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

Percentage Accurate: 78.9% → 87.1%

Time: 15.6s

Alternatives: 16

Speedup: 0.9×

• 36.6% 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: 78.9% 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: 87.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\\\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ c\_s \cdot \begin{array}{l} \mathbf{if}\;c\_m \leq 5 \cdot 10^{+65}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, 9 \cdot y, \mathsf{fma}\left(a, -4 \cdot \left(z \cdot t\right), b\right)\right)}{z} \cdot \frac{1}{c\_m}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a, t \cdot \frac{-4}{c\_m}, \mathsf{fma}\left(x, \frac{9 \cdot y}{c\_m \cdot z}, \frac{b}{c\_m \cdot z}\right)\right)\\ \end{array} \end{array} \]

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 5e+65)
    (* (/ (fma x (* 9.0 y) (fma a (* -4.0 (* z t)) 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 <= 5e+65) {
		tmp = (fma(x, (9.0 * y), fma(a, (-4.0 * (z * t)), 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 <= 5e+65)
		tmp = Float64(Float64(fma(x, Float64(9.0 * y), fma(a, Float64(-4.0 * Float64(z * t)), 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, 5e+65], N[(N[(N[(x * N[(9.0 * y), $MachinePrecision] + N[(a * N[(-4.0 * N[(z * t), $MachinePrecision]), $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 < 4.99999999999999973e65

   1. Initial program 82.6%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lift--.f64 N/A

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

      7. lift-+.f64 N/A

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

      8. *-rgt-identity N/A

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

      9. frac-times N/A

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

      10. lower-*.f64 N/A

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

   4. Applied egg-rr 85.9%

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

   if 4.99999999999999973e65 < c

   1. Initial program 58.9%

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

   3. Taylor expanded in x around 0

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. associate-/l* N/A

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

      6. associate-*r* N/A

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

      7. *-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. *-commutative N/A

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

      10. associate-*l/ N/A

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

      11. associate-/l* N/A

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

      12. lower-*.f64 N/A

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

      13. lower-/.f64 N/A

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

      14. *-commutative N/A

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

      15. associate-/l* N/A

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

      16. associate-*l* N/A

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

      17. *-commutative N/A

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

   5. Simplified 85.9%

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

4. Final simplification 85.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq 5 \cdot 10^{+65}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, 9 \cdot y, \mathsf{fma}\left(a, -4 \cdot \left(z \cdot t\right), b\right)\right)}{z} \cdot \frac{1}{c}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a, t \cdot \frac{-4}{c}, \mathsf{fma}\left(x, \frac{9 \cdot y}{c \cdot z}, \frac{b}{c \cdot z}\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 85.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\\\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ \begin{array}{l} t_1 := \mathsf{fma}\left(x, 9 \cdot y, \mathsf{fma}\left(a, -4 \cdot \left(z \cdot t\right), b\right)\right)\\ t_2 := \frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{c\_m \cdot z}\\ c\_s \cdot \begin{array}{l} \mathbf{if}\;t\_2 \leq -5 \cdot 10^{+26}:\\ \;\;\;\;t\_1 \cdot \frac{1}{c\_m \cdot z}\\ \mathbf{elif}\;t\_2 \leq \infty:\\ \;\;\;\;\frac{\frac{1}{c\_m}}{\frac{z}{t\_1}}\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(t \cdot \frac{-4}{c\_m}\right)\\ \end{array} \end{array} \end{array} \]

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 x (* 9.0 y) (fma a (* -4.0 (* z t)) b)))
        (t_2 (/ (+ b (- (* y (* x 9.0)) (* a (* t (* z 4.0))))) (* c_m z))))
   (*
    c_s
    (if (<= t_2 -5e+26)
      (* t_1 (/ 1.0 (* c_m z)))
      (if (<= t_2 INFINITY)
        (/ (/ 1.0 c_m) (/ z t_1))
        (* a (* t (/ -4.0 c_m))))))))

C

c\_m = fabs(c);
c\_s = copysign(1.0, c);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
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(x, (9.0 * y), fma(a, (-4.0 * (z * t)), b));
	double t_2 = (b + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (c_m * z);
	double tmp;
	if (t_2 <= -5e+26) {
		tmp = t_1 * (1.0 / (c_m * z));
	} else if (t_2 <= ((double) INFINITY)) {
		tmp = (1.0 / c_m) / (z / t_1);
	} else {
		tmp = a * (t * (-4.0 / c_m));
	}
	return c_s * tmp;
}

Julia

c\_m = abs(c)
c\_s = copysign(1.0, c)
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
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(x, Float64(9.0 * y), fma(a, Float64(-4.0 * Float64(z * t)), b))
	t_2 = Float64(Float64(b + Float64(Float64(y * Float64(x * 9.0)) - Float64(a * Float64(t * Float64(z * 4.0))))) / Float64(c_m * z))
	tmp = 0.0
	if (t_2 <= -5e+26)
		tmp = Float64(t_1 * Float64(1.0 / Float64(c_m * z)));
	elseif (t_2 <= Inf)
		tmp = Float64(Float64(1.0 / c_m) / Float64(z / t_1));
	else
		tmp = Float64(a * Float64(t * Float64(-4.0 / c_m)));
	end
	return Float64(c_s * tmp)
end

Wolfram

c\_m = N[Abs[c], $MachinePrecision]
c\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
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[(x * N[(9.0 * y), $MachinePrecision] + N[(a * N[(-4.0 * N[(z * t), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b + N[(N[(y * N[(x * 9.0), $MachinePrecision]), $MachinePrecision] - N[(a * N[(t * N[(z * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision]}, N[(c$95$s * If[LessEqual[t$95$2, -5e+26], N[(t$95$1 * N[(1.0 / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, Infinity], N[(N[(1.0 / c$95$m), $MachinePrecision] / N[(z / t$95$1), $MachinePrecision]), $MachinePrecision], N[(a * N[(t * N[(-4.0 / c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x #s(literal 9 binary64)) y) (*.f64 (*.f64 (*.f64 z #s(literal 4 binary64)) t) a)) b) (*.f64 z c)) < -5.0000000000000001e26

   1. Initial program 88.7%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lift--.f64 N/A

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

      7. lift-+.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. div-inv N/A

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

      10. lower-*.f64 N/A

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

   4. Applied egg-rr 88.7%

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

   if -5.0000000000000001e26 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x #s(literal 9 binary64)) y) (*.f64 (*.f64 (*.f64 z #s(literal 4 binary64)) t) a)) b) (*.f64 z c)) < +inf.0

   1. Initial program 85.6%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lift--.f64 N/A

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

      7. lift-+.f64 N/A

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

      8. associate-/r* N/A

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

      9. clear-num N/A

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

      10. associate-/l/ N/A

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

      11. associate-/r* N/A

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

      12. lower-/.f64 N/A

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

      13. lower-/.f64 N/A

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

      14. lower-/.f64 88.8

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

   4. Applied egg-rr 89.4%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in 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 4.9

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

   5. Simplified 4.9%

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

   6. Taylor expanded in a around inf

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

      1. lower-*.f64 N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 68.9

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

   8. Simplified 68.9%

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

   9. Taylor expanded in t around inf

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

       1. associate-*r/ N/A

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

       2. lower-/.f64 N/A

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

       3. lower-*.f64 68.9

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

   11. Simplified 68.9%

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

       1. *-commutative N/A

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

       2. associate-/l* N/A

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

       3. lower-*.f64 N/A

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

       4. lower-/.f64 68.8

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

   13. Applied egg-rr 68.8%

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

4. Final simplification 87.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{c \cdot z} \leq -5 \cdot 10^{+26}:\\ \;\;\;\;\mathsf{fma}\left(x, 9 \cdot y, \mathsf{fma}\left(a, -4 \cdot \left(z \cdot t\right), b\right)\right) \cdot \frac{1}{c \cdot z}\\ \mathbf{elif}\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{c \cdot z} \leq \infty:\\ \;\;\;\;\frac{\frac{1}{c}}{\frac{z}{\mathsf{fma}\left(x, 9 \cdot y, \mathsf{fma}\left(a, -4 \cdot \left(z \cdot t\right), b\right)\right)}}\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(t \cdot \frac{-4}{c}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 83.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\\\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ \begin{array}{l} t_1 := t \cdot \mathsf{fma}\left(-4, \frac{a}{c\_m}, \frac{b}{c\_m \cdot \left(z \cdot t\right)}\right)\\ c\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{+84}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.16 \cdot 10^{+95}:\\ \;\;\;\;\mathsf{fma}\left(x, 9 \cdot y, \mathsf{fma}\left(a, -4 \cdot \left(z \cdot t\right), b\right)\right) \cdot \frac{1}{c\_m \cdot z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \end{array} \]

