{+175}:\\ \;\;\;\;\frac{\mathsf{fma}\left(9, x \cdot y, b\right)}{c\_m \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t\_1}{c\_m}\\ \end{array} \end{array} \end{array} \]

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.
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 (* -4.0 (* a t))))
   (*
    c_s
    (if (<= z -3.6e+53)
      (/ 1.0 (/ c_m t_1))
      (if (<= z 3.6e+175) (/ (fma 9.0 (* x y) b) (* c_m z)) (/ t_1 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);
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 = -4.0 * (a * t);
	double tmp;
	if (z <= -3.6e+53) {
		tmp = 1.0 / (c_m / t_1);
	} else if (z <= 3.6e+175) {
		tmp = fma(9.0, (x * y), b) / (c_m * z);
	} else {
		tmp = t_1 / 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])
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(-4.0 * Float64(a * t))
	tmp = 0.0
	if (z <= -3.6e+53)
		tmp = Float64(1.0 / Float64(c_m / t_1));
	elseif (z <= 3.6e+175)
		tmp = Float64(fma(9.0, Float64(x * y), b) / Float64(c_m * z));
	else
		tmp = Float64(t_1 / 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.
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[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision]}, N[(c$95$s * If[LessEqual[z, -3.6e+53], N[(1.0 / N[(c$95$m / t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.6e+175], N[(N[(9.0 * N[(x * y), $MachinePrecision] + b), $MachinePrecision] / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision], N[(t$95$1 / c$95$m), $MachinePrecision]]]), $MachinePrecision]]

Derivation

1. Split input into 3 regimes

2. if z < -3.6e53

   1. Initial program 42.9%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/r* N/A

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

      4. lower-/.f64 N/A

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

   4. Applied rewrites 57.6%

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

   5. Taylor expanded in a around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 60.7

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

   7. Applied rewrites 60.7%

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

      1. lift-/.f64 N/A

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

      2. clear-num N/A

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

      3. lower-/.f64 N/A

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

      4. lower-/.f64 60.8

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

   9. Applied rewrites 60.8%

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

   if -3.6e53 < z < 3.60000000000000034e175

   1. Initial program 89.3%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-*.f64 71.3

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

   5. Applied rewrites 71.3%

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

   if 3.60000000000000034e175 < z

   1. Initial program 48.6%

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

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 74.7

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

   5. Applied rewrites 74.7%

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

4. Final simplification 69.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{+53}:\\ \;\;\;\;\frac{1}{\frac{c}{-4 \cdot \left(a \cdot t\right)}}\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{+175}:\\ \;\;\;\;\frac{\mathsf{fma}\left(9, x \cdot y, b\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right)}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 68.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\\\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ \begin{array}{l} t_1 := \frac{-4 \cdot \left(a \cdot t\right)}{c\_m}\\ c\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{+53}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{+175}:\\ \;\;\;\;\frac{\mathsf{fma}\left(9, x \cdot y, b\right)}{c\_m \cdot z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \end{array} \]

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.
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 (/ (* -4.0 (* a t)) c_m)))
   (*
    c_s
    (if (<= z -3.6e+53)
      t_1
      (if (<= z 3.6e+175) (/ (fma 9.0 (* x y) b) (* c_m z)) 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);
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 = (-4.0 * (a * t)) / c_m;
	double tmp;
	if (z <= -3.6e+53) {
		tmp = t_1;
	} else if (z <= 3.6e+175) {
		tmp = fma(9.0, (x * y), b) / (c_m * z);
	} 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])
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(-4.0 * Float64(a * t)) / c_m)
	tmp = 0.0
	if (z <= -3.6e+53)
		tmp = t_1;
	elseif (z <= 3.6e+175)
		tmp = Float64(fma(9.0, Float64(x * y), b) / Float64(c_m * z));
	else
		tmp = t_1;
	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.
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[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision] / c$95$m), $MachinePrecision]}, N[(c$95$s * If[LessEqual[z, -3.6e+53], t$95$1, If[LessEqual[z, 3.6e+175], N[(N[(9.0 * N[(x * y), $MachinePrecision] + b), $MachinePrecision] / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision], t$95$1]]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.6e53 or 3.60000000000000034e175 < z

