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

Percentage Accurate: 80.1% → 88.7%

Time: 16.8s

Alternatives: 19

Speedup: 0.5×

• 38.0% 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: 80.1% 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: 88.7% accurate, 0.1× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\\\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ \begin{array}{l} t_1 := \frac{b - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - \left(x \cdot 9\right) \cdot y\right)}{z \cdot c\_m}\\ c\_s \cdot \begin{array}{l} \mathbf{if}\;t\_1 \leq -5 \cdot 10^{-225}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_1 \leq 0:\\ \;\;\;\;\frac{1}{\frac{z}{\mathsf{fma}\left(-4, \frac{z \cdot \left(t \cdot a\right)}{c\_m}, \mathsf{fma}\left(9, x \cdot \frac{y}{c\_m}, \frac{b}{c\_m}\right)\right)}}\\ \mathbf{elif}\;t\_1 \leq \infty:\\ \;\;\;\;\frac{b + \left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right)}{z \cdot c\_m}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(\frac{\mathsf{fma}\left(-4, a \cdot \frac{t}{c\_m}, \frac{b}{z \cdot c\_m}\right)}{y} - \frac{x}{z} \cdot \frac{-9}{c\_m}\right)\\ \end{array} \end{array} \end{array} \]

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 (/ (- b (- (* (* (* z 4.0) t) a) (* (* x 9.0) y))) (* z c_m))))
   (*
    c_s
    (if (<= t_1 -5e-225)
      t_1
      (if (<= t_1 0.0)
        (/
         1.0
         (/
          z
          (fma
           -4.0
           (/ (* z (* t a)) c_m)
           (fma 9.0 (* x (/ y c_m)) (/ b c_m)))))
        (if (<= t_1 INFINITY)
          (/ (+ b (- (* x (* 9.0 y)) (* (* z 4.0) (* t a)))) (* z c_m))
          (*
           y
           (-
            (/ (fma -4.0 (* a (/ t c_m)) (/ b (* z c_m))) y)
            (* (/ x z) (/ -9.0 c_m))))))))))

C

c\_m = fabs(c);
c\_s = copysign(1.0, c);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
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 - ((((z * 4.0) * t) * a) - ((x * 9.0) * y))) / (z * c_m);
	double tmp;
	if (t_1 <= -5e-225) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = 1.0 / (z / fma(-4.0, ((z * (t * a)) / c_m), fma(9.0, (x * (y / c_m)), (b / c_m))));
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = (b + ((x * (9.0 * y)) - ((z * 4.0) * (t * a)))) / (z * c_m);
	} else {
		tmp = y * ((fma(-4.0, (a * (t / c_m)), (b / (z * c_m))) / y) - ((x / z) * (-9.0 / c_m)));
	}
	return c_s * tmp;
}

Julia

c\_m = abs(c)
c\_s = copysign(1.0, c)
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
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 - Float64(Float64(Float64(Float64(z * 4.0) * t) * a) - Float64(Float64(x * 9.0) * y))) / Float64(z * c_m))
	tmp = 0.0
	if (t_1 <= -5e-225)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = Float64(1.0 / Float64(z / fma(-4.0, Float64(Float64(z * Float64(t * a)) / c_m), fma(9.0, Float64(x * Float64(y / c_m)), Float64(b / c_m)))));
	elseif (t_1 <= Inf)
		tmp = Float64(Float64(b + Float64(Float64(x * Float64(9.0 * y)) - Float64(Float64(z * 4.0) * Float64(t * a)))) / Float64(z * c_m));
	else
		tmp = Float64(y * Float64(Float64(fma(-4.0, Float64(a * Float64(t / c_m)), Float64(b / Float64(z * c_m))) / y) - Float64(Float64(x / z) * Float64(-9.0 / c_m))));
	end
	return Float64(c_s * tmp)
end

Wolfram

c\_m = N[Abs[c], $MachinePrecision]
c\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
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 - N[(N[(N[(N[(z * 4.0), $MachinePrecision] * t), $MachinePrecision] * a), $MachinePrecision] - N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c$95$m), $MachinePrecision]), $MachinePrecision]}, N[(c$95$s * If[LessEqual[t$95$1, -5e-225], t$95$1, If[LessEqual[t$95$1, 0.0], N[(1.0 / N[(z / N[(-4.0 * N[(N[(z * N[(t * a), $MachinePrecision]), $MachinePrecision] / c$95$m), $MachinePrecision] + N[(9.0 * N[(x * N[(y / c$95$m), $MachinePrecision]), $MachinePrecision] + N[(b / c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, Infinity], N[(N[(b + N[(N[(x * N[(9.0 * y), $MachinePrecision]), $MachinePrecision] - N[(N[(z * 4.0), $MachinePrecision] * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c$95$m), $MachinePrecision]), $MachinePrecision], N[(y * N[(N[(N[(-4.0 * N[(a * N[(t / c$95$m), $MachinePrecision]), $MachinePrecision] + N[(b / N[(z * c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision] - N[(N[(x / z), $MachinePrecision] * N[(-9.0 / c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]), $MachinePrecision]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x #s(literal 9 binary64)) y) (*.f64 (*.f64 (*.f64 z #s(literal 4 binary64)) t) a)) b) (*.f64 z c)) < -5.0000000000000001e-225

   1. Initial program 93.4%

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

   if -5.0000000000000001e-225 < (/.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)) < 0.0

   1. Initial program 57.4%

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

   3. Simplified 60.7%

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

   5. Taylor expanded in z around 0 91.9%

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

      1. clear-num 89.1%

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

      2. inv-pow 89.1%

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

      3. fma-define 89.1%

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

      4. associate-/l* 89.1%

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

      5. *-commutative 89.1%

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

      6. fma-define 89.1%

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

      7. associate-/l* 89.1%

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

   7. Applied egg-rr 89.1%

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

      1. unpow-1 89.1%

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

      2. associate-*r/ 89.1%

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

      3. *-commutative 89.1%

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

      4. associate-*r* 93.0%

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

   9. Simplified 93.0%

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

   if 0.0 < (/.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)) < +inf.0

   1. Initial program 86.9%

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

      1. associate-+l- 86.9%

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

      2. *-commutative 86.9%

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

      3. associate-*r* 87.5%

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

      4. *-commutative 87.5%

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

      5. associate-+l- 87.5%

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

      6. associate-*l* 87.5%

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

      7. associate-*l* 86.5%

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

      8. *-commutative 86.5%

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

   3. Simplified 86.5%

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

   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%

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

   3. Simplified 18.0%

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

   5. Taylor expanded in y around -inf 45.0%

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

   7. Simplified 70.1%

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

4. Final simplification 88.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{b - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - \left(x \cdot 9\right) \cdot y\right)}{z \cdot c} \leq -5 \cdot 10^{-225}:\\ \;\;\;\;\frac{b - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - \left(x \cdot 9\right) \cdot y\right)}{z \cdot c}\\ \mathbf{elif}\;\frac{b - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - \left(x \cdot 9\right) \cdot y\right)}{z \cdot c} \leq 0:\\ \;\;\;\;\frac{1}{\frac{z}{\mathsf{fma}\left(-4, \frac{z \cdot \left(t \cdot a\right)}{c}, \mathsf{fma}\left(9, x \cdot \frac{y}{c}, \frac{b}{c}\right)\right)}}\\ \mathbf{elif}\;\frac{b - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - \left(x \cdot 9\right) \cdot y\right)}{z \cdot c} \leq \infty:\\ \;\;\;\;\frac{b + \left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(\frac{\mathsf{fma}\left(-4, a \cdot \frac{t}{c}, \frac{b}{z \cdot c}\right)}{y} - \frac{x}{z} \cdot \frac{-9}{c}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 88.9% accurate, 0.1× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\\\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ \begin{array}{l} t_1 := \frac{b - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - \left(x \cdot 9\right) \cdot y\right)}{z \cdot c\_m}\\ c\_s \cdot \begin{array}{l} \mathbf{if}\;t\_1 \leq -5 \cdot 10^{-251}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_1 \leq 0:\\ \;\;\;\;\frac{-4 \cdot \frac{a \cdot \left(z \cdot t\right)}{c\_m} + \left(\frac{b}{c\_m} + 9 \cdot \left(x \cdot \frac{y}{c\_m}\right)\right)}{z}\\ \mathbf{elif}\;t\_1 \leq \infty:\\ \;\;\;\;\frac{b + \left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right)}{z \cdot c\_m}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(\frac{\mathsf{fma}\left(-4, a \cdot \frac{t}{c\_m}, \frac{b}{z \cdot c\_m}\right)}{y} - \frac{x}{z} \cdot \frac{-9}{c\_m}\right)\\ \end{array} \end{array} \end{array} \]

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 (/ (- b (- (* (* (* z 4.0) t) a) (* (* x 9.0) y))) (* z c_m))))
   (*
    c_s
    (if (<= t_1 -5e-251)
      t_1
      (if (<= t_1 0.0)
        (/
         (+
          (* -4.0 (/ (* a (* z t)) c_m))
          (+ (/ b c_m) (* 9.0 (* x (/ y c_m)))))
         z)
        (if (<= t_1 INFINITY)
          (/ (+ b (- (* x (* 9.0 y)) (* (* z 4.0) (* t a)))) (* z c_m))
          (*
           y
           (-
            (/ (fma -4.0 (* a (/ t c_m)) (/ b (* z c_m))) y)
            (* (/ x z) (/ -9.0 c_m))))))))))

C

c\_m = fabs(c);
c\_s = copysign(1.0, c);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
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 - ((((z * 4.0) * t) * a) - ((x * 9.0) * y))) / (z * c_m);
	double tmp;
	if (t_1 <= -5e-251) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = ((-4.0 * ((a * (z * t)) / c_m)) + ((b / c_m) + (9.0 * (x * (y / c_m))))) / z;
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = (b + ((x * (9.0 * y)) - ((z * 4.0) * (t * a)))) / (z * c_m);
	} else {
		tmp = y * ((fma(-4.0, (a * (t / c_m)), (b / (z * c_m))) / y) - ((x / z) * (-9.0 / c_m)));
	}
	return c_s * tmp;
}

Julia

c\_m = abs(c)
c\_s = copysign(1.0, c)
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
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 - Float64(Float64(Float64(Float64(z * 4.0) * t) * a) - Float64(Float64(x * 9.0) * y))) / Float64(z * c_m))
	tmp = 0.0
	if (t_1 <= -5e-251)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = Float64(Float64(Float64(-4.0 * Float64(Float64(a * Float64(z * t)) / c_m)) + Float64(Float64(b / c_m) + Float64(9.0 * Float64(x * Float64(y / c_m))))) / z);
	elseif (t_1 <= Inf)
		tmp = Float64(Float64(b + Float64(Float64(x * Float64(9.0 * y)) - Float64(Float64(z * 4.0) * Float64(t * a)))) / Float64(z * c_m));
	else
		tmp = Float64(y * Float64(Float64(fma(-4.0, Float64(a * Float64(t / c_m)), Float64(b / Float64(z * c_m))) / y) - Float64(Float64(x / z) * Float64(-9.0 / c_m))));
	end
	return Float64(c_s * tmp)
end

Wolfram

c\_m = N[Abs[c], $MachinePrecision]
c\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
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 - N[(N[(N[(N[(z * 4.0), $MachinePrecision] * t), $MachinePrecision] * a), $MachinePrecision] - N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c$95$m), $MachinePrecision]), $MachinePrecision]}, N[(c$95$s * If[LessEqual[t$95$1, -5e-251], t$95$1, If[LessEqual[t$95$1, 0.0], N[(N[(N[(-4.0 * N[(N[(a * N[(z * t), $MachinePrecision]), $MachinePrecision] / c$95$m), $MachinePrecision]), $MachinePrecision] + N[(N[(b / c$95$m), $MachinePrecision] + N[(9.0 * N[(x * N[(y / c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t$95$1, Infinity], N[(N[(b + N[(N[(x * N[(9.0 * y), $MachinePrecision]), $MachinePrecision] - N[(N[(z * 4.0), $MachinePrecision] * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c$95$m), $MachinePrecision]), $MachinePrecision], N[(y * N[(N[(N[(-4.0 * N[(a * N[(t / c$95$m), $MachinePrecision]), $MachinePrecision] + N[(b / N[(z * c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision] - N[(N[(x / z), $MachinePrecision] * N[(-9.0 / c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]), $MachinePrecision]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x #s(literal 9 binary64)) y) (*.f64 (*.f64 (*.f64 z #s(literal 4 binary64)) t) a)) b) (*.f64 z c)) < -5.0000000000000003e-251

   1. Initial program 92.6%

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

   if -5.0000000000000003e-251 < (/.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)) < 0.0

   1. Initial program 57.9%

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

   3. Simplified 57.3%

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

   5. Taylor expanded in z around 0 95.5%

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

      1. associate-/l* 95.5%

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

   7. Applied egg-rr 95.5%

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

   if 0.0 < (/.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)) < +inf.0

   1. Initial program 86.9%

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

      1. associate-+l- 86.9%

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

      2. *-commutative 86.9%

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

      3. associate-*r* 87.5%

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

      4. *-commutative 87.5%

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

      5. associate-+l- 87.5%

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

      6. associate-*l* 87.5%

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

      7. associate-*l* 86.5%

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

      8. *-commutative 86.5%

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

   3. Simplified 86.5%

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

   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%

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

   3. Simplified 18.0%

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

   5. Taylor expanded in y around -inf 45.0%

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

   7. Simplified 70.1%

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

4. Final simplification 88.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{b - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - \left(x \cdot 9\right) \cdot y\right)}{z \cdot c} \leq -5 \cdot 10^{-251}:\\ \;\;\;\;\frac{b - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - \left(x \cdot 9\right) \cdot y\right)}{z \cdot c}\\ \mathbf{elif}\;\frac{b - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - \left(x \cdot 9\right) \cdot y\right)}{z \cdot c} \leq 0:\\ \;\;\;\;\frac{-4 \cdot \frac{a \cdot \left(z \cdot t\right)}{c} + \left(\frac{b}{c} + 9 \cdot \left(x \cdot \frac{y}{c}\right)\right)}{z}\\ \mathbf{elif}\;\frac{b - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - \left(x \cdot 9\right) \cdot y\right)}{z \cdot c} \leq \infty:\\ \;\;\;\;\frac{b + \left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(\frac{\mathsf{fma}\left(-4, a \cdot \frac{t}{c}, \frac{b}{z \cdot c}\right)}{y} - \frac{x}{z} \cdot \frac{-9}{c}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 89.1% accurate, 0.1× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\\\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ \begin{array}{l} t_1 := \frac{b - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - \left(x \cdot 9\right) \cdot y\right)}{z \cdot c\_m}\\ c\_s \cdot \begin{array}{l} \mathbf{if}\;t\_1 \leq -5 \cdot 10^{-251}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_1 \leq 0:\\ \;\;\;\;\frac{-4 \cdot \frac{a \cdot \left(z \cdot t\right)}{c\_m} + \left(\frac{b}{c\_m} + 9 \cdot \left(x \cdot \frac{y}{c\_m}\right)\right)}{z}\\ \mathbf{elif}\;t\_1 \leq \infty:\\ \;\;\;\;\frac{b + \left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right)}{z \cdot c\_m}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{\mathsf{fma}\left(-4, a \cdot \frac{t}{c\_m}, \frac{b}{z \cdot c\_m}\right)}{x} - \frac{y}{z} \cdot \frac{-9}{c\_m}\right)\\ \end{array} \end{array} \end{array} \]

