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

Percentage Accurate: 79.0% → 88.2%

Time: 20.4s

Alternatives: 18

Speedup: 0.9×

• 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: 79.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 88.2% accurate, 0.1× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} t_1 := \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\\ \mathbf{if}\;t_1 \leq -2 \cdot 10^{-73}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq 0:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, 9 \cdot y, \mathsf{fma}\left(t, z \cdot \left(a \cdot -4\right), b\right)\right)}{z} \cdot \frac{1}{c}\\ \mathbf{elif}\;t_1 \leq \infty:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a \cdot \frac{-t}{-c}, -4, \mathsf{fma}\left(9, \frac{x}{z} \cdot \frac{y}{c}, \frac{b}{z \cdot c}\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c))))
   (if (<= t_1 -2e-73)
     t_1
     (if (<= t_1 0.0)
       (* (/ (fma x (* 9.0 y) (fma t (* z (* a -4.0)) b)) z) (/ 1.0 c))
       (if (<= t_1 INFINITY)
         t_1
         (fma
          (* a (/ (- t) (- c)))
          -4.0
          (fma 9.0 (* (/ x z) (/ y c)) (/ b (* z c)))))))))

C

assert(x < y);
assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c);
	double tmp;
	if (t_1 <= -2e-73) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = (fma(x, (9.0 * y), fma(t, (z * (a * -4.0)), b)) / z) * (1.0 / c);
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = fma((a * (-t / -c)), -4.0, fma(9.0, ((x / z) * (y / c)), (b / (z * c))));
	}
	return tmp;
}

Julia

x, y = sort([x, y])
t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(Float64(Float64(Float64(x * 9.0) * y) - Float64(Float64(Float64(z * 4.0) * t) * a)) + b) / Float64(z * c))
	tmp = 0.0
	if (t_1 <= -2e-73)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = Float64(Float64(fma(x, Float64(9.0 * y), fma(t, Float64(z * Float64(a * -4.0)), b)) / z) * Float64(1.0 / c));
	elseif (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = fma(Float64(a * Float64(Float64(-t) / Float64(-c))), -4.0, fma(9.0, Float64(Float64(x / z) * Float64(y / c)), Float64(b / Float64(z * c))));
	end
	return tmp
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = 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]}, If[LessEqual[t$95$1, -2e-73], t$95$1, If[LessEqual[t$95$1, 0.0], N[(N[(N[(x * N[(9.0 * y), $MachinePrecision] + N[(t * N[(z * N[(a * -4.0), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] * N[(1.0 / c), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, Infinity], t$95$1, N[(N[(a * N[((-t) / (-c)), $MachinePrecision]), $MachinePrecision] * -4.0 + N[(9.0 * N[(N[(x / z), $MachinePrecision] * N[(y / c), $MachinePrecision]), $MachinePrecision] + N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)) b) (*.f64 z c)) < -1.99999999999999999e-73 or -0.0 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)) b) (*.f64 z c)) < +inf.0

   1. Initial program 94.6%

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

   if -1.99999999999999999e-73 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)) b) (*.f64 z c)) < -0.0

   1. Initial program 60.5%

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

      1. associate-+l- 60.5%

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

      2. div-sub 60.5%

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

      3. *-commutative 60.5%

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

      4. associate-*r* 56.2%

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

      5. *-commutative 56.2%

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

      6. div-sub 56.2%

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

      7. associate-+l- 56.2%

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

   3. Simplified 60.4%

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

      1. associate-+l- 60.4%

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

      2. associate-+l- 60.4%

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

      3. sub-neg 60.4%

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

      4. associate-+l+ 60.4%

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

      5. distribute-lft-neg-in 60.4%

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

      6. *-commutative 60.4%

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

      7. associate-*r* 56.2%

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

      8. distribute-rgt-neg-in 56.2%

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

      9. metadata-eval 56.2%

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

      10. associate-*r* 56.2%

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

      11. *-commutative 56.2%

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

      12. *-commutative 56.2%

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

      13. +-commutative 56.2%

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

      14. fma-udef 56.2%

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

   5. Applied egg-rr 84.0%

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

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

   1. Initial program 0.0%

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

      1. associate-+l- 0.0%

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

      2. div-sub 0.0%

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

      3. *-commutative 0.0%

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

      4. associate-*r* 0.7%

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

      5. *-commutative 0.7%

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

      6. div-sub 0.7%

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

      7. associate-+l- 0.7%

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

   3. Simplified 0.7%

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

   4. Taylor expanded in x around 0 32.9%

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

      1. cancel-sign-sub-inv 32.9%

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

      2. metadata-eval 32.9%

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

      3. +-commutative 32.9%

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

      4. *-commutative 32.9%

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

      5. fma-def 32.9%

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

      6. associate-/l* 50.1%

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

      7. associate-/r/ 38.6%

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

      8. fma-def 38.6%

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

      9. *-commutative 38.6%

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

      10. times-frac 79.4%

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

      11. *-commutative 79.4%

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

   6. Simplified 79.4%

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

      1. *-commutative 79.4%

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

      2. frac-2neg 79.4%

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

      3. associate-*r/ 73.7%

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

   8. Applied egg-rr 73.7%

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

      1. associate-/l* 78.0%

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

      2. associate-/r/ 90.5%

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

   10. Simplified 90.5%

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

4. Final simplification 93.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \leq -2 \cdot 10^{-73}:\\ \;\;\;\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\\ \mathbf{elif}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \leq 0:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, 9 \cdot y, \mathsf{fma}\left(t, z \cdot \left(a \cdot -4\right), b\right)\right)}{z} \cdot \frac{1}{c}\\ \mathbf{elif}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \leq \infty:\\ \;\;\;\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a \cdot \frac{-t}{-c}, -4, \mathsf{fma}\left(9, \frac{x}{z} \cdot \frac{y}{c}, \frac{b}{z \cdot c}\right)\right)\\ \end{array} \]

Alternative 2: 88.0% accurate, 0.1× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} t_1 := \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\\ \mathbf{if}\;t_1 \leq -2 \cdot 10^{-73}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq 0:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, 9 \cdot y, \mathsf{fma}\left(t, z \cdot \left(a \cdot -4\right), b\right)\right)}{z} \cdot \frac{1}{c}\\ \mathbf{elif}\;t_1 \leq \infty:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t \cdot \frac{a}{c}, -4, \mathsf{fma}\left(9, \frac{x}{z} \cdot \frac{y}{c}, \frac{b}{z \cdot c}\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c))))
   (if (<= t_1 -2e-73)
     t_1
     (if (<= t_1 0.0)
       (* (/ (fma x (* 9.0 y) (fma t (* z (* a -4.0)) b)) z) (/ 1.0 c))
       (if (<= t_1 INFINITY)
         t_1
         (fma
          (* t (/ a c))
          -4.0
          (fma 9.0 (* (/ x z) (/ y c)) (/ b (* z c)))))))))

C

assert(x < y);
assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c);
	double tmp;
	if (t_1 <= -2e-73) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = (fma(x, (9.0 * y), fma(t, (z * (a * -4.0)), b)) / z) * (1.0 / c);
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = fma((t * (a / c)), -4.0, fma(9.0, ((x / z) * (y / c)), (b / (z * c))));
	}
	return tmp;
}

Julia

x, y = sort([x, y])
t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(Float64(Float64(Float64(x * 9.0) * y) - Float64(Float64(Float64(z * 4.0) * t) * a)) + b) / Float64(z * c))
	tmp = 0.0
	if (t_1 <= -2e-73)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = Float64(Float64(fma(x, Float64(9.0 * y), fma(t, Float64(z * Float64(a * -4.0)), b)) / z) * Float64(1.0 / c));
	elseif (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = fma(Float64(t * Float64(a / c)), -4.0, fma(9.0, Float64(Float64(x / z) * Float64(y / c)), Float64(b / Float64(z * c))));
	end
	return tmp
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = 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]}, If[LessEqual[t$95$1, -2e-73], t$95$1, If[LessEqual[t$95$1, 0.0], N[(N[(N[(x * N[(9.0 * y), $MachinePrecision] + N[(t * N[(z * N[(a * -4.0), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] * N[(1.0 / c), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, Infinity], t$95$1, N[(N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision] * -4.0 + N[(9.0 * N[(N[(x / z), $MachinePrecision] * N[(y / c), $MachinePrecision]), $MachinePrecision] + N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)) b) (*.f64 z c)) < -1.99999999999999999e-73 or -0.0 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)) b) (*.f64 z c)) < +inf.0

   1. Initial program 94.6%

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

   if -1.99999999999999999e-73 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)) b) (*.f64 z c)) < -0.0

