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

Percentage Accurate: 80.2% → 94.0%

Time: 14.1s

Alternatives: 13

Speedup: 0.7×

• 37.2% 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: 80.2% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	return ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c);
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    code = ((((x * 9.0d0) * y) - (((z * 4.0d0) * t) * a)) + b) / (z * c)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	return ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c);
}

Python

def code(x, y, z, t, a, b, c):
	return ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c)

Julia

function code(x, y, z, t, a, b, c)
	return Float64(Float64(Float64(Float64(Float64(x * 9.0) * y) - Float64(Float64(Float64(z * 4.0) * t) * a)) + b) / Float64(z * c))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c)
	tmp = ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c);
end

Wolfram

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

Alternative 1: 94.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\\\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ c\_s \cdot \begin{array}{l} \mathbf{if}\;c\_m \leq 130000:\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right) + \frac{b + x \cdot \left(y \cdot 9\right)}{z}}{c\_m}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c\_m}\right) + \frac{\frac{b}{c\_m} - x \cdot \left(\frac{y}{c\_m} \cdot -9\right)}{z}\\ \end{array} \end{array} \]

FPCore

c\_m = (fabs.f64 c)
c\_s = (copysign.f64 #s(literal 1 binary64) c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
(FPCore (c_s x y z t a b c_m)
 :precision binary64
 (*
  c_s
  (if (<= c_m 130000.0)
    (/ (+ (* -4.0 (* a t)) (/ (+ b (* x (* y 9.0))) z)) c_m)
    (+
     (* -4.0 (* t (/ a c_m)))
     (/ (- (/ b c_m) (* x (* (/ y c_m) -9.0))) z)))))

C

c\_m = fabs(c);
c\_s = copysign(1.0, c);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if (c_m <= 130000.0) {
		tmp = ((-4.0 * (a * t)) + ((b + (x * (y * 9.0))) / z)) / c_m;
	} else {
		tmp = (-4.0 * (t * (a / c_m))) + (((b / c_m) - (x * ((y / c_m) * -9.0))) / 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 (c_m <= 130000.0d0) then
        tmp = (((-4.0d0) * (a * t)) + ((b + (x * (y * 9.0d0))) / z)) / c_m
    else
        tmp = ((-4.0d0) * (t * (a / c_m))) + (((b / c_m) - (x * ((y / c_m) * (-9.0d0)))) / 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 (c_m <= 130000.0) {
		tmp = ((-4.0 * (a * t)) + ((b + (x * (y * 9.0))) / z)) / c_m;
	} else {
		tmp = (-4.0 * (t * (a / c_m))) + (((b / c_m) - (x * ((y / c_m) * -9.0))) / 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 c_m <= 130000.0:
		tmp = ((-4.0 * (a * t)) + ((b + (x * (y * 9.0))) / z)) / c_m
	else:
		tmp = (-4.0 * (t * (a / c_m))) + (((b / c_m) - (x * ((y / c_m) * -9.0))) / z)
	return c_s * tmp

Julia

c\_m = abs(c)
c\_s = copysign(1.0, c)
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
function code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0
	if (c_m <= 130000.0)
		tmp = Float64(Float64(Float64(-4.0 * Float64(a * t)) + Float64(Float64(b + Float64(x * Float64(y * 9.0))) / z)) / c_m);
	else
		tmp = Float64(Float64(-4.0 * Float64(t * Float64(a / c_m))) + Float64(Float64(Float64(b / c_m) - Float64(x * Float64(Float64(y / c_m) * -9.0))) / 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 (c_m <= 130000.0)
		tmp = ((-4.0 * (a * t)) + ((b + (x * (y * 9.0))) / z)) / c_m;
	else
		tmp = (-4.0 * (t * (a / c_m))) + (((b / c_m) - (x * ((y / c_m) * -9.0))) / 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[c$95$m, 130000.0], N[(N[(N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision] + N[(N[(b + N[(x * N[(y * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] / c$95$m), $MachinePrecision], N[(N[(-4.0 * N[(t * N[(a / c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(b / c$95$m), $MachinePrecision] - N[(x * N[(N[(y / c$95$m), $MachinePrecision] * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if c < 1.3e5

   1. Initial program 83.5%

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

   3. Simplified 85.1%

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

      1. associate-/r* 88.0%

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

      2. div-inv 88.0%

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

      3. +-commutative 88.0%

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

      4. associate-*r* 88.0%

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

      5. *-commutative 88.0%

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

      6. associate-*l* 88.0%

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

   6. Applied egg-rr 88.0%

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

   7. Taylor expanded in b around 0 87.8%

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

   8. Taylor expanded in c around 0 87.8%

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

   9. Taylor expanded in z around 0 90.4%

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

       1. *-commutative 90.4%

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

       2. associate-*l* 90.4%

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

   11. Simplified 90.4%

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

   if 1.3e5 < c

   1. Initial program 65.3%

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

   3. Simplified 63.9%

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

      1. associate-/r* 62.9%

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

      2. div-inv 62.9%

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

      3. +-commutative 62.9%

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

      4. associate-*r* 62.9%

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

      5. *-commutative 62.9%

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

      6. associate-*l* 62.9%

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

   6. Applied egg-rr 62.9%

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

   7. Taylor expanded in b around 0 70.6%

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

   8. Taylor expanded in c around 0 70.6%

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

   9. Taylor expanded in z around -inf 81.2%

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

       1. mul-1-neg 81.2%

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

       2. unsub-neg 81.2%

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

       3. associate-*r/ 81.2%

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

       4. associate-*r* 81.2%

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

       5. associate-*l/ 84.9%

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

       6. associate-*r/ 84.8%

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

       7. associate-*l* 84.8%

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

       8. neg-mul-1 84.8%

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

       9. unsub-neg 84.8%

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

       10. *-commutative 84.8%

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

       11. associate-/l* 93.9%

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

       12. associate-*l* 93.8%

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

   11. Simplified 93.8%

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

4. Final simplification 91.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq 130000:\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right) + \frac{b + x \cdot \left(y \cdot 9\right)}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right) + \frac{\frac{b}{c} - x \cdot \left(\frac{y}{c} \cdot -9\right)}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 88.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\\\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot 9\right)\\ c\_s \cdot \begin{array}{l} \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;\left(x \cdot \frac{y}{c\_m}\right) \cdot \frac{9}{z}\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+288}:\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right) + \frac{b + x \cdot \left(y \cdot 9\right)}{z}}{c\_m}\\ \mathbf{else}:\\ \;\;\;\;9 \cdot \left(\frac{y}{c\_m} \cdot \frac{x}{z}\right)\\ \end{array} \end{array} \end{array} \]