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 (* t (fma -4.0 (/ a c_m) (/ b (* c_m (* z t)))))))
   (*
    c_s
    (if (<= z -1.65e+84)
      t_1
      (if (<= z 1.16e+95)
        (* (fma x (* 9.0 y) (fma a (* -4.0 (* z t)) 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 = t * fma(-4.0, (a / c_m), (b / (c_m * (z * t))));
	double tmp;
	if (z <= -1.65e+84) {
		tmp = t_1;
	} else if (z <= 1.16e+95) {
		tmp = fma(x, (9.0 * y), fma(a, (-4.0 * (z * t)), 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(t * fma(-4.0, Float64(a / c_m), Float64(b / Float64(c_m * Float64(z * t)))))
	tmp = 0.0
	if (z <= -1.65e+84)
		tmp = t_1;
	elseif (z <= 1.16e+95)
		tmp = Float64(fma(x, Float64(9.0 * y), fma(a, Float64(-4.0 * Float64(z * t)), b)) * Float64(1.0 / 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[(t * N[(-4.0 * N[(a / c$95$m), $MachinePrecision] + N[(b / N[(c$95$m * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, N[(c$95$s * If[LessEqual[z, -1.65e+84], t$95$1, If[LessEqual[z, 1.16e+95], N[(N[(x * N[(9.0 * y), $MachinePrecision] + N[(a * N[(-4.0 * N[(z * t), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] * 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 < -1.65000000000000008e84 or 1.1599999999999999e95 < z

   1. Initial program 50.1%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   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 46.4

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

   5. Simplified 46.4%

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

   6. Taylor expanded in t around inf

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

      1. lower-*.f64 N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. lower-*.f64 75.8

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

   8. Simplified 75.8%

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

   if -1.65000000000000008e84 < z < 1.1599999999999999e95

   1. Initial program 95.2%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lift--.f64 N/A

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

      7. lift-+.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. div-inv N/A

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

      10. lower-*.f64 N/A

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

   4. Applied egg-rr 95.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, 9 \cdot y, \mathsf{fma}\left(a, -4 \cdot \left(z \cdot t\right), b\right)\right) \cdot \frac{1}{z \cdot c}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 88.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{+84}:\\ \;\;\;\;t \cdot \mathsf{fma}\left(-4, \frac{a}{c}, \frac{b}{c \cdot \left(z \cdot t\right)}\right)\\ \mathbf{elif}\;z \leq 1.16 \cdot 10^{+95}:\\ \;\;\;\;\mathsf{fma}\left(x, 9 \cdot y, \mathsf{fma}\left(a, -4 \cdot \left(z \cdot t\right), b\right)\right) \cdot \frac{1}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \mathsf{fma}\left(-4, \frac{a}{c}, \frac{b}{c \cdot \left(z \cdot t\right)}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 83.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\\\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ \begin{array}{l} t_1 := t \cdot \mathsf{fma}\left(-4, \frac{a}{c\_m}, \frac{b}{c\_m \cdot \left(z \cdot t\right)}\right)\\ c\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{+84}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.12 \cdot 10^{+95}:\\ \;\;\;\;\frac{\mathsf{fma}\left(a \cdot \left(-4 \cdot z\right), t, \mathsf{fma}\left(x, 9 \cdot y, b\right)\right)}{c\_m \cdot z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \end{array} \]

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 (* t (fma -4.0 (/ a c_m) (/ b (* c_m (* z t)))))))
   (*
    c_s
    (if (<= z -1.25e+84)
      t_1
      (if (<= z 1.12e+95)
        (/ (fma (* a (* -4.0 z)) t (fma x (* 9.0 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 = t * fma(-4.0, (a / c_m), (b / (c_m * (z * t))));
	double tmp;
	if (z <= -1.25e+84) {
		tmp = t_1;
	} else if (z <= 1.12e+95) {
		tmp = fma((a * (-4.0 * z)), t, fma(x, (9.0 * 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(t * fma(-4.0, Float64(a / c_m), Float64(b / Float64(c_m * Float64(z * t)))))
	tmp = 0.0
	if (z <= -1.25e+84)
		tmp = t_1;
	elseif (z <= 1.12e+95)
		tmp = Float64(fma(Float64(a * Float64(-4.0 * z)), t, fma(x, Float64(9.0 * 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[(t * N[(-4.0 * N[(a / c$95$m), $MachinePrecision] + N[(b / N[(c$95$m * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, N[(c$95$s * If[LessEqual[z, -1.25e+84], t$95$1, If[LessEqual[z, 1.12e+95], N[(N[(N[(a * N[(-4.0 * z), $MachinePrecision]), $MachinePrecision] * t + N[(x * N[(9.0 * y), $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 < -1.25e84 or 1.11999999999999999e95 < z

   1. Initial program 50.1%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   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 46.4

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

   5. Simplified 46.4%

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

   6. Taylor expanded in t around inf

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

      1. lower-*.f64 N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. lower-*.f64 75.8

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

   8. Simplified 75.8%

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

   if -1.25e84 < z < 1.11999999999999999e95

   1. Initial program 95.2%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. sub-neg N/A

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

      7. +-commutative N/A

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

      8. associate-+l+ N/A

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

      9. lift-*.f64 N/A

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

      10. lift-*.f64 N/A

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

      11. associate-*l* N/A

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

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

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

      13. *-commutative N/A

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

      14. associate-*r* N/A

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

      15. lower-fma.f64 N/A

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

   4. Applied egg-rr 96.3%

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

4. Final simplification 89.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{+84}:\\ \;\;\;\;t \cdot \mathsf{fma}\left(-4, \frac{a}{c}, \frac{b}{c \cdot \left(z \cdot t\right)}\right)\\ \mathbf{elif}\;z \leq 1.12 \cdot 10^{+95}:\\ \;\;\;\;\frac{\mathsf{fma}\left(a \cdot \left(-4 \cdot z\right), t, \mathsf{fma}\left(x, 9 \cdot y, b\right)\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \mathsf{fma}\left(-4, \frac{a}{c}, \frac{b}{c \cdot \left(z \cdot t\right)}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 83.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\\\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ \begin{array}{l} t_1 := t \cdot \mathsf{fma}\left(-4, \frac{a}{c\_m}, \frac{b}{c\_m \cdot \left(z \cdot t\right)}\right)\\ c\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{+84}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.12 \cdot 10^{+95}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x \cdot 9, y, \mathsf{fma}\left(a, -4 \cdot \left(z \cdot t\right), b\right)\right)}{c\_m \cdot z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \end{array} \]

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 (* t (fma -4.0 (/ a c_m) (/ b (* c_m (* z t)))))))
   (*
    c_s
    (if (<= z -1.65e+84)
      t_1
      (if (<= z 1.12e+95)
        (/ (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 = t * fma(-4.0, (a / c_m), (b / (c_m * (z * t))));
	double tmp;
	if (z <= -1.65e+84) {
		tmp = t_1;
	} else if (z <= 1.12e+95) {
		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 = Float64(t * fma(-4.0, Float64(a / c_m), Float64(b / Float64(c_m * Float64(z * t)))))
	tmp = 0.0
	if (z <= -1.65e+84)
		tmp = t_1;
	elseif (z <= 1.12e+95)
		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[(t * N[(-4.0 * N[(a / c$95$m), $MachinePrecision] + N[(b / N[(c$95$m * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, N[(c$95$s * If[LessEqual[z, -1.65e+84], t$95$1, If[LessEqual[z, 1.12e+95], 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 < -1.65000000000000008e84 or 1.11999999999999999e95 < z

   1. Initial program 50.1%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   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 46.4

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

   5. Simplified 46.4%

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

   6. Taylor expanded in t around inf

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

      1. lower-*.f64 N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. lower-*.f64 75.8