   1. Initial program 60.5%

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

      1. associate-+l- 60.5%

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

      2. div-sub 60.5%

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

      3. *-commutative 60.5%

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

      4. associate-*r* 56.2%

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

      5. *-commutative 56.2%

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

      6. div-sub 56.2%

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

      7. associate-+l- 56.2%

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

   3. Simplified 60.4%

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

      1. associate-+l- 60.4%

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

      2. associate-+l- 60.4%

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

      3. sub-neg 60.4%

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

      4. associate-+l+ 60.4%

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

      5. distribute-lft-neg-in 60.4%

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

      6. *-commutative 60.4%

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

      7. associate-*r* 56.2%

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

      8. distribute-rgt-neg-in 56.2%

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

      9. metadata-eval 56.2%

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

      10. associate-*r* 56.2%

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

      11. *-commutative 56.2%

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

      12. *-commutative 56.2%

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

      13. +-commutative 56.2%

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

      14. fma-udef 56.2%

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

   5. Applied egg-rr 84.0%

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

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

   1. Initial program 0.0%

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

      1. associate-+l- 0.0%

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

      2. div-sub 0.0%

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

      3. *-commutative 0.0%

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

      4. associate-*r* 0.7%

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

      5. *-commutative 0.7%

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

      6. div-sub 0.7%

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

      7. associate-+l- 0.7%

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

   3. Simplified 0.7%

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

   4. Taylor expanded in x around 0 32.9%

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

      1. cancel-sign-sub-inv 32.9%

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

      2. metadata-eval 32.9%

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

      3. +-commutative 32.9%

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

      4. *-commutative 32.9%

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

      5. fma-def 32.9%

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

      6. associate-/l* 50.1%

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

      7. associate-/r/ 38.6%

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

      8. fma-def 38.6%

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

      9. *-commutative 38.6%

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

      10. times-frac 79.4%

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

      11. *-commutative 79.4%

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

   6. Simplified 79.4%

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

4. Final simplification 92.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \leq -2 \cdot 10^{-73}:\\ \;\;\;\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\\ \mathbf{elif}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \leq 0:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, 9 \cdot y, \mathsf{fma}\left(t, z \cdot \left(a \cdot -4\right), b\right)\right)}{z} \cdot \frac{1}{c}\\ \mathbf{elif}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \leq \infty:\\ \;\;\;\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t \cdot \frac{a}{c}, -4, \mathsf{fma}\left(9, \frac{x}{z} \cdot \frac{y}{c}, \frac{b}{z \cdot c}\right)\right)\\ \end{array} \]

Alternative 3: 88.6% accurate, 0.1× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+108} \lor \neg \left(z \leq 4.3 \cdot 10^{+70}\right):\\ \;\;\;\;\left(\frac{b}{z \cdot c} + 9 \cdot \frac{x \cdot y}{z \cdot c}\right) - 4 \cdot \frac{t \cdot a}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{z} \cdot \frac{\mathsf{fma}\left(x, 9 \cdot y, \mathsf{fma}\left(t, z \cdot \left(a \cdot -4\right), b\right)\right)}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= z -2e+108) (not (<= z 4.3e+70)))
   (- (+ (/ b (* z c)) (* 9.0 (/ (* x y) (* z c)))) (* 4.0 (/ (* t a) c)))
   (* (/ 1.0 z) (/ (fma x (* 9.0 y) (fma t (* z (* a -4.0)) b)) c))))

C

assert(x < y);
assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((z <= -2e+108) || !(z <= 4.3e+70)) {
		tmp = ((b / (z * c)) + (9.0 * ((x * y) / (z * c)))) - (4.0 * ((t * a) / c));
	} else {
		tmp = (1.0 / z) * (fma(x, (9.0 * y), fma(t, (z * (a * -4.0)), b)) / c);
	}
	return tmp;
}

Julia

x, y = sort([x, y])
t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((z <= -2e+108) || !(z <= 4.3e+70))
		tmp = Float64(Float64(Float64(b / Float64(z * c)) + Float64(9.0 * Float64(Float64(x * y) / Float64(z * c)))) - Float64(4.0 * Float64(Float64(t * a) / c)));
	else
		tmp = Float64(Float64(1.0 / z) * Float64(fma(x, Float64(9.0 * y), fma(t, Float64(z * Float64(a * -4.0)), b)) / c));
	end
	return tmp
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[z, -2e+108], N[Not[LessEqual[z, 4.3e+70]], $MachinePrecision]], N[(N[(N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision] + N[(9.0 * N[(N[(x * y), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * N[(N[(t * a), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(1.0 / z), $MachinePrecision] * N[(N[(x * N[(9.0 * y), $MachinePrecision] + N[(t * N[(z * N[(a * -4.0), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.0000000000000001e108 or 4.3000000000000001e70 < z

   1. Initial program 60.8%

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

      1. associate-+l- 60.8%

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

      2. div-sub 60.8%

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

      3. *-commutative 60.8%

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

      4. associate-*r* 60.3%

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

      5. *-commutative 60.3%

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

      6. div-sub 60.4%

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

      7. associate-+l- 60.4%

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

   3. Simplified 64.5%

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

   4. Taylor expanded in x around 0 81.6%

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

   if -2.0000000000000001e108 < z < 4.3000000000000001e70

   1. Initial program 92.1%

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

      1. associate-+l- 92.1%

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

      2. div-sub 80.8%

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

      3. *-commutative 80.8%

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

      4. associate-*r* 80.8%

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

      5. *-commutative 80.8%

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

      6. div-sub 92.1%

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

      7. associate-+l- 92.1%

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

   3. Simplified 90.0%

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

      1. sub-neg 90.0%

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

      2. associate-+l+ 90.0%

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

      3. distribute-lft-neg-in 90.0%

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

      4. *-commutative 90.0%

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

      5. associate-*r* 92.1%

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

      6. distribute-rgt-neg-in 92.1%

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

      7. metadata-eval 92.1%

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

      8. associate-*r* 92.1%

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

      9. *-commutative 92.1%

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

      10. *-commutative 92.1%

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

      11. +-commutative 92.1%

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

      12. *-un-lft-identity 92.1%

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

      13. fma-udef 92.1%

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

   5. Applied egg-rr 94.8%

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

4. Final simplification 90.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+108} \lor \neg \left(z \leq 4.3 \cdot 10^{+70}\right):\\ \;\;\;\;\left(\frac{b}{z \cdot c} + 9 \cdot \frac{x \cdot y}{z \cdot c}\right) - 4 \cdot \frac{t \cdot a}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{z} \cdot \frac{\mathsf{fma}\left(x, 9 \cdot y, \mathsf{fma}\left(t, z \cdot \left(a \cdot -4\right), b\right)\right)}{c}\\ \end{array} \]

Alternative 4: 88.5% accurate, 0.1× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.95 \cdot 10^{+108} \lor \neg \left(z \leq 1.75 \cdot 10^{+70}\right):\\ \;\;\;\;\left(\frac{b}{z \cdot c} + 9 \cdot \frac{x \cdot y}{z \cdot c}\right) - 4 \cdot \frac{t \cdot a}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{1}{z}}{\frac{c}{\mathsf{fma}\left(x, 9 \cdot y, \mathsf{fma}\left(t, z \cdot \left(a \cdot -4\right), b\right)\right)}}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= z -1.95e+108) (not (<= z 1.75e+70)))
   (- (+ (/ b (* z c)) (* 9.0 (/ (* x y) (* z c)))) (* 4.0 (/ (* t a) c)))
   (/ (/ 1.0 z) (/ c (fma x (* 9.0 y) (fma t (* z (* a -4.0)) b))))))

C

assert(x < y);
assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((z <= -1.95e+108) || !(z <= 1.75e+70)) {
		tmp = ((b / (z * c)) + (9.0 * ((x * y) / (z * c)))) - (4.0 * ((t * a) / c));
	} else {
		tmp = (1.0 / z) / (c / fma(x, (9.0 * y), fma(t, (z * (a * -4.0)), b)));
	}
	return tmp;
}

Julia

x, y = sort([x, y])
t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((z <= -1.95e+108) || !(z <= 1.75e+70))
		tmp = Float64(Float64(Float64(b / Float64(z * c)) + Float64(9.0 * Float64(Float64(x * y) / Float64(z * c)))) - Float64(4.0 * Float64(Float64(t * a) / c)));
	else
		tmp = Float64(Float64(1.0 / z) / Float64(c / fma(x, Float64(9.0 * y), fma(t, Float64(z * Float64(a * -4.0)), b))));
	end
	return tmp
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[z, -1.95e+108], N[Not[LessEqual[z, 1.75e+70]], $MachinePrecision]], N[(N[(N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision] + N[(9.0 * N[(N[(x * y), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * N[(N[(t * a), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(1.0 / z), $MachinePrecision] / N[(c / N[(x * N[(9.0 * y), $MachinePrecision] + N[(t * N[(z * N[(a * -4.0), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.94999999999999992e108 or 1.75000000000000001e70 < z

   1. Initial program 60.8%

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

      1. associate-+l- 60.8%

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

      2. div-sub 60.8%

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

      3. *-commutative 60.8%

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

      4. associate-*r* 60.3%

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

      5. *-commutative 60.3%

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

      6. div-sub 60.4%

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

      7. associate-+l- 60.4%

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

   3. Simplified 64.5%

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

   4. Taylor expanded in x around 0 81.6%

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

   if -1.94999999999999992e108 < z < 1.75000000000000001e70

   1. Initial program 92.1%

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

      1. associate-+l- 92.1%

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

      2. div-sub 80.8%

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

      3. *-commutative 80.8%

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

      4. associate-*r* 80.8%

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

      5. *-commutative 80.8%

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

      6. div-sub 92.1%

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

      7. associate-+l- 92.1%

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

   3. Simplified 90.0%

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

      1. sub-neg 90.0%

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

      2. associate-+l+ 90.0%

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

      3. distribute-lft-neg-in 90.0%

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

      4. *-commutative 90.0%

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

      5. associate-*r* 92.1%

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

      6. distribute-rgt-neg-in 92.1%

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

      7. metadata-eval 92.1%

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

      8. associate-*r* 92.1%

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

      9. *-commutative 92.1%

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

      10. *-commutative 92.1%

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

      11. +-commutative 92.1%

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

      12. *-un-lft-identity 92.1%

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

      13. fma-udef 92.1%

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

   5. Applied egg-rr 94.8%

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

      1. clear-num 94.8%

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

      2. un-div-inv 94.8%

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

   7. Applied egg-rr 94.8%

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

4. Final simplification 90.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.95 \cdot 10^{+108} \lor \neg \left(z \leq 1.75 \cdot 10^{+70}\right):\\ \;\;\;\;\left(\frac{b}{z \cdot c} + 9 \cdot \frac{x \cdot y}{z \cdot c}\right) - 4 \cdot \frac{t \cdot a}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{1}{z}}{\frac{c}{\mathsf{fma}\left(x, 9 \cdot y, \mathsf{fma}\left(t, z \cdot \left(a \cdot -4\right), b\right)\right)}}\\ \end{array} \]