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 (* y (* x 9.0))))
   (*
    c_s
    (if (<= t_1 (- INFINITY))
      (* (* x (/ y c_m)) (/ 9.0 z))
      (if (<= t_1 5e+288)
        (/ (+ (* -4.0 (* a t)) (/ (+ b (* x (* y 9.0))) 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 t_1 = y * (x * 9.0);
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = (x * (y / c_m)) * (9.0 / z);
	} else if (t_1 <= 5e+288) {
		tmp = ((-4.0 * (a * t)) + ((b + (x * (y * 9.0))) / z)) / c_m;
	} else {
		tmp = 9.0 * ((y / c_m) * (x / z));
	}
	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 = y * (x * 9.0);
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = (x * (y / c_m)) * (9.0 / z);
	} else if (t_1 <= 5e+288) {
		tmp = ((-4.0 * (a * t)) + ((b + (x * (y * 9.0))) / 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):
	t_1 = y * (x * 9.0)
	tmp = 0
	if t_1 <= -math.inf:
		tmp = (x * (y / c_m)) * (9.0 / z)
	elif t_1 <= 5e+288:
		tmp = ((-4.0 * (a * t)) + ((b + (x * (y * 9.0))) / 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)
	t_1 = Float64(y * Float64(x * 9.0))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(Float64(x * Float64(y / c_m)) * Float64(9.0 / z));
	elseif (t_1 <= 5e+288)
		tmp = Float64(Float64(Float64(-4.0 * Float64(a * t)) + Float64(Float64(b + Float64(x * Float64(y * 9.0))) / 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)
	t_1 = y * (x * 9.0);
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = (x * (y / c_m)) * (9.0 / z);
	elseif (t_1 <= 5e+288)
		tmp = ((-4.0 * (a * t)) + ((b + (x * (y * 9.0))) / 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_] := Block[{t$95$1 = N[(y * N[(x * 9.0), $MachinePrecision]), $MachinePrecision]}, N[(c$95$s * If[LessEqual[t$95$1, (-Infinity)], N[(N[(x * N[(y / c$95$m), $MachinePrecision]), $MachinePrecision] * N[(9.0 / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+288], N[(N[(N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision] + N[(N[(b + N[(x * N[(y * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] / c$95$m), $MachinePrecision], N[(9.0 * N[(N[(y / c$95$m), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 x #s(literal 9 binary64)) y) < -inf.0

   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 67.9%

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

   5. Taylor expanded in x around inf 80.7%

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

      1. associate-*r/ 74.5%

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

      2. *-commutative 74.5%

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

      3. times-frac 80.9%

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

      4. associate-/l* 99.8%

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

   7. Simplified 99.8%

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

   if -inf.0 < (*.f64 (*.f64 x #s(literal 9 binary64)) y) < 5.0000000000000003e288

   1. Initial program 82.6%

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

   3. Simplified 84.0%

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

      1. associate-/r* 86.3%

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

      2. div-inv 86.3%

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

      3. +-commutative 86.3%

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

      4. associate-*r* 86.3%

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

      5. *-commutative 86.3%

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

      6. associate-*l* 86.3%

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

   6. Applied egg-rr 86.3%

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

   7. Taylor expanded in b around 0 89.6%

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

   8. Taylor expanded in c around 0 89.7%

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

   9. Taylor expanded in z around 0 90.6%

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

       1. *-commutative 90.6%

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

       2. associate-*l* 90.6%

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

   11. Simplified 90.6%

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

   if 5.0000000000000003e288 < (*.f64 (*.f64 x #s(literal 9 binary64)) y)

   1. Initial program 49.4%

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

   3. Simplified 49.4%

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

      1. associate-/r* 50.0%

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

      2. div-inv 50.0%

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

      3. +-commutative 50.0%

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

      4. associate-*r* 50.0%

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

      5. *-commutative 50.0%

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

      6. associate-*l* 50.0%

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

   6. Applied egg-rr 50.0%

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

   7. Taylor expanded in x around inf 53.8%

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

      1. *-commutative 53.8%

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

      2. times-frac 79.1%

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

   9. Simplified 79.1%

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

4. Final simplification 90.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \left(x \cdot 9\right) \leq -\infty:\\ \;\;\;\;\left(x \cdot \frac{y}{c}\right) \cdot \frac{9}{z}\\ \mathbf{elif}\;y \cdot \left(x \cdot 9\right) \leq 5 \cdot 10^{+288}:\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right) + \frac{b + x \cdot \left(y \cdot 9\right)}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;9 \cdot \left(\frac{y}{c} \cdot \frac{x}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 50.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\\\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ \begin{array}{l} t_1 := 9 \cdot \left(x \cdot \frac{y}{c\_m \cdot z}\right)\\ c\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -24000000:\\ \;\;\;\;-4 \cdot \frac{a \cdot t}{c\_m}\\ \mathbf{elif}\;z \leq -1.02 \cdot 10^{-227}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{-151}:\\ \;\;\;\;\frac{\frac{b}{c\_m}}{z}\\ \mathbf{elif}\;z \leq 0.0017:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c\_m}\right)\\ \end{array} \end{array} \end{array} \]

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 (* 9.0 (* x (/ y (* c_m z))))))
   (*
    c_s
    (if (<= z -24000000.0)
      (* -4.0 (/ (* a t) c_m))
      (if (<= z -1.02e-227)
        t_1
        (if (<= z 6.2e-151)
          (/ (/ b c_m) z)
          (if (<= z 0.0017) t_1 (* -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 t_1 = 9.0 * (x * (y / (c_m * z)));
	double tmp;
	if (z <= -24000000.0) {
		tmp = -4.0 * ((a * t) / c_m);
	} else if (z <= -1.02e-227) {
		tmp = t_1;
	} else if (z <= 6.2e-151) {
		tmp = (b / c_m) / z;
	} else if (z <= 0.0017) {
		tmp = t_1;
	} else {
		tmp = -4.0 * (t * (a / 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 = 9.0d0 * (x * (y / (c_m * z)))
    if (z <= (-24000000.0d0)) then
        tmp = (-4.0d0) * ((a * t) / c_m)
    else if (z <= (-1.02d-227)) then
        tmp = t_1
    else if (z <= 6.2d-151) then
        tmp = (b / c_m) / z
    else if (z <= 0.0017d0) then
        tmp = t_1
    else
        tmp = (-4.0d0) * (t * (a / 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 = 9.0 * (x * (y / (c_m * z)));
	double tmp;
	if (z <= -24000000.0) {
		tmp = -4.0 * ((a * t) / c_m);
	} else if (z <= -1.02e-227) {
		tmp = t_1;
	} else if (z <= 6.2e-151) {
		tmp = (b / c_m) / z;
	} else if (z <= 0.0017) {
		tmp = t_1;
	} else {
		tmp = -4.0 * (t * (a / 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 = 9.0 * (x * (y / (c_m * z)))
	tmp = 0
	if z <= -24000000.0:
		tmp = -4.0 * ((a * t) / c_m)
	elif z <= -1.02e-227:
		tmp = t_1
	elif z <= 6.2e-151:
		tmp = (b / c_m) / z
	elif z <= 0.0017:
		tmp = t_1
	else:
		tmp = -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)
	t_1 = Float64(9.0 * Float64(x * Float64(y / Float64(c_m * z))))
	tmp = 0.0
	if (z <= -24000000.0)
		tmp = Float64(-4.0 * Float64(Float64(a * t) / c_m));
	elseif (z <= -1.02e-227)
		tmp = t_1;
	elseif (z <= 6.2e-151)
		tmp = Float64(Float64(b / c_m) / z);
	elseif (z <= 0.0017)
		tmp = t_1;
	else
		tmp = Float64(-4.0 * Float64(t * Float64(a / 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 = 9.0 * (x * (y / (c_m * z)));
	tmp = 0.0;
	if (z <= -24000000.0)
		tmp = -4.0 * ((a * t) / c_m);
	elseif (z <= -1.02e-227)
		tmp = t_1;
	elseif (z <= 6.2e-151)
		tmp = (b / c_m) / z;
	elseif (z <= 0.0017)
		tmp = t_1;
	else
		tmp = -4.0 * (t * (a / 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[(9.0 * N[(x * N[(y / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, N[(c$95$s * If[LessEqual[z, -24000000.0], N[(-4.0 * N[(N[(a * t), $MachinePrecision] / c$95$m), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.02e-227], t$95$1, If[LessEqual[z, 6.2e-151], N[(N[(b / c$95$m), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, 0.0017], t$95$1, N[(-4.0 * N[(t * N[(a / c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]), $MachinePrecision]]