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 (/ (- b (- (* (* (* z 4.0) t) a) (* (* x 9.0) y))) (* z c_m))))
   (*
    c_s
    (if (<= t_1 -5e-251)
      t_1
      (if (<= t_1 0.0)
        (/
         (+
          (* -4.0 (/ (* a (* z t)) c_m))
          (+ (/ b c_m) (* 9.0 (* x (/ y c_m)))))
         z)
        (if (<= t_1 INFINITY)
          (/ (+ b (- (* x (* 9.0 y)) (* (* z 4.0) (* t a)))) (* z c_m))
          (*
           x
           (-
            (/ (fma -4.0 (* a (/ t c_m)) (/ b (* z c_m))) x)
            (* (/ y z) (/ -9.0 c_m))))))))))

C

c\_m = fabs(c);
c\_s = copysign(1.0, c);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
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 - ((((z * 4.0) * t) * a) - ((x * 9.0) * y))) / (z * c_m);
	double tmp;
	if (t_1 <= -5e-251) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = ((-4.0 * ((a * (z * t)) / c_m)) + ((b / c_m) + (9.0 * (x * (y / c_m))))) / z;
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = (b + ((x * (9.0 * y)) - ((z * 4.0) * (t * a)))) / (z * c_m);
	} else {
		tmp = x * ((fma(-4.0, (a * (t / c_m)), (b / (z * c_m))) / x) - ((y / z) * (-9.0 / c_m)));
	}
	return c_s * tmp;
}

Julia

c\_m = abs(c)
c\_s = copysign(1.0, c)
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
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 - Float64(Float64(Float64(Float64(z * 4.0) * t) * a) - Float64(Float64(x * 9.0) * y))) / Float64(z * c_m))
	tmp = 0.0
	if (t_1 <= -5e-251)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = Float64(Float64(Float64(-4.0 * Float64(Float64(a * Float64(z * t)) / c_m)) + Float64(Float64(b / c_m) + Float64(9.0 * Float64(x * Float64(y / c_m))))) / z);
	elseif (t_1 <= Inf)
		tmp = Float64(Float64(b + Float64(Float64(x * Float64(9.0 * y)) - Float64(Float64(z * 4.0) * Float64(t * a)))) / Float64(z * c_m));
	else
		tmp = Float64(x * Float64(Float64(fma(-4.0, Float64(a * Float64(t / c_m)), Float64(b / Float64(z * c_m))) / x) - Float64(Float64(y / z) * Float64(-9.0 / c_m))));
	end
	return Float64(c_s * tmp)
end

Wolfram

c\_m = N[Abs[c], $MachinePrecision]
c\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
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 - N[(N[(N[(N[(z * 4.0), $MachinePrecision] * t), $MachinePrecision] * a), $MachinePrecision] - N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c$95$m), $MachinePrecision]), $MachinePrecision]}, N[(c$95$s * If[LessEqual[t$95$1, -5e-251], t$95$1, If[LessEqual[t$95$1, 0.0], N[(N[(N[(-4.0 * N[(N[(a * N[(z * t), $MachinePrecision]), $MachinePrecision] / c$95$m), $MachinePrecision]), $MachinePrecision] + N[(N[(b / c$95$m), $MachinePrecision] + N[(9.0 * N[(x * N[(y / c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t$95$1, Infinity], N[(N[(b + N[(N[(x * N[(9.0 * y), $MachinePrecision]), $MachinePrecision] - N[(N[(z * 4.0), $MachinePrecision] * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c$95$m), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(N[(-4.0 * N[(a * N[(t / c$95$m), $MachinePrecision]), $MachinePrecision] + N[(b / N[(z * c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision] - N[(N[(y / z), $MachinePrecision] * N[(-9.0 / c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]), $MachinePrecision]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x #s(literal 9 binary64)) y) (*.f64 (*.f64 (*.f64 z #s(literal 4 binary64)) t) a)) b) (*.f64 z c)) < -5.0000000000000003e-251

   1. Initial program 92.6%

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

   if -5.0000000000000003e-251 < (/.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)) < 0.0

   1. Initial program 57.9%

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

   3. Simplified 57.3%

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

   5. Taylor expanded in z around 0 95.5%

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

      1. associate-/l* 95.5%

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

   7. Applied egg-rr 95.5%

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

   if 0.0 < (/.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)) < +inf.0

   1. Initial program 86.9%

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

      1. associate-+l- 86.9%

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

      2. *-commutative 86.9%

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

      3. associate-*r* 87.5%

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

      4. *-commutative 87.5%

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

      5. associate-+l- 87.5%

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

      6. associate-*l* 87.5%

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

      7. associate-*l* 86.5%

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

      8. *-commutative 86.5%

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

   3. Simplified 86.5%

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

   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%

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

   3. Simplified 18.0%

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

   5. Taylor expanded in x around -inf 49.1%

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

   7. Simplified 74.4%

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

4. Final simplification 88.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{b - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - \left(x \cdot 9\right) \cdot y\right)}{z \cdot c} \leq -5 \cdot 10^{-251}:\\ \;\;\;\;\frac{b - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - \left(x \cdot 9\right) \cdot y\right)}{z \cdot c}\\ \mathbf{elif}\;\frac{b - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - \left(x \cdot 9\right) \cdot y\right)}{z \cdot c} \leq 0:\\ \;\;\;\;\frac{-4 \cdot \frac{a \cdot \left(z \cdot t\right)}{c} + \left(\frac{b}{c} + 9 \cdot \left(x \cdot \frac{y}{c}\right)\right)}{z}\\ \mathbf{elif}\;\frac{b - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - \left(x \cdot 9\right) \cdot y\right)}{z \cdot c} \leq \infty:\\ \;\;\;\;\frac{b + \left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{\mathsf{fma}\left(-4, a \cdot \frac{t}{c}, \frac{b}{z \cdot c}\right)}{x} - \frac{y}{z} \cdot \frac{-9}{c}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 84.4% accurate, 0.1× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\\\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ c\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -950000000:\\ \;\;\;\;x \cdot \left(\left(9 \cdot \frac{y}{z \cdot c\_m} + \frac{b}{c\_m \cdot \left(x \cdot z\right)}\right) - 4 \cdot \frac{t \cdot a}{x \cdot c\_m}\right)\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+141}:\\ \;\;\;\;\frac{b + \mathsf{fma}\left(x, 9 \cdot y, t \cdot \left(a \cdot \left(z \cdot -4\right)\right)\right)}{z \cdot c\_m}\\ \mathbf{else}:\\ \;\;\;\;\frac{9 \cdot \frac{x \cdot y}{z} - 4 \cdot \left(t \cdot a\right)}{c\_m}\\ \end{array} \end{array} \]

FPCore

c\_m = (fabs.f64 c)
c\_s = (copysign.f64 #s(literal 1 binary64) c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
(FPCore (c_s x y z t a b c_m)
 :precision binary64
 (*
  c_s
  (if (<= z -950000000.0)
    (*
     x
     (-
      (+ (* 9.0 (/ y (* z c_m))) (/ b (* c_m (* x z))))
      (* 4.0 (/ (* t a) (* x c_m)))))
    (if (<= z 1.5e+141)
      (/ (+ b (fma x (* 9.0 y) (* t (* a (* z -4.0))))) (* z c_m))
      (/ (- (* 9.0 (/ (* x y) z)) (* 4.0 (* t a))) 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 tmp;
	if (z <= -950000000.0) {
		tmp = x * (((9.0 * (y / (z * c_m))) + (b / (c_m * (x * z)))) - (4.0 * ((t * a) / (x * c_m))));
	} else if (z <= 1.5e+141) {
		tmp = (b + fma(x, (9.0 * y), (t * (a * (z * -4.0))))) / (z * c_m);
	} else {
		tmp = ((9.0 * ((x * y) / z)) - (4.0 * (t * a))) / 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)
	tmp = 0.0
	if (z <= -950000000.0)
		tmp = Float64(x * Float64(Float64(Float64(9.0 * Float64(y / Float64(z * c_m))) + Float64(b / Float64(c_m * Float64(x * z)))) - Float64(4.0 * Float64(Float64(t * a) / Float64(x * c_m)))));
	elseif (z <= 1.5e+141)
		tmp = Float64(Float64(b + fma(x, Float64(9.0 * y), Float64(t * Float64(a * Float64(z * -4.0))))) / Float64(z * c_m));
	else
		tmp = Float64(Float64(Float64(9.0 * Float64(Float64(x * y) / z)) - Float64(4.0 * Float64(t * a))) / 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_] := N[(c$95$s * If[LessEqual[z, -950000000.0], N[(x * N[(N[(N[(9.0 * N[(y / N[(z * c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b / N[(c$95$m * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * N[(N[(t * a), $MachinePrecision] / N[(x * c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.5e+141], N[(N[(b + N[(x * N[(9.0 * y), $MachinePrecision] + N[(t * N[(a * N[(z * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c$95$m), $MachinePrecision]), $MachinePrecision], N[(N[(N[(9.0 * N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] - N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c$95$m), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if z < -9.5e8

   1. Initial program 59.3%

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

      1. associate-+l- 59.3%

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

      2. *-commutative 59.3%

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

      3. associate-*r* 57.6%

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

      4. *-commutative 57.6%

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

      5. associate-+l- 57.6%

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

      6. associate-*l* 57.6%

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

      7. associate-*l* 62.4%

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

      8. *-commutative 62.4%

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

   3. Simplified 62.4%

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

   5. Taylor expanded in x around inf 73.4%

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

   if -9.5e8 < z < 1.4999999999999999e141

   1. Initial program 93.5%

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

   3. Simplified 94.5%

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

   if 1.4999999999999999e141 < z

   1. Initial program 45.1%

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

      1. associate-+l- 45.1%

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

      2. *-commutative 45.1%

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

      3. associate-*r* 41.7%

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

      4. *-commutative 41.7%

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

      5. associate-+l- 41.7%

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

      6. associate-*l* 41.8%

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

      7. associate-*l* 51.1%

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

      8. *-commutative 51.1%

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

   3. Simplified 51.1%

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

   5. Taylor expanded in z around inf 54.4%

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

   6. Taylor expanded in b around 0 67.1%

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

4. Final simplification 85.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -950000000:\\ \;\;\;\;x \cdot \left(\left(9 \cdot \frac{y}{z \cdot c} + \frac{b}{c \cdot \left(x \cdot z\right)}\right) - 4 \cdot \frac{t \cdot a}{x \cdot c}\right)\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+141}:\\ \;\;\;\;\frac{b + \mathsf{fma}\left(x, 9 \cdot y, t \cdot \left(a \cdot \left(z \cdot -4\right)\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{9 \cdot \frac{x \cdot y}{z} - 4 \cdot \left(t \cdot a\right)}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 88.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\\\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ \begin{array}{l} t_1 := \frac{b - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - \left(x \cdot 9\right) \cdot y\right)}{z \cdot c\_m}\\ c\_s \cdot \begin{array}{l} \mathbf{if}\;t\_1 \leq -5 \cdot 10^{-251}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_1 \leq 0:\\ \;\;\;\;\frac{-4 \cdot \frac{a \cdot \left(z \cdot t\right)}{c\_m} + \left(\frac{b}{c\_m} + 9 \cdot \left(x \cdot \frac{y}{c\_m}\right)\right)}{z}\\ \mathbf{elif}\;t\_1 \leq \infty:\\ \;\;\;\;\frac{b + \left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right)}{z \cdot c\_m}\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{1}{\frac{c\_m}{t \cdot -4}}\\ \end{array} \end{array} \end{array} \]

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 (- (* (* (* z 4.0) t) a) (* (* x 9.0) y))) (* z c_m))))
   (*
    c_s
    (if (<= t_1 -5e-251)
      t_1
      (if (<= t_1 0.0)
        (/
         (+
          (* -4.0 (/ (* a (* z t)) c_m))
          (+ (/ b c_m) (* 9.0 (* x (/ y c_m)))))
         z)
        (if (<= t_1 INFINITY)
          (/ (+ b (- (* x (* 9.0 y)) (* (* z 4.0) (* t a)))) (* z c_m))
          (* a (/ 1.0 (/ c_m (* t -4.0))))))))))

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 - ((((z * 4.0) * t) * a) - ((x * 9.0) * y))) / (z * c_m);
	double tmp;
	if (t_1 <= -5e-251) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = ((-4.0 * ((a * (z * t)) / c_m)) + ((b / c_m) + (9.0 * (x * (y / c_m))))) / z;
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = (b + ((x * (9.0 * y)) - ((z * 4.0) * (t * a)))) / (z * c_m);
	} else {
		tmp = a * (1.0 / (c_m / (t * -4.0)));
	}
	return c_s * tmp;
}