   1. Initial program 44.3%

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

   3. Taylor expanded in z around inf

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 64.1

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

   5. Applied rewrites 64.1%

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

   if -3.6e53 < z < 3.60000000000000034e175

   1. Initial program 89.3%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-*.f64 71.3

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

   5. Applied rewrites 71.3%

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

4. Final simplification 69.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{+53}:\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right)}{c}\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{+175}:\\ \;\;\;\;\frac{\mathsf{fma}\left(9, x \cdot y, b\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right)}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 50.5% accurate, 1.4× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\\\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ \begin{array}{l} t_1 := \frac{-4 \cdot \left(a \cdot t\right)}{c\_m}\\ c\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -1660000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 0.108:\\ \;\;\;\;b \cdot \frac{1}{c\_m \cdot z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \end{array} \]

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.
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 (/ (* -4.0 (* a t)) c_m)))
   (*
    c_s
    (if (<= z -1660000.0) t_1 (if (<= z 0.108) (* b (/ 1.0 (* c_m z))) 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);
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 = (-4.0 * (a * t)) / c_m;
	double tmp;
	if (z <= -1660000.0) {
		tmp = t_1;
	} else if (z <= 0.108) {
		tmp = b * (1.0 / (c_m * z));
	} 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.
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) :: tmp
    t_1 = ((-4.0d0) * (a * t)) / c_m
    if (z <= (-1660000.0d0)) then
        tmp = t_1
    else if (z <= 0.108d0) then
        tmp = b * (1.0d0 / (c_m * z))
    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;
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 = (-4.0 * (a * t)) / c_m;
	double tmp;
	if (z <= -1660000.0) {
		tmp = t_1;
	} else if (z <= 0.108) {
		tmp = b * (1.0 / (c_m * z));
	} 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])
[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 = (-4.0 * (a * t)) / c_m
	tmp = 0
	if z <= -1660000.0:
		tmp = t_1
	elif z <= 0.108:
		tmp = b * (1.0 / (c_m * z))
	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])
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(-4.0 * Float64(a * t)) / c_m)
	tmp = 0.0
	if (z <= -1660000.0)
		tmp = t_1;
	elseif (z <= 0.108)
		tmp = Float64(b * Float64(1.0 / Float64(c_m * z)));
	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])){:}
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 = (-4.0 * (a * t)) / c_m;
	tmp = 0.0;
	if (z <= -1660000.0)
		tmp = t_1;
	elseif (z <= 0.108)
		tmp = b * (1.0 / (c_m * z));
	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.
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[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision] / c$95$m), $MachinePrecision]}, N[(c$95$s * If[LessEqual[z, -1660000.0], t$95$1, If[LessEqual[z, 0.108], N[(b * N[(1.0 / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.66e6 or 0.107999999999999999 < z

   1. Initial program 60.3%

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

   3. Taylor expanded in z around inf

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 53.5

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

   5. Applied rewrites 53.5%

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

   if -1.66e6 < z < 0.107999999999999999

   1. Initial program 92.4%

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

   3. Taylor expanded in b around inf

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 51.7

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

   5. Applied rewrites 51.7%

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

   7. Applied rewrites 52.3%

      \[\leadsto \frac{1}{z \cdot c} \cdot \color{blue}{b} \]
3. Recombined 2 regimes into one program.

4. Final simplification 52.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1660000:\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right)}{c}\\ \mathbf{elif}\;z \leq 0.108:\\ \;\;\;\;b \cdot \frac{1}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right)}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 35.4% accurate, 2.2× speedup

Math

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

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.
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 (/ 1.0 (* 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);
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 * (1.0 / (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.
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 * (1.0d0 / (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;
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 * (1.0 / (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])
[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 * (1.0 / (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])
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(1.0 / 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])){:}
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 * (1.0 / (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.
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[(1.0 / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 75.6%

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

3. Taylor expanded in b around inf

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

   1. lower-/.f64 N/A

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

   2. *-commutative N/A

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

   3. lower-*.f64 35.6

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

5. Applied rewrites 35.6%

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

7. Applied rewrites 36.0%

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

8. Final simplification 36.0%

   \[\leadsto b \cdot \frac{1}{c \cdot z} \]
9. Add Preprocessing

Alternative 16: 35.2% accurate, 2.8× speedup

Math

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

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.
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);
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.
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;
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])
[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])
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])){:}
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.
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 75.6%

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

3. Taylor expanded in b around inf

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

   1. lower-/.f64 N/A

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

   2. *-commutative N/A

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

   3. lower-*.f64 35.6

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

5. Applied rewrites 35.6%

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

6. Final simplification 35.6%

   \[\leadsto \frac{b}{c \cdot z} \]
7. Add Preprocessing

Developer Target 1: 80.5% 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 2024226 
(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)))