Derivation

1. Split input into 4 regimes

2. if z < -2.4e7

   1. Initial program 67.9%

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

   3. Simplified 77.3%

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

   5. Taylor expanded in z around inf 53.6%

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

   if -2.4e7 < z < -1.02e-227 or 6.19999999999999969e-151 < z < 0.00169999999999999991

   1. Initial program 89.7%

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

   3. Simplified 86.2%

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

   5. Taylor expanded in x around inf 52.8%

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

      1. associate-/l* 56.1%

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

      2. *-commutative 56.1%

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

   7. Simplified 56.1%

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

   if -1.02e-227 < z < 6.19999999999999969e-151

   1. Initial program 95.0%

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

   3. Simplified 91.7%

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

      1. associate-/r* 82.1%

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

      2. div-inv 82.1%

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

      3. +-commutative 82.1%

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

      4. associate-*r* 82.1%

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

      5. *-commutative 82.1%

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

      6. associate-*l* 82.1%

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

   6. Applied egg-rr 82.1%

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

   7. Taylor expanded in b around inf 68.5%

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

      1. associate-/r* 70.0%

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

   9. Simplified 70.0%

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

   if 0.00169999999999999991 < z

   1. Initial program 59.8%

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

   3. Simplified 63.2%

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

      1. associate-/r* 76.9%

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

      2. div-inv 76.9%

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

      3. +-commutative 76.9%

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

      4. associate-*r* 76.9%

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

      5. *-commutative 76.9%

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

      6. associate-*l* 76.9%

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

   6. Applied egg-rr 76.9%

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

   7. Taylor expanded in b around 0 89.1%

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

   8. Taylor expanded in c around 0 89.0%

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

   9. Taylor expanded in a around inf 67.1%

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

       1. associate-*r/ 67.1%

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

       2. associate-*r* 67.1%

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

       3. associate-*l/ 61.7%

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

       4. associate-*r/ 61.6%

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

       5. associate-*l* 61.6%

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

   11. Simplified 61.6%

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

4. Final simplification 60.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -24000000:\\ \;\;\;\;-4 \cdot \frac{a \cdot t}{c}\\ \mathbf{elif}\;z \leq -1.02 \cdot 10^{-227}:\\ \;\;\;\;9 \cdot \left(x \cdot \frac{y}{c \cdot z}\right)\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{-151}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;z \leq 0.0017:\\ \;\;\;\;9 \cdot \left(x \cdot \frac{y}{c \cdot z}\right)\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 94.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\\\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ c\_s \cdot \begin{array}{l} \mathbf{if}\;c\_m \leq 4000000:\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right) + \frac{b + x \cdot \left(y \cdot 9\right)}{z}}{c\_m}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(a \cdot \frac{t}{c\_m}\right) + \frac{\frac{b}{c\_m} - \left(x \cdot \frac{y}{c\_m}\right) \cdot -9}{z}\\ \end{array} \end{array} \]

FPCore

c\_m = (fabs.f64 c)
c\_s = (copysign.f64 #s(literal 1 binary64) c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
(FPCore (c_s x y z t a b c_m)
 :precision binary64
 (*
  c_s
  (if (<= c_m 4000000.0)
    (/ (+ (* -4.0 (* a t)) (/ (+ b (* x (* y 9.0))) z)) c_m)
    (+
     (* -4.0 (* a (/ t c_m)))
     (/ (- (/ b c_m) (* (* x (/ y c_m)) -9.0)) z)))))

C

c\_m = fabs(c);
c\_s = copysign(1.0, c);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
assert(x < y && y < z && z < t && t < a && a < b && b < c_m);
double code(double c_s, double x, double y, double z, double t, double a, double b, double c_m) {
	double tmp;
	if (c_m <= 4000000.0) {
		tmp = ((-4.0 * (a * t)) + ((b + (x * (y * 9.0))) / z)) / c_m;
	} else {
		tmp = (-4.0 * (a * (t / c_m))) + (((b / c_m) - ((x * (y / c_m)) * -9.0)) / 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 (c_m <= 4000000.0d0) then
        tmp = (((-4.0d0) * (a * t)) + ((b + (x * (y * 9.0d0))) / z)) / c_m
    else
        tmp = ((-4.0d0) * (a * (t / c_m))) + (((b / c_m) - ((x * (y / c_m)) * (-9.0d0))) / 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 (c_m <= 4000000.0) {
		tmp = ((-4.0 * (a * t)) + ((b + (x * (y * 9.0))) / z)) / c_m;
	} else {
		tmp = (-4.0 * (a * (t / c_m))) + (((b / c_m) - ((x * (y / c_m)) * -9.0)) / 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 c_m <= 4000000.0:
		tmp = ((-4.0 * (a * t)) + ((b + (x * (y * 9.0))) / z)) / c_m
	else:
		tmp = (-4.0 * (a * (t / c_m))) + (((b / c_m) - ((x * (y / c_m)) * -9.0)) / z)
	return c_s * tmp

Julia

c\_m = abs(c)
c\_s = copysign(1.0, c)
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
x, y, z, t, a, b, c_m = sort([x, y, z, t, a, b, c_m])
function code(c_s, x, y, z, t, a, b, c_m)
	tmp = 0.0
	if (c_m <= 4000000.0)
		tmp = Float64(Float64(Float64(-4.0 * Float64(a * t)) + Float64(Float64(b + Float64(x * Float64(y * 9.0))) / z)) / c_m);
	else
		tmp = Float64(Float64(-4.0 * Float64(a * Float64(t / c_m))) + Float64(Float64(Float64(b / c_m) - Float64(Float64(x * Float64(y / c_m)) * -9.0)) / 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 (c_m <= 4000000.0)
		tmp = ((-4.0 * (a * t)) + ((b + (x * (y * 9.0))) / z)) / c_m;
	else
		tmp = (-4.0 * (a * (t / c_m))) + (((b / c_m) - ((x * (y / c_m)) * -9.0)) / 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[c$95$m, 4000000.0], N[(N[(N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision] + N[(N[(b + N[(x * N[(y * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] / c$95$m), $MachinePrecision], N[(N[(-4.0 * N[(a * N[(t / c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(b / c$95$m), $MachinePrecision] - N[(N[(x * N[(y / c$95$m), $MachinePrecision]), $MachinePrecision] * -9.0), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if c < 4e6