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 - ((((z * 4.0) * t) * a) - ((x * 9.0) * y))) / (z * c_m);
	double tmp;
	if (t_1 <= -5e-251) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = ((-4.0 * ((a * (z * t)) / c_m)) + ((b / c_m) + (9.0 * (x * (y / c_m))))) / z;
	} else if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = (b + ((x * (9.0 * y)) - ((z * 4.0) * (t * a)))) / (z * c_m);
	} else {
		tmp = a * (1.0 / (c_m / (t * -4.0)));
	}
	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 - ((((z * 4.0) * t) * a) - ((x * 9.0) * y))) / (z * c_m)
	tmp = 0
	if t_1 <= -5e-251:
		tmp = t_1
	elif t_1 <= 0.0:
		tmp = ((-4.0 * ((a * (z * t)) / c_m)) + ((b / c_m) + (9.0 * (x * (y / c_m))))) / z
	elif t_1 <= math.inf:
		tmp = (b + ((x * (9.0 * y)) - ((z * 4.0) * (t * a)))) / (z * c_m)
	else:
		tmp = a * (1.0 / (c_m / (t * -4.0)))
	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 - Float64(Float64(Float64(Float64(z * 4.0) * t) * a) - Float64(Float64(x * 9.0) * y))) / Float64(z * c_m))
	tmp = 0.0
	if (t_1 <= -5e-251)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = Float64(Float64(Float64(-4.0 * Float64(Float64(a * Float64(z * t)) / c_m)) + Float64(Float64(b / c_m) + Float64(9.0 * Float64(x * Float64(y / c_m))))) / z);
	elseif (t_1 <= Inf)
		tmp = Float64(Float64(b + Float64(Float64(x * Float64(9.0 * y)) - Float64(Float64(z * 4.0) * Float64(t * a)))) / Float64(z * c_m));
	else
		tmp = Float64(a * Float64(1.0 / Float64(c_m / Float64(t * -4.0))));
	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 - ((((z * 4.0) * t) * a) - ((x * 9.0) * y))) / (z * c_m);
	tmp = 0.0;
	if (t_1 <= -5e-251)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = ((-4.0 * ((a * (z * t)) / c_m)) + ((b / c_m) + (9.0 * (x * (y / c_m))))) / z;
	elseif (t_1 <= Inf)
		tmp = (b + ((x * (9.0 * y)) - ((z * 4.0) * (t * a)))) / (z * c_m);
	else
		tmp = a * (1.0 / (c_m / (t * -4.0)));
	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 - N[(N[(N[(N[(z * 4.0), $MachinePrecision] * t), $MachinePrecision] * a), $MachinePrecision] - N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c$95$m), $MachinePrecision]), $MachinePrecision]}, N[(c$95$s * If[LessEqual[t$95$1, -5e-251], t$95$1, If[LessEqual[t$95$1, 0.0], N[(N[(N[(-4.0 * N[(N[(a * N[(z * t), $MachinePrecision]), $MachinePrecision] / c$95$m), $MachinePrecision]), $MachinePrecision] + N[(N[(b / c$95$m), $MachinePrecision] + N[(9.0 * N[(x * N[(y / c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t$95$1, Infinity], N[(N[(b + N[(N[(x * N[(9.0 * y), $MachinePrecision]), $MachinePrecision] - N[(N[(z * 4.0), $MachinePrecision] * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c$95$m), $MachinePrecision]), $MachinePrecision], N[(a * N[(1.0 / N[(c$95$m / N[(t * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]), $MachinePrecision]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x #s(literal 9 binary64)) y) (*.f64 (*.f64 (*.f64 z #s(literal 4 binary64)) t) a)) b) (*.f64 z c)) < -5.0000000000000003e-251

   1. Initial program 92.6%

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

   if -5.0000000000000003e-251 < (/.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)) < 0.0

   1. Initial program 57.9%

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

   3. Simplified 57.3%

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

   5. Taylor expanded in z around 0 95.5%

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

      1. associate-/l* 95.5%

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

   7. Applied egg-rr 95.5%

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

   if 0.0 < (/.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)) < +inf.0

   1. Initial program 86.9%

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

      1. associate-+l- 86.9%

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

      2. *-commutative 86.9%

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

      3. associate-*r* 87.5%

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

      4. *-commutative 87.5%

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

      5. associate-+l- 87.5%

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

      6. associate-*l* 87.5%

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

      7. associate-*l* 86.5%

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

      8. *-commutative 86.5%

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

   3. Simplified 86.5%

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

   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%

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

   3. Simplified 18.0%

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

   5. Taylor expanded in t around inf 45.0%

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

      1. *-commutative 45.0%

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

      2. associate-/l* 49.1%

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

      3. associate-*r* 49.1%

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

      4. *-commutative 49.1%

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

      5. *-commutative 49.1%

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

      6. associate-*l/ 49.1%

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

   7. Simplified 49.1%

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

      1. clear-num 49.1%

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

      2. inv-pow 49.1%

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

      3. *-commutative 49.1%

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

   9. Applied egg-rr 49.1%

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

       1. unpow-1 49.1%

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

   11. Simplified 49.1%

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

4. Final simplification 86.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{b - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - \left(x \cdot 9\right) \cdot y\right)}{z \cdot c} \leq -5 \cdot 10^{-251}:\\ \;\;\;\;\frac{b - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - \left(x \cdot 9\right) \cdot y\right)}{z \cdot c}\\ \mathbf{elif}\;\frac{b - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - \left(x \cdot 9\right) \cdot y\right)}{z \cdot c} \leq 0:\\ \;\;\;\;\frac{-4 \cdot \frac{a \cdot \left(z \cdot t\right)}{c} + \left(\frac{b}{c} + 9 \cdot \left(x \cdot \frac{y}{c}\right)\right)}{z}\\ \mathbf{elif}\;\frac{b - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - \left(x \cdot 9\right) \cdot y\right)}{z \cdot c} \leq \infty:\\ \;\;\;\;\frac{b + \left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{1}{\frac{c}{t \cdot -4}}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 83.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\\\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ \begin{array}{l} t_1 := \left(x \cdot 9\right) \cdot y\\ c\_s \cdot \begin{array}{l} \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+296} \lor \neg \left(t\_1 \leq 10^{+235}\right):\\ \;\;\;\;9 \cdot \left(\frac{y}{z} \cdot \frac{x}{c\_m}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{b - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - t\_1\right)}{z \cdot c\_m}\\ \end{array} \end{array} \end{array} \]

FPCore

c\_m = (fabs.f64 c)
c\_s = (copysign.f64 #s(literal 1 binary64) c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
(FPCore (c_s x y z t a b c_m)
 :precision binary64
 (let* ((t_1 (* (* x 9.0) y)))
   (*
    c_s
    (if (or (<= t_1 -1e+296) (not (<= t_1 1e+235)))
      (* 9.0 (* (/ y z) (/ x c_m)))
      (/ (- b (- (* (* (* z 4.0) t) a) t_1)) (* z c_m))))))

C

c\_m = fabs(c);
c\_s = copysign(1.0, c);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double t_1 = (x * 9.0) * y;
	double tmp;
	if ((t_1 <= -1e+296) || !(t_1 <= 1e+235)) {
		tmp = 9.0 * ((y / z) * (x / c_m));
	} else {
		tmp = (b - ((((z * 4.0) * t) * a) - t_1)) / (z * c_m);
	}
	return c_s * tmp;
}

Fortran

c\_m = abs(c)
c\_s = copysign(1.0d0, c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
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 = (x * 9.0d0) * y
    if ((t_1 <= (-1d+296)) .or. (.not. (t_1 <= 1d+235))) then
        tmp = 9.0d0 * ((y / z) * (x / c_m))
    else
        tmp = (b - ((((z * 4.0d0) * t) * a) - t_1)) / (z * c_m)
    end if
    code = c_s * tmp
end function

Java

c\_m = Math.abs(c);
c\_s = Math.copySign(1.0, c);
assert x < y && y < z && z < t && t < a && a < b && b < c_m;
assert x < y && y < z && z < t && t < a && a < b && b < c_m;
public static double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double t_1 = (x * 9.0) * y;
	double tmp;
	if ((t_1 <= -1e+296) || !(t_1 <= 1e+235)) {
		tmp = 9.0 * ((y / z) * (x / c_m));
	} else {
		tmp = (b - ((((z * 4.0) * t) * a) - t_1)) / (z * c_m);
	}
	return c_s * tmp;
}

Python

c\_m = math.fabs(c)
c\_s = math.copysign(1.0, c)
[x, y, z, t, a, b, c_m] = sort([x, y, z, t, a, b, c_m])
[x, y, z, t, a, b, c_m] = sort([x, y, z, t, a, b, c_m])
def code(c_s, x, y, z, t, a, b, c_m):
	t_1 = (x * 9.0) * y
	tmp = 0
	if (t_1 <= -1e+296) or not (t_1 <= 1e+235):
		tmp = 9.0 * ((y / z) * (x / c_m))
	else:
		tmp = (b - ((((z * 4.0) * t) * a) - t_1)) / (z * c_m)
	return c_s * tmp

Julia

c\_m = abs(c)
c\_s = copysign(1.0, c)
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
function code(c_s, x, y, z, t, a, b, c_m)
	t_1 = Float64(Float64(x * 9.0) * y)
	tmp = 0.0
	if ((t_1 <= -1e+296) || !(t_1 <= 1e+235))
		tmp = Float64(9.0 * Float64(Float64(y / z) * Float64(x / c_m)));
	else
		tmp = Float64(Float64(b - Float64(Float64(Float64(Float64(z * 4.0) * t) * a) - t_1)) / Float64(z * c_m));
	end
	return Float64(c_s * tmp)
end

MATLAB

c\_m = abs(c);
c\_s = sign(c) * abs(1.0);
x, y, z, t, a, b, c_m = num2cell(sort([x, y, z, t, a, b, c_m])){:}
x, y, z, t, a, b, c_m = num2cell(sort([x, y, z, t, a, b, c_m])){:}
function tmp_2 = code(c_s, x, y, z, t, a, b, c_m)
	t_1 = (x * 9.0) * y;
	tmp = 0.0;
	if ((t_1 <= -1e+296) || ~((t_1 <= 1e+235)))
		tmp = 9.0 * ((y / z) * (x / c_m));
	else
		tmp = (b - ((((z * 4.0) * t) * a) - t_1)) / (z * c_m);
	end
	tmp_2 = c_s * tmp;
end

Wolfram

c\_m = N[Abs[c], $MachinePrecision]
c\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
code[c$95$s_, x_, y_, z_, t_, a_, b_, c$95$m_] := Block[{t$95$1 = N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision]}, N[(c$95$s * If[Or[LessEqual[t$95$1, -1e+296], N[Not[LessEqual[t$95$1, 1e+235]], $MachinePrecision]], N[(9.0 * N[(N[(y / z), $MachinePrecision] * N[(x / c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b - N[(N[(N[(N[(z * 4.0), $MachinePrecision] * t), $MachinePrecision] * a), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision] / N[(z * c$95$m), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -9.99999999999999981e295 or 1.0000000000000001e235 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 51.1%

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

   3. Simplified 59.1%

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

   5. Taylor expanded in x around inf 57.1%

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

      1. +-commutative 57.1%

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

      2. fma-define 57.1%

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

      3. *-commutative 57.1%

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

      4. associate-/l* 57.2%

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

      5. associate-*l* 57.2%

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

      6. *-commutative 57.2%

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

      7. associate-/l* 63.3%

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

   7. Simplified 63.3%

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

   8. Taylor expanded in x around inf 57.3%

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

      1. times-frac 88.2%

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

      2. *-commutative 88.2%

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

   10. Simplified 88.2%

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

   if -9.99999999999999981e295 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 1.0000000000000001e235

   1. Initial program 85.7%

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

4. Final simplification 86.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x \cdot 9\right) \cdot y \leq -1 \cdot 10^{+296} \lor \neg \left(\left(x \cdot 9\right) \cdot y \leq 10^{+235}\right):\\ \;\;\;\;9 \cdot \left(\frac{y}{z} \cdot \frac{x}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{b - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - \left(x \cdot 9\right) \cdot y\right)}{z \cdot c}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 51.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\\\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ c\_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -1.32 \cdot 10^{-11}:\\ \;\;\;\;9 \cdot \left(x \cdot \frac{y}{z \cdot c\_m}\right)\\ \mathbf{elif}\;y \leq -1.25 \cdot 10^{-206}:\\ \;\;\;\;\frac{1}{\frac{\frac{c\_m \cdot -0.25}{t}}{a}}\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{-267}:\\ \;\;\;\;\frac{1}{c\_m \cdot \frac{z}{b}}\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{+63}:\\ \;\;\;\;-4 \cdot \frac{t \cdot a}{c\_m}\\ \mathbf{else}:\\ \;\;\;\;9 \cdot \left(\frac{y}{c\_m} \cdot \frac{x}{z}\right)\\ \end{array} \end{array} \]