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

   8. Simplified 75.8%

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

   if -1.65000000000000008e84 < z < 1.11999999999999999e95

   1. Initial program 95.2%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. associate-+l- N/A

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

      7. sub-neg N/A

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

      8. lift-*.f64 N/A

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

      9. lower-fma.f64 N/A

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

      10. neg-sub0 N/A

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

      11. associate-+l- N/A

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

      12. neg-sub0 N/A

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

      13. lift-*.f64 N/A

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

      14. *-commutative N/A

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

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

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

      16. lower-fma.f64 N/A

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

   4. Applied egg-rr 95.2%

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

4. Final simplification 88.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{+84}:\\ \;\;\;\;t \cdot \mathsf{fma}\left(-4, \frac{a}{c}, \frac{b}{c \cdot \left(z \cdot t\right)}\right)\\ \mathbf{elif}\;z \leq 1.12 \cdot 10^{+95}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x \cdot 9, y, \mathsf{fma}\left(a, -4 \cdot \left(z \cdot t\right), b\right)\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \mathsf{fma}\left(-4, \frac{a}{c}, \frac{b}{c \cdot \left(z \cdot t\right)}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 73.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\\\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ \begin{array}{l} t_1 := t \cdot \mathsf{fma}\left(-4, \frac{a}{c\_m}, \frac{b}{c\_m \cdot \left(z \cdot t\right)}\right)\\ c\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{+27}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 8 \cdot 10^{+42}:\\ \;\;\;\;\frac{\mathsf{fma}\left(9, x \cdot y, b\right)}{c\_m \cdot z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \end{array} \]

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 (* t (fma -4.0 (/ a c_m) (/ b (* c_m (* z t)))))))
   (*
    c_s
    (if (<= z -1.65e+27)
      t_1
      (if (<= z 8e+42) (/ (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 = t * fma(-4.0, (a / c_m), (b / (c_m * (z * t))));
	double tmp;
	if (z <= -1.65e+27) {
		tmp = t_1;
	} else if (z <= 8e+42) {
		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(t * fma(-4.0, Float64(a / c_m), Float64(b / Float64(c_m * Float64(z * t)))))
	tmp = 0.0
	if (z <= -1.65e+27)
		tmp = t_1;
	elseif (z <= 8e+42)
		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[(t * N[(-4.0 * N[(a / c$95$m), $MachinePrecision] + N[(b / N[(c$95$m * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, N[(c$95$s * If[LessEqual[z, -1.65e+27], t$95$1, If[LessEqual[z, 8e+42], 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 < -1.6499999999999999e27 or 8.00000000000000036e42 < z

   1. Initial program 58.7%

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

   3. Taylor expanded in x around 0

      \[\leadsto \frac{\color{blue}{b - 4 \cdot \left(a \cdot \left(t \cdot z\right)\right)}}{z \cdot c} \]
   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 50.7

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

   5. Simplified 50.7%

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

   6. Taylor expanded in t around inf

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

      1. lower-*.f64 N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. lower-*.f64 72.7

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

   8. Simplified 72.7%

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

   if -1.6499999999999999e27 < z < 8.00000000000000036e42

   1. Initial program 96.4%

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

   3. Taylor expanded in z around 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 84.5

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

   5. Simplified 84.5%

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

4. Final simplification 79.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{+27}:\\ \;\;\;\;t \cdot \mathsf{fma}\left(-4, \frac{a}{c}, \frac{b}{c \cdot \left(z \cdot t\right)}\right)\\ \mathbf{elif}\;z \leq 8 \cdot 10^{+42}:\\ \;\;\;\;\frac{\mathsf{fma}\left(9, x \cdot y, b\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \mathsf{fma}\left(-4, \frac{a}{c}, \frac{b}{c \cdot \left(z \cdot t\right)}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 66.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\\\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ c\_s \cdot \begin{array}{l} \mathbf{if}\;t \leq -2.6 \cdot 10^{+110}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(z \cdot t, a \cdot -4, b\right)}{c\_m}}{z}\\ \mathbf{elif}\;t \leq 3.8 \cdot 10^{-77}:\\ \;\;\;\;\frac{\mathsf{fma}\left(9, x \cdot y, b\right)}{c\_m \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{c\_m} \cdot \left(-4 \cdot t\right)\\ \end{array} \end{array} \]

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 (<= t -2.6e+110)
    (/ (/ (fma (* z t) (* a -4.0) b) c_m) z)
    (if (<= t 3.8e-77)
      (/ (fma 9.0 (* x y) b) (* c_m z))
      (* (/ a c_m) (* -4.0 t))))))

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 (t <= -2.6e+110) {
		tmp = (fma((z * t), (a * -4.0), b) / c_m) / z;
	} else if (t <= 3.8e-77) {
		tmp = fma(9.0, (x * y), b) / (c_m * z);
	} else {
		tmp = (a / c_m) * (-4.0 * t);
	}
	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 (t <= -2.6e+110)
		tmp = Float64(Float64(fma(Float64(z * t), Float64(a * -4.0), b) / c_m) / z);
	elseif (t <= 3.8e-77)
		tmp = Float64(fma(9.0, Float64(x * y), b) / Float64(c_m * z));
	else
		tmp = Float64(Float64(a / c_m) * Float64(-4.0 * t));
	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[t, -2.6e+110], N[(N[(N[(N[(z * t), $MachinePrecision] * N[(a * -4.0), $MachinePrecision] + b), $MachinePrecision] / c$95$m), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t, 3.8e-77], N[(N[(9.0 * N[(x * y), $MachinePrecision] + b), $MachinePrecision] / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision], N[(N[(a / c$95$m), $MachinePrecision] * N[(-4.0 * t), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if t < -2.6e110

   1. Initial program 75.1%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   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 72.9

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

   5. Simplified 72.9%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lift-*.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lift-fma.f64 N/A

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

      8. *-commutative N/A

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

      9. associate-/r* N/A

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

      10. lower-/.f64 N/A

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

   7. Applied egg-rr 77.6%

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

   if -2.6e110 < t < 3.7999999999999999e-77

   1. Initial program 83.3%

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

   3. Taylor expanded in 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 74.5

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

   5. Simplified 74.5%

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

   if 3.7999999999999999e-77 < t

   1. Initial program 74.0%

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

   3. Taylor expanded in x around 0

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. associate-*l* N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower-*.f64 56.9

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

   5. Simplified 56.9%

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

   6. Taylor expanded in a around inf

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

      1. lower-*.f64 N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 66.3

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

   8. Simplified 66.3%

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

   9. Taylor expanded in t around inf

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

       1. associate-*r/ N/A

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

       2. lower-/.f64 N/A

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

       3. lower-*.f64 55.9

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

   11. Simplified 55.9%

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

       1. lift-*.f64 N/A

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

       2. clear-num N/A

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

       3. associate-*r/ N/A

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

       4. div-inv N/A

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

       5. times-frac N/A

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

       6. lift-*.f64 N/A

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

       7. *-commutative N/A

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

       8. metadata-eval N/A

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

       9. div-inv N/A

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

       10. clear-num N/A

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

       11. clear-num N/A

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

       12. div-inv N/A

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

       13. metadata-eval N/A

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

       14. *-commutative N/A

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

       15. lift-*.f64 N/A

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

       16. lower-*.f64 N/A

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

       17. lower-/.f64 52.0

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

   13. Applied egg-rr 52.0%

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

4. Final simplification 68.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.6 \cdot 10^{+110}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(z \cdot t, a \cdot -4, b\right)}{c}}{z}\\ \mathbf{elif}\;t \leq 3.8 \cdot 10^{-77}:\\ \;\;\;\;\frac{\mathsf{fma}\left(9, x \cdot y, b\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{c} \cdot \left(-4 \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 68.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\\\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ c\_s \cdot \begin{array}{l} \mathbf{if}\;t \leq -6.5 \cdot 10^{+114}:\\ \;\;\;\;\frac{\mathsf{fma}\left(z \cdot \left(a \cdot -4\right), t, b\right)}{c\_m \cdot z}\\ \mathbf{elif}\;t \leq 3.8 \cdot 10^{-77}:\\ \;\;\;\;\frac{\mathsf{fma}\left(9, x \cdot y, b\right)}{c\_m \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{c\_m} \cdot \left(-4 \cdot t\right)\\ \end{array} \end{array} \]

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 (<= t -6.5e+114)
    (/ (fma (* z (* a -4.0)) t b) (* c_m z))
    (if (<= t 3.8e-77)
      (/ (fma 9.0 (* x y) b) (* c_m z))
      (* (/ a c_m) (* -4.0 t))))))