   1. Initial program 83.6%

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

   3. Simplified 85.2%

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

      1. associate-/r* 88.1%

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

      2. div-inv 88.1%

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

      3. +-commutative 88.1%

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

      4. associate-*r* 88.1%

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

      5. *-commutative 88.1%

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

      6. associate-*l* 88.1%

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

   6. Applied egg-rr 88.1%

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

   7. Taylor expanded in b around 0 87.8%

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

   8. Taylor expanded in c around 0 87.9%

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

   9. Taylor expanded in z around 0 90.5%

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

       1. *-commutative 90.5%

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

       2. associate-*l* 90.5%

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

   11. Simplified 90.5%

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

   if 4e6 < c

   1. Initial program 64.8%

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

   3. Simplified 63.3%

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

      1. associate-/r* 62.3%

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

      2. div-inv 62.3%

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

      3. +-commutative 62.3%

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

      4. associate-*r* 62.3%

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

      5. *-commutative 62.3%

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

      6. associate-*l* 62.3%

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

   6. Applied egg-rr 62.3%

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

   7. Taylor expanded in b around 0 70.2%

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

   8. Taylor expanded in z around -inf 80.9%

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

      1. mul-1-neg 80.9%

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

      2. unsub-neg 80.9%

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

      3. associate-/l* 85.7%

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

      4. fma-define 85.7%

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

      5. associate-*r/ 95.0%

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

      6. neg-mul-1 95.0%

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

      7. fmm-undef 95.0%

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

   10. Simplified 95.0%

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

4. Final simplification 91.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq 4000000:\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right) + \frac{b + x \cdot \left(y \cdot 9\right)}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(a \cdot \frac{t}{c}\right) + \frac{\frac{b}{c} - \left(x \cdot \frac{y}{c}\right) \cdot -9}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 72.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\\\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ c\_s \cdot \begin{array}{l} \mathbf{if}\;b \leq -7 \cdot 10^{-95}:\\ \;\;\;\;\frac{b + x \cdot \left(y \cdot 9\right)}{c\_m \cdot z}\\ \mathbf{elif}\;b \leq 2 \cdot 10^{-12}:\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right) + 9 \cdot \frac{x \cdot y}{z}}{c\_m}\\ \mathbf{else}:\\ \;\;\;\;\frac{b - 4 \cdot \left(a \cdot \left(t \cdot z\right)\right)}{c\_m \cdot z}\\ \end{array} \end{array} \]

FPCore

c\_m = (fabs.f64 c)
c\_s = (copysign.f64 #s(literal 1 binary64) c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
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 -7e-95)
    (/ (+ b (* x (* y 9.0))) (* c_m z))
    (if (<= b 2e-12)
      (/ (+ (* -4.0 (* a t)) (* 9.0 (/ (* x y) z))) c_m)
      (/ (- b (* 4.0 (* a (* t z)))) (* 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 <= -7e-95) {
		tmp = (b + (x * (y * 9.0))) / (c_m * z);
	} else if (b <= 2e-12) {
		tmp = ((-4.0 * (a * t)) + (9.0 * ((x * y) / z))) / c_m;
	} else {
		tmp = (b - (4.0 * (a * (t * z)))) / (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 <= (-7d-95)) then
        tmp = (b + (x * (y * 9.0d0))) / (c_m * z)
    else if (b <= 2d-12) then
        tmp = (((-4.0d0) * (a * t)) + (9.0d0 * ((x * y) / z))) / c_m
    else
        tmp = (b - (4.0d0 * (a * (t * z)))) / (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 <= -7e-95) {
		tmp = (b + (x * (y * 9.0))) / (c_m * z);
	} else if (b <= 2e-12) {
		tmp = ((-4.0 * (a * t)) + (9.0 * ((x * y) / z))) / c_m;
	} else {
		tmp = (b - (4.0 * (a * (t * z)))) / (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 <= -7e-95:
		tmp = (b + (x * (y * 9.0))) / (c_m * z)
	elif b <= 2e-12:
		tmp = ((-4.0 * (a * t)) + (9.0 * ((x * y) / z))) / c_m
	else:
		tmp = (b - (4.0 * (a * (t * z)))) / (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 <= -7e-95)
		tmp = Float64(Float64(b + Float64(x * Float64(y * 9.0))) / Float64(c_m * z));
	elseif (b <= 2e-12)
		tmp = Float64(Float64(Float64(-4.0 * Float64(a * t)) + Float64(9.0 * Float64(Float64(x * y) / z))) / c_m);
	else
		tmp = Float64(Float64(b - Float64(4.0 * Float64(a * Float64(t * z)))) / Float64(c_m * z));
	end
	return Float64(c_s * tmp)
end

MATLAB

c\_m = abs(c);
c\_s = sign(c) * abs(1.0);
x, y, z, t, a, b, c_m = num2cell(sort([x, y, z, t, a, b, c_m])){:}
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 <= -7e-95)
		tmp = (b + (x * (y * 9.0))) / (c_m * z);
	elseif (b <= 2e-12)
		tmp = ((-4.0 * (a * t)) + (9.0 * ((x * y) / z))) / c_m;
	else
		tmp = (b - (4.0 * (a * (t * z)))) / (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, -7e-95], N[(N[(b + N[(x * N[(y * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2e-12], N[(N[(N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision] + N[(9.0 * N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c$95$m), $MachinePrecision], N[(N[(b - N[(4.0 * N[(a * N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if b < -6.9999999999999994e-95