FPCore

c\_m = (fabs.f64 c)
c\_s = (copysign.f64 #s(literal 1 binary64) c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
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 (<= y -1.32e-11)
    (* 9.0 (* x (/ y (* z c_m))))
    (if (<= y -1.25e-206)
      (/ 1.0 (/ (/ (* c_m -0.25) t) a))
      (if (<= y 1.05e-267)
        (/ 1.0 (* c_m (/ z b)))
        (if (<= y 5.5e+63)
          (* -4.0 (/ (* t a) c_m))
          (* 9.0 (* (/ y c_m) (/ x 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 (y <= -1.32e-11) {
		tmp = 9.0 * (x * (y / (z * c_m)));
	} else if (y <= -1.25e-206) {
		tmp = 1.0 / (((c_m * -0.25) / t) / a);
	} else if (y <= 1.05e-267) {
		tmp = 1.0 / (c_m * (z / b));
	} else if (y <= 5.5e+63) {
		tmp = -4.0 * ((t * a) / c_m);
	} else {
		tmp = 9.0 * ((y / c_m) * (x / 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 (y <= (-1.32d-11)) then
        tmp = 9.0d0 * (x * (y / (z * c_m)))
    else if (y <= (-1.25d-206)) then
        tmp = 1.0d0 / (((c_m * (-0.25d0)) / t) / a)
    else if (y <= 1.05d-267) then
        tmp = 1.0d0 / (c_m * (z / b))
    else if (y <= 5.5d+63) then
        tmp = (-4.0d0) * ((t * a) / c_m)
    else
        tmp = 9.0d0 * ((y / c_m) * (x / 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 (y <= -1.32e-11) {
		tmp = 9.0 * (x * (y / (z * c_m)));
	} else if (y <= -1.25e-206) {
		tmp = 1.0 / (((c_m * -0.25) / t) / a);
	} else if (y <= 1.05e-267) {
		tmp = 1.0 / (c_m * (z / b));
	} else if (y <= 5.5e+63) {
		tmp = -4.0 * ((t * a) / c_m);
	} else {
		tmp = 9.0 * ((y / c_m) * (x / 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 y <= -1.32e-11:
		tmp = 9.0 * (x * (y / (z * c_m)))
	elif y <= -1.25e-206:
		tmp = 1.0 / (((c_m * -0.25) / t) / a)
	elif y <= 1.05e-267:
		tmp = 1.0 / (c_m * (z / b))
	elif y <= 5.5e+63:
		tmp = -4.0 * ((t * a) / c_m)
	else:
		tmp = 9.0 * ((y / c_m) * (x / 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 (y <= -1.32e-11)
		tmp = Float64(9.0 * Float64(x * Float64(y / Float64(z * c_m))));
	elseif (y <= -1.25e-206)
		tmp = Float64(1.0 / Float64(Float64(Float64(c_m * -0.25) / t) / a));
	elseif (y <= 1.05e-267)
		tmp = Float64(1.0 / Float64(c_m * Float64(z / b)));
	elseif (y <= 5.5e+63)
		tmp = Float64(-4.0 * Float64(Float64(t * a) / c_m));
	else
		tmp = Float64(9.0 * Float64(Float64(y / c_m) * Float64(x / 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 (y <= -1.32e-11)
		tmp = 9.0 * (x * (y / (z * c_m)));
	elseif (y <= -1.25e-206)
		tmp = 1.0 / (((c_m * -0.25) / t) / a);
	elseif (y <= 1.05e-267)
		tmp = 1.0 / (c_m * (z / b));
	elseif (y <= 5.5e+63)
		tmp = -4.0 * ((t * a) / c_m);
	else
		tmp = 9.0 * ((y / c_m) * (x / 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[y, -1.32e-11], N[(9.0 * N[(x * N[(y / N[(z * c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.25e-206], N[(1.0 / N[(N[(N[(c$95$m * -0.25), $MachinePrecision] / t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.05e-267], N[(1.0 / N[(c$95$m * N[(z / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.5e+63], N[(-4.0 * N[(N[(t * a), $MachinePrecision] / c$95$m), $MachinePrecision]), $MachinePrecision], N[(9.0 * N[(N[(y / c$95$m), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]), $MachinePrecision]

Derivation

1. Split input into 5 regimes

2. if y < -1.32e-11

   1. Initial program 72.3%

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

   3. Simplified 70.7%

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

   5. Taylor expanded in x around inf 44.6%

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

      1. associate-/l* 51.2%

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

      2. *-commutative 51.2%

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

   7. Simplified 51.2%

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

   if -1.32e-11 < y < -1.25e-206

   1. Initial program 93.1%

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

   3. Simplified 89.9%

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

   5. Taylor expanded in z around 0 82.5%

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

      1. clear-num 82.5%

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

      2. inv-pow 82.5%

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

      3. fma-define 82.5%

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

      4. associate-/l* 79.0%

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

      5. *-commutative 79.0%

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

      6. fma-define 79.0%

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

      7. associate-/l* 77.4%

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

   7. Applied egg-rr 77.4%

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

      1. unpow-1 77.4%

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

      2. associate-*r/ 80.2%

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

      3. *-commutative 80.2%

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

      4. associate-*r* 80.2%

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

   9. Simplified 80.2%

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

   10. Taylor expanded in z around inf 52.4%

       \[\leadsto \frac{1}{\color{blue}{-0.25 \cdot \frac{c}{a \cdot t}}} \]
   11. Step-by-step derivation

       1. associate-*r/ 52.4%

          \[\leadsto \frac{1}{\color{blue}{\frac{-0.25 \cdot c}{a \cdot t}}} \]

   12. Simplified 52.4%

       \[\leadsto \frac{1}{\color{blue}{\frac{-0.25 \cdot c}{a \cdot t}}} \]

   13. Taylor expanded in c around 0 52.4%

       \[\leadsto \frac{1}{\color{blue}{-0.25 \cdot \frac{c}{a \cdot t}}} \]
   14. Step-by-step derivation

       1. associate-*r/ 52.4%

          \[\leadsto \frac{1}{\color{blue}{\frac{-0.25 \cdot c}{a \cdot t}}} \]

       2. times-frac 57.2%

          \[\leadsto \frac{1}{\color{blue}{\frac{-0.25}{a} \cdot \frac{c}{t}}} \]

       3. associate-*l/ 57.3%

          \[\leadsto \frac{1}{\color{blue}{\frac{-0.25 \cdot \frac{c}{t}}{a}}} \]

       4. associate-*r/ 57.3%

          \[\leadsto \frac{1}{\frac{\color{blue}{\frac{-0.25 \cdot c}{t}}}{a}} \]

       5. *-commutative 57.3%

          \[\leadsto \frac{1}{\frac{\frac{\color{blue}{c \cdot -0.25}}{t}}{a}} \]

   15. Simplified 57.3%

       \[\leadsto \frac{1}{\color{blue}{\frac{\frac{c \cdot -0.25}{t}}{a}}} \]

   if -1.25e-206 < y < 1.0500000000000001e-267

   1. Initial program 83.7%

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

   3. Simplified 83.7%

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

   5. Taylor expanded in b around inf 68.0%

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

      1. *-commutative 68.0%

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

   7. Simplified 68.0%

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

   8. Taylor expanded in b around 0 68.0%

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

      1. associate-/r* 54.2%

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

   10. Simplified 54.2%

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

       1. clear-num 54.2%

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

       2. inv-pow 54.2%

          \[\leadsto \color{blue}{{\left(\frac{z}{\frac{b}{c}}\right)}^{-1}} \]

   12. Applied egg-rr 54.2%

       \[\leadsto \color{blue}{{\left(\frac{z}{\frac{b}{c}}\right)}^{-1}} \]
   13. Step-by-step derivation

       1. unpow-1 54.2%

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

       2. associate-/r/ 63.9%

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

   14. Simplified 63.9%

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

   if 1.0500000000000001e-267 < y < 5.50000000000000004e63

   1. Initial program 85.9%

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

   3. Simplified 86.8%

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

   5. Taylor expanded in t around inf 51.9%

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

   if 5.50000000000000004e63 < y

   1. Initial program 65.0%

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

   3. Simplified 71.8%

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

   5. Taylor expanded in x around inf 50.0%

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

      1. *-commutative 50.0%

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

      2. *-commutative 50.0%

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

      3. *-commutative 50.0%

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

      4. times-frac 63.5%

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

   7. Simplified 63.5%

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

4. Final simplification 56.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.32 \cdot 10^{-11}:\\ \;\;\;\;9 \cdot \left(x \cdot \frac{y}{z \cdot c}\right)\\ \mathbf{elif}\;y \leq -1.25 \cdot 10^{-206}:\\ \;\;\;\;\frac{1}{\frac{\frac{c \cdot -0.25}{t}}{a}}\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{-267}:\\ \;\;\;\;\frac{1}{c \cdot \frac{z}{b}}\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{+63}:\\ \;\;\;\;-4 \cdot \frac{t \cdot a}{c}\\ \mathbf{else}:\\ \;\;\;\;9 \cdot \left(\frac{y}{c} \cdot \frac{x}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 51.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\\\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ c\_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{-15}:\\ \;\;\;\;9 \cdot \left(x \cdot \frac{y}{z \cdot c\_m}\right)\\ \mathbf{elif}\;y \leq -3.2 \cdot 10^{-208}:\\ \;\;\;\;a \cdot \left(t \cdot \frac{-4}{c\_m}\right)\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{-268}:\\ \;\;\;\;\frac{1}{c\_m \cdot \frac{z}{b}}\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{+63}:\\ \;\;\;\;-4 \cdot \frac{t \cdot a}{c\_m}\\ \mathbf{else}:\\ \;\;\;\;9 \cdot \left(\frac{y}{c\_m} \cdot \frac{x}{z}\right)\\ \end{array} \end{array} \]

FPCore

c\_m = (fabs.f64 c)
c\_s = (copysign.f64 #s(literal 1 binary64) c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
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 (<= y -1.9e-15)
    (* 9.0 (* x (/ y (* z c_m))))
    (if (<= y -3.2e-208)
      (* a (* t (/ -4.0 c_m)))
      (if (<= y 3.1e-268)
        (/ 1.0 (* c_m (/ z b)))
        (if (<= y 8.2e+63)
          (* -4.0 (/ (* t a) c_m))
          (* 9.0 (* (/ y c_m) (/ x 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 (y <= -1.9e-15) {
		tmp = 9.0 * (x * (y / (z * c_m)));
	} else if (y <= -3.2e-208) {
		tmp = a * (t * (-4.0 / c_m));
	} else if (y <= 3.1e-268) {
		tmp = 1.0 / (c_m * (z / b));
	} else if (y <= 8.2e+63) {
		tmp = -4.0 * ((t * a) / c_m);
	} else {
		tmp = 9.0 * ((y / c_m) * (x / 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 (y <= (-1.9d-15)) then
        tmp = 9.0d0 * (x * (y / (z * c_m)))
    else if (y <= (-3.2d-208)) then
        tmp = a * (t * ((-4.0d0) / c_m))
    else if (y <= 3.1d-268) then
        tmp = 1.0d0 / (c_m * (z / b))
    else if (y <= 8.2d+63) then
        tmp = (-4.0d0) * ((t * a) / c_m)
    else
        tmp = 9.0d0 * ((y / c_m) * (x / 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 (y <= -1.9e-15) {
		tmp = 9.0 * (x * (y / (z * c_m)));
	} else if (y <= -3.2e-208) {
		tmp = a * (t * (-4.0 / c_m));
	} else if (y <= 3.1e-268) {
		tmp = 1.0 / (c_m * (z / b));
	} else if (y <= 8.2e+63) {
		tmp = -4.0 * ((t * a) / c_m);
	} else {
		tmp = 9.0 * ((y / c_m) * (x / 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 y <= -1.9e-15:
		tmp = 9.0 * (x * (y / (z * c_m)))
	elif y <= -3.2e-208:
		tmp = a * (t * (-4.0 / c_m))
	elif y <= 3.1e-268:
		tmp = 1.0 / (c_m * (z / b))
	elif y <= 8.2e+63:
		tmp = -4.0 * ((t * a) / c_m)
	else:
		tmp = 9.0 * ((y / c_m) * (x / 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 (y <= -1.9e-15)
		tmp = Float64(9.0 * Float64(x * Float64(y / Float64(z * c_m))));
	elseif (y <= -3.2e-208)
		tmp = Float64(a * Float64(t * Float64(-4.0 / c_m)));
	elseif (y <= 3.1e-268)
		tmp = Float64(1.0 / Float64(c_m * Float64(z / b)));
	elseif (y <= 8.2e+63)
		tmp = Float64(-4.0 * Float64(Float64(t * a) / c_m));
	else
		tmp = Float64(9.0 * Float64(Float64(y / c_m) * Float64(x / 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 (y <= -1.9e-15)
		tmp = 9.0 * (x * (y / (z * c_m)));
	elseif (y <= -3.2e-208)
		tmp = a * (t * (-4.0 / c_m));
	elseif (y <= 3.1e-268)
		tmp = 1.0 / (c_m * (z / b));
	elseif (y <= 8.2e+63)
		tmp = -4.0 * ((t * a) / c_m);
	else
		tmp = 9.0 * ((y / c_m) * (x / 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[y, -1.9e-15], N[(9.0 * N[(x * N[(y / N[(z * c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -3.2e-208], N[(a * N[(t * N[(-4.0 / c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.1e-268], N[(1.0 / N[(c$95$m * N[(z / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 8.2e+63], N[(-4.0 * N[(N[(t * a), $MachinePrecision] / c$95$m), $MachinePrecision]), $MachinePrecision], N[(9.0 * N[(N[(y / c$95$m), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]), $MachinePrecision]

Derivation

1. Split input into 5 regimes

2. if y < -1.9000000000000001e-15

   1. Initial program 72.7%

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

   3. Simplified 71.2%

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

   5. Taylor expanded in x around inf 43.9%

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

      1. associate-/l* 50.4%

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

      2. *-commutative 50.4%

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

   7. Simplified 50.4%

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

   if -1.9000000000000001e-15 < y < -3.2000000000000001e-208

   1. Initial program 93.0%

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

   3. Simplified 89.7%

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

   5. Taylor expanded in t around inf 51.2%

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

      1. *-commutative 51.2%

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

      2. associate-/l* 56.2%

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

      3. associate-*r* 56.2%

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

      4. *-commutative 56.2%

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

      5. *-commutative 56.2%

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

      6. associate-*l/ 56.2%

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

   7. Simplified 56.2%

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

      1. associate-/l* 56.2%

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

   9. Applied egg-rr 56.2%

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

   if -3.2000000000000001e-208 < y < 3.0999999999999998e-268

   1. Initial program 83.7%

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

   3. Simplified 83.7%

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

   5. Taylor expanded in b around inf 68.0%

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

      1. *-commutative 68.0%

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

   7. Simplified 68.0%

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

   8. Taylor expanded in b around 0 68.0%

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

      1. associate-/r* 54.2%

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

   10. Simplified 54.2%

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

       1. clear-num 54.2%

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

       2. inv-pow 54.2%

          \[\leadsto \color{blue}{{\left(\frac{z}{\frac{b}{c}}\right)}^{-1}} \]

   12. Applied egg-rr 54.2%

       \[\leadsto \color{blue}{{\left(\frac{z}{\frac{b}{c}}\right)}^{-1}} \]
   13. Step-by-step derivation