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 (t <= -6.5e+114) {
		tmp = fma((z * (a * -4.0)), t, b) / (c_m * z);
	} else if (t <= 3.8e-77) {
		tmp = fma(9.0, (x * y), b) / (c_m * z);
	} else {
		tmp = (a / c_m) * (-4.0 * t);
	}
	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 (t <= -6.5e+114)
		tmp = Float64(fma(Float64(z * Float64(a * -4.0)), t, b) / Float64(c_m * z));
	elseif (t <= 3.8e-77)
		tmp = Float64(fma(9.0, Float64(x * y), b) / Float64(c_m * z));
	else
		tmp = Float64(Float64(a / c_m) * Float64(-4.0 * t));
	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[t, -6.5e+114], N[(N[(N[(z * N[(a * -4.0), $MachinePrecision]), $MachinePrecision] * t + b), $MachinePrecision] / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.8e-77], N[(N[(9.0 * N[(x * y), $MachinePrecision] + b), $MachinePrecision] / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision], N[(N[(a / c$95$m), $MachinePrecision] * N[(-4.0 * t), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if t < -6.5000000000000001e114

   1. Initial program 75.1%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   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 72.9

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

   5. Simplified 72.9%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. associate-*r* N/A

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

      7. associate-*r* N/A

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

      8. *-commutative N/A

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

      9. lift-*.f64 N/A

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

      10. lift-*.f64 N/A

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

      11. lower-fma.f64 75.2

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

      12. lift-*.f64 N/A

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

      13. *-commutative N/A

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

      14. lift-*.f64 N/A

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

      15. associate-*l* N/A

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

      16. *-commutative N/A

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

      17. lower-*.f64 N/A

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

      18. lower-*.f64 75.2

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

   7. Applied egg-rr 75.2%

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

   if -6.5000000000000001e114 < t < 3.7999999999999999e-77

   1. Initial program 83.3%

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

   3. Taylor expanded in 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 74.5

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

   5. Simplified 74.5%

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

   if 3.7999999999999999e-77 < t

   1. Initial program 74.0%

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

   3. Taylor expanded in x around 0

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. associate-*l* N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower-*.f64 56.9

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

   5. Simplified 56.9%

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

   6. Taylor expanded in a around inf

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

      1. lower-*.f64 N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 66.3

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

   8. Simplified 66.3%

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

   9. Taylor expanded in t around inf

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

       1. associate-*r/ N/A

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

       2. lower-/.f64 N/A

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

       3. lower-*.f64 55.9

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

   11. Simplified 55.9%

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

       1. lift-*.f64 N/A

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

       2. clear-num N/A

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

       3. associate-*r/ N/A

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

       4. div-inv N/A

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

       5. times-frac N/A

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

       6. lift-*.f64 N/A

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

       7. *-commutative N/A

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

       8. metadata-eval N/A

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

       9. div-inv N/A

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

       10. clear-num N/A

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

       11. clear-num N/A

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

       12. div-inv N/A

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

       13. metadata-eval N/A

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

       14. *-commutative N/A

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

       15. lift-*.f64 N/A

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

       16. lower-*.f64 N/A

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

       17. lower-/.f64 52.0

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

   13. Applied egg-rr 52.0%

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

4. Final simplification 68.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.5 \cdot 10^{+114}:\\ \;\;\;\;\frac{\mathsf{fma}\left(z \cdot \left(a \cdot -4\right), t, b\right)}{c \cdot z}\\ \mathbf{elif}\;t \leq 3.8 \cdot 10^{-77}:\\ \;\;\;\;\frac{\mathsf{fma}\left(9, x \cdot y, b\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{c} \cdot \left(-4 \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 66.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\\\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ c\_s \cdot \begin{array}{l} \mathbf{if}\;t \leq -2.6 \cdot 10^{+110}:\\ \;\;\;\;\frac{\mathsf{fma}\left(a, -4 \cdot \left(z \cdot t\right), b\right)}{c\_m \cdot z}\\ \mathbf{elif}\;t \leq 3.8 \cdot 10^{-77}:\\ \;\;\;\;\frac{\mathsf{fma}\left(9, x \cdot y, b\right)}{c\_m \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{c\_m} \cdot \left(-4 \cdot t\right)\\ \end{array} \end{array} \]

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 (<= t -2.6e+110)
    (/ (fma a (* -4.0 (* z t)) b) (* c_m z))
    (if (<= t 3.8e-77)
      (/ (fma 9.0 (* x y) b) (* c_m z))
      (* (/ a c_m) (* -4.0 t))))))

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 (t <= -2.6e+110) {
		tmp = fma(a, (-4.0 * (z * t)), b) / (c_m * z);
	} else if (t <= 3.8e-77) {
		tmp = fma(9.0, (x * y), b) / (c_m * z);
	} else {
		tmp = (a / c_m) * (-4.0 * t);
	}
	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 (t <= -2.6e+110)
		tmp = Float64(fma(a, Float64(-4.0 * Float64(z * t)), b) / Float64(c_m * z));
	elseif (t <= 3.8e-77)
		tmp = Float64(fma(9.0, Float64(x * y), b) / Float64(c_m * z));
	else
		tmp = Float64(Float64(a / c_m) * Float64(-4.0 * t));
	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[t, -2.6e+110], N[(N[(a * N[(-4.0 * N[(z * t), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision] / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.8e-77], N[(N[(9.0 * N[(x * y), $MachinePrecision] + b), $MachinePrecision] / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision], N[(N[(a / c$95$m), $MachinePrecision] * N[(-4.0 * t), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if t < -2.6e110

   1. Initial program 75.1%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   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 72.9

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

   5. Simplified 72.9%

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

   if -2.6e110 < t < 3.7999999999999999e-77

   1. Initial program 83.3%

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

   3. Taylor expanded in 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 74.5

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

   5. Simplified 74.5%

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

   if 3.7999999999999999e-77 < t

   1. Initial program 74.0%

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

   3. Taylor expanded in x around 0

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. associate-*l* N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower-*.f64 56.9

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

   5. Simplified 56.9%

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

   6. Taylor expanded in a around inf

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

      1. lower-*.f64 N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 66.3

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

   8. Simplified 66.3%

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

   9. Taylor expanded in t around inf

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

       1. associate-*r/ N/A

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

       2. lower-/.f64 N/A

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

       3. lower-*.f64 55.9

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

   11. Simplified 55.9%

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

       1. lift-*.f64 N/A

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

       2. clear-num N/A

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

       3. associate-*r/ N/A

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

       4. div-inv N/A

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

       5. times-frac N/A

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

       6. lift-*.f64 N/A

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

       7. *-commutative N/A

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

       8. metadata-eval N/A

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

       9. div-inv N/A

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

       10. clear-num N/A

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

       11. clear-num N/A

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

       12. div-inv N/A

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

       13. metadata-eval N/A

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

       14. *-commutative N/A

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

       15. lift-*.f64 N/A

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

       16. lower-*.f64 N/A

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

       17. lower-/.f64 52.0

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

   13. Applied egg-rr 52.0%

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

4. Final simplification 67.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.6 \cdot 10^{+110}:\\ \;\;\;\;\frac{\mathsf{fma}\left(a, -4 \cdot \left(z \cdot t\right), b\right)}{c \cdot z}\\ \mathbf{elif}\;t \leq 3.8 \cdot 10^{-77}:\\ \;\;\;\;\frac{\mathsf{fma}\left(9, x \cdot y, b\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{c} \cdot \left(-4 \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 68.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\\\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ \begin{array}{l} t_1 := \frac{a}{c\_m} \cdot \left(-4 \cdot t\right)\\ c\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{+53}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 7.4 \cdot 10^{+43}:\\ \;\;\;\;\frac{\mathsf{fma}\left(9, x \cdot y, b\right)}{c\_m \cdot z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \end{array} \]

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 (* (/ a c_m) (* -4.0 t))))
   (*
    c_s
    (if (<= z -5.5e+53)
      t_1
      (if (<= z 7.4e+43) (/ (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 = (a / c_m) * (-4.0 * t);
	double tmp;
	if (z <= -5.5e+53) {
		tmp = t_1;
	} else if (z <= 7.4e+43) {
		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(a / c_m) * Float64(-4.0 * t))
	tmp = 0.0
	if (z <= -5.5e+53)
		tmp = t_1;
	elseif (z <= 7.4e+43)
		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[(a / c$95$m), $MachinePrecision] * N[(-4.0 * t), $MachinePrecision]), $MachinePrecision]}, N[(c$95$s * If[LessEqual[z, -5.5e+53], t$95$1, If[LessEqual[z, 7.4e+43], 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 < -5.49999999999999975e53 or 7.4000000000000002e43 < z

   1. Initial program 56.5%

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

   3. Taylor expanded in x around 0

      \[\leadsto \frac{\color{blue}{b - 4 \cdot \left(a \cdot \left(t \cdot z\right)\right)}}{z \cdot c} \]
   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 48.9