   1. Initial program 83.6%

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

   3. Simplified 83.6%

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

      1. associate-/r* 78.7%

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

      2. div-inv 78.7%

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

      3. +-commutative 78.7%

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

      4. associate-*r* 78.7%

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

      5. *-commutative 78.7%

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

      6. associate-*l* 78.7%

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

   6. Applied egg-rr 78.7%

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

   7. Taylor expanded in z around 0 77.2%

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

      1. +-commutative 77.2%

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

      2. associate-*r* 77.2%

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

      3. *-commutative 77.2%

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

      4. associate-*r* 77.2%

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

      5. *-commutative 77.2%

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

   9. Simplified 77.2%

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

   if -6.9999999999999994e-95 < b < 1.99999999999999996e-12

   1. Initial program 74.1%

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

   3. Simplified 77.6%

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

      1. associate-/r* 87.4%

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

      2. div-inv 87.3%

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

      3. +-commutative 87.3%

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

      4. associate-*r* 87.3%

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

      5. *-commutative 87.3%

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

      6. associate-*l* 87.3%

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

   6. Applied egg-rr 87.3%

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

   7. Taylor expanded in b around 0 91.4%

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

   8. Taylor expanded in b around 0 85.5%

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

   if 1.99999999999999996e-12 < b

   1. Initial program 82.8%

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

      1. associate-+l- 82.8%

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

      2. *-commutative 82.8%

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

      3. associate-*r* 81.5%

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

      4. *-commutative 81.5%

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

      5. associate-+l- 81.5%

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

      6. associate-*l* 81.5%

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

      7. associate-*l* 80.1%

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

      8. *-commutative 80.1%

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

   3. Simplified 80.1%

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

   5. Taylor expanded in x around 0 72.9%

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

4. Final simplification 79.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -7 \cdot 10^{-95}:\\ \;\;\;\;\frac{b + x \cdot \left(y \cdot 9\right)}{c \cdot z}\\ \mathbf{elif}\;b \leq 2 \cdot 10^{-12}:\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right) + 9 \cdot \frac{x \cdot y}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b - 4 \cdot \left(a \cdot \left(t \cdot z\right)\right)}{c \cdot z}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 67.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\\\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ c\_s \cdot \begin{array}{l} \mathbf{if}\;t \leq -1.6 \cdot 10^{+114}:\\ \;\;\;\;a \cdot \left(-4 \cdot \frac{t}{c\_m}\right)\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{-98}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{c\_m \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + a \cdot \left(z \cdot \left(-4 \cdot t\right)\right)}{z} \cdot \frac{1}{c\_m}\\ \end{array} \end{array} \]

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 (<= t -1.6e+114)
    (* a (* -4.0 (/ t c_m)))
    (if (<= t 9.5e-98)
      (/ (+ b (* 9.0 (* x y))) (* c_m z))
      (* (/ (+ b (* a (* z (* -4.0 t)))) z) (/ 1.0 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 <= -1.6e+114) {
		tmp = a * (-4.0 * (t / c_m));
	} else if (t <= 9.5e-98) {
		tmp = (b + (9.0 * (x * y))) / (c_m * z);
	} else {
		tmp = ((b + (a * (z * (-4.0 * t)))) / z) * (1.0 / 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 <= (-1.6d+114)) then
        tmp = a * ((-4.0d0) * (t / c_m))
    else if (t <= 9.5d-98) then
        tmp = (b + (9.0d0 * (x * y))) / (c_m * z)
    else
        tmp = ((b + (a * (z * ((-4.0d0) * t)))) / z) * (1.0d0 / 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 <= -1.6e+114) {
		tmp = a * (-4.0 * (t / c_m));
	} else if (t <= 9.5e-98) {
		tmp = (b + (9.0 * (x * y))) / (c_m * z);
	} else {
		tmp = ((b + (a * (z * (-4.0 * t)))) / z) * (1.0 / 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 <= -1.6e+114:
		tmp = a * (-4.0 * (t / c_m))
	elif t <= 9.5e-98:
		tmp = (b + (9.0 * (x * y))) / (c_m * z)
	else:
		tmp = ((b + (a * (z * (-4.0 * t)))) / z) * (1.0 / 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 <= -1.6e+114)
		tmp = Float64(a * Float64(-4.0 * Float64(t / c_m)));
	elseif (t <= 9.5e-98)
		tmp = Float64(Float64(b + Float64(9.0 * Float64(x * y))) / Float64(c_m * z));
	else
		tmp = Float64(Float64(Float64(b + Float64(a * Float64(z * Float64(-4.0 * t)))) / z) * Float64(1.0 / 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 <= -1.6e+114)
		tmp = a * (-4.0 * (t / c_m));
	elseif (t <= 9.5e-98)
		tmp = (b + (9.0 * (x * y))) / (c_m * z);
	else
		tmp = ((b + (a * (z * (-4.0 * t)))) / z) * (1.0 / 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, -1.6e+114], N[(a * N[(-4.0 * N[(t / c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 9.5e-98], N[(N[(b + N[(9.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision], N[(N[(N[(b + N[(a * N[(z * N[(-4.0 * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] * N[(1.0 / c$95$m), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if t < -1.6e114

   1. Initial program 74.0%

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

   3. Simplified 68.3%

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

   5. Taylor expanded in z around inf 58.9%

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

      1. associate-/l* 69.8%

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

      2. associate-*r* 69.8%

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

      3. *-commutative 69.8%

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

      4. associate-*r* 69.8%

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

   7. Simplified 69.8%

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

   if -1.6e114 < t < 9.5000000000000001e-98

   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 84.5%

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

   5. Taylor expanded in z around 0 75.6%

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

      1. +-commutative 75.6%

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

      2. *-commutative 75.6%

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

   7. Simplified 75.6%

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

   if 9.5000000000000001e-98 < 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 77.8%

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

      1. associate-/r* 83.1%

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

      2. div-inv 83.0%

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

      3. +-commutative 83.0%

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

      4. associate-*r* 83.0%

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

      5. *-commutative 83.0%

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

      6. associate-*l* 83.0%

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

   6. Applied egg-rr 83.0%

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

   7. Taylor expanded in x around 0 58.9%

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

      1. *-commutative 58.9%

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

      2. *-commutative 58.9%

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

      3. associate-*r* 57.8%

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

      4. associate-*l* 57.8%

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

      5. *-commutative 57.8%

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

   9. Simplified 57.8%

      \[\leadsto \frac{b + \color{blue}{a \cdot \left(z \cdot \left(-4 \cdot t\right)\right)}}{z} \cdot \frac{1}{c} \]
3. Recombined 3 regimes into one program.

4. Final simplification 68.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.6 \cdot 10^{+114}:\\ \;\;\;\;a \cdot \left(-4 \cdot \frac{t}{c}\right)\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{-98}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + a \cdot \left(z \cdot \left(-4 \cdot t\right)\right)}{z} \cdot \frac{1}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 67.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\\\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ c\_s \cdot \begin{array}{l} \mathbf{if}\;t \leq -7 \cdot 10^{+118}:\\ \;\;\;\;a \cdot \left(-4 \cdot \frac{t}{c\_m}\right)\\ \mathbf{elif}\;t \leq 8.6 \cdot 10^{-97}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{c\_m \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{b - 4 \cdot \left(a \cdot \left(t \cdot z\right)\right)}{c\_m \cdot z}\\ \end{array} \end{array} \]