       1. unpow-1 54.2%

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

       2. associate-/r/ 63.9%

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

   14. Simplified 63.9%

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

   if 3.0999999999999998e-268 < y < 8.19999999999999985e63

   1. Initial program 85.9%

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

   3. Simplified 86.8%

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

   5. Taylor expanded in t around inf 51.9%

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

   if 8.19999999999999985e63 < y

   1. Initial program 65.0%

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

   3. Simplified 71.8%

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

   5. Taylor expanded in x around inf 50.0%

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

      1. *-commutative 50.0%

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

      2. *-commutative 50.0%

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

      3. *-commutative 50.0%

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

      4. times-frac 63.5%

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

   7. Simplified 63.5%

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

4. Final simplification 55.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{-15}:\\ \;\;\;\;9 \cdot \left(x \cdot \frac{y}{z \cdot c}\right)\\ \mathbf{elif}\;y \leq -3.2 \cdot 10^{-208}:\\ \;\;\;\;a \cdot \left(t \cdot \frac{-4}{c}\right)\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{-268}:\\ \;\;\;\;\frac{1}{c \cdot \frac{z}{b}}\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{+63}:\\ \;\;\;\;-4 \cdot \frac{t \cdot a}{c}\\ \mathbf{else}:\\ \;\;\;\;9 \cdot \left(\frac{y}{c} \cdot \frac{x}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 67.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\\\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ c\_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -3.1 \cdot 10^{-9}:\\ \;\;\;\;9 \cdot \left(x \cdot \frac{y}{z \cdot c\_m}\right)\\ \mathbf{elif}\;y \leq 2 \cdot 10^{+68}:\\ \;\;\;\;\frac{b + z \cdot \left(a \cdot \left(t \cdot -4\right)\right)}{z \cdot c\_m}\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{+196}:\\ \;\;\;\;\frac{\left(x \cdot 9\right) \cdot y + b}{z \cdot c\_m}\\ \mathbf{else}:\\ \;\;\;\;9 \cdot \left(\frac{y}{c\_m} \cdot \frac{x}{z}\right)\\ \end{array} \end{array} \]

FPCore

c\_m = (fabs.f64 c)
c\_s = (copysign.f64 #s(literal 1 binary64) c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
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 (<= y -3.1e-9)
    (* 9.0 (* x (/ y (* z c_m))))
    (if (<= y 2e+68)
      (/ (+ b (* z (* a (* t -4.0)))) (* z c_m))
      (if (<= y 2.2e+196)
        (/ (+ (* (* x 9.0) y) b) (* z c_m))
        (* 9.0 (* (/ y c_m) (/ x 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 (y <= -3.1e-9) {
		tmp = 9.0 * (x * (y / (z * c_m)));
	} else if (y <= 2e+68) {
		tmp = (b + (z * (a * (t * -4.0)))) / (z * c_m);
	} else if (y <= 2.2e+196) {
		tmp = (((x * 9.0) * y) + b) / (z * c_m);
	} else {
		tmp = 9.0 * ((y / c_m) * (x / 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 (y <= (-3.1d-9)) then
        tmp = 9.0d0 * (x * (y / (z * c_m)))
    else if (y <= 2d+68) then
        tmp = (b + (z * (a * (t * (-4.0d0))))) / (z * c_m)
    else if (y <= 2.2d+196) then
        tmp = (((x * 9.0d0) * y) + b) / (z * c_m)
    else
        tmp = 9.0d0 * ((y / c_m) * (x / 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 (y <= -3.1e-9) {
		tmp = 9.0 * (x * (y / (z * c_m)));
	} else if (y <= 2e+68) {
		tmp = (b + (z * (a * (t * -4.0)))) / (z * c_m);
	} else if (y <= 2.2e+196) {
		tmp = (((x * 9.0) * y) + b) / (z * c_m);
	} else {
		tmp = 9.0 * ((y / c_m) * (x / 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 y <= -3.1e-9:
		tmp = 9.0 * (x * (y / (z * c_m)))
	elif y <= 2e+68:
		tmp = (b + (z * (a * (t * -4.0)))) / (z * c_m)
	elif y <= 2.2e+196:
		tmp = (((x * 9.0) * y) + b) / (z * c_m)
	else:
		tmp = 9.0 * ((y / c_m) * (x / 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 (y <= -3.1e-9)
		tmp = Float64(9.0 * Float64(x * Float64(y / Float64(z * c_m))));
	elseif (y <= 2e+68)
		tmp = Float64(Float64(b + Float64(z * Float64(a * Float64(t * -4.0)))) / Float64(z * c_m));
	elseif (y <= 2.2e+196)
		tmp = Float64(Float64(Float64(Float64(x * 9.0) * y) + b) / Float64(z * c_m));
	else
		tmp = Float64(9.0 * Float64(Float64(y / c_m) * Float64(x / 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 (y <= -3.1e-9)
		tmp = 9.0 * (x * (y / (z * c_m)));
	elseif (y <= 2e+68)
		tmp = (b + (z * (a * (t * -4.0)))) / (z * c_m);
	elseif (y <= 2.2e+196)
		tmp = (((x * 9.0) * y) + b) / (z * c_m);
	else
		tmp = 9.0 * ((y / c_m) * (x / 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[y, -3.1e-9], N[(9.0 * N[(x * N[(y / N[(z * c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2e+68], N[(N[(b + N[(z * N[(a * N[(t * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c$95$m), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.2e+196], N[(N[(N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision] + b), $MachinePrecision] / N[(z * c$95$m), $MachinePrecision]), $MachinePrecision], N[(9.0 * N[(N[(y / c$95$m), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]), $MachinePrecision]

Derivation

1. Split input into 4 regimes

2. if y < -3.10000000000000005e-9

   1. Initial program 72.3%

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

   3. Simplified 70.7%

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

   5. Taylor expanded in x around inf 44.6%

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

      1. associate-/l* 51.2%

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

      2. *-commutative 51.2%

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

   7. Simplified 51.2%

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

   if -3.10000000000000005e-9 < y < 1.99999999999999991e68

   1. Initial program 87.6%

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

   3. Simplified 87.2%

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

   5. Taylor expanded in x around inf 83.4%

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

      1. +-commutative 83.4%

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

      2. fma-define 83.4%

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

      3. *-commutative 83.4%

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

      4. associate-/l* 79.0%

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

      5. associate-*l* 79.0%

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

      6. *-commutative 79.0%

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

      7. associate-/l* 77.3%

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

   7. Simplified 77.3%

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

   8. Taylor expanded in x around 0 77.7%

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

      1. *-commutative 77.7%

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

      2. *-commutative 77.7%

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

      3. associate-*r* 78.3%

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

      4. *-commutative 78.3%

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

      5. associate-*l* 78.8%

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

      6. associate-*r* 78.8%

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

      7. *-commutative 78.8%

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

      8. associate-*r* 78.8%

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

      9. *-commutative 78.8%

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

      10. associate-*l* 78.8%

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

   10. Simplified 78.8%

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

   if 1.99999999999999991e68 < y < 2.19999999999999998e196

   1. Initial program 77.8%

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

   3. Simplified 81.2%

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

   5. Taylor expanded in x around inf 74.7%

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

      1. +-commutative 74.7%

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

      2. fma-define 74.7%

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

      3. *-commutative 74.7%

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

      4. associate-/l* 73.7%

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

      5. associate-*l* 73.7%

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

      6. *-commutative 73.7%

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

      7. associate-/l* 77.1%

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

   7. Simplified 77.1%

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

   8. Taylor expanded in x around inf 68.3%

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

      1. *-commutative 68.3%

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

      2. associate-*r* 68.4%

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

      3. *-commutative 68.4%

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

      4. associate-*r* 68.3%

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

   10. Simplified 68.3%

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

   if 2.19999999999999998e196 < y

   1. Initial program 51.3%

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

   3. Simplified 61.8%

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

   5. Taylor expanded in x around inf 48.0%

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

      1. *-commutative 48.0%

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

      2. *-commutative 48.0%

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

      3. *-commutative 48.0%

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

      4. times-frac 72.1%

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

   7. Simplified 72.1%

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

4. Final simplification 70.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.1 \cdot 10^{-9}:\\ \;\;\;\;9 \cdot \left(x \cdot \frac{y}{z \cdot c}\right)\\ \mathbf{elif}\;y \leq 2 \cdot 10^{+68}:\\ \;\;\;\;\frac{b + z \cdot \left(a \cdot \left(t \cdot -4\right)\right)}{z \cdot c}\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{+196}:\\ \;\;\;\;\frac{\left(x \cdot 9\right) \cdot y + b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;9 \cdot \left(\frac{y}{c} \cdot \frac{x}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 72.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\\\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ c\_s \cdot \begin{array}{l} \mathbf{if}\;b \leq -2.3 \cdot 10^{-92}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c\_m}\\ \mathbf{elif}\;b \leq 1.75 \cdot 10^{+68}:\\ \;\;\;\;\frac{9 \cdot \frac{x \cdot y}{z} - 4 \cdot \left(t \cdot a\right)}{c\_m}\\ \mathbf{else}:\\ \;\;\;\;\frac{b - 4 \cdot \left(a \cdot \left(z \cdot t\right)\right)}{z \cdot c\_m}\\ \end{array} \end{array} \]

FPCore

c\_m = (fabs.f64 c)
c\_s = (copysign.f64 #s(literal 1 binary64) c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
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-92)
    (/ (+ b (* 9.0 (* x y))) (* z c_m))
    (if (<= b 1.75e+68)
      (/ (- (* 9.0 (/ (* x y) z)) (* 4.0 (* t a))) c_m)
      (/ (- b (* 4.0 (* a (* z t)))) (* z c_m))))))

C

c\_m = fabs(c);
c\_s = copysign(1.0, c);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
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-92) {
		tmp = (b + (9.0 * (x * y))) / (z * c_m);
	} else if (b <= 1.75e+68) {
		tmp = ((9.0 * ((x * y) / z)) - (4.0 * (t * a))) / c_m;
	} else {
		tmp = (b - (4.0 * (a * (z * t)))) / (z * c_m);
	}
	return c_s * tmp;
}

Fortran

c\_m = abs(c)
c\_s = copysign(1.0d0, c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
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-92)) then
        tmp = (b + (9.0d0 * (x * y))) / (z * c_m)
    else if (b <= 1.75d+68) then
        tmp = ((9.0d0 * ((x * y) / z)) - (4.0d0 * (t * a))) / c_m
    else
        tmp = (b - (4.0d0 * (a * (z * t)))) / (z * c_m)
    end if
    code = c_s * tmp
end function

Java

c\_m = Math.abs(c);
c\_s = Math.copySign(1.0, c);
assert x < y && y < z && z < t && t < a && a < b && b < c_m;
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-92) {
		tmp = (b + (9.0 * (x * y))) / (z * c_m);
	} else if (b <= 1.75e+68) {
		tmp = ((9.0 * ((x * y) / z)) - (4.0 * (t * a))) / c_m;
	} else {
		tmp = (b - (4.0 * (a * (z * t)))) / (z * c_m);
	}
	return c_s * tmp;
}

Python

c\_m = math.fabs(c)
c\_s = math.copysign(1.0, c)
[x, y, z, t, a, b, c_m] = sort([x, y, z, t, a, b, c_m])
[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-92:
		tmp = (b + (9.0 * (x * y))) / (z * c_m)
	elif b <= 1.75e+68:
		tmp = ((9.0 * ((x * y) / z)) - (4.0 * (t * a))) / c_m
	else:
		tmp = (b - (4.0 * (a * (z * t)))) / (z * c_m)
	return c_s * tmp

Julia

c\_m = abs(c)
c\_s = copysign(1.0, c)
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
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-92)
		tmp = Float64(Float64(b + Float64(9.0 * Float64(x * y))) / Float64(z * c_m));
	elseif (b <= 1.75e+68)
		tmp = Float64(Float64(Float64(9.0 * Float64(Float64(x * y) / z)) - Float64(4.0 * Float64(t * a))) / c_m);
	else
		tmp = Float64(Float64(b - Float64(4.0 * Float64(a * Float64(z * t)))) / Float64(z * c_m));
	end
	return Float64(c_s * tmp)
end

MATLAB

c\_m = abs(c);
c\_s = sign(c) * abs(1.0);
x, y, z, t, a, b, c_m = num2cell(sort([x, y, z, t, a, b, c_m])){:}
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-92)
		tmp = (b + (9.0 * (x * y))) / (z * c_m);
	elseif (b <= 1.75e+68)
		tmp = ((9.0 * ((x * y) / z)) - (4.0 * (t * a))) / c_m;
	else
		tmp = (b - (4.0 * (a * (z * t)))) / (z * c_m);
	end
	tmp_2 = c_s * tmp;
end

Wolfram

c\_m = N[Abs[c], $MachinePrecision]
c\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
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-92], N[(N[(b + N[(9.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c$95$m), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.75e+68], N[(N[(N[(9.0 * N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] - N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c$95$m), $MachinePrecision], N[(N[(b - N[(4.0 * N[(a * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c$95$m), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if b < -2.30000000000000016e-92