Alternative 5: 84.8% accurate, 0.2× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} t_1 := \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\\ \mathbf{if}\;t_1 \leq -2 \cdot 10^{-294}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq 0:\\ \;\;\;\;\frac{x \cdot 9}{z \cdot \frac{c}{y}}\\ \mathbf{elif}\;t_1 \leq \infty:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{a \cdot -4}{\frac{c}{t}}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c))))
   (if (<= t_1 -2e-294)
     t_1
     (if (<= t_1 0.0)
       (/ (* x 9.0) (* z (/ c y)))
       (if (<= t_1 INFINITY) t_1 (/ (* a -4.0) (/ c t)))))))

C

assert(x < y);
assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c);
	double tmp;
	if (t_1 <= -2e-294) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = (x * 9.0) / (z * (c / y));
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = (a * -4.0) / (c / t);
	}
	return tmp;
}

Java

assert x < y;
assert t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c);
	double tmp;
	if (t_1 <= -2e-294) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = (x * 9.0) / (z * (c / y));
	} else if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else {
		tmp = (a * -4.0) / (c / t);
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	t_1 = ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c)
	tmp = 0
	if t_1 <= -2e-294:
		tmp = t_1
	elif t_1 <= 0.0:
		tmp = (x * 9.0) / (z * (c / y))
	elif t_1 <= math.inf:
		tmp = t_1
	else:
		tmp = (a * -4.0) / (c / t)
	return tmp

Julia

x, y = sort([x, y])
t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(Float64(Float64(Float64(x * 9.0) * y) - Float64(Float64(Float64(z * 4.0) * t) * a)) + b) / Float64(z * c))
	tmp = 0.0
	if (t_1 <= -2e-294)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = Float64(Float64(x * 9.0) / Float64(z * Float64(c / y)));
	elseif (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = Float64(Float64(a * -4.0) / Float64(c / t));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c);
	tmp = 0.0;
	if (t_1 <= -2e-294)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = (x * 9.0) / (z * (c / y));
	elseif (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = (a * -4.0) / (c / t);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = 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]}, If[LessEqual[t$95$1, -2e-294], t$95$1, If[LessEqual[t$95$1, 0.0], N[(N[(x * 9.0), $MachinePrecision] / N[(z * N[(c / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, Infinity], t$95$1, N[(N[(a * -4.0), $MachinePrecision] / N[(c / t), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)) b) (*.f64 z c)) < -2.00000000000000003e-294 or -0.0 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)) b) (*.f64 z c)) < +inf.0

   1. Initial program 94.9%

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

   if -2.00000000000000003e-294 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)) b) (*.f64 z c)) < -0.0

   1. Initial program 38.9%

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

      1. associate-+l- 38.9%

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

      2. div-sub 38.9%

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

      3. *-commutative 38.9%

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

      4. associate-*r* 32.3%

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

      5. *-commutative 32.3%

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

      6. div-sub 32.3%

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

      7. associate-+l- 32.3%

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

   3. Simplified 38.9%

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

   4. Taylor expanded in x around inf 38.9%

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

      1. *-commutative 38.9%

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

      2. associate-/l* 38.9%

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

      3. associate-*l/ 38.9%

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

      4. *-commutative 38.9%

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

      5. *-un-lft-identity 38.9%

         \[\leadsto \frac{x \cdot 9}{\frac{z \cdot c}{\color{blue}{1 \cdot y}}} \]

      6. times-frac 53.2%

         \[\leadsto \frac{x \cdot 9}{\color{blue}{\frac{z}{1} \cdot \frac{c}{y}}} \]

      7. /-rgt-identity 53.2%

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

   6. Applied egg-rr 53.2%

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

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

   1. Initial program 0.0%

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

      1. associate-+l- 0.0%

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

      2. div-sub 0.0%

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

      3. *-commutative 0.0%

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

      4. associate-*r* 0.7%

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

      5. *-commutative 0.7%

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

      6. div-sub 0.7%

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

      7. associate-+l- 0.7%

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

   3. Simplified 0.7%

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

   4. Taylor expanded in z around inf 38.4%

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

      1. associate-/l* 55.6%

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

      2. associate-*r/ 55.6%

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

      3. *-commutative 55.6%

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

   6. Simplified 55.6%

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

4. Final simplification 88.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \leq -2 \cdot 10^{-294}:\\ \;\;\;\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\\ \mathbf{elif}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \leq 0:\\ \;\;\;\;\frac{x \cdot 9}{z \cdot \frac{c}{y}}\\ \mathbf{elif}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \leq \infty:\\ \;\;\;\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{a \cdot -4}{\frac{c}{t}}\\ \end{array} \]

Alternative 6: 88.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -4.4 \cdot 10^{+128} \lor \neg \left(z \leq 1.16 \cdot 10^{+19}\right):\\ \;\;\;\;\left(\frac{b}{z \cdot c} + 9 \cdot \frac{x \cdot y}{z \cdot c}\right) - 4 \cdot \frac{t \cdot a}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= z -4.4e+128) (not (<= z 1.16e+19)))
   (- (+ (/ b (* z c)) (* 9.0 (/ (* x y) (* z c)))) (* 4.0 (/ (* t a) c)))
   (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c))))

C

assert(x < y);
assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((z <= -4.4e+128) || !(z <= 1.16e+19)) {
		tmp = ((b / (z * c)) + (9.0 * ((x * y) / (z * c)))) - (4.0 * ((t * a) / c));
	} else {
		tmp = ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c);
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
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) :: tmp
    if ((z <= (-4.4d+128)) .or. (.not. (z <= 1.16d+19))) then
        tmp = ((b / (z * c)) + (9.0d0 * ((x * y) / (z * c)))) - (4.0d0 * ((t * a) / c))
    else
        tmp = ((((x * 9.0d0) * y) - (((z * 4.0d0) * t) * a)) + b) / (z * c)
    end if
    code = tmp
end function

Java

assert x < y;
assert t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((z <= -4.4e+128) || !(z <= 1.16e+19)) {
		tmp = ((b / (z * c)) + (9.0 * ((x * y) / (z * c)))) - (4.0 * ((t * a) / c));
	} else {
		tmp = ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c);
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if (z <= -4.4e+128) or not (z <= 1.16e+19):
		tmp = ((b / (z * c)) + (9.0 * ((x * y) / (z * c)))) - (4.0 * ((t * a) / c))
	else:
		tmp = ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c)
	return tmp

Julia

x, y = sort([x, y])
t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((z <= -4.4e+128) || !(z <= 1.16e+19))
		tmp = Float64(Float64(Float64(b / Float64(z * c)) + Float64(9.0 * Float64(Float64(x * y) / Float64(z * c)))) - Float64(4.0 * Float64(Float64(t * a) / c)));
	else
		tmp = Float64(Float64(Float64(Float64(Float64(x * 9.0) * y) - Float64(Float64(Float64(z * 4.0) * t) * a)) + b) / Float64(z * c));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((z <= -4.4e+128) || ~((z <= 1.16e+19)))
		tmp = ((b / (z * c)) + (9.0 * ((x * y) / (z * c)))) - (4.0 * ((t * a) / c));
	else
		tmp = ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[z, -4.4e+128], N[Not[LessEqual[z, 1.16e+19]], $MachinePrecision]], N[(N[(N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision] + N[(9.0 * N[(N[(x * y), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * N[(N[(t * a), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision] - N[(N[(N[(z * 4.0), $MachinePrecision] * t), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.40000000000000033e128 or 1.16e19 < z

   1. Initial program 63.7%

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

      1. associate-+l- 63.7%

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

      2. div-sub 63.7%

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

      3. *-commutative 63.7%

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

      4. associate-*r* 62.3%

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

      5. *-commutative 62.3%

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

      6. div-sub 62.3%

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

      7. associate-+l- 62.3%

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

   3. Simplified 66.0%

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

   4. Taylor expanded in x around 0 81.8%

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

   if -4.40000000000000033e128 < z < 1.16e19

   1. Initial program 92.8%

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

4. Final simplification 88.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.4 \cdot 10^{+128} \lor \neg \left(z \leq 1.16 \cdot 10^{+19}\right):\\ \;\;\;\;\left(\frac{b}{z \cdot c} + 9 \cdot \frac{x \cdot y}{z \cdot c}\right) - 4 \cdot \frac{t \cdot a}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\\ \end{array} \]

Alternative 7: 82.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq 6.6 \cdot 10^{+167}:\\ \;\;\;\;\frac{b + \left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{z \cdot c} + -4 \cdot \frac{t \cdot a}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= z 6.6e+167)
   (/ (+ b (- (* x (* 9.0 y)) (* (* z 4.0) (* t a)))) (* z c))
   (+ (/ b (* z c)) (* -4.0 (/ (* t a) c)))))

C

assert(x < y);
assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (z <= 6.6e+167) {
		tmp = (b + ((x * (9.0 * y)) - ((z * 4.0) * (t * a)))) / (z * c);
	} else {
		tmp = (b / (z * c)) + (-4.0 * ((t * a) / c));
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
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) :: tmp
    if (z <= 6.6d+167) then
        tmp = (b + ((x * (9.0d0 * y)) - ((z * 4.0d0) * (t * a)))) / (z * c)
    else
        tmp = (b / (z * c)) + ((-4.0d0) * ((t * a) / c))
    end if
    code = tmp
end function