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

   5. Simplified 48.9%

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

   6. Taylor expanded in a around inf

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

      1. lower-*.f64 N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 73.0

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

   8. Simplified 73.0%

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

   9. Taylor expanded in t around inf

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

       1. associate-*r/ N/A

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

       2. lower-/.f64 N/A

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

       3. lower-*.f64 63.5

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

   11. Simplified 63.5%

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

       1. lift-*.f64 N/A

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

       2. clear-num N/A

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

       3. associate-*r/ N/A

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

       4. div-inv N/A

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

       5. times-frac N/A

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

       6. lift-*.f64 N/A

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

       7. *-commutative N/A

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

       8. metadata-eval N/A

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

       9. div-inv N/A

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

       10. clear-num N/A

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

       11. clear-num N/A

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

       12. div-inv N/A

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

       13. metadata-eval N/A

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

       14. *-commutative N/A

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

       15. lift-*.f64 N/A

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

       16. lower-*.f64 N/A

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

       17. lower-/.f64 61.8

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

   13. Applied egg-rr 61.8%

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

   if -5.49999999999999975e53 < z < 7.4000000000000002e43

   1. Initial program 96.5%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. 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 83.1

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

   5. Simplified 83.1%

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

4. Final simplification 73.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{+53}:\\ \;\;\;\;\frac{a}{c} \cdot \left(-4 \cdot t\right)\\ \mathbf{elif}\;z \leq 7.4 \cdot 10^{+43}:\\ \;\;\;\;\frac{\mathsf{fma}\left(9, x \cdot y, b\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{c} \cdot \left(-4 \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 50.5% accurate, 1.4× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\\\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ c\_s \cdot \begin{array}{l} \mathbf{if}\;b \leq -2.3 \cdot 10^{+26}:\\ \;\;\;\;\frac{1}{\frac{c\_m \cdot z}{b}}\\ \mathbf{elif}\;b \leq 7.9 \cdot 10^{+43}:\\ \;\;\;\;\frac{a}{c\_m} \cdot \left(-4 \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{c\_m}}{z}\\ \end{array} \end{array} \]

FPCore

c\_m = (fabs.f64 c)
c\_s = (copysign.f64 #s(literal 1 binary64) c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
(FPCore (c_s x y z t a b c_m)
 :precision binary64
 (*
  c_s
  (if (<= b -2.3e+26)
    (/ 1.0 (/ (* c_m z) b))
    (if (<= b 7.9e+43) (* (/ a c_m) (* -4.0 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 (b <= -2.3e+26) {
		tmp = 1.0 / ((c_m * z) / b);
	} else if (b <= 7.9e+43) {
		tmp = (a / c_m) * (-4.0 * t);
	} else {
		tmp = (b / c_m) / z;
	}
	return c_s * tmp;
}

Fortran

c\_m = abs(c)
c\_s = copysign(1.0d0, c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
real(8) function code(c_s, x, y, z, t, a, b, c_m)
    real(8), intent (in) :: c_s
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c_m
    real(8) :: tmp
    if (b <= (-2.3d+26)) then
        tmp = 1.0d0 / ((c_m * z) / b)
    else if (b <= 7.9d+43) then
        tmp = (a / c_m) * ((-4.0d0) * t)
    else
        tmp = (b / c_m) / z
    end if
    code = c_s * tmp
end function

Java

c\_m = Math.abs(c);
c\_s = Math.copySign(1.0, c);
assert x < y && y < z && z < t && t < a && a < b && b < c_m;
assert x < y && y < z && z < t && t < a && a < b && b < c_m;
public static double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if (b <= -2.3e+26) {
		tmp = 1.0 / ((c_m * z) / b);
	} else if (b <= 7.9e+43) {
		tmp = (a / c_m) * (-4.0 * t);
	} else {
		tmp = (b / c_m) / z;
	}
	return c_s * tmp;
}

Python

c\_m = math.fabs(c)
c\_s = math.copysign(1.0, c)
[x, y, z, t, a, b, c_m] = sort([x, y, z, t, a, b, c_m])
[x, y, z, t, a, b, c_m] = sort([x, y, z, t, a, b, c_m])
def code(c_s, x, y, z, t, a, b, c_m):
	tmp = 0
	if b <= -2.3e+26:
		tmp = 1.0 / ((c_m * z) / b)
	elif b <= 7.9e+43:
		tmp = (a / c_m) * (-4.0 * t)
	else:
		tmp = (b / c_m) / z
	return c_s * tmp

Julia

c\_m = abs(c)
c\_s = copysign(1.0, c)
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
function code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0
	if (b <= -2.3e+26)
		tmp = Float64(1.0 / Float64(Float64(c_m * z) / b));
	elseif (b <= 7.9e+43)
		tmp = Float64(Float64(a / c_m) * Float64(-4.0 * t));
	else
		tmp = Float64(Float64(b / c_m) / z);
	end
	return Float64(c_s * tmp)
end

MATLAB

c\_m = abs(c);
c\_s = sign(c) * abs(1.0);
x, y, z, t, a, b, c_m = num2cell(sort([x, y, z, t, a, b, c_m])){:}
x, y, z, t, a, b, c_m = num2cell(sort([x, y, z, t, a, b, c_m])){:}
function tmp_2 = code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0;
	if (b <= -2.3e+26)
		tmp = 1.0 / ((c_m * z) / b);
	elseif (b <= 7.9e+43)
		tmp = (a / c_m) * (-4.0 * t);
	else
		tmp = (b / c_m) / z;
	end
	tmp_2 = c_s * tmp;
end

Wolfram

c\_m = N[Abs[c], $MachinePrecision]
c\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
code[c$95$s_, x_, y_, z_, t_, a_, b_, c$95$m_] := N[(c$95$s * If[LessEqual[b, -2.3e+26], N[(1.0 / N[(N[(c$95$m * z), $MachinePrecision] / b), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 7.9e+43], N[(N[(a / c$95$m), $MachinePrecision] * N[(-4.0 * t), $MachinePrecision]), $MachinePrecision], N[(N[(b / c$95$m), $MachinePrecision] / z), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if b < -2.3000000000000001e26

   1. Initial program 88.5%

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

   3. Taylor expanded in b around 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 62.2

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

   5. Simplified 62.2%

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

      1. lift-*.f64 N/A

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

      2. clear-num N/A

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

      3. lower-/.f64 N/A

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

      4. lower-/.f64 62.2

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 62.2

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

   7. Applied egg-rr 62.2%

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

   if -2.3000000000000001e26 < b < 7.89999999999999963e43

   1. Initial program 73.4%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. 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 47.9

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

   5. Simplified 47.9%

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

   6. Taylor expanded in a around inf

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

      1. lower-*.f64 N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 59.5

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

   8. Simplified 59.5%

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

   9. Taylor expanded in t around inf

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

       1. associate-*r/ N/A

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

       2. lower-/.f64 N/A

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

       3. lower-*.f64 52.3

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

   11. Simplified 52.3%

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

       1. lift-*.f64 N/A

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

       2. clear-num N/A

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

       3. associate-*r/ N/A

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

       4. div-inv N/A

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

       5. times-frac N/A

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

       6. lift-*.f64 N/A

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

       7. *-commutative N/A

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

       8. metadata-eval N/A

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

       9. div-inv N/A

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

       10. clear-num N/A

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

       11. clear-num N/A

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

       12. div-inv N/A

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

       13. metadata-eval N/A

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

       14. *-commutative N/A

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

       15. lift-*.f64 N/A

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

       16. lower-*.f64 N/A

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

       17. lower-/.f64 53.4

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

   13. Applied egg-rr 53.4%

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

   if 7.89999999999999963e43 < b

   1. Initial program 87.6%

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

   3. 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 68.7

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

   5. Simplified 68.7%

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

      1. *-commutative N/A

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

      2. associate-/r* N/A

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

      3. lower-/.f64 N/A

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

      4. lower-/.f64 71.8

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

   7. Applied egg-rr 71.8%

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

Alternative 12: 50.8% accurate, 1.4× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\\\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ \begin{array}{l} t_1 := \frac{\frac{b}{c\_m}}{z}\\ c\_s \cdot \begin{array}{l} \mathbf{if}\;b \leq -2.3 \cdot 10^{+26}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 7.9 \cdot 10^{+43}:\\ \;\;\;\;\frac{a}{c\_m} \cdot \left(-4 \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \end{array} \]