   1. Initial program 73.3%

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

   3. Simplified 74.6%

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

   5. Taylor expanded in t around 0 67.5%

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

      1. +-commutative 67.5%

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

      2. *-commutative 67.5%

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

   7. Simplified 67.5%

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

   if -2.30000000000000016e-92 < b < 1.74999999999999989e68

   1. Initial program 80.1%

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

      1. associate-+l- 80.1%

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

      2. *-commutative 80.1%

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

      3. associate-*r* 79.0%

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

      4. *-commutative 79.0%

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

      5. associate-+l- 79.0%

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

      6. associate-*l* 79.1%

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

      7. associate-*l* 80.6%

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

      8. *-commutative 80.6%

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

   3. Simplified 80.6%

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

   5. Taylor expanded in z around inf 79.9%

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

   6. Taylor expanded in b around 0 78.8%

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

   if 1.74999999999999989e68 < b

   1. Initial program 83.6%

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

      1. associate-+l- 83.6%

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

      2. *-commutative 83.6%

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

      3. associate-*r* 85.3%

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

      4. *-commutative 85.3%

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

      5. associate-+l- 85.3%

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

      6. associate-*l* 85.3%

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

      7. associate-*l* 83.5%

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

      8. *-commutative 83.5%

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

   3. Simplified 83.5%

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

   5. Taylor expanded in x around 0 79.3%

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

4. Final simplification 75.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.3 \cdot 10^{-92}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \mathbf{elif}\;b \leq 1.75 \cdot 10^{+68}:\\ \;\;\;\;\frac{9 \cdot \frac{x \cdot y}{z} - 4 \cdot \left(t \cdot a\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b - 4 \cdot \left(a \cdot \left(z \cdot t\right)\right)}{z \cdot c}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 49.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\\\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ c\_s \cdot \begin{array}{l} \mathbf{if}\;x \leq -1.34 \cdot 10^{+73}:\\ \;\;\;\;9 \cdot \left(x \cdot \frac{y}{z \cdot c\_m}\right)\\ \mathbf{elif}\;x \leq -7 \cdot 10^{-94}:\\ \;\;\;\;-4 \cdot \frac{t \cdot a}{c\_m}\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{-83}:\\ \;\;\;\;b \cdot \frac{1}{z \cdot c\_m}\\ \mathbf{else}:\\ \;\;\;\;9 \cdot \left(y \cdot \frac{\frac{x}{c\_m}}{z}\right)\\ \end{array} \end{array} \]

FPCore

c\_m = (fabs.f64 c)
c\_s = (copysign.f64 #s(literal 1 binary64) c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
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 (<= x -1.34e+73)
    (* 9.0 (* x (/ y (* z c_m))))
    (if (<= x -7e-94)
      (* -4.0 (/ (* t a) c_m))
      (if (<= x 4.2e-83)
        (* b (/ 1.0 (* z c_m)))
        (* 9.0 (* y (/ (/ x 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 (x <= -1.34e+73) {
		tmp = 9.0 * (x * (y / (z * c_m)));
	} else if (x <= -7e-94) {
		tmp = -4.0 * ((t * a) / c_m);
	} else if (x <= 4.2e-83) {
		tmp = b * (1.0 / (z * c_m));
	} else {
		tmp = 9.0 * (y * ((x / 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 (x <= (-1.34d+73)) then
        tmp = 9.0d0 * (x * (y / (z * c_m)))
    else if (x <= (-7d-94)) then
        tmp = (-4.0d0) * ((t * a) / c_m)
    else if (x <= 4.2d-83) then
        tmp = b * (1.0d0 / (z * c_m))
    else
        tmp = 9.0d0 * (y * ((x / 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 (x <= -1.34e+73) {
		tmp = 9.0 * (x * (y / (z * c_m)));
	} else if (x <= -7e-94) {
		tmp = -4.0 * ((t * a) / c_m);
	} else if (x <= 4.2e-83) {
		tmp = b * (1.0 / (z * c_m));
	} else {
		tmp = 9.0 * (y * ((x / 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 x <= -1.34e+73:
		tmp = 9.0 * (x * (y / (z * c_m)))
	elif x <= -7e-94:
		tmp = -4.0 * ((t * a) / c_m)
	elif x <= 4.2e-83:
		tmp = b * (1.0 / (z * c_m))
	else:
		tmp = 9.0 * (y * ((x / 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 (x <= -1.34e+73)
		tmp = Float64(9.0 * Float64(x * Float64(y / Float64(z * c_m))));
	elseif (x <= -7e-94)
		tmp = Float64(-4.0 * Float64(Float64(t * a) / c_m));
	elseif (x <= 4.2e-83)
		tmp = Float64(b * Float64(1.0 / Float64(z * c_m)));
	else
		tmp = Float64(9.0 * Float64(y * Float64(Float64(x / 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 (x <= -1.34e+73)
		tmp = 9.0 * (x * (y / (z * c_m)));
	elseif (x <= -7e-94)
		tmp = -4.0 * ((t * a) / c_m);
	elseif (x <= 4.2e-83)
		tmp = b * (1.0 / (z * c_m));
	else
		tmp = 9.0 * (y * ((x / 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[x, -1.34e+73], N[(9.0 * N[(x * N[(y / N[(z * c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -7e-94], N[(-4.0 * N[(N[(t * a), $MachinePrecision] / c$95$m), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4.2e-83], N[(b * N[(1.0 / N[(z * c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(9.0 * N[(y * N[(N[(x / c$95$m), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]), $MachinePrecision]

Derivation

1. Split input into 4 regimes

2. if x < -1.34e73

   1. Initial program 78.4%

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

   3. Simplified 78.5%

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

   5. Taylor expanded in x around inf 54.2%

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

      1. associate-/l* 58.9%

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

      2. *-commutative 58.9%

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

   7. Simplified 58.9%

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

   if -1.34e73 < x < -6.99999999999999996e-94

   1. Initial program 75.4%

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

   3. Simplified 77.3%

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

   5. Taylor expanded in t around inf 47.2%

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

   if -6.99999999999999996e-94 < x < 4.1999999999999998e-83

   1. Initial program 83.4%

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

   3. Simplified 84.1%

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

   5. Taylor expanded in b around inf 54.7%

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

      1. *-commutative 54.7%

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

   7. Simplified 54.7%

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

      1. div-inv 54.7%

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

   9. Applied egg-rr 54.7%

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

   if 4.1999999999999998e-83 < x

   1. Initial program 75.5%

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

   3. Simplified 76.9%

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

   5. Taylor expanded in z around 0 67.6%

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

      1. clear-num 67.6%

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

      2. inv-pow 67.6%

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

      3. fma-define 67.6%

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

      4. associate-/l* 68.8%

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

      5. *-commutative 68.8%

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

      6. fma-define 68.8%

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

      7. associate-/l* 78.1%

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

   7. Applied egg-rr 78.1%

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

      1. unpow-1 78.1%

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

      2. associate-*r/ 76.8%

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

      3. *-commutative 76.8%

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

      4. associate-*r* 75.5%

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

   9. Simplified 75.5%

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

   10. Taylor expanded in x around inf 42.9%

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

       1. *-commutative 42.9%

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

       2. *-commutative 42.9%

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

       3. associate-/l* 50.9%

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

       4. *-commutative 50.9%

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

       5. associate-/r* 52.3%

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

   12. Simplified 52.3%

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

4. Final simplification 53.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.34 \cdot 10^{+73}:\\ \;\;\;\;9 \cdot \left(x \cdot \frac{y}{z \cdot c}\right)\\ \mathbf{elif}\;x \leq -7 \cdot 10^{-94}:\\ \;\;\;\;-4 \cdot \frac{t \cdot a}{c}\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{-83}:\\ \;\;\;\;b \cdot \frac{1}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;9 \cdot \left(y \cdot \frac{\frac{x}{c}}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 78.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\\\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ c\_s \cdot \begin{array}{l} \mathbf{if}\;y \leq 3.2 \cdot 10^{+198}:\\ \;\;\;\;\frac{b + \left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right)}{z \cdot c\_m}\\ \mathbf{else}:\\ \;\;\;\;9 \cdot \left(\frac{y}{z} \cdot \frac{x}{c\_m}\right)\\ \end{array} \end{array} \]

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 (<= y 3.2e+198)
    (/ (+ b (- (* x (* 9.0 y)) (* (* z 4.0) (* t a)))) (* z c_m))
    (* 9.0 (* (/ y z) (/ x 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 tmp;
	if (y <= 3.2e+198) {
		tmp = (b + ((x * (9.0 * y)) - ((z * 4.0) * (t * a)))) / (z * c_m);
	} else {
		tmp = 9.0 * ((y / z) * (x / c_m));
	}
	return c_s * tmp;
}

Fortran

c\_m = abs(c)
c\_s = copysign(1.0d0, c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
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 (y <= 3.2d+198) then
        tmp = (b + ((x * (9.0d0 * y)) - ((z * 4.0d0) * (t * a)))) / (z * c_m)
    else
        tmp = 9.0d0 * ((y / z) * (x / c_m))
    end if
    code = c_s * tmp
end function

Java

c\_m = Math.abs(c);
c\_s = Math.copySign(1.0, c);
assert x < y && y < z && z < t && t < a && a < b && b < c_m;
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 (y <= 3.2e+198) {
		tmp = (b + ((x * (9.0 * y)) - ((z * 4.0) * (t * a)))) / (z * c_m);
	} else {
		tmp = 9.0 * ((y / z) * (x / c_m));
	}
	return c_s * tmp;
}

Python

c\_m = math.fabs(c)
c\_s = math.copysign(1.0, c)
[x, y, z, t, a, b, c_m] = sort([x, y, z, t, a, b, c_m])
[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 y <= 3.2e+198:
		tmp = (b + ((x * (9.0 * y)) - ((z * 4.0) * (t * a)))) / (z * c_m)
	else:
		tmp = 9.0 * ((y / z) * (x / 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)
	tmp = 0.0
	if (y <= 3.2e+198)
		tmp = Float64(Float64(b + Float64(Float64(x * Float64(9.0 * y)) - Float64(Float64(z * 4.0) * Float64(t * a)))) / Float64(z * c_m));
	else
		tmp = Float64(9.0 * Float64(Float64(y / z) * Float64(x / c_m)));
	end
	return Float64(c_s * tmp)
end

MATLAB

c\_m = abs(c);
c\_s = sign(c) * abs(1.0);
x, y, z, t, a, b, c_m = num2cell(sort([x, y, z, t, a, b, c_m])){:}
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 (y <= 3.2e+198)
		tmp = (b + ((x * (9.0 * y)) - ((z * 4.0) * (t * a)))) / (z * c_m);
	else
		tmp = 9.0 * ((y / z) * (x / c_m));
	end
	tmp_2 = c_s * tmp;
end

Wolfram

c\_m = N[Abs[c], $MachinePrecision]
c\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
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[y, 3.2e+198], N[(N[(b + N[(N[(x * N[(9.0 * y), $MachinePrecision]), $MachinePrecision] - N[(N[(z * 4.0), $MachinePrecision] * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c$95$m), $MachinePrecision]), $MachinePrecision], N[(9.0 * N[(N[(y / z), $MachinePrecision] * N[(x / c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if y < 3.1999999999999998e198

   1. Initial program 82.0%

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

      1. associate-+l- 82.0%

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

      2. *-commutative 82.0%

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

      3. associate-*r* 81.7%

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

      4. *-commutative 81.7%

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

      5. associate-+l- 81.7%

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

      6. associate-*l* 81.7%

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

      7. associate-*l* 81.4%

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

      8. *-commutative 81.4%

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

   3. Simplified 81.4%

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

   if 3.1999999999999998e198 < y

   1. Initial program 53.0%

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

   3. Simplified 63.9%

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

   5. Taylor expanded in x around inf 60.6%

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

      1. +-commutative 60.6%

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

      2. fma-define 60.6%

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

      3. *-commutative 60.6%

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

      4. associate-/l* 57.1%

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

      5. associate-*l* 57.1%

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

      6. *-commutative 57.1%

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

      7. associate-/l* 60.8%

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

   7. Simplified 60.8%

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

   8. Taylor expanded in x around inf 49.6%

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

      1. times-frac 67.5%

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

      2. *-commutative 67.5%

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

   10. Simplified 67.5%

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

4. Final simplification 79.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 3.2 \cdot 10^{+198}:\\ \;\;\;\;\frac{b + \left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;9 \cdot \left(\frac{y}{z} \cdot \frac{x}{c}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 48.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\\\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ c\_s \cdot \begin{array}{l} \mathbf{if}\;b \leq -2.9 \cdot 10^{-77}:\\ \;\;\;\;b \cdot \frac{1}{z \cdot c\_m}\\ \mathbf{elif}\;b \leq -2.25 \cdot 10^{-187}:\\ \;\;\;\;9 \cdot \left(x \cdot \frac{y}{z \cdot c\_m}\right)\\ \mathbf{elif}\;b \leq 1.65 \cdot 10^{+81}:\\ \;\;\;\;-4 \cdot \frac{t \cdot a}{c\_m}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{c\_m}}{z}\\ \end{array} \end{array} \]

FPCore

c\_m = (fabs.f64 c)
c\_s = (copysign.f64 #s(literal 1 binary64) c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
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 -2.9e-77)
    (* b (/ 1.0 (* z c_m)))
    (if (<= b -2.25e-187)
      (* 9.0 (* x (/ y (* z c_m))))
      (if (<= b 1.65e+81) (* -4.0 (/ (* t a) c_m)) (/ (/ b c_m) z))))))

C

c\_m = fabs(c);
c\_s = copysign(1.0, c);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
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 <= -2.9e-77) {
		tmp = b * (1.0 / (z * c_m));
	} else if (b <= -2.25e-187) {
		tmp = 9.0 * (x * (y / (z * c_m)));
	} else if (b <= 1.65e+81) {
		tmp = -4.0 * ((t * a) / c_m);
	} else {
		tmp = (b / c_m) / z;
	}
	return c_s * tmp;
}

Fortran

c\_m = abs(c)
c\_s = copysign(1.0d0, c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
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 <= (-2.9d-77)) then
        tmp = b * (1.0d0 / (z * c_m))
    else if (b <= (-2.25d-187)) then
        tmp = 9.0d0 * (x * (y / (z * c_m)))
    else if (b <= 1.65d+81) then
        tmp = (-4.0d0) * ((t * a) / c_m)
    else
        tmp = (b / c_m) / z
    end if
    code = c_s * tmp
end function

Java

c\_m = Math.abs(c);
c\_s = Math.copySign(1.0, c);
assert x < y && y < z && z < t && t < a && a < b && b < c_m;
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 <= -2.9e-77) {
		tmp = b * (1.0 / (z * c_m));
	} else if (b <= -2.25e-187) {
		tmp = 9.0 * (x * (y / (z * c_m)));
	} else if (b <= 1.65e+81) {
		tmp = -4.0 * ((t * a) / c_m);
	} else {
		tmp = (b / c_m) / z;
	}
	return c_s * tmp;
}

Python

c\_m = math.fabs(c)
c\_s = math.copysign(1.0, c)
[x, y, z, t, a, b, c_m] = sort([x, y, z, t, a, b, c_m])
[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 <= -2.9e-77:
		tmp = b * (1.0 / (z * c_m))
	elif b <= -2.25e-187:
		tmp = 9.0 * (x * (y / (z * c_m)))
	elif b <= 1.65e+81:
		tmp = -4.0 * ((t * a) / c_m)
	else:
		tmp = (b / c_m) / z
	return c_s * tmp