FPCore

c\_m = (fabs.f64 c)
c\_s = (copysign.f64 #s(literal 1 binary64) c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
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 -7e+118)
    (* a (* -4.0 (/ t c_m)))
    (if (<= t 8.6e-97)
      (/ (+ b (* 9.0 (* x y))) (* c_m z))
      (/ (- b (* 4.0 (* a (* t z)))) (* 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 (t <= -7e+118) {
		tmp = a * (-4.0 * (t / c_m));
	} else if (t <= 8.6e-97) {
		tmp = (b + (9.0 * (x * y))) / (c_m * z);
	} else {
		tmp = (b - (4.0 * (a * (t * z)))) / (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 (t <= (-7d+118)) then
        tmp = a * ((-4.0d0) * (t / c_m))
    else if (t <= 8.6d-97) then
        tmp = (b + (9.0d0 * (x * y))) / (c_m * z)
    else
        tmp = (b - (4.0d0 * (a * (t * z)))) / (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 (t <= -7e+118) {
		tmp = a * (-4.0 * (t / c_m));
	} else if (t <= 8.6e-97) {
		tmp = (b + (9.0 * (x * y))) / (c_m * z);
	} else {
		tmp = (b - (4.0 * (a * (t * z)))) / (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 t <= -7e+118:
		tmp = a * (-4.0 * (t / c_m))
	elif t <= 8.6e-97:
		tmp = (b + (9.0 * (x * y))) / (c_m * z)
	else:
		tmp = (b - (4.0 * (a * (t * z)))) / (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 (t <= -7e+118)
		tmp = Float64(a * Float64(-4.0 * Float64(t / c_m)));
	elseif (t <= 8.6e-97)
		tmp = Float64(Float64(b + Float64(9.0 * Float64(x * y))) / Float64(c_m * z));
	else
		tmp = Float64(Float64(b - Float64(4.0 * Float64(a * Float64(t * z)))) / Float64(c_m * z));
	end
	return Float64(c_s * tmp)
end

MATLAB

c\_m = abs(c);
c\_s = sign(c) * abs(1.0);
x, y, z, t, a, b, c_m = num2cell(sort([x, y, z, t, a, b, c_m])){:}
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 <= -7e+118)
		tmp = a * (-4.0 * (t / c_m));
	elseif (t <= 8.6e-97)
		tmp = (b + (9.0 * (x * y))) / (c_m * z);
	else
		tmp = (b - (4.0 * (a * (t * z)))) / (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[t, -7e+118], N[(a * N[(-4.0 * N[(t / c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 8.6e-97], N[(N[(b + N[(9.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision], N[(N[(b - N[(4.0 * N[(a * N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if t < -7.00000000000000033e118

   1. Initial program 74.0%

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

   3. Simplified 68.3%

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

   5. Taylor expanded in z around inf 58.9%

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

      1. associate-/l* 69.8%

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

      2. associate-*r* 69.8%

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

      3. *-commutative 69.8%

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

      4. associate-*r* 69.8%

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

   7. Simplified 69.8%

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

   if -7.00000000000000033e118 < t < 8.6e-97

   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 84.5%

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

   5. Taylor expanded in z around 0 75.6%

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

      1. +-commutative 75.6%

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

      2. *-commutative 75.6%

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

   7. Simplified 75.6%

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

   if 8.6e-97 < t

   1. Initial program 74.5%

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

      1. associate-+l- 74.5%

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

      2. *-commutative 74.5%

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

      3. associate-*r* 79.9%

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

      4. *-commutative 79.9%

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

      5. associate-+l- 79.9%

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

      6. associate-*l* 79.9%

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

      7. associate-*l* 77.8%

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

      8. *-commutative 77.8%

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

   3. Simplified 77.8%

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

   5. Taylor expanded in x around 0 59.9%

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

4. Final simplification 69.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7 \cdot 10^{+118}:\\ \;\;\;\;a \cdot \left(-4 \cdot \frac{t}{c}\right)\\ \mathbf{elif}\;t \leq 8.6 \cdot 10^{-97}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{b - 4 \cdot \left(a \cdot \left(t \cdot z\right)\right)}{c \cdot z}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 50.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\\\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ c\_s \cdot \begin{array}{l} \mathbf{if}\;t \leq -6.2 \cdot 10^{+118}:\\ \;\;\;\;a \cdot \left(-4 \cdot \frac{t}{c\_m}\right)\\ \mathbf{elif}\;t \leq -1.15 \cdot 10^{-71}:\\ \;\;\;\;9 \cdot \left(\frac{x}{c\_m} \cdot \frac{y}{z}\right)\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{-86}:\\ \;\;\;\;\frac{\frac{b}{c\_m}}{z}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c\_m}\right)\\ \end{array} \end{array} \]

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 -6.2e+118)
    (* a (* -4.0 (/ t c_m)))
    (if (<= t -1.15e-71)
      (* 9.0 (* (/ x c_m) (/ y z)))
      (if (<= t 5.5e-86) (/ (/ b c_m) 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 (t <= -6.2e+118) {
		tmp = a * (-4.0 * (t / c_m));
	} else if (t <= -1.15e-71) {
		tmp = 9.0 * ((x / c_m) * (y / z));
	} else if (t <= 5.5e-86) {
		tmp = (b / c_m) / z;
	} else {
		tmp = -4.0 * (t * (a / 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 <= (-6.2d+118)) then
        tmp = a * ((-4.0d0) * (t / c_m))
    else if (t <= (-1.15d-71)) then
        tmp = 9.0d0 * ((x / c_m) * (y / z))
    else if (t <= 5.5d-86) then
        tmp = (b / c_m) / z
    else
        tmp = (-4.0d0) * (t * (a / 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 <= -6.2e+118) {
		tmp = a * (-4.0 * (t / c_m));
	} else if (t <= -1.15e-71) {
		tmp = 9.0 * ((x / c_m) * (y / z));
	} else if (t <= 5.5e-86) {
		tmp = (b / c_m) / z;
	} else {
		tmp = -4.0 * (t * (a / 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 <= -6.2e+118:
		tmp = a * (-4.0 * (t / c_m))
	elif t <= -1.15e-71:
		tmp = 9.0 * ((x / c_m) * (y / z))
	elif t <= 5.5e-86:
		tmp = (b / c_m) / z
	else:
		tmp = -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 (t <= -6.2e+118)
		tmp = Float64(a * Float64(-4.0 * Float64(t / c_m)));
	elseif (t <= -1.15e-71)
		tmp = Float64(9.0 * Float64(Float64(x / c_m) * Float64(y / z)));
	elseif (t <= 5.5e-86)
		tmp = Float64(Float64(b / c_m) / z);
	else
		tmp = Float64(-4.0 * Float64(t * Float64(a / 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 <= -6.2e+118)
		tmp = a * (-4.0 * (t / c_m));
	elseif (t <= -1.15e-71)
		tmp = 9.0 * ((x / c_m) * (y / z));
	elseif (t <= 5.5e-86)
		tmp = (b / c_m) / z;
	else
		tmp = -4.0 * (t * (a / 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, -6.2e+118], N[(a * N[(-4.0 * N[(t / c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.15e-71], N[(9.0 * N[(N[(x / c$95$m), $MachinePrecision] * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.5e-86], N[(N[(b / c$95$m), $MachinePrecision] / z), $MachinePrecision], N[(-4.0 * N[(t * N[(a / c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]), $MachinePrecision]