Java

assert x < y;
assert t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (z <= 6.6e+167) {
		tmp = (b + ((x * (9.0 * y)) - ((z * 4.0) * (t * a)))) / (z * c);
	} else {
		tmp = (b / (z * c)) + (-4.0 * ((t * a) / c));
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if z <= 6.6e+167:
		tmp = (b + ((x * (9.0 * y)) - ((z * 4.0) * (t * a)))) / (z * c)
	else:
		tmp = (b / (z * c)) + (-4.0 * ((t * a) / c))
	return tmp

Julia

x, y = sort([x, y])
t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (z <= 6.6e+167)
		tmp = Float64(Float64(b + Float64(Float64(x * Float64(9.0 * y)) - Float64(Float64(z * 4.0) * Float64(t * a)))) / Float64(z * c));
	else
		tmp = Float64(Float64(b / Float64(z * c)) + Float64(-4.0 * Float64(Float64(t * a) / c)));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (z <= 6.6e+167)
		tmp = (b + ((x * (9.0 * y)) - ((z * 4.0) * (t * a)))) / (z * c);
	else
		tmp = (b / (z * c)) + (-4.0 * ((t * a) / c));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[z, 6.6e+167], N[(N[(b + N[(N[(x * N[(9.0 * y), $MachinePrecision]), $MachinePrecision] - N[(N[(z * 4.0), $MachinePrecision] * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision] + N[(-4.0 * N[(N[(t * a), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 6.60000000000000036e167

   1. Initial program 87.0%

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

      1. associate-+l- 87.0%

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

      2. div-sub 78.2%

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

      3. *-commutative 78.2%

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

      4. associate-*r* 78.1%

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

      5. *-commutative 78.1%

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

      6. div-sub 86.9%

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

      7. associate-+l- 86.9%

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

   3. Simplified 86.6%

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

   if 6.60000000000000036e167 < z

   1. Initial program 45.8%

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

      1. associate-+l- 45.8%

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

      2. div-sub 45.8%

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

      3. *-commutative 45.8%

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

      4. associate-*r* 45.6%

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

      5. *-commutative 45.6%

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

      6. div-sub 45.6%

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

      7. associate-+l- 45.6%

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

   3. Simplified 46.1%

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

   4. Taylor expanded in x around 0 36.2%

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

   5. Taylor expanded in b around 0 70.4%

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

4. Final simplification 84.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 6.6 \cdot 10^{+167}:\\ \;\;\;\;\frac{b + \left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{z \cdot c} + -4 \cdot \frac{t \cdot a}{c}\\ \end{array} \]

Alternative 8: 49.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} t_1 := \frac{\frac{1}{z}}{\frac{c}{b}}\\ t_2 := 9 \cdot \left(y \cdot \frac{x}{z \cdot c}\right)\\ \mathbf{if}\;b \leq -2.2 \cdot 10^{+36}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -5.4 \cdot 10^{-22}:\\ \;\;\;\;a \cdot \left(t \cdot \frac{-4}{c}\right)\\ \mathbf{elif}\;b \leq -3.8 \cdot 10^{-264}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 5.2 \cdot 10^{-89}:\\ \;\;\;\;-4 \cdot \left(\frac{1}{c} \cdot \left(t \cdot a\right)\right)\\ \mathbf{elif}\;b \leq 9.5 \cdot 10^{+67}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (/ 1.0 z) (/ c b))) (t_2 (* 9.0 (* y (/ x (* z c))))))
   (if (<= b -2.2e+36)
     t_1
     (if (<= b -5.4e-22)
       (* a (* t (/ -4.0 c)))
       (if (<= b -3.8e-264)
         t_2
         (if (<= b 5.2e-89)
           (* -4.0 (* (/ 1.0 c) (* t a)))
           (if (<= b 9.5e+67) t_2 t_1)))))))

C

assert(x < y);
assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (1.0 / z) / (c / b);
	double t_2 = 9.0 * (y * (x / (z * c)));
	double tmp;
	if (b <= -2.2e+36) {
		tmp = t_1;
	} else if (b <= -5.4e-22) {
		tmp = a * (t * (-4.0 / c));
	} else if (b <= -3.8e-264) {
		tmp = t_2;
	} else if (b <= 5.2e-89) {
		tmp = -4.0 * ((1.0 / c) * (t * a));
	} else if (b <= 9.5e+67) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
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) :: tmp
    t_1 = (1.0d0 / z) / (c / b)
    t_2 = 9.0d0 * (y * (x / (z * c)))
    if (b <= (-2.2d+36)) then
        tmp = t_1
    else if (b <= (-5.4d-22)) then
        tmp = a * (t * ((-4.0d0) / c))
    else if (b <= (-3.8d-264)) then
        tmp = t_2
    else if (b <= 5.2d-89) then
        tmp = (-4.0d0) * ((1.0d0 / c) * (t * a))
    else if (b <= 9.5d+67) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y;
assert t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (1.0 / z) / (c / b);
	double t_2 = 9.0 * (y * (x / (z * c)));
	double tmp;
	if (b <= -2.2e+36) {
		tmp = t_1;
	} else if (b <= -5.4e-22) {
		tmp = a * (t * (-4.0 / c));
	} else if (b <= -3.8e-264) {
		tmp = t_2;
	} else if (b <= 5.2e-89) {
		tmp = -4.0 * ((1.0 / c) * (t * a));
	} else if (b <= 9.5e+67) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	t_1 = (1.0 / z) / (c / b)
	t_2 = 9.0 * (y * (x / (z * c)))
	tmp = 0
	if b <= -2.2e+36:
		tmp = t_1
	elif b <= -5.4e-22:
		tmp = a * (t * (-4.0 / c))
	elif b <= -3.8e-264:
		tmp = t_2
	elif b <= 5.2e-89:
		tmp = -4.0 * ((1.0 / c) * (t * a))
	elif b <= 9.5e+67:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

x, y = sort([x, y])
t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(1.0 / z) / Float64(c / b))
	t_2 = Float64(9.0 * Float64(y * Float64(x / Float64(z * c))))
	tmp = 0.0
	if (b <= -2.2e+36)
		tmp = t_1;
	elseif (b <= -5.4e-22)
		tmp = Float64(a * Float64(t * Float64(-4.0 / c)));
	elseif (b <= -3.8e-264)
		tmp = t_2;
	elseif (b <= 5.2e-89)
		tmp = Float64(-4.0 * Float64(Float64(1.0 / c) * Float64(t * a)));
	elseif (b <= 9.5e+67)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (1.0 / z) / (c / b);
	t_2 = 9.0 * (y * (x / (z * c)));
	tmp = 0.0;
	if (b <= -2.2e+36)
		tmp = t_1;
	elseif (b <= -5.4e-22)
		tmp = a * (t * (-4.0 / c));
	elseif (b <= -3.8e-264)
		tmp = t_2;
	elseif (b <= 5.2e-89)
		tmp = -4.0 * ((1.0 / c) * (t * a));
	elseif (b <= 9.5e+67)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(1.0 / z), $MachinePrecision] / N[(c / b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(9.0 * N[(y * N[(x / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2.2e+36], t$95$1, If[LessEqual[b, -5.4e-22], N[(a * N[(t * N[(-4.0 / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -3.8e-264], t$95$2, If[LessEqual[b, 5.2e-89], N[(-4.0 * N[(N[(1.0 / c), $MachinePrecision] * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 9.5e+67], t$95$2, t$95$1]]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -2.2e36 or 9.5000000000000002e67 < b

   1. Initial program 84.0%

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

      1. associate-+l- 84.0%

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

      2. div-sub 78.3%

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

      3. *-commutative 78.3%

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

      4. associate-*r* 76.3%

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

      5. *-commutative 76.3%

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

      6. div-sub 82.0%

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

      7. associate-+l- 82.0%

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

   3. Simplified 82.3%

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

      1. sub-neg 82.3%

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

      2. associate-+l+ 82.3%

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

      3. distribute-lft-neg-in 82.3%

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

      4. *-commutative 82.3%

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

      5. associate-*r* 82.0%

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

      6. distribute-rgt-neg-in 82.0%

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

      7. metadata-eval 82.0%

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

      8. associate-*r* 82.0%

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

      9. *-commutative 82.0%

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

      10. *-commutative 82.0%

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

      11. +-commutative 82.0%

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

      12. *-un-lft-identity 82.0%

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

      13. fma-udef 82.1%

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

   5. Applied egg-rr 83.4%

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

      1. clear-num 83.3%

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

      2. un-div-inv 83.9%

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

   7. Applied egg-rr 83.9%

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

   8. Taylor expanded in b around inf 61.5%

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

   if -2.2e36 < b < -5.4000000000000004e-22

   1. Initial program 79.8%

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

      1. associate-+l- 79.8%

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

      2. div-sub 74.8%

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

      3. *-commutative 74.8%

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

      4. associate-*r* 74.9%

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

      5. *-commutative 74.9%

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

      6. div-sub 79.9%

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

      7. associate-+l- 79.9%

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

   3. Simplified 79.9%

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

      1. sub-neg 79.9%

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

      2. associate-+l+ 79.9%

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

      3. distribute-lft-neg-in 79.9%

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

      4. *-commutative 79.9%

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

      5. associate-*r* 79.9%

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

      6. distribute-rgt-neg-in 79.9%

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

      7. metadata-eval 79.9%

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

      8. associate-*r* 79.9%

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

      9. *-commutative 79.9%

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

      10. *-commutative 79.9%

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

      11. +-commutative 79.9%

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

      12. *-un-lft-identity 79.9%

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

      13. fma-udef 79.9%

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

   5. Applied egg-rr 80.5%

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

   6. Taylor expanded in z around inf 70.3%

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

      1. associate-*l/ 62.8%

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

      2. *-commutative 62.8%

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

   8. Simplified 62.8%

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

      1. *-commutative 62.8%

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

      2. associate-*r/ 70.3%

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

      3. associate-*l/ 70.3%

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

   10. Applied egg-rr 70.3%

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

   11. Taylor expanded in t around 0 70.3%

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

       1. associate-/l* 75.1%

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

       2. associate-*r/ 75.1%

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

       3. *-commutative 75.1%

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

       4. associate-/l* 70.3%

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

       5. associate-*l/ 62.8%

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

       6. associate-*r/ 62.8%

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

       7. metadata-eval 62.8%

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

       8. associate-*r/ 62.8%

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

       9. associate-*l* 75.1%

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

       10. associate-*r/ 75.1%

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

       11. metadata-eval 75.1%

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

   13. Simplified 75.1%

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

   if -5.4000000000000004e-22 < b < -3.80000000000000013e-264 or 5.1999999999999997e-89 < b < 9.5000000000000002e67