Julia

c\_m = abs(c)
c\_s = copysign(1.0, c)
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
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 <= -2.9e-77)
		tmp = Float64(b * Float64(1.0 / Float64(z * c_m)));
	elseif (b <= -2.25e-187)
		tmp = Float64(9.0 * Float64(x * Float64(y / Float64(z * c_m))));
	elseif (b <= 1.65e+81)
		tmp = Float64(-4.0 * Float64(Float64(t * a) / c_m));
	else
		tmp = Float64(Float64(b / c_m) / z);
	end
	return Float64(c_s * tmp)
end

MATLAB

c\_m = abs(c);
c\_s = sign(c) * abs(1.0);
x, y, z, t, a, b, c_m = num2cell(sort([x, y, z, t, a, b, c_m])){:}
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 <= -2.9e-77)
		tmp = b * (1.0 / (z * c_m));
	elseif (b <= -2.25e-187)
		tmp = 9.0 * (x * (y / (z * c_m)));
	elseif (b <= 1.65e+81)
		tmp = -4.0 * ((t * a) / c_m);
	else
		tmp = (b / c_m) / z;
	end
	tmp_2 = c_s * tmp;
end

Wolfram

c\_m = N[Abs[c], $MachinePrecision]
c\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
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, -2.9e-77], N[(b * N[(1.0 / N[(z * c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -2.25e-187], N[(9.0 * N[(x * N[(y / N[(z * c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.65e+81], N[(-4.0 * N[(N[(t * a), $MachinePrecision] / c$95$m), $MachinePrecision]), $MachinePrecision], N[(N[(b / c$95$m), $MachinePrecision] / z), $MachinePrecision]]]]), $MachinePrecision]

Derivation

1. Split input into 4 regimes

2. if b < -2.8999999999999999e-77

   1. Initial program 71.7%

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

   3. Simplified 73.1%

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

   5. Taylor expanded in b around inf 47.2%

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

      1. *-commutative 47.2%

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

   7. Simplified 47.2%

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

      1. div-inv 47.2%

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

   9. Applied egg-rr 47.2%

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

   if -2.8999999999999999e-77 < b < -2.2499999999999999e-187

   1. Initial program 84.1%

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

   3. Simplified 80.9%

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

   5. Taylor expanded in x around inf 59.6%

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

      1. associate-/l* 60.1%

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

      2. *-commutative 60.1%

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

   7. Simplified 60.1%

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

   if -2.2499999999999999e-187 < b < 1.65e81

   1. Initial program 79.9%

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

   3. Simplified 81.4%

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

   5. Taylor expanded in t around inf 55.7%

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

   if 1.65e81 < b

   1. Initial program 83.3%

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

   3. Simplified 85.0%

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

   5. Taylor expanded in b around inf 71.4%

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

      1. *-commutative 71.4%

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

   7. Simplified 71.4%

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

   8. Taylor expanded in b around 0 71.4%

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

      1. associate-/r* 74.2%

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

   10. Simplified 74.2%

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

4. Final simplification 57.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.9 \cdot 10^{-77}:\\ \;\;\;\;b \cdot \frac{1}{z \cdot c}\\ \mathbf{elif}\;b \leq -2.25 \cdot 10^{-187}:\\ \;\;\;\;9 \cdot \left(x \cdot \frac{y}{z \cdot c}\right)\\ \mathbf{elif}\;b \leq 1.65 \cdot 10^{+81}:\\ \;\;\;\;-4 \cdot \frac{t \cdot a}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 68.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\\\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ c\_s \cdot \begin{array}{l} \mathbf{if}\;t \leq -3.4 \cdot 10^{+185}:\\ \;\;\;\;a \cdot \frac{t \cdot -4}{c\_m}\\ \mathbf{elif}\;t \leq 10^{-64}:\\ \;\;\;\;\frac{\left(x \cdot 9\right) \cdot y + b}{z \cdot c\_m}\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(t \cdot \frac{-4}{c\_m}\right)\\ \end{array} \end{array} \]

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 -3.4e+185)
    (* a (/ (* t -4.0) c_m))
    (if (<= t 1e-64)
      (/ (+ (* (* x 9.0) y) b) (* z c_m))
      (* 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 tmp;
	if (t <= -3.4e+185) {
		tmp = a * ((t * -4.0) / c_m);
	} else if (t <= 1e-64) {
		tmp = (((x * 9.0) * y) + b) / (z * c_m);
	} else {
		tmp = a * (t * (-4.0 / c_m));
	}
	return c_s * tmp;
}

Fortran

c\_m = abs(c)
c\_s = copysign(1.0d0, c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
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 (t <= (-3.4d+185)) then
        tmp = a * ((t * (-4.0d0)) / c_m)
    else if (t <= 1d-64) then
        tmp = (((x * 9.0d0) * y) + b) / (z * c_m)
    else
        tmp = a * (t * ((-4.0d0) / c_m))
    end if
    code = c_s * tmp
end function

Java

c\_m = Math.abs(c);
c\_s = Math.copySign(1.0, c);
assert x < y && y < z && z < t && t < a && a < b && b < c_m;
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 (t <= -3.4e+185) {
		tmp = a * ((t * -4.0) / c_m);
	} else if (t <= 1e-64) {
		tmp = (((x * 9.0) * y) + b) / (z * c_m);
	} else {
		tmp = a * (t * (-4.0 / c_m));
	}
	return c_s * tmp;
}

Python

c\_m = math.fabs(c)
c\_s = math.copysign(1.0, c)
[x, y, z, t, a, b, c_m] = sort([x, y, z, t, a, b, c_m])
[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 t <= -3.4e+185:
		tmp = a * ((t * -4.0) / c_m)
	elif t <= 1e-64:
		tmp = (((x * 9.0) * y) + b) / (z * c_m)
	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)
	tmp = 0.0
	if (t <= -3.4e+185)
		tmp = Float64(a * Float64(Float64(t * -4.0) / c_m));
	elseif (t <= 1e-64)
		tmp = Float64(Float64(Float64(Float64(x * 9.0) * y) + b) / Float64(z * c_m));
	else
		tmp = Float64(a * Float64(t * Float64(-4.0 / c_m)));
	end
	return Float64(c_s * tmp)
end

MATLAB

c\_m = abs(c);
c\_s = sign(c) * abs(1.0);
x, y, z, t, a, b, c_m = num2cell(sort([x, y, z, t, a, b, c_m])){:}
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 (t <= -3.4e+185)
		tmp = a * ((t * -4.0) / c_m);
	elseif (t <= 1e-64)
		tmp = (((x * 9.0) * y) + b) / (z * c_m);
	else
		tmp = a * (t * (-4.0 / c_m));
	end
	tmp_2 = c_s * tmp;
end

Wolfram

c\_m = N[Abs[c], $MachinePrecision]
c\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
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, -3.4e+185], N[(a * N[(N[(t * -4.0), $MachinePrecision] / c$95$m), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1e-64], N[(N[(N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision] + b), $MachinePrecision] / N[(z * c$95$m), $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 t < -3.40000000000000017e185

   1. Initial program 73.6%

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

   3. Simplified 81.3%

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

   5. Taylor expanded in t around inf 70.0%

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

      1. *-commutative 70.0%

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

      2. associate-/l* 66.6%

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

      3. associate-*r* 66.6%

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

      4. *-commutative 66.6%

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

      5. *-commutative 66.6%

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

      6. associate-*l/ 66.6%

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

   7. Simplified 66.6%

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

   if -3.40000000000000017e185 < t < 9.99999999999999965e-65

   1. Initial program 82.5%

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

   3. Simplified 80.1%

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

   5. Taylor expanded in x around inf 77.2%

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

      1. +-commutative 77.2%

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

      2. fma-define 77.2%

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

      3. *-commutative 77.2%

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

      4. associate-/l* 73.6%

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

      5. associate-*l* 73.6%

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

      6. *-commutative 73.6%

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

      7. associate-/l* 73.3%

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

   7. Simplified 73.3%

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

   8. Taylor expanded in x around inf 67.1%

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

      1. *-commutative 67.1%

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

      2. associate-*r* 67.1%

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

      3. *-commutative 67.1%

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

      4. associate-*r* 67.1%

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

   10. Simplified 67.1%

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

   if 9.99999999999999965e-65 < t

   1. Initial program 74.5%

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

   3. Simplified 79.0%

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

   5. Taylor expanded in t around inf 41.5%

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

      1. *-commutative 41.5%

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

      2. associate-/l* 46.9%

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

      3. associate-*r* 46.9%

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

      4. *-commutative 46.9%

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

      5. *-commutative 46.9%

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

      6. associate-*l/ 46.9%

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

   7. Simplified 46.9%

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

      1. associate-/l* 46.9%

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

   9. Applied egg-rr 46.9%

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

4. Final simplification 60.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.4 \cdot 10^{+185}:\\ \;\;\;\;a \cdot \frac{t \cdot -4}{c}\\ \mathbf{elif}\;t \leq 10^{-64}:\\ \;\;\;\;\frac{\left(x \cdot 9\right) \cdot y + b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(t \cdot \frac{-4}{c}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 68.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\\\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ c\_s \cdot \begin{array}{l} \mathbf{if}\;t \leq -2.8 \cdot 10^{+185}:\\ \;\;\;\;a \cdot \frac{t \cdot -4}{c\_m}\\ \mathbf{elif}\;t \leq 10^{-64}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c\_m}\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(t \cdot \frac{-4}{c\_m}\right)\\ \end{array} \end{array} \]

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 -2.8e+185)
    (* a (/ (* t -4.0) c_m))
    (if (<= t 1e-64)
      (/ (+ b (* 9.0 (* x y))) (* z c_m))
      (* 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 tmp;
	if (t <= -2.8e+185) {
		tmp = a * ((t * -4.0) / c_m);
	} else if (t <= 1e-64) {
		tmp = (b + (9.0 * (x * y))) / (z * c_m);
	} else {
		tmp = a * (t * (-4.0 / c_m));
	}
	return c_s * tmp;
}

Fortran

c\_m = abs(c)
c\_s = copysign(1.0d0, c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
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 (t <= (-2.8d+185)) then
        tmp = a * ((t * (-4.0d0)) / c_m)
    else if (t <= 1d-64) then
        tmp = (b + (9.0d0 * (x * y))) / (z * c_m)
    else
        tmp = a * (t * ((-4.0d0) / c_m))
    end if
    code = c_s * tmp
end function

Java

c\_m = Math.abs(c);
c\_s = Math.copySign(1.0, c);
assert x < y && y < z && z < t && t < a && a < b && b < c_m;
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 (t <= -2.8e+185) {
		tmp = a * ((t * -4.0) / c_m);
	} else if (t <= 1e-64) {
		tmp = (b + (9.0 * (x * y))) / (z * c_m);
	} else {
		tmp = a * (t * (-4.0 / c_m));
	}
	return c_s * tmp;
}

Python

c\_m = math.fabs(c)
c\_s = math.copysign(1.0, c)
[x, y, z, t, a, b, c_m] = sort([x, y, z, t, a, b, c_m])
[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 t <= -2.8e+185:
		tmp = a * ((t * -4.0) / c_m)
	elif t <= 1e-64:
		tmp = (b + (9.0 * (x * y))) / (z * c_m)
	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)
	tmp = 0.0
	if (t <= -2.8e+185)
		tmp = Float64(a * Float64(Float64(t * -4.0) / c_m));
	elseif (t <= 1e-64)
		tmp = Float64(Float64(b + Float64(9.0 * Float64(x * y))) / Float64(z * c_m));
	else
		tmp = Float64(a * Float64(t * Float64(-4.0 / c_m)));
	end
	return Float64(c_s * tmp)
end

MATLAB

c\_m = abs(c);
c\_s = sign(c) * abs(1.0);
x, y, z, t, a, b, c_m = num2cell(sort([x, y, z, t, a, b, c_m])){:}
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 (t <= -2.8e+185)
		tmp = a * ((t * -4.0) / c_m);
	elseif (t <= 1e-64)
		tmp = (b + (9.0 * (x * y))) / (z * c_m);
	else
		tmp = a * (t * (-4.0 / c_m));
	end
	tmp_2 = c_s * tmp;
end

Wolfram

c\_m = N[Abs[c], $MachinePrecision]
c\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
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, -2.8e+185], N[(a * N[(N[(t * -4.0), $MachinePrecision] / c$95$m), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1e-64], N[(N[(b + N[(9.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c$95$m), $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 t < -2.79999999999999982e185

   1. Initial program 73.6%

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

   3. Simplified 81.3%

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

   5. Taylor expanded in t around inf 70.0%

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

      1. *-commutative 70.0%

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

      2. associate-/l* 66.6%

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

      3. associate-*r* 66.6%

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

      4. *-commutative 66.6%

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

      5. *-commutative 66.6%

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

      6. associate-*l/ 66.6%

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

   7. Simplified 66.6%

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

   if -2.79999999999999982e185 < t < 9.99999999999999965e-65

   1. Initial program 82.5%

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

   3. Simplified 80.1%

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

   5. Taylor expanded in t around 0 67.1%

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

      1. +-commutative 67.1%

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

      2. *-commutative 67.1%

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

   7. Simplified 67.1%

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

   if 9.99999999999999965e-65 < t

   1. Initial program 74.5%

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

   3. Simplified 79.0%

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

   5. Taylor expanded in t around inf 41.5%

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

      1. *-commutative 41.5%

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

      2. associate-/l* 46.9%

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

      3. associate-*r* 46.9%

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

      4. *-commutative 46.9%

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

      5. *-commutative 46.9%

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

      6. associate-*l/ 46.9%

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

   7. Simplified 46.9%

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

      1. associate-/l* 46.9%

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

   9. Applied egg-rr 46.9%

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

4. Final simplification 60.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.8 \cdot 10^{+185}:\\ \;\;\;\;a \cdot \frac{t \cdot -4}{c}\\ \mathbf{elif}\;t \leq 10^{-64}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(t \cdot \frac{-4}{c}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 49.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\\\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ c\_s \cdot \begin{array}{l} \mathbf{if}\;b \leq -9 \cdot 10^{+123}:\\ \;\;\;\;\frac{b}{z \cdot c\_m}\\ \mathbf{elif}\;b \leq 1.2 \cdot 10^{+81}:\\ \;\;\;\;a \cdot \frac{t \cdot -4}{c\_m}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{c\_m}}{z}\\ \end{array} \end{array} \]