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 (/ (/ b c_m) z)))
   (*
    c_s
    (if (<= b -2.3e+26)
      t_1
      (if (<= b 7.9e+43) (* (/ a c_m) (* -4.0 t)) 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 = (b / c_m) / z;
	double tmp;
	if (b <= -2.3e+26) {
		tmp = t_1;
	} else if (b <= 7.9e+43) {
		tmp = (a / c_m) * (-4.0 * t);
	} 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 = (b / c_m) / z
    if (b <= (-2.3d+26)) then
        tmp = t_1
    else if (b <= 7.9d+43) then
        tmp = (a / c_m) * ((-4.0d0) * t)
    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 = (b / c_m) / z;
	double tmp;
	if (b <= -2.3e+26) {
		tmp = t_1;
	} else if (b <= 7.9e+43) {
		tmp = (a / c_m) * (-4.0 * t);
	} 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 = (b / c_m) / z
	tmp = 0
	if b <= -2.3e+26:
		tmp = t_1
	elif b <= 7.9e+43:
		tmp = (a / c_m) * (-4.0 * t)
	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(b / c_m) / z)
	tmp = 0.0
	if (b <= -2.3e+26)
		tmp = t_1;
	elseif (b <= 7.9e+43)
		tmp = Float64(Float64(a / c_m) * Float64(-4.0 * t));
	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 = (b / c_m) / z;
	tmp = 0.0;
	if (b <= -2.3e+26)
		tmp = t_1;
	elseif (b <= 7.9e+43)
		tmp = (a / c_m) * (-4.0 * t);
	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[(b / c$95$m), $MachinePrecision] / z), $MachinePrecision]}, N[(c$95$s * If[LessEqual[b, -2.3e+26], t$95$1, If[LessEqual[b, 7.9e+43], N[(N[(a / c$95$m), $MachinePrecision] * N[(-4.0 * t), $MachinePrecision]), $MachinePrecision], t$95$1]]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -2.3000000000000001e26 or 7.89999999999999963e43 < b

   1. Initial program 88.0%

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

   3. 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 66.1

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

   5. Simplified 66.1%

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

      1. *-commutative N/A

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

      2. associate-/r* N/A

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

      3. lower-/.f64 N/A

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

      4. lower-/.f64 68.0

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

   7. Applied egg-rr 68.0%

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

   if -2.3000000000000001e26 < b < 7.89999999999999963e43

   1. Initial program 73.4%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. 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 47.9

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

   5. Simplified 47.9%

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

   6. Taylor expanded in a around inf

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

      1. lower-*.f64 N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 59.5

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

   8. Simplified 59.5%

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

   9. Taylor expanded in t around inf

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

       1. associate-*r/ N/A

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

       2. lower-/.f64 N/A

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

       3. lower-*.f64 52.3

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

   11. Simplified 52.3%

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

       1. lift-*.f64 N/A

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

       2. clear-num N/A

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

       3. associate-*r/ N/A

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

       4. div-inv N/A

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

       5. times-frac N/A

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

       6. lift-*.f64 N/A

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

       7. *-commutative N/A

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

       8. metadata-eval N/A

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

       9. div-inv N/A

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

       10. clear-num N/A

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

       11. clear-num N/A

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

       12. div-inv N/A

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

       13. metadata-eval N/A

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

       14. *-commutative N/A

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

       15. lift-*.f64 N/A

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

       16. lower-*.f64 N/A

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

       17. lower-/.f64 53.4

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

   13. Applied egg-rr 53.4%

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

Alternative 13: 50.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\\\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ \begin{array}{l} t_1 := \frac{b}{c\_m \cdot z}\\ c\_s \cdot \begin{array}{l} \mathbf{if}\;b \leq -2.3 \cdot 10^{+26}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1.42 \cdot 10^{+44}:\\ \;\;\;\;\frac{a}{c\_m} \cdot \left(-4 \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \end{array} \]

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 (/ b (* c_m z))))
   (*
    c_s
    (if (<= b -2.3e+26)
      t_1
      (if (<= b 1.42e+44) (* (/ a c_m) (* -4.0 t)) 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 = b / (c_m * z);
	double tmp;
	if (b <= -2.3e+26) {
		tmp = t_1;
	} else if (b <= 1.42e+44) {
		tmp = (a / c_m) * (-4.0 * t);
	} 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 = b / (c_m * z)
    if (b <= (-2.3d+26)) then
        tmp = t_1
    else if (b <= 1.42d+44) then
        tmp = (a / c_m) * ((-4.0d0) * t)
    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 = b / (c_m * z);
	double tmp;
	if (b <= -2.3e+26) {
		tmp = t_1;
	} else if (b <= 1.42e+44) {
		tmp = (a / c_m) * (-4.0 * t);
	} 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 = b / (c_m * z)
	tmp = 0
	if b <= -2.3e+26:
		tmp = t_1
	elif b <= 1.42e+44:
		tmp = (a / c_m) * (-4.0 * t)
	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(b / Float64(c_m * z))
	tmp = 0.0
	if (b <= -2.3e+26)
		tmp = t_1;
	elseif (b <= 1.42e+44)
		tmp = Float64(Float64(a / c_m) * Float64(-4.0 * t));
	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 = b / (c_m * z);
	tmp = 0.0;
	if (b <= -2.3e+26)
		tmp = t_1;
	elseif (b <= 1.42e+44)
		tmp = (a / c_m) * (-4.0 * t);
	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[(b / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision]}, N[(c$95$s * If[LessEqual[b, -2.3e+26], t$95$1, If[LessEqual[b, 1.42e+44], N[(N[(a / c$95$m), $MachinePrecision] * N[(-4.0 * t), $MachinePrecision]), $MachinePrecision], t$95$1]]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -2.3000000000000001e26 or 1.41999999999999994e44 < b

   1. Initial program 88.0%

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

   3. 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 66.1

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

   5. Simplified 66.1%

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

   if -2.3000000000000001e26 < b < 1.41999999999999994e44

   1. Initial program 73.4%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. 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 47.9

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

   5. Simplified 47.9%

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

   6. Taylor expanded in a around inf

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

      1. lower-*.f64 N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 59.5

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

   8. Simplified 59.5%

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

   9. Taylor expanded in t around inf

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

       1. associate-*r/ N/A

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

       2. lower-/.f64 N/A

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

       3. lower-*.f64 52.3

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

   11. Simplified 52.3%

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

       1. lift-*.f64 N/A

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

       2. clear-num N/A

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

       3. associate-*r/ N/A

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

       4. div-inv N/A

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

       5. times-frac N/A

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

       6. lift-*.f64 N/A

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

       7. *-commutative N/A

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

       8. metadata-eval N/A

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

       9. div-inv N/A

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

       10. clear-num N/A

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

       11. clear-num N/A

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

       12. div-inv N/A

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

       13. metadata-eval N/A

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

       14. *-commutative N/A

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

       15. lift-*.f64 N/A

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

       16. lower-*.f64 N/A

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

       17. lower-/.f64 53.4

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

   13. Applied egg-rr 53.4%

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

4. Final simplification 58.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.3 \cdot 10^{+26}:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \mathbf{elif}\;b \leq 1.42 \cdot 10^{+44}:\\ \;\;\;\;\frac{a}{c} \cdot \left(-4 \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 50.3% accurate, 1.4× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\\\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ \begin{array}{l} t_1 := \frac{b}{c\_m \cdot z}\\ c\_s \cdot \begin{array}{l} \mathbf{if}\;b \leq -2.2 \cdot 10^{+31}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1.42 \cdot 10^{+44}:\\ \;\;\;\;a \cdot \frac{-4 \cdot t}{c\_m}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \end{array} \]

FPCore

c\_m = (fabs.f64 c)
c\_s = (copysign.f64 #s(literal 1 binary64) c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
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 (/ b (* c_m z))))
   (*
    c_s
    (if (<= b -2.2e+31)
      t_1
      (if (<= b 1.42e+44) (* a (/ (* -4.0 t) c_m)) t_1)))))

C

c\_m = fabs(c);
c\_s = copysign(1.0, c);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
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 = b / (c_m * z);
	double tmp;
	if (b <= -2.2e+31) {
		tmp = t_1;
	} else if (b <= 1.42e+44) {
		tmp = a * ((-4.0 * t) / c_m);
	} else {
		tmp = t_1;
	}
	return c_s * tmp;
}

Fortran

c\_m = abs(c)
c\_s = copysign(1.0d0, c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
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 = b / (c_m * z)
    if (b <= (-2.2d+31)) then
        tmp = t_1
    else if (b <= 1.42d+44) then
        tmp = a * (((-4.0d0) * t) / c_m)
    else
        tmp = t_1
    end if
    code = c_s * tmp
end function