   1. Initial program 84.7%

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

      1. associate-+l- 84.7%

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

      2. div-sub 72.8%

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

      3. *-commutative 72.8%

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

      4. associate-*r* 72.8%

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

      5. *-commutative 72.8%

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

      6. div-sub 84.7%

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

      7. associate-+l- 84.7%

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

   3. Simplified 83.6%

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

   4. Taylor expanded in x around inf 58.5%

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

      1. associate-/l* 61.9%

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

      2. associate-/r/ 56.4%

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

      3. *-commutative 56.4%

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

   6. Applied egg-rr 56.4%

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

   if -3.80000000000000013e-264 < b < 5.1999999999999997e-89

   1. Initial program 75.5%

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

      1. associate-+l- 75.5%

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

      2. div-sub 69.1%

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

      3. *-commutative 69.1%

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

      4. associate-*r* 72.6%

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

      5. *-commutative 72.6%

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

      6. div-sub 79.0%

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

      7. associate-+l- 79.0%

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

   3. Simplified 79.5%

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

      1. sub-neg 79.5%

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

      2. associate-+l+ 79.5%

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

      3. distribute-lft-neg-in 79.5%

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

      4. *-commutative 79.5%

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

      5. associate-*r* 79.0%

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

      6. distribute-rgt-neg-in 79.0%

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

      7. metadata-eval 79.0%

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

      8. associate-*r* 79.0%

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

      9. *-commutative 79.0%

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

      10. *-commutative 79.0%

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

      11. +-commutative 79.0%

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

      12. *-un-lft-identity 79.0%

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

      13. fma-udef 79.0%

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

   5. Applied egg-rr 83.2%

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

   6. Taylor expanded in z around inf 58.5%

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

      1. associate-*l/ 58.5%

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

      2. *-commutative 58.5%

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

   8. Simplified 58.5%

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

      1. associate-*r/ 58.5%

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

      2. clear-num 58.4%

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

   10. Applied egg-rr 58.4%

       \[\leadsto -4 \cdot \color{blue}{\frac{1}{\frac{c}{t \cdot a}}} \]
   11. Step-by-step derivation

       1. associate-/r/ 58.5%

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

       2. *-commutative 58.5%

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

   12. Simplified 58.5%

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

4. Final simplification 60.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.2 \cdot 10^{+36}:\\ \;\;\;\;\frac{\frac{1}{z}}{\frac{c}{b}}\\ \mathbf{elif}\;b \leq -5.4 \cdot 10^{-22}:\\ \;\;\;\;a \cdot \left(t \cdot \frac{-4}{c}\right)\\ \mathbf{elif}\;b \leq -3.8 \cdot 10^{-264}:\\ \;\;\;\;9 \cdot \left(y \cdot \frac{x}{z \cdot c}\right)\\ \mathbf{elif}\;b \leq 5.2 \cdot 10^{-89}:\\ \;\;\;\;-4 \cdot \left(\frac{1}{c} \cdot \left(t \cdot a\right)\right)\\ \mathbf{elif}\;b \leq 9.5 \cdot 10^{+67}:\\ \;\;\;\;9 \cdot \left(y \cdot \frac{x}{z \cdot c}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{1}{z}}{\frac{c}{b}}\\ \end{array} \]

Alternative 9: 49.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} t_1 := \frac{\frac{1}{z}}{\frac{c}{b}}\\ \mathbf{if}\;b \leq -4.5 \cdot 10^{+42}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -2.4 \cdot 10^{-22}:\\ \;\;\;\;a \cdot \left(t \cdot \frac{-4}{c}\right)\\ \mathbf{elif}\;b \leq -1.75 \cdot 10^{-264}:\\ \;\;\;\;9 \cdot \left(y \cdot \frac{x}{z \cdot c}\right)\\ \mathbf{elif}\;b \leq 2.3 \cdot 10^{-92}:\\ \;\;\;\;-4 \cdot \left(\frac{1}{c} \cdot \left(t \cdot a\right)\right)\\ \mathbf{elif}\;b \leq 8 \cdot 10^{+66}:\\ \;\;\;\;9 \cdot \frac{x}{\frac{z \cdot c}{y}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (/ 1.0 z) (/ c b))))
   (if (<= b -4.5e+42)
     t_1
     (if (<= b -2.4e-22)
       (* a (* t (/ -4.0 c)))
       (if (<= b -1.75e-264)
         (* 9.0 (* y (/ x (* z c))))
         (if (<= b 2.3e-92)
           (* -4.0 (* (/ 1.0 c) (* t a)))
           (if (<= b 8e+66) (* 9.0 (/ x (/ (* z c) y))) t_1)))))))

C

assert(x < y);
assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (1.0 / z) / (c / b);
	double tmp;
	if (b <= -4.5e+42) {
		tmp = t_1;
	} else if (b <= -2.4e-22) {
		tmp = a * (t * (-4.0 / c));
	} else if (b <= -1.75e-264) {
		tmp = 9.0 * (y * (x / (z * c)));
	} else if (b <= 2.3e-92) {
		tmp = -4.0 * ((1.0 / c) * (t * a));
	} else if (b <= 8e+66) {
		tmp = 9.0 * (x / ((z * c) / y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
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) :: tmp
    t_1 = (1.0d0 / z) / (c / b)
    if (b <= (-4.5d+42)) then
        tmp = t_1
    else if (b <= (-2.4d-22)) then
        tmp = a * (t * ((-4.0d0) / c))
    else if (b <= (-1.75d-264)) then
        tmp = 9.0d0 * (y * (x / (z * c)))
    else if (b <= 2.3d-92) then
        tmp = (-4.0d0) * ((1.0d0 / c) * (t * a))
    else if (b <= 8d+66) then
        tmp = 9.0d0 * (x / ((z * c) / y))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y;
assert t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (1.0 / z) / (c / b);
	double tmp;
	if (b <= -4.5e+42) {
		tmp = t_1;
	} else if (b <= -2.4e-22) {
		tmp = a * (t * (-4.0 / c));
	} else if (b <= -1.75e-264) {
		tmp = 9.0 * (y * (x / (z * c)));
	} else if (b <= 2.3e-92) {
		tmp = -4.0 * ((1.0 / c) * (t * a));
	} else if (b <= 8e+66) {
		tmp = 9.0 * (x / ((z * c) / y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	t_1 = (1.0 / z) / (c / b)
	tmp = 0
	if b <= -4.5e+42:
		tmp = t_1
	elif b <= -2.4e-22:
		tmp = a * (t * (-4.0 / c))
	elif b <= -1.75e-264:
		tmp = 9.0 * (y * (x / (z * c)))
	elif b <= 2.3e-92:
		tmp = -4.0 * ((1.0 / c) * (t * a))
	elif b <= 8e+66:
		tmp = 9.0 * (x / ((z * c) / y))
	else:
		tmp = t_1
	return tmp

Julia

x, y = sort([x, y])
t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(1.0 / z) / Float64(c / b))
	tmp = 0.0
	if (b <= -4.5e+42)
		tmp = t_1;
	elseif (b <= -2.4e-22)
		tmp = Float64(a * Float64(t * Float64(-4.0 / c)));
	elseif (b <= -1.75e-264)
		tmp = Float64(9.0 * Float64(y * Float64(x / Float64(z * c))));
	elseif (b <= 2.3e-92)
		tmp = Float64(-4.0 * Float64(Float64(1.0 / c) * Float64(t * a)));
	elseif (b <= 8e+66)
		tmp = Float64(9.0 * Float64(x / Float64(Float64(z * c) / y)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (1.0 / z) / (c / b);
	tmp = 0.0;
	if (b <= -4.5e+42)
		tmp = t_1;
	elseif (b <= -2.4e-22)
		tmp = a * (t * (-4.0 / c));
	elseif (b <= -1.75e-264)
		tmp = 9.0 * (y * (x / (z * c)));
	elseif (b <= 2.3e-92)
		tmp = -4.0 * ((1.0 / c) * (t * a));
	elseif (b <= 8e+66)
		tmp = 9.0 * (x / ((z * c) / y));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(1.0 / z), $MachinePrecision] / N[(c / b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -4.5e+42], t$95$1, If[LessEqual[b, -2.4e-22], N[(a * N[(t * N[(-4.0 / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -1.75e-264], N[(9.0 * N[(y * N[(x / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.3e-92], N[(-4.0 * N[(N[(1.0 / c), $MachinePrecision] * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 8e+66], N[(9.0 * N[(x / N[(N[(z * c), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -4.50000000000000012e42 or 7.99999999999999956e66 < b