FPCore

c\_m = (fabs.f64 c)
c\_s = (copysign.f64 #s(literal 1 binary64) c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
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 -9e+123)
    (/ b (* z c_m))
    (if (<= b 1.2e+81) (* a (/ (* t -4.0) c_m)) (/ (/ b c_m) z)))))

C

c\_m = fabs(c);
c\_s = copysign(1.0, c);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
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 <= -9e+123) {
		tmp = b / (z * c_m);
	} else if (b <= 1.2e+81) {
		tmp = a * ((t * -4.0) / c_m);
	} else {
		tmp = (b / c_m) / z;
	}
	return c_s * tmp;
}

Fortran

c\_m = abs(c)
c\_s = copysign(1.0d0, c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
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 <= (-9d+123)) then
        tmp = b / (z * c_m)
    else if (b <= 1.2d+81) then
        tmp = a * ((t * (-4.0d0)) / c_m)
    else
        tmp = (b / c_m) / z
    end if
    code = c_s * tmp
end function

Java

c\_m = Math.abs(c);
c\_s = Math.copySign(1.0, c);
assert x < y && y < z && z < t && t < a && a < b && b < c_m;
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 <= -9e+123) {
		tmp = b / (z * c_m);
	} else if (b <= 1.2e+81) {
		tmp = a * ((t * -4.0) / c_m);
	} else {
		tmp = (b / c_m) / z;
	}
	return c_s * tmp;
}

Python

c\_m = math.fabs(c)
c\_s = math.copysign(1.0, c)
[x, y, z, t, a, b, c_m] = sort([x, y, z, t, a, b, c_m])
[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 <= -9e+123:
		tmp = b / (z * c_m)
	elif b <= 1.2e+81:
		tmp = a * ((t * -4.0) / c_m)
	else:
		tmp = (b / c_m) / z
	return c_s * tmp

Julia

c\_m = abs(c)
c\_s = copysign(1.0, c)
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
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 <= -9e+123)
		tmp = Float64(b / Float64(z * c_m));
	elseif (b <= 1.2e+81)
		tmp = Float64(a * Float64(Float64(t * -4.0) / c_m));
	else
		tmp = Float64(Float64(b / c_m) / z);
	end
	return Float64(c_s * tmp)
end

MATLAB

c\_m = abs(c);
c\_s = sign(c) * abs(1.0);
x, y, z, t, a, b, c_m = num2cell(sort([x, y, z, t, a, b, c_m])){:}
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 <= -9e+123)
		tmp = b / (z * c_m);
	elseif (b <= 1.2e+81)
		tmp = a * ((t * -4.0) / c_m);
	else
		tmp = (b / c_m) / z;
	end
	tmp_2 = c_s * tmp;
end

Wolfram

c\_m = N[Abs[c], $MachinePrecision]
c\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
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, -9e+123], N[(b / N[(z * c$95$m), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.2e+81], N[(a * N[(N[(t * -4.0), $MachinePrecision] / c$95$m), $MachinePrecision]), $MachinePrecision], N[(N[(b / c$95$m), $MachinePrecision] / z), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if b < -8.99999999999999965e123

   1. Initial program 78.4%

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

   3. Simplified 78.4%

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

   5. Taylor expanded in b around inf 65.5%

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

      1. *-commutative 65.5%

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

   7. Simplified 65.5%

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

   if -8.99999999999999965e123 < b < 1.19999999999999995e81

   1. Initial program 77.7%

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

   3. Simplified 78.6%

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

   5. Taylor expanded in t around inf 49.1%

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

      1. *-commutative 49.1%

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

      2. associate-/l* 48.0%

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

      3. associate-*r* 48.0%

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

      4. *-commutative 48.0%

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

      5. *-commutative 48.0%

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

      6. associate-*l/ 48.0%

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

   7. Simplified 48.0%

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

   if 1.19999999999999995e81 < b

   1. Initial program 83.3%

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

   3. Simplified 85.0%

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

   5. Taylor expanded in b around inf 71.4%

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

      1. *-commutative 71.4%

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

   7. Simplified 71.4%

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

   8. Taylor expanded in b around 0 71.4%

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

      1. associate-/r* 74.2%

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

   10. Simplified 74.2%

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

Alternative 17: 49.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\\\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ c\_s \cdot \begin{array}{l} \mathbf{if}\;b \leq -9.2 \cdot 10^{+123}:\\ \;\;\;\;\frac{b}{z \cdot c\_m}\\ \mathbf{elif}\;b \leq 3.7 \cdot 10^{+81}:\\ \;\;\;\;a \cdot \left(t \cdot \frac{-4}{c\_m}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{c\_m}}{z}\\ \end{array} \end{array} \]

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 -9.2e+123)
    (/ b (* z c_m))
    (if (<= b 3.7e+81) (* a (* t (/ -4.0 c_m))) (/ (/ b c_m) z)))))

C

c\_m = fabs(c);
c\_s = copysign(1.0, c);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
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 <= -9.2e+123) {
		tmp = b / (z * c_m);
	} else if (b <= 3.7e+81) {
		tmp = a * (t * (-4.0 / c_m));
	} else {
		tmp = (b / c_m) / z;
	}
	return c_s * tmp;
}

Fortran

c\_m = abs(c)
c\_s = copysign(1.0d0, c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
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 <= (-9.2d+123)) then
        tmp = b / (z * c_m)
    else if (b <= 3.7d+81) then
        tmp = a * (t * ((-4.0d0) / c_m))
    else
        tmp = (b / c_m) / z
    end if
    code = c_s * tmp
end function

Java

c\_m = Math.abs(c);
c\_s = Math.copySign(1.0, c);
assert x < y && y < z && z < t && t < a && a < b && b < c_m;
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 <= -9.2e+123) {
		tmp = b / (z * c_m);
	} else if (b <= 3.7e+81) {
		tmp = a * (t * (-4.0 / c_m));
	} else {
		tmp = (b / c_m) / z;
	}
	return c_s * tmp;
}

Python

c\_m = math.fabs(c)
c\_s = math.copysign(1.0, c)
[x, y, z, t, a, b, c_m] = sort([x, y, z, t, a, b, c_m])
[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 <= -9.2e+123:
		tmp = b / (z * c_m)
	elif b <= 3.7e+81:
		tmp = a * (t * (-4.0 / c_m))
	else:
		tmp = (b / c_m) / z
	return c_s * tmp

Julia

c\_m = abs(c)
c\_s = copysign(1.0, c)
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
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 <= -9.2e+123)
		tmp = Float64(b / Float64(z * c_m));
	elseif (b <= 3.7e+81)
		tmp = Float64(a * Float64(t * Float64(-4.0 / c_m)));
	else
		tmp = Float64(Float64(b / c_m) / z);
	end
	return Float64(c_s * tmp)
end

MATLAB

c\_m = abs(c);
c\_s = sign(c) * abs(1.0);
x, y, z, t, a, b, c_m = num2cell(sort([x, y, z, t, a, b, c_m])){:}
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 <= -9.2e+123)
		tmp = b / (z * c_m);
	elseif (b <= 3.7e+81)
		tmp = a * (t * (-4.0 / c_m));
	else
		tmp = (b / c_m) / z;
	end
	tmp_2 = c_s * tmp;
end

Wolfram

c\_m = N[Abs[c], $MachinePrecision]
c\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
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, -9.2e+123], N[(b / N[(z * c$95$m), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.7e+81], N[(a * N[(t * N[(-4.0 / c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b / c$95$m), $MachinePrecision] / z), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if b < -9.19999999999999962e123

   1. Initial program 78.4%

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

   3. Simplified 78.4%

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

   5. Taylor expanded in b around inf 65.5%

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

      1. *-commutative 65.5%

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

   7. Simplified 65.5%

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

   if -9.19999999999999962e123 < b < 3.7000000000000001e81

   1. Initial program 77.7%

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

   3. Simplified 78.6%

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

   5. Taylor expanded in t around inf 49.1%

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

      1. *-commutative 49.1%

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

      2. associate-/l* 48.0%

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

      3. associate-*r* 48.0%

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

      4. *-commutative 48.0%

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

      5. *-commutative 48.0%

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

      6. associate-*l/ 48.0%

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

   7. Simplified 48.0%

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

      1. associate-/l* 48.0%

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

   9. Applied egg-rr 48.0%

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

   if 3.7000000000000001e81 < b

   1. Initial program 83.3%

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

   3. Simplified 85.0%

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

   5. Taylor expanded in b around inf 71.4%

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

      1. *-commutative 71.4%

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

   7. Simplified 71.4%

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

   8. Taylor expanded in b around 0 71.4%

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

      1. associate-/r* 74.2%

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

   10. Simplified 74.2%

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

Alternative 18: 48.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\\\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ c\_s \cdot \begin{array}{l} \mathbf{if}\;b \leq -9 \cdot 10^{+123}:\\ \;\;\;\;\frac{b}{z \cdot c\_m}\\ \mathbf{elif}\;b \leq 1.7 \cdot 10^{+83}:\\ \;\;\;\;-4 \cdot \frac{t \cdot a}{c\_m}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{c\_m}}{z}\\ \end{array} \end{array} \]

FPCore

c\_m = (fabs.f64 c)
c\_s = (copysign.f64 #s(literal 1 binary64) c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
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 -9e+123)
    (/ b (* z c_m))
    (if (<= b 1.7e+83) (* -4.0 (/ (* t a) c_m)) (/ (/ b c_m) z)))))

C

c\_m = fabs(c);
c\_s = copysign(1.0, c);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
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 <= -9e+123) {
		tmp = b / (z * c_m);
	} else if (b <= 1.7e+83) {
		tmp = -4.0 * ((t * a) / c_m);
	} else {
		tmp = (b / c_m) / z;
	}
	return c_s * tmp;
}

Fortran

c\_m = abs(c)
c\_s = copysign(1.0d0, c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
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 <= (-9d+123)) then
        tmp = b / (z * c_m)
    else if (b <= 1.7d+83) then
        tmp = (-4.0d0) * ((t * a) / c_m)
    else
        tmp = (b / c_m) / z
    end if
    code = c_s * tmp
end function

Java

c\_m = Math.abs(c);
c\_s = Math.copySign(1.0, c);
assert x < y && y < z && z < t && t < a && a < b && b < c_m;
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 <= -9e+123) {
		tmp = b / (z * c_m);
	} else if (b <= 1.7e+83) {
		tmp = -4.0 * ((t * a) / c_m);
	} else {
		tmp = (b / c_m) / z;
	}
	return c_s * tmp;
}

Python

c\_m = math.fabs(c)
c\_s = math.copysign(1.0, c)
[x, y, z, t, a, b, c_m] = sort([x, y, z, t, a, b, c_m])
[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 <= -9e+123:
		tmp = b / (z * c_m)
	elif b <= 1.7e+83:
		tmp = -4.0 * ((t * a) / c_m)
	else:
		tmp = (b / c_m) / z
	return c_s * tmp

Julia

c\_m = abs(c)
c\_s = copysign(1.0, c)
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
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 <= -9e+123)
		tmp = Float64(b / Float64(z * c_m));
	elseif (b <= 1.7e+83)
		tmp = Float64(-4.0 * Float64(Float64(t * a) / c_m));
	else
		tmp = Float64(Float64(b / c_m) / z);
	end
	return Float64(c_s * tmp)
end

MATLAB

c\_m = abs(c);
c\_s = sign(c) * abs(1.0);
x, y, z, t, a, b, c_m = num2cell(sort([x, y, z, t, a, b, c_m])){:}
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 <= -9e+123)
		tmp = b / (z * c_m);
	elseif (b <= 1.7e+83)
		tmp = -4.0 * ((t * a) / c_m);
	else
		tmp = (b / c_m) / z;
	end
	tmp_2 = c_s * tmp;
end

Wolfram

c\_m = N[Abs[c], $MachinePrecision]
c\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[c]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
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, -9e+123], N[(b / N[(z * c$95$m), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.7e+83], N[(-4.0 * N[(N[(t * a), $MachinePrecision] / c$95$m), $MachinePrecision]), $MachinePrecision], N[(N[(b / c$95$m), $MachinePrecision] / z), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if b < -8.99999999999999965e123

   1. Initial program 78.4%

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

   3. Simplified 78.4%

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

   5. Taylor expanded in b around inf 65.5%

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

      1. *-commutative 65.5%

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

   7. Simplified 65.5%

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

   if -8.99999999999999965e123 < b < 1.6999999999999999e83

   1. Initial program 77.7%

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

   3. Simplified 78.6%

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

   5. Taylor expanded in t around inf 49.1%

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

   if 1.6999999999999999e83 < b

   1. Initial program 83.3%

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

   3. Simplified 85.0%

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

   5. Taylor expanded in b around inf 71.4%

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

      1. *-commutative 71.4%

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

   7. Simplified 71.4%

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

   8. Taylor expanded in b around 0 71.4%

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

      1. associate-/r* 74.2%

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

   10. Simplified 74.2%

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

4. Final simplification 56.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -9 \cdot 10^{+123}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;b \leq 1.7 \cdot 10^{+83}:\\ \;\;\;\;-4 \cdot \frac{t \cdot a}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 35.0% accurate, 3.8× speedup

Math

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

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 (* z c_m))))

C

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

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 / (z * c_m))
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 / (z * c_m));
}

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 / (z * c_m))

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(z * c_m)))
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 / (z * c_m));
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[(z * c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 78.9%

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

3. Simplified 79.8%

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

5. Taylor expanded in b around inf 38.5%

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

   1. *-commutative 38.5%

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

7. Simplified 38.5%

   \[\leadsto \color{blue}{\frac{b}{z \cdot c}} \]
8. 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 2024137 
(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)))