Java

c\_m = Math.abs(c);
c\_s = Math.copySign(1.0, c);
assert x < y && y < z && z < t && t < a && a < b && b < c_m;
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 = b / (c_m * z);
	double tmp;
	if (b <= -2.2e+31) {
		tmp = t_1;
	} else if (b <= 1.42e+44) {
		tmp = a * ((-4.0 * t) / c_m);
	} else {
		tmp = t_1;
	}
	return c_s * tmp;
}

Python

c\_m = math.fabs(c)
c\_s = math.copysign(1.0, c)
[x, y, z, t, a, b, c_m] = sort([x, y, z, t, a, b, c_m])
[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 = b / (c_m * z)
	tmp = 0
	if b <= -2.2e+31:
		tmp = t_1
	elif b <= 1.42e+44:
		tmp = a * ((-4.0 * t) / c_m)
	else:
		tmp = t_1
	return c_s * tmp

Julia

c\_m = abs(c)
c\_s = copysign(1.0, c)
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
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(b / Float64(c_m * z))
	tmp = 0.0
	if (b <= -2.2e+31)
		tmp = t_1;
	elseif (b <= 1.42e+44)
		tmp = Float64(a * Float64(Float64(-4.0 * t) / c_m));
	else
		tmp = t_1;
	end
	return Float64(c_s * tmp)
end

MATLAB

c\_m = abs(c);
c\_s = sign(c) * abs(1.0);
x, y, z, t, a, b, c_m = num2cell(sort([x, y, z, t, a, b, c_m])){:}
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 = b / (c_m * z);
	tmp = 0.0;
	if (b <= -2.2e+31)
		tmp = t_1;
	elseif (b <= 1.42e+44)
		tmp = a * ((-4.0 * t) / c_m);
	else
		tmp = t_1;
	end
	tmp_2 = c_s * tmp;
end

Wolfram

c\_m = N[Abs[c], $MachinePrecision]
c\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
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[(b / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision]}, N[(c$95$s * If[LessEqual[b, -2.2e+31], t$95$1, If[LessEqual[b, 1.42e+44], N[(a * N[(N[(-4.0 * t), $MachinePrecision] / c$95$m), $MachinePrecision]), $MachinePrecision], t$95$1]]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -2.2000000000000001e31 or 1.41999999999999994e44 < b

   1. Initial program 88.0%

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

   3. 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 66.1

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

   5. Simplified 66.1%

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

   if -2.2000000000000001e31 < b < 1.41999999999999994e44

   1. Initial program 73.4%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. 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 47.9

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

   5. Simplified 47.9%

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

   6. Taylor expanded in a around inf

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

      1. lower-*.f64 N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 59.5

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

   8. Simplified 59.5%

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

   9. Taylor expanded in t around inf

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

       1. associate-*r/ N/A

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

       2. lower-/.f64 N/A

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

       3. lower-*.f64 52.3

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

   11. Simplified 52.3%

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

4. Final simplification 57.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.2 \cdot 10^{+31}:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \mathbf{elif}\;b \leq 1.42 \cdot 10^{+44}:\\ \;\;\;\;a \cdot \frac{-4 \cdot t}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 50.4% accurate, 1.4× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\\\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ \begin{array}{l} t_1 := \frac{b}{c\_m \cdot z}\\ c\_s \cdot \begin{array}{l} \mathbf{if}\;b \leq -2.2 \cdot 10^{+31}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1.42 \cdot 10^{+44}:\\ \;\;\;\;a \cdot \left(t \cdot \frac{-4}{c\_m}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \end{array} \]

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 (/ b (* c_m z))))
   (*
    c_s
    (if (<= b -2.2e+31)
      t_1
      (if (<= b 1.42e+44) (* a (* t (/ -4.0 c_m))) t_1)))))

C

c\_m = fabs(c);
c\_s = copysign(1.0, c);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
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 = b / (c_m * z);
	double tmp;
	if (b <= -2.2e+31) {
		tmp = t_1;
	} else if (b <= 1.42e+44) {
		tmp = a * (t * (-4.0 / c_m));
	} else {
		tmp = t_1;
	}
	return c_s * tmp;
}

Fortran

c\_m = abs(c)
c\_s = copysign(1.0d0, c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
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 = b / (c_m * z)
    if (b <= (-2.2d+31)) then
        tmp = t_1
    else if (b <= 1.42d+44) then
        tmp = a * (t * ((-4.0d0) / c_m))
    else
        tmp = t_1
    end if
    code = c_s * tmp
end function

Java

c\_m = Math.abs(c);
c\_s = Math.copySign(1.0, c);
assert x < y && y < z && z < t && t < a && a < b && b < c_m;
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 = b / (c_m * z);
	double tmp;
	if (b <= -2.2e+31) {
		tmp = t_1;
	} else if (b <= 1.42e+44) {
		tmp = a * (t * (-4.0 / c_m));
	} else {
		tmp = t_1;
	}
	return c_s * tmp;
}

Python

c\_m = math.fabs(c)
c\_s = math.copysign(1.0, c)
[x, y, z, t, a, b, c_m] = sort([x, y, z, t, a, b, c_m])
[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 = b / (c_m * z)
	tmp = 0
	if b <= -2.2e+31:
		tmp = t_1
	elif b <= 1.42e+44:
		tmp = a * (t * (-4.0 / c_m))
	else:
		tmp = t_1
	return c_s * tmp

Julia

c\_m = abs(c)
c\_s = copysign(1.0, c)
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
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(b / Float64(c_m * z))
	tmp = 0.0
	if (b <= -2.2e+31)
		tmp = t_1;
	elseif (b <= 1.42e+44)
		tmp = Float64(a * Float64(t * Float64(-4.0 / c_m)));
	else
		tmp = t_1;
	end
	return Float64(c_s * tmp)
end

MATLAB

c\_m = abs(c);
c\_s = sign(c) * abs(1.0);
x, y, z, t, a, b, c_m = num2cell(sort([x, y, z, t, a, b, c_m])){:}
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 = b / (c_m * z);
	tmp = 0.0;
	if (b <= -2.2e+31)
		tmp = t_1;
	elseif (b <= 1.42e+44)
		tmp = a * (t * (-4.0 / c_m));
	else
		tmp = t_1;
	end
	tmp_2 = c_s * tmp;
end

Wolfram

c\_m = N[Abs[c], $MachinePrecision]
c\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
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[(b / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision]}, N[(c$95$s * If[LessEqual[b, -2.2e+31], t$95$1, If[LessEqual[b, 1.42e+44], N[(a * N[(t * N[(-4.0 / c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -2.2000000000000001e31 or 1.41999999999999994e44 < b

   1. Initial program 88.0%

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

   3. 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 66.1

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

   5. Simplified 66.1%

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

   if -2.2000000000000001e31 < b < 1.41999999999999994e44

   1. Initial program 73.4%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. 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 47.9

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

   5. Simplified 47.9%

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

   6. Taylor expanded in a around inf

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

      1. lower-*.f64 N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 59.5

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

   8. Simplified 59.5%

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

   9. Taylor expanded in t around inf

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

       1. associate-*r/ N/A

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

       2. lower-/.f64 N/A

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

       3. lower-*.f64 52.3

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

   11. Simplified 52.3%

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

       1. *-commutative N/A

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

       2. associate-/l* N/A

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

       3. lower-*.f64 N/A

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

       4. lower-/.f64 52.2

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

   13. Applied egg-rr 52.2%

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

4. Final simplification 57.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.2 \cdot 10^{+31}:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \mathbf{elif}\;b \leq 1.42 \cdot 10^{+44}:\\ \;\;\;\;a \cdot \left(t \cdot \frac{-4}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 35.7% 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 79.3%