   1. Initial program 84.0%

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

      1. associate-+l- 84.0%

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

      2. div-sub 78.3%

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

      3. *-commutative 78.3%

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

      4. associate-*r* 76.3%

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

      5. *-commutative 76.3%

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

      6. div-sub 82.0%

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

      7. associate-+l- 82.0%

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

   3. Simplified 82.3%

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

      1. sub-neg 82.3%

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

      2. associate-+l+ 82.3%

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

      3. distribute-lft-neg-in 82.3%

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

      4. *-commutative 82.3%

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

      5. associate-*r* 82.0%

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

      6. distribute-rgt-neg-in 82.0%

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

      7. metadata-eval 82.0%

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

      8. associate-*r* 82.0%

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

      9. *-commutative 82.0%

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

      10. *-commutative 82.0%

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

      11. +-commutative 82.0%

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

      12. *-un-lft-identity 82.0%

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

      13. fma-udef 82.1%

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

   5. Applied egg-rr 83.4%

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

      1. clear-num 83.3%

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

      2. un-div-inv 83.9%

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

   7. Applied egg-rr 83.9%

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

   8. Taylor expanded in b around inf 61.5%

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

   if -4.50000000000000012e42 < b < -2.40000000000000002e-22

   1. Initial program 79.8%

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

      1. associate-+l- 79.8%

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

      2. div-sub 74.8%

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

      3. *-commutative 74.8%

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

      4. associate-*r* 74.9%

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

      5. *-commutative 74.9%

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

      6. div-sub 79.9%

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

      7. associate-+l- 79.9%

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

   3. Simplified 79.9%

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

      1. sub-neg 79.9%

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

      2. associate-+l+ 79.9%

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

      3. distribute-lft-neg-in 79.9%

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

      4. *-commutative 79.9%

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

      5. associate-*r* 79.9%

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

      6. distribute-rgt-neg-in 79.9%

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

      7. metadata-eval 79.9%

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

      8. associate-*r* 79.9%

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

      9. *-commutative 79.9%

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

      10. *-commutative 79.9%

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

      11. +-commutative 79.9%

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

      12. *-un-lft-identity 79.9%

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

      13. fma-udef 79.9%

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

   5. Applied egg-rr 80.5%

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

   6. Taylor expanded in z around inf 70.3%

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

      1. associate-*l/ 62.8%

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

      2. *-commutative 62.8%

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

   8. Simplified 62.8%

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

      1. *-commutative 62.8%

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

      2. associate-*r/ 70.3%

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

      3. associate-*l/ 70.3%

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

   10. Applied egg-rr 70.3%

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

   11. Taylor expanded in t around 0 70.3%

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

       1. associate-/l* 75.1%

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

       2. associate-*r/ 75.1%

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

       3. *-commutative 75.1%

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

       4. associate-/l* 70.3%

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

       5. associate-*l/ 62.8%

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

       6. associate-*r/ 62.8%

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

       7. metadata-eval 62.8%

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

       8. associate-*r/ 62.8%

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

       9. associate-*l* 75.1%

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

       10. associate-*r/ 75.1%

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

       11. metadata-eval 75.1%

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

   13. Simplified 75.1%

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

   if -2.40000000000000002e-22 < b < -1.75e-264

   1. Initial program 77.6%

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

      1. associate-+l- 77.6%

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

      2. div-sub 67.1%

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

      3. *-commutative 67.1%

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

      4. associate-*r* 67.2%

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

      5. *-commutative 67.2%

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

      6. div-sub 77.7%

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

      7. associate-+l- 77.7%

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

   3. Simplified 75.9%

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

   4. Taylor expanded in x around inf 57.7%

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

      1. associate-/l* 61.1%

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

      2. associate-/r/ 56.3%

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

      3. *-commutative 56.3%

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

   6. Applied egg-rr 56.3%

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

   if -1.75e-264 < b < 2.30000000000000016e-92

   1. Initial program 75.5%

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

      1. associate-+l- 75.5%

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

      2. div-sub 69.1%

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

      3. *-commutative 69.1%

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

      4. associate-*r* 72.6%

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

      5. *-commutative 72.6%

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

      6. div-sub 79.0%

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

      7. associate-+l- 79.0%

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

   3. Simplified 79.5%

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

      1. sub-neg 79.5%

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

      2. associate-+l+ 79.5%

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

      3. distribute-lft-neg-in 79.5%

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

      4. *-commutative 79.5%

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

      5. associate-*r* 79.0%

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

      6. distribute-rgt-neg-in 79.0%

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

      7. metadata-eval 79.0%

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

      8. associate-*r* 79.0%

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

      9. *-commutative 79.0%

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

      10. *-commutative 79.0%

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

      11. +-commutative 79.0%

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

      12. *-un-lft-identity 79.0%

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

      13. fma-udef 79.0%

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

   5. Applied egg-rr 83.2%

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

   6. Taylor expanded in z around inf 58.5%

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

      1. associate-*l/ 58.5%

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

      2. *-commutative 58.5%

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

   8. Simplified 58.5%

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

      1. associate-*r/ 58.5%

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

      2. clear-num 58.4%

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

   10. Applied egg-rr 58.4%

       \[\leadsto -4 \cdot \color{blue}{\frac{1}{\frac{c}{t \cdot a}}} \]
   11. Step-by-step derivation

       1. associate-/r/ 58.5%

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

       2. *-commutative 58.5%

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

   12. Simplified 58.5%

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

   if 2.30000000000000016e-92 < b < 7.99999999999999956e66

   1. Initial program 99.6%

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

      1. associate-+l- 99.6%

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

      2. div-sub 84.8%

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

      3. *-commutative 84.8%

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

      4. associate-*r* 84.8%

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

      5. *-commutative 84.8%

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

      6. div-sub 99.6%

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

      7. associate-+l- 99.6%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around inf 60.1%

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

      1. *-commutative 60.1%

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

      2. associate-/l* 63.6%

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

   6. Simplified 63.6%

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

4. Final simplification 61.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.5 \cdot 10^{+42}:\\ \;\;\;\;\frac{\frac{1}{z}}{\frac{c}{b}}\\ \mathbf{elif}\;b \leq -2.4 \cdot 10^{-22}:\\ \;\;\;\;a \cdot \left(t \cdot \frac{-4}{c}\right)\\ \mathbf{elif}\;b \leq -1.75 \cdot 10^{-264}:\\ \;\;\;\;9 \cdot \left(y \cdot \frac{x}{z \cdot c}\right)\\ \mathbf{elif}\;b \leq 2.3 \cdot 10^{-92}:\\ \;\;\;\;-4 \cdot \left(\frac{1}{c} \cdot \left(t \cdot a\right)\right)\\ \mathbf{elif}\;b \leq 8 \cdot 10^{+66}:\\ \;\;\;\;9 \cdot \frac{x}{\frac{z \cdot c}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{1}{z}}{\frac{c}{b}}\\ \end{array} \]

Alternative 10: 49.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} t_1 := \frac{\frac{1}{z}}{\frac{c}{b}}\\ \mathbf{if}\;b \leq -4.1 \cdot 10^{+42}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -1.32 \cdot 10^{-18}:\\ \;\;\;\;a \cdot \left(t \cdot \frac{-4}{c}\right)\\ \mathbf{elif}\;b \leq -4.9 \cdot 10^{-265}:\\ \;\;\;\;\frac{y}{\frac{c}{x}} \cdot \frac{9}{z}\\ \mathbf{elif}\;b \leq 4 \cdot 10^{-86}:\\ \;\;\;\;-4 \cdot \left(\frac{1}{c} \cdot \left(t \cdot a\right)\right)\\ \mathbf{elif}\;b \leq 1.05 \cdot 10^{+69}:\\ \;\;\;\;9 \cdot \frac{x}{\frac{z \cdot c}{y}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (/ 1.0 z) (/ c b))))
   (if (<= b -4.1e+42)
     t_1
     (if (<= b -1.32e-18)
       (* a (* t (/ -4.0 c)))
       (if (<= b -4.9e-265)
         (* (/ y (/ c x)) (/ 9.0 z))
         (if (<= b 4e-86)
           (* -4.0 (* (/ 1.0 c) (* t a)))
           (if (<= b 1.05e+69) (* 9.0 (/ x (/ (* z c) y))) t_1)))))))

C

assert(x < y);
assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (1.0 / z) / (c / b);
	double tmp;
	if (b <= -4.1e+42) {
		tmp = t_1;
	} else if (b <= -1.32e-18) {
		tmp = a * (t * (-4.0 / c));
	} else if (b <= -4.9e-265) {
		tmp = (y / (c / x)) * (9.0 / z);
	} else if (b <= 4e-86) {
		tmp = -4.0 * ((1.0 / c) * (t * a));
	} else if (b <= 1.05e+69) {
		tmp = 9.0 * (x / ((z * c) / y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
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) :: tmp
    t_1 = (1.0d0 / z) / (c / b)
    if (b <= (-4.1d+42)) then
        tmp = t_1
    else if (b <= (-1.32d-18)) then
        tmp = a * (t * ((-4.0d0) / c))
    else if (b <= (-4.9d-265)) then
        tmp = (y / (c / x)) * (9.0d0 / z)
    else if (b <= 4d-86) then
        tmp = (-4.0d0) * ((1.0d0 / c) * (t * a))
    else if (b <= 1.05d+69) then
        tmp = 9.0d0 * (x / ((z * c) / y))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y;
assert t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (1.0 / z) / (c / b);
	double tmp;
	if (b <= -4.1e+42) {
		tmp = t_1;
	} else if (b <= -1.32e-18) {
		tmp = a * (t * (-4.0 / c));
	} else if (b <= -4.9e-265) {
		tmp = (y / (c / x)) * (9.0 / z);
	} else if (b <= 4e-86) {
		tmp = -4.0 * ((1.0 / c) * (t * a));
	} else if (b <= 1.05e+69) {
		tmp = 9.0 * (x / ((z * c) / y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	t_1 = (1.0 / z) / (c / b)
	tmp = 0
	if b <= -4.1e+42:
		tmp = t_1
	elif b <= -1.32e-18:
		tmp = a * (t * (-4.0 / c))
	elif b <= -4.9e-265:
		tmp = (y / (c / x)) * (9.0 / z)
	elif b <= 4e-86:
		tmp = -4.0 * ((1.0 / c) * (t * a))
	elif b <= 1.05e+69:
		tmp = 9.0 * (x / ((z * c) / y))
	else:
		tmp = t_1
	return tmp