Derivation

1. Split input into 4 regimes

2. if t < -6.19999999999999973e118

   1. Initial program 74.0%

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

   3. Simplified 68.3%

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

   5. Taylor expanded in z around inf 58.9%

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

      1. associate-/l* 69.8%

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

      2. associate-*r* 69.8%

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

      3. *-commutative 69.8%

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

      4. associate-*r* 69.8%

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

   7. Simplified 69.8%

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

   if -6.19999999999999973e118 < t < -1.1499999999999999e-71

   1. Initial program 77.1%

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

   3. Simplified 79.6%

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

   5. Taylor expanded in x around inf 46.8%

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

      1. times-frac 48.5%

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

   7. Applied egg-rr 48.5%

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

   if -1.1499999999999999e-71 < t < 5.5e-86

   1. Initial program 86.1%

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

   3. Simplified 86.1%

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

      1. associate-/r* 87.3%

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

      2. div-inv 87.3%

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

      3. +-commutative 87.3%

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

      4. associate-*r* 87.3%

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

      5. *-commutative 87.3%

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

      6. associate-*l* 87.3%

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

   6. Applied egg-rr 87.3%

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

   7. Taylor expanded in b around inf 51.8%

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

      1. associate-/r* 48.7%

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

   9. Simplified 48.7%

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

   if 5.5e-86 < t

   1. Initial program 74.9%

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

   3. Simplified 78.3%

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

      1. associate-/r* 82.7%

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

      2. div-inv 82.7%

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

      3. +-commutative 82.7%

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

      4. associate-*r* 82.7%

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

      5. *-commutative 82.7%

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

      6. associate-*l* 82.7%

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

   6. Applied egg-rr 82.7%

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

   7. Taylor expanded in b around 0 83.6%

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

   8. Taylor expanded in c around 0 83.6%

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

   9. Taylor expanded in a around inf 51.9%

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

       1. associate-*r/ 51.9%

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

       2. associate-*r* 51.9%

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

       3. associate-*l/ 52.3%

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

       4. associate-*r/ 52.2%

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

       5. associate-*l* 52.2%

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

   11. Simplified 52.2%

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

4. Final simplification 52.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.2 \cdot 10^{+118}:\\ \;\;\;\;a \cdot \left(-4 \cdot \frac{t}{c}\right)\\ \mathbf{elif}\;t \leq -1.15 \cdot 10^{-71}:\\ \;\;\;\;9 \cdot \left(\frac{x}{c} \cdot \frac{y}{z}\right)\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{-86}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 68.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\\\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ c\_s \cdot \begin{array}{l} \mathbf{if}\;t \leq -3.9 \cdot 10^{+115}:\\ \;\;\;\;a \cdot \left(-4 \cdot \frac{t}{c\_m}\right)\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{-84}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{c\_m \cdot z}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c\_m}\right)\\ \end{array} \end{array} \]

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 -3.9e+115)
    (* a (* -4.0 (/ t c_m)))
    (if (<= t 2.7e-84)
      (/ (+ b (* 9.0 (* x y))) (* c_m 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 (t <= -3.9e+115) {
		tmp = a * (-4.0 * (t / c_m));
	} else if (t <= 2.7e-84) {
		tmp = (b + (9.0 * (x * y))) / (c_m * z);
	} else {
		tmp = -4.0 * (t * (a / 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 <= (-3.9d+115)) then
        tmp = a * ((-4.0d0) * (t / c_m))
    else if (t <= 2.7d-84) then
        tmp = (b + (9.0d0 * (x * y))) / (c_m * z)
    else
        tmp = (-4.0d0) * (t * (a / 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 <= -3.9e+115) {
		tmp = a * (-4.0 * (t / c_m));
	} else if (t <= 2.7e-84) {
		tmp = (b + (9.0 * (x * y))) / (c_m * z);
	} else {
		tmp = -4.0 * (t * (a / 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 <= -3.9e+115:
		tmp = a * (-4.0 * (t / c_m))
	elif t <= 2.7e-84:
		tmp = (b + (9.0 * (x * y))) / (c_m * z)
	else:
		tmp = -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 (t <= -3.9e+115)
		tmp = Float64(a * Float64(-4.0 * Float64(t / c_m)));
	elseif (t <= 2.7e-84)
		tmp = Float64(Float64(b + Float64(9.0 * Float64(x * y))) / Float64(c_m * z));
	else
		tmp = Float64(-4.0 * Float64(t * Float64(a / 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 <= -3.9e+115)
		tmp = a * (-4.0 * (t / c_m));
	elseif (t <= 2.7e-84)
		tmp = (b + (9.0 * (x * y))) / (c_m * z);
	else
		tmp = -4.0 * (t * (a / 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, -3.9e+115], N[(a * N[(-4.0 * N[(t / c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.7e-84], N[(N[(b + N[(9.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision], N[(-4.0 * N[(t * N[(a / c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if t < -3.90000000000000006e115

   1. Initial program 74.0%

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

   3. Simplified 68.3%

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

   5. Taylor expanded in z around inf 58.9%

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

      1. associate-/l* 69.8%

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

      2. associate-*r* 69.8%

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

      3. *-commutative 69.8%

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

      4. associate-*r* 69.8%

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

   7. Simplified 69.8%

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

   if -3.90000000000000006e115 < t < 2.6999999999999999e-84

   1. Initial program 83.2%

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

   3. Simplified 84.1%

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

   5. Taylor expanded in z around 0 75.3%

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

      1. +-commutative 75.3%

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

      2. *-commutative 75.3%

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

   7. Simplified 75.3%

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

   if 2.6999999999999999e-84 < t

   1. Initial program 74.9%

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

   3. Simplified 78.3%

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

      1. associate-/r* 82.7%

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

      2. div-inv 82.7%

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

      3. +-commutative 82.7%

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

      4. associate-*r* 82.7%

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

      5. *-commutative 82.7%

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

      6. associate-*l* 82.7%

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

   6. Applied egg-rr 82.7%

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

   7. Taylor expanded in b around 0 83.6%

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

   8. Taylor expanded in c around 0 83.6%

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

   9. Taylor expanded in a around inf 51.9%

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

       1. associate-*r/ 51.9%

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

       2. associate-*r* 51.9%

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

       3. associate-*l/ 52.3%

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

       4. associate-*r/ 52.2%

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

       5. associate-*l* 52.2%

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

   11. Simplified 52.2%

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

4. Final simplification 66.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.9 \cdot 10^{+115}:\\ \;\;\;\;a \cdot \left(-4 \cdot \frac{t}{c}\right)\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{-84}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 50.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\\\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ c\_s \cdot \begin{array}{l} \mathbf{if}\;a \leq -4.2 \cdot 10^{-82} \lor \neg \left(a \leq 2.2 \cdot 10^{+56}\right):\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c\_m}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{c\_m \cdot z}\\ \end{array} \end{array} \]

FPCore

c\_m = (fabs.f64 c)
c\_s = (copysign.f64 #s(literal 1 binary64) c)
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, and c_m should be sorted in increasing order before calling this function.
(FPCore (c_s x y z t a b c_m)
 :precision binary64
 (*
  c_s
  (if (or (<= a -4.2e-82) (not (<= a 2.2e+56)))
    (* -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 ((a <= -4.2e-82) || !(a <= 2.2e+56)) {
		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 ((a <= (-4.2d-82)) .or. (.not. (a <= 2.2d+56))) 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 ((a <= -4.2e-82) || !(a <= 2.2e+56)) {
		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 (a <= -4.2e-82) or not (a <= 2.2e+56):
		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 ((a <= -4.2e-82) || !(a <= 2.2e+56))
		tmp = Float64(-4.0 * Float64(t * Float64(a / c_m)));
	else
		tmp = Float64(b / Float64(c_m * z));
	end
	return Float64(c_s * tmp)
end