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

3. Taylor expanded in 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 37.5

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

5. Simplified 37.5%

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

6. Final simplification 37.5%

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

Developer Target 1: 80.7% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{b}{c \cdot z}\\ t_2 := 4 \cdot \frac{a \cdot t}{c}\\ t_3 := \left(x \cdot 9\right) \cdot y\\ t_4 := \left(t\_3 - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b\\ t_5 := \frac{t\_4}{z \cdot c}\\ t_6 := \frac{\left(t\_3 - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}\\ \mathbf{if}\;t\_5 < -1.100156740804105 \cdot 10^{-171}:\\ \;\;\;\;t\_6\\ \mathbf{elif}\;t\_5 < 0:\\ \;\;\;\;\frac{\frac{t\_4}{z}}{c}\\ \mathbf{elif}\;t\_5 < 1.1708877911747488 \cdot 10^{-53}:\\ \;\;\;\;t\_6\\ \mathbf{elif}\;t\_5 < 2.876823679546137 \cdot 10^{+130}:\\ \;\;\;\;\left(\left(9 \cdot \frac{y}{c}\right) \cdot \frac{x}{z} + t\_1\right) - t\_2\\ \mathbf{elif}\;t\_5 < 1.3838515042456319 \cdot 10^{+158}:\\ \;\;\;\;t\_6\\ \mathbf{else}:\\ \;\;\;\;\left(9 \cdot \left(\frac{y}{c \cdot z} \cdot x\right) + t\_1\right) - t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ b (* c z)))
        (t_2 (* 4.0 (/ (* a t) c)))
        (t_3 (* (* x 9.0) y))
        (t_4 (+ (- t_3 (* (* (* z 4.0) t) a)) b))
        (t_5 (/ t_4 (* z c)))
        (t_6 (/ (+ (- t_3 (* (* z 4.0) (* t a))) b) (* z c))))
   (if (< t_5 -1.100156740804105e-171)
     t_6
     (if (< t_5 0.0)
       (/ (/ t_4 z) c)
       (if (< t_5 1.1708877911747488e-53)
         t_6
         (if (< t_5 2.876823679546137e+130)
           (- (+ (* (* 9.0 (/ y c)) (/ x z)) t_1) t_2)
           (if (< t_5 1.3838515042456319e+158)
             t_6
             (- (+ (* 9.0 (* (/ y (* c z)) x)) t_1) t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = b / (c * z);
	double t_2 = 4.0 * ((a * t) / c);
	double t_3 = (x * 9.0) * y;
	double t_4 = (t_3 - (((z * 4.0) * t) * a)) + b;
	double t_5 = t_4 / (z * c);
	double t_6 = ((t_3 - ((z * 4.0) * (t * a))) + b) / (z * c);
	double tmp;
	if (t_5 < -1.100156740804105e-171) {
		tmp = t_6;
	} else if (t_5 < 0.0) {
		tmp = (t_4 / z) / c;
	} else if (t_5 < 1.1708877911747488e-53) {
		tmp = t_6;
	} else if (t_5 < 2.876823679546137e+130) {
		tmp = (((9.0 * (y / c)) * (x / z)) + t_1) - t_2;
	} else if (t_5 < 1.3838515042456319e+158) {
		tmp = t_6;
	} else {
		tmp = ((9.0 * ((y / (c * z)) * x)) + t_1) - t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: tmp
    t_1 = b / (c * z)
    t_2 = 4.0d0 * ((a * t) / c)
    t_3 = (x * 9.0d0) * y
    t_4 = (t_3 - (((z * 4.0d0) * t) * a)) + b
    t_5 = t_4 / (z * c)
    t_6 = ((t_3 - ((z * 4.0d0) * (t * a))) + b) / (z * c)
    if (t_5 < (-1.100156740804105d-171)) then
        tmp = t_6
    else if (t_5 < 0.0d0) then
        tmp = (t_4 / z) / c
    else if (t_5 < 1.1708877911747488d-53) then
        tmp = t_6
    else if (t_5 < 2.876823679546137d+130) then
        tmp = (((9.0d0 * (y / c)) * (x / z)) + t_1) - t_2
    else if (t_5 < 1.3838515042456319d+158) then
        tmp = t_6
    else
        tmp = ((9.0d0 * ((y / (c * z)) * x)) + t_1) - t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = b / (c * z);
	double t_2 = 4.0 * ((a * t) / c);
	double t_3 = (x * 9.0) * y;
	double t_4 = (t_3 - (((z * 4.0) * t) * a)) + b;
	double t_5 = t_4 / (z * c);
	double t_6 = ((t_3 - ((z * 4.0) * (t * a))) + b) / (z * c);
	double tmp;
	if (t_5 < -1.100156740804105e-171) {
		tmp = t_6;
	} else if (t_5 < 0.0) {
		tmp = (t_4 / z) / c;
	} else if (t_5 < 1.1708877911747488e-53) {
		tmp = t_6;
	} else if (t_5 < 2.876823679546137e+130) {
		tmp = (((9.0 * (y / c)) * (x / z)) + t_1) - t_2;
	} else if (t_5 < 1.3838515042456319e+158) {
		tmp = t_6;
	} else {
		tmp = ((9.0 * ((y / (c * z)) * x)) + t_1) - t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = b / (c * z)
	t_2 = 4.0 * ((a * t) / c)
	t_3 = (x * 9.0) * y
	t_4 = (t_3 - (((z * 4.0) * t) * a)) + b
	t_5 = t_4 / (z * c)
	t_6 = ((t_3 - ((z * 4.0) * (t * a))) + b) / (z * c)
	tmp = 0
	if t_5 < -1.100156740804105e-171:
		tmp = t_6
	elif t_5 < 0.0:
		tmp = (t_4 / z) / c
	elif t_5 < 1.1708877911747488e-53:
		tmp = t_6
	elif t_5 < 2.876823679546137e+130:
		tmp = (((9.0 * (y / c)) * (x / z)) + t_1) - t_2
	elif t_5 < 1.3838515042456319e+158:
		tmp = t_6
	else:
		tmp = ((9.0 * ((y / (c * z)) * x)) + t_1) - t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(b / Float64(c * z))
	t_2 = Float64(4.0 * Float64(Float64(a * t) / c))
	t_3 = Float64(Float64(x * 9.0) * y)
	t_4 = Float64(Float64(t_3 - Float64(Float64(Float64(z * 4.0) * t) * a)) + b)
	t_5 = Float64(t_4 / Float64(z * c))
	t_6 = Float64(Float64(Float64(t_3 - Float64(Float64(z * 4.0) * Float64(t * a))) + b) / Float64(z * c))
	tmp = 0.0
	if (t_5 < -1.100156740804105e-171)
		tmp = t_6;
	elseif (t_5 < 0.0)
		tmp = Float64(Float64(t_4 / z) / c);
	elseif (t_5 < 1.1708877911747488e-53)
		tmp = t_6;
	elseif (t_5 < 2.876823679546137e+130)
		tmp = Float64(Float64(Float64(Float64(9.0 * Float64(y / c)) * Float64(x / z)) + t_1) - t_2);
	elseif (t_5 < 1.3838515042456319e+158)
		tmp = t_6;
	else
		tmp = Float64(Float64(Float64(9.0 * Float64(Float64(y / Float64(c * z)) * x)) + t_1) - t_2);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = b / (c * z);
	t_2 = 4.0 * ((a * t) / c);
	t_3 = (x * 9.0) * y;
	t_4 = (t_3 - (((z * 4.0) * t) * a)) + b;
	t_5 = t_4 / (z * c);
	t_6 = ((t_3 - ((z * 4.0) * (t * a))) + b) / (z * c);
	tmp = 0.0;
	if (t_5 < -1.100156740804105e-171)
		tmp = t_6;
	elseif (t_5 < 0.0)
		tmp = (t_4 / z) / c;
	elseif (t_5 < 1.1708877911747488e-53)
		tmp = t_6;
	elseif (t_5 < 2.876823679546137e+130)
		tmp = (((9.0 * (y / c)) * (x / z)) + t_1) - t_2;
	elseif (t_5 < 1.3838515042456319e+158)
		tmp = t_6;
	else
		tmp = ((9.0 * ((y / (c * z)) * x)) + t_1) - t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(b / N[(c * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(4.0 * N[(N[(a * t), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision]}, Block[{t$95$4 = N[(N[(t$95$3 - N[(N[(N[(z * 4.0), $MachinePrecision] * t), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]}, Block[{t$95$5 = N[(t$95$4 / N[(z * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(N[(N[(t$95$3 - N[(N[(z * 4.0), $MachinePrecision] * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]}, If[Less[t$95$5, -1.100156740804105e-171], t$95$6, If[Less[t$95$5, 0.0], N[(N[(t$95$4 / z), $MachinePrecision] / c), $MachinePrecision], If[Less[t$95$5, 1.1708877911747488e-53], t$95$6, If[Less[t$95$5, 2.876823679546137e+130], N[(N[(N[(N[(9.0 * N[(y / c), $MachinePrecision]), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision] - t$95$2), $MachinePrecision], If[Less[t$95$5, 1.3838515042456319e+158], t$95$6, N[(N[(N[(9.0 * N[(N[(y / N[(c * z), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision] - t$95$2), $MachinePrecision]]]]]]]]]]]]

Reproduce

herbie shell --seed 2024208 
(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)))