Julia

x, y = sort([x, y])
t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(1.0 / z) / Float64(c / b))
	tmp = 0.0
	if (b <= -4.1e+42)
		tmp = t_1;
	elseif (b <= -1.32e-18)
		tmp = Float64(a * Float64(t * Float64(-4.0 / c)));
	elseif (b <= -4.9e-265)
		tmp = Float64(Float64(y / Float64(c / x)) * Float64(9.0 / z));
	elseif (b <= 4e-86)
		tmp = Float64(-4.0 * Float64(Float64(1.0 / c) * Float64(t * a)));
	elseif (b <= 1.05e+69)
		tmp = Float64(9.0 * Float64(x / Float64(Float64(z * c) / y)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (1.0 / z) / (c / b);
	tmp = 0.0;
	if (b <= -4.1e+42)
		tmp = t_1;
	elseif (b <= -1.32e-18)
		tmp = a * (t * (-4.0 / c));
	elseif (b <= -4.9e-265)
		tmp = (y / (c / x)) * (9.0 / z);
	elseif (b <= 4e-86)
		tmp = -4.0 * ((1.0 / c) * (t * a));
	elseif (b <= 1.05e+69)
		tmp = 9.0 * (x / ((z * c) / y));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(1.0 / z), $MachinePrecision] / N[(c / b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -4.1e+42], t$95$1, If[LessEqual[b, -1.32e-18], N[(a * N[(t * N[(-4.0 / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -4.9e-265], N[(N[(y / N[(c / x), $MachinePrecision]), $MachinePrecision] * N[(9.0 / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 4e-86], N[(-4.0 * N[(N[(1.0 / c), $MachinePrecision] * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.05e+69], N[(9.0 * N[(x / N[(N[(z * c), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -4.1e42 or 1.05000000000000008e69 < b

   1. Initial program 84.0%

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

      1. associate-+l- 84.0%

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

      2. div-sub 78.3%

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

      3. *-commutative 78.3%

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

      4. associate-*r* 76.3%

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

      5. *-commutative 76.3%

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

      6. div-sub 82.0%

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

      7. associate-+l- 82.0%

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

   3. Simplified 82.3%

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

      1. sub-neg 82.3%

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

      2. associate-+l+ 82.3%

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

      3. distribute-lft-neg-in 82.3%

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

      4. *-commutative 82.3%

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

      5. associate-*r* 82.0%

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

      6. distribute-rgt-neg-in 82.0%

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

      7. metadata-eval 82.0%

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

      8. associate-*r* 82.0%

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

      9. *-commutative 82.0%

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

      10. *-commutative 82.0%

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

      11. +-commutative 82.0%

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

      12. *-un-lft-identity 82.0%

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

      13. fma-udef 82.1%

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

   5. Applied egg-rr 83.4%

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

      1. clear-num 83.3%

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

      2. un-div-inv 83.9%

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

   7. Applied egg-rr 83.9%

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

   8. Taylor expanded in b around inf 61.5%

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

   if -4.1e42 < b < -1.3199999999999999e-18

   1. Initial program 78.8%

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

      1. associate-+l- 78.8%

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

      2. div-sub 73.5%

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

      3. *-commutative 73.5%

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

      4. associate-*r* 73.6%

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

      5. *-commutative 73.6%

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

      6. div-sub 78.9%

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

      7. associate-+l- 78.9%

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

   3. Simplified 78.9%

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

      1. sub-neg 78.9%

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

      2. associate-+l+ 78.9%

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

      3. distribute-lft-neg-in 78.9%

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

      4. *-commutative 78.9%

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

      5. associate-*r* 78.9%

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

      6. distribute-rgt-neg-in 78.9%

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

      7. metadata-eval 78.9%

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

      8. associate-*r* 78.9%

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

      9. *-commutative 78.9%

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

      10. *-commutative 78.9%

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

      11. +-commutative 78.9%

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

      12. *-un-lft-identity 78.9%

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

      13. fma-udef 78.9%

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

   5. Applied egg-rr 79.5%

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

   6. Taylor expanded in z around inf 68.8%

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

      1. associate-*l/ 60.8%

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

      2. *-commutative 60.8%

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

   8. Simplified 60.8%

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

      1. *-commutative 60.8%

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

      2. associate-*r/ 68.8%

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

      3. associate-*l/ 68.8%

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

   10. Applied egg-rr 68.8%

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

   11. Taylor expanded in t around 0 68.8%

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

       1. associate-/l* 73.8%

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

       2. associate-*r/ 73.8%

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

       3. *-commutative 73.8%

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

       4. associate-/l* 68.8%

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

       5. associate-*l/ 60.8%

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

       6. associate-*r/ 60.8%

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

       7. metadata-eval 60.8%

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

       8. associate-*r/ 60.8%

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

       9. associate-*l* 73.8%

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

       10. associate-*r/ 73.8%

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

       11. metadata-eval 73.8%

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

   13. Simplified 73.8%

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

   if -1.3199999999999999e-18 < b < -4.89999999999999999e-265

   1. Initial program 78.0%

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

      1. associate-+l- 78.0%

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

      2. div-sub 67.6%

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

      3. *-commutative 67.6%

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

      4. associate-*r* 67.7%

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

      5. *-commutative 67.7%

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

      6. div-sub 78.1%

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

      7. associate-+l- 78.1%

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

   3. Simplified 76.4%

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

   4. Taylor expanded in x around inf 58.4%

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

      1. *-commutative 58.4%

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

      2. associate-*r/ 58.4%

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

      3. *-commutative 58.4%

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

      4. *-commutative 58.4%

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

      5. times-frac 58.6%

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

      6. *-commutative 58.6%

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

      7. associate-/l* 57.9%

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

   6. Simplified 57.9%

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

   if -4.89999999999999999e-265 < b < 4.00000000000000034e-86

   1. Initial program 75.5%

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

      1. associate-+l- 75.5%

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

      2. div-sub 69.1%

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

      3. *-commutative 69.1%

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

      4. associate-*r* 72.6%

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

      5. *-commutative 72.6%

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

      6. div-sub 79.0%

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

      7. associate-+l- 79.0%

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

   3. Simplified 79.5%

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

      1. sub-neg 79.5%

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

      2. associate-+l+ 79.5%

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

      3. distribute-lft-neg-in 79.5%

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

      4. *-commutative 79.5%

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

      5. associate-*r* 79.0%

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

      6. distribute-rgt-neg-in 79.0%

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

      7. metadata-eval 79.0%

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

      8. associate-*r* 79.0%

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

      9. *-commutative 79.0%

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

      10. *-commutative 79.0%

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

      11. +-commutative 79.0%

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

      12. *-un-lft-identity 79.0%

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

      13. fma-udef 79.0%

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

   5. Applied egg-rr 83.2%

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

   6. Taylor expanded in z around inf 58.5%

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

      1. associate-*l/ 58.5%

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

      2. *-commutative 58.5%

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

   8. Simplified 58.5%

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

      1. associate-*r/ 58.5%

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

      2. clear-num 58.4%

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

   10. Applied egg-rr 58.4%

       \[\leadsto -4 \cdot \color{blue}{\frac{1}{\frac{c}{t \cdot a}}} \]
   11. Step-by-step derivation

       1. associate-/r/ 58.5%

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

       2. *-commutative 58.5%

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

   12. Simplified 58.5%

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

   if 4.00000000000000034e-86 < b < 1.05000000000000008e69

   1. Initial program 99.6%

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

      1. associate-+l- 99.6%

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

      2. div-sub 84.8%

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

      3. *-commutative 84.8%

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

      4. associate-*r* 84.8%

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

      5. *-commutative 84.8%

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

      6. div-sub 99.6%

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

      7. associate-+l- 99.6%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around inf 60.1%

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

      1. *-commutative 60.1%

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

      2. associate-/l* 63.6%

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

   6. Simplified 63.6%

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

4. Final simplification 61.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.1 \cdot 10^{+42}:\\ \;\;\;\;\frac{\frac{1}{z}}{\frac{c}{b}}\\ \mathbf{elif}\;b \leq -1.32 \cdot 10^{-18}:\\ \;\;\;\;a \cdot \left(t \cdot \frac{-4}{c}\right)\\ \mathbf{elif}\;b \leq -4.9 \cdot 10^{-265}:\\ \;\;\;\;\frac{y}{\frac{c}{x}} \cdot \frac{9}{z}\\ \mathbf{elif}\;b \leq 4 \cdot 10^{-86}:\\ \;\;\;\;-4 \cdot \left(\frac{1}{c} \cdot \left(t \cdot a\right)\right)\\ \mathbf{elif}\;b \leq 1.05 \cdot 10^{+69}:\\ \;\;\;\;9 \cdot \frac{x}{\frac{z \cdot c}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{1}{z}}{\frac{c}{b}}\\ \end{array} \]