MATLAB

c\_m = abs(c);
c\_s = sign(c) * abs(1.0);
x, y, z, t, a, b, c_m = num2cell(sort([x, y, z, t, a, b, c_m])){:}
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 ((a <= -4.2e-82) || ~((a <= 2.2e+56)))
		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[Or[LessEqual[a, -4.2e-82], N[Not[LessEqual[a, 2.2e+56]], $MachinePrecision]], N[(-4.0 * N[(t * N[(a / c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if a < -4.2000000000000001e-82 or 2.20000000000000016e56 < a

   1. Initial program 76.3%

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

   3. Simplified 73.6%

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

      1. associate-/r* 77.2%

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

      2. div-inv 77.2%

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

      3. +-commutative 77.2%

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

      4. associate-*r* 77.2%

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

      5. *-commutative 77.2%

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

      6. associate-*l* 77.2%

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

   6. Applied egg-rr 77.2%

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

   7. Taylor expanded in b around 0 80.4%

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

   8. Taylor expanded in c around 0 80.4%

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

   9. Taylor expanded in a around inf 48.0%

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

       1. associate-*r/ 48.0%

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

       2. associate-*r* 48.0%

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

       3. associate-*l/ 51.3%

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

       4. associate-*r/ 51.3%

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

       5. associate-*l* 51.3%

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

   11. Simplified 51.3%

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

   if -4.2000000000000001e-82 < a < 2.20000000000000016e56

   1. Initial program 82.7%

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

   3. Simplified 88.0%

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

   5. Taylor expanded in b around inf 50.6%

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

      1. *-commutative 50.6%

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

   7. Simplified 50.6%

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

4. Final simplification 51.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.2 \cdot 10^{-82} \lor \neg \left(a \leq 2.2 \cdot 10^{+56}\right):\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 50.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} c\_m = \left|c\right| \\ c\_s = \mathsf{copysign}\left(1, c\right) \\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\\\ [x, y, z, t, a, b, c_m] = \mathsf{sort}([x, y, z, t, a, b, c_m])\\ \\ c\_s \cdot \begin{array}{l} \mathbf{if}\;a \leq -9 \cdot 10^{-83}:\\ \;\;\;\;a \cdot \left(-4 \cdot \frac{t}{c\_m}\right)\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{+56}:\\ \;\;\;\;\frac{b}{c\_m \cdot z}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c\_m}\right)\\ \end{array} \end{array} \]

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 (<= a -9e-83)
    (* a (* -4.0 (/ t c_m)))
    (if (<= a 1.1e+56) (/ b (* c_m 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 (a <= -9e-83) {
		tmp = a * (-4.0 * (t / c_m));
	} else if (a <= 1.1e+56) {
		tmp = b / (c_m * z);
	} else {
		tmp = -4.0 * (t * (a / 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 (a <= (-9d-83)) then
        tmp = a * ((-4.0d0) * (t / c_m))
    else if (a <= 1.1d+56) then
        tmp = b / (c_m * z)
    else
        tmp = (-4.0d0) * (t * (a / 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 (a <= -9e-83) {
		tmp = a * (-4.0 * (t / c_m));
	} else if (a <= 1.1e+56) {
		tmp = b / (c_m * z);
	} else {
		tmp = -4.0 * (t * (a / 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 a <= -9e-83:
		tmp = a * (-4.0 * (t / c_m))
	elif a <= 1.1e+56:
		tmp = b / (c_m * z)
	else:
		tmp = -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 (a <= -9e-83)
		tmp = Float64(a * Float64(-4.0 * Float64(t / c_m)));
	elseif (a <= 1.1e+56)
		tmp = Float64(b / Float64(c_m * z));
	else
		tmp = Float64(-4.0 * Float64(t * Float64(a / 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 (a <= -9e-83)
		tmp = a * (-4.0 * (t / c_m));
	elseif (a <= 1.1e+56)
		tmp = b / (c_m * z);
	else
		tmp = -4.0 * (t * (a / 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[a, -9e-83], N[(a * N[(-4.0 * N[(t / c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.1e+56], N[(b / N[(c$95$m * z), $MachinePrecision]), $MachinePrecision], N[(-4.0 * N[(t * N[(a / c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if a < -8.99999999999999995e-83

   1. Initial program 71.2%

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

   3. Simplified 70.3%

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

   5. Taylor expanded in z around inf 45.9%

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

      1. associate-/l* 47.9%

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

      2. associate-*r* 47.9%

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

      3. *-commutative 47.9%

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

      4. associate-*r* 47.9%

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

   7. Simplified 47.9%

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

   if -8.99999999999999995e-83 < a < 1.10000000000000008e56

   1. Initial program 82.7%

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

   3. Simplified 88.0%

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

   5. Taylor expanded in b around inf 50.6%

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

      1. *-commutative 50.6%

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

   7. Simplified 50.6%

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

   if 1.10000000000000008e56 < a

   1. Initial program 86.1%

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

   3. Simplified 80.0%

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

      1. associate-/r* 72.7%

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

      2. div-inv 72.8%

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

      3. +-commutative 72.8%

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

      4. associate-*r* 72.8%

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

      5. *-commutative 72.8%

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

      6. associate-*l* 72.8%

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

   6. Applied egg-rr 72.8%

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

   7. Taylor expanded in b around 0 70.7%

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

   8. Taylor expanded in c around 0 70.6%

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

   9. Taylor expanded in a around inf 52.0%

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

       1. associate-*r/ 52.0%

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

       2. associate-*r* 52.0%

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

       3. associate-*l/ 57.9%

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

       4. associate-*r/ 57.9%

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

       5. associate-*l* 57.9%

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

   11. Simplified 57.9%

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

4. Final simplification 51.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -9 \cdot 10^{-83}:\\ \;\;\;\;a \cdot \left(-4 \cdot \frac{t}{c}\right)\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{+56}:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 35.1% accurate, 3.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 79.1%

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

3. Simplified 80.0%

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

   1. associate-/r* 81.9%

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

   2. div-inv 81.9%

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

   3. +-commutative 81.9%

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

   4. associate-*r* 81.9%

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

   5. *-commutative 81.9%

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

   6. associate-*l* 81.9%

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

6. Applied egg-rr 81.9%

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

7. Taylor expanded in b around inf 37.8%

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

   1. associate-/r* 38.1%

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

9. Simplified 38.1%

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

Alternative 13: 35.5% accurate, 3.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 79.1%

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

3. Simplified 80.0%

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

5. Taylor expanded in b around inf 37.8%

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

   1. *-commutative 37.8%

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

7. Simplified 37.8%

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

8. Final simplification 37.8%

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

Developer Target 1: 80.8% 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 2024170 
(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)))