Alternative 11: 67.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq -2.8 \cdot 10^{+73} \lor \neg \left(a \leq 1.06 \cdot 10^{+101} \lor \neg \left(a \leq 8.3 \cdot 10^{+204}\right) \land a \leq 1.6 \cdot 10^{+219}\right):\\ \;\;\;\;\frac{t \cdot -4}{\frac{c}{a}}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= a -2.8e+73)
         (not
          (or (<= a 1.06e+101) (and (not (<= a 8.3e+204)) (<= a 1.6e+219)))))
   (/ (* t -4.0) (/ c a))
   (/ (+ b (* 9.0 (* x y))) (* z c))))

C

assert(x < y);
assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((a <= -2.8e+73) || !((a <= 1.06e+101) || (!(a <= 8.3e+204) && (a <= 1.6e+219)))) {
		tmp = (t * -4.0) / (c / a);
	} else {
		tmp = (b + (9.0 * (x * y))) / (z * c);
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
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) :: tmp
    if ((a <= (-2.8d+73)) .or. (.not. (a <= 1.06d+101) .or. (.not. (a <= 8.3d+204)) .and. (a <= 1.6d+219))) then
        tmp = (t * (-4.0d0)) / (c / a)
    else
        tmp = (b + (9.0d0 * (x * y))) / (z * c)
    end if
    code = tmp
end function

Java

assert x < y;
assert t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((a <= -2.8e+73) || !((a <= 1.06e+101) || (!(a <= 8.3e+204) && (a <= 1.6e+219)))) {
		tmp = (t * -4.0) / (c / a);
	} else {
		tmp = (b + (9.0 * (x * y))) / (z * c);
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if (a <= -2.8e+73) or not ((a <= 1.06e+101) or (not (a <= 8.3e+204) and (a <= 1.6e+219))):
		tmp = (t * -4.0) / (c / a)
	else:
		tmp = (b + (9.0 * (x * y))) / (z * c)
	return tmp

Julia

x, y = sort([x, y])
t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((a <= -2.8e+73) || !((a <= 1.06e+101) || (!(a <= 8.3e+204) && (a <= 1.6e+219))))
		tmp = Float64(Float64(t * -4.0) / Float64(c / a));
	else
		tmp = Float64(Float64(b + Float64(9.0 * Float64(x * y))) / Float64(z * c));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((a <= -2.8e+73) || ~(((a <= 1.06e+101) || (~((a <= 8.3e+204)) && (a <= 1.6e+219)))))
		tmp = (t * -4.0) / (c / a);
	else
		tmp = (b + (9.0 * (x * y))) / (z * c);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[a, -2.8e+73], N[Not[Or[LessEqual[a, 1.06e+101], And[N[Not[LessEqual[a, 8.3e+204]], $MachinePrecision], LessEqual[a, 1.6e+219]]]], $MachinePrecision]], N[(N[(t * -4.0), $MachinePrecision] / N[(c / a), $MachinePrecision]), $MachinePrecision], N[(N[(b + N[(9.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -2.80000000000000008e73 or 1.06e101 < a < 8.3000000000000004e204 or 1.60000000000000013e219 < a

   1. Initial program 81.3%

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

      1. associate-+l- 81.3%

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

      2. div-sub 77.0%

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

      3. *-commutative 77.0%

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

      4. associate-*r* 75.5%

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

      5. *-commutative 75.5%

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

      6. div-sub 79.8%

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

      7. associate-+l- 79.8%

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

   3. Simplified 78.1%

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

      1. sub-neg 78.1%

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

      2. associate-+l+ 78.1%

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

      3. distribute-lft-neg-in 78.1%

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

      4. *-commutative 78.1%

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

      5. associate-*r* 79.8%

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

      6. distribute-rgt-neg-in 79.8%

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

      7. metadata-eval 79.8%

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

      8. associate-*r* 79.8%

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

      9. *-commutative 79.8%

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

      10. *-commutative 79.8%

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

      11. +-commutative 79.8%

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

      12. *-un-lft-identity 79.8%

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

      13. fma-udef 79.9%

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

   5. Applied egg-rr 82.2%

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

   6. Taylor expanded in z around inf 55.1%

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

      1. associate-*l/ 61.2%

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

      2. *-commutative 61.2%

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

   8. Simplified 61.2%

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

      1. associate-*r* 61.2%

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

      2. clear-num 61.2%

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

      3. un-div-inv 61.5%

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

      4. *-commutative 61.5%

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

   10. Applied egg-rr 61.5%

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

   if -2.80000000000000008e73 < a < 1.06e101 or 8.3000000000000004e204 < a < 1.60000000000000013e219

   1. Initial program 83.0%

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

      1. associate-+l- 83.0%

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

      2. div-sub 73.1%

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

      3. *-commutative 73.1%

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

      4. associate-*r* 73.7%

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

      5. *-commutative 73.7%

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

      6. div-sub 83.6%

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

      7. associate-+l- 83.6%

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

   3. Simplified 84.2%

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

   4. Taylor expanded in x around inf 73.8%

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

4. Final simplification 69.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.8 \cdot 10^{+73} \lor \neg \left(a \leq 1.06 \cdot 10^{+101} \lor \neg \left(a \leq 8.3 \cdot 10^{+204}\right) \land a \leq 1.6 \cdot 10^{+219}\right):\\ \;\;\;\;\frac{t \cdot -4}{\frac{c}{a}}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \end{array} \]

Alternative 12: 69.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} t_1 := \frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ t_2 := \frac{t \cdot -4}{\frac{c}{a}}\\ \mathbf{if}\;a \leq -1.46 \cdot 10^{+72}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 8 \cdot 10^{+100}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.95 \cdot 10^{+206}:\\ \;\;\;\;\frac{b}{z \cdot c} + -4 \cdot \frac{t \cdot a}{c}\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{+219}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (+ b (* 9.0 (* x y))) (* z c))) (t_2 (/ (* t -4.0) (/ c a))))
   (if (<= a -1.46e+72)
     t_2
     (if (<= a 8e+100)
       t_1
       (if (<= a 1.95e+206)
         (+ (/ b (* z c)) (* -4.0 (/ (* t a) c)))
         (if (<= a 1.6e+219) t_1 t_2))))))

C

assert(x < y);
assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (b + (9.0 * (x * y))) / (z * c);
	double t_2 = (t * -4.0) / (c / a);
	double tmp;
	if (a <= -1.46e+72) {
		tmp = t_2;
	} else if (a <= 8e+100) {
		tmp = t_1;
	} else if (a <= 1.95e+206) {
		tmp = (b / (z * c)) + (-4.0 * ((t * a) / c));
	} else if (a <= 1.6e+219) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
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) :: tmp
    t_1 = (b + (9.0d0 * (x * y))) / (z * c)
    t_2 = (t * (-4.0d0)) / (c / a)
    if (a <= (-1.46d+72)) then
        tmp = t_2
    else if (a <= 8d+100) then
        tmp = t_1
    else if (a <= 1.95d+206) then
        tmp = (b / (z * c)) + ((-4.0d0) * ((t * a) / c))
    else if (a <= 1.6d+219) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

assert x < y;
assert t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (b + (9.0 * (x * y))) / (z * c);
	double t_2 = (t * -4.0) / (c / a);
	double tmp;
	if (a <= -1.46e+72) {
		tmp = t_2;
	} else if (a <= 8e+100) {
		tmp = t_1;
	} else if (a <= 1.95e+206) {
		tmp = (b / (z * c)) + (-4.0 * ((t * a) / c));
	} else if (a <= 1.6e+219) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	t_1 = (b + (9.0 * (x * y))) / (z * c)
	t_2 = (t * -4.0) / (c / a)
	tmp = 0
	if a <= -1.46e+72:
		tmp = t_2
	elif a <= 8e+100:
		tmp = t_1
	elif a <= 1.95e+206:
		tmp = (b / (z * c)) + (-4.0 * ((t * a) / c))
	elif a <= 1.6e+219:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

x, y = sort([x, y])
t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(b + Float64(9.0 * Float64(x * y))) / Float64(z * c))
	t_2 = Float64(Float64(t * -4.0) / Float64(c / a))
	tmp = 0.0
	if (a <= -1.46e+72)
		tmp = t_2;
	elseif (a <= 8e+100)
		tmp = t_1;
	elseif (a <= 1.95e+206)
		tmp = Float64(Float64(b / Float64(z * c)) + Float64(-4.0 * Float64(Float64(t * a) / c)));
	elseif (a <= 1.6e+219)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (b + (9.0 * (x * y))) / (z * c);
	t_2 = (t * -4.0) / (c / a);
	tmp = 0.0;
	if (a <= -1.46e+72)
		tmp = t_2;
	elseif (a <= 8e+100)
		tmp = t_1;
	elseif (a <= 1.95e+206)
		tmp = (b / (z * c)) + (-4.0 * ((t * a) / c));
	elseif (a <= 1.6e+219)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(b + N[(9.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t * -4.0), $MachinePrecision] / N[(c / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.46e+72], t$95$2, If[LessEqual[a, 8e+100], t$95$1, If[LessEqual[a, 1.95e+206], N[(N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision] + N[(-4.0 * N[(N[(t * a), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.6e+219], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.45999999999999999e72 or 1.60000000000000013e219 < a

   1. Initial program 81.7%

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

      1. associate-+l- 81.7%

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

      2. div-sub 75.9%

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

      3. *-commutative 75.9%

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

      4. associate-*r* 74.2%

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

      5. *-commutative 74.2%

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

      6. div-sub 80.0%

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

      7. associate-+l- 80.0%

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

   3. Simplified 77.5%

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

      1. sub-neg 77.5%

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

      2. associate-+l+ 77.5%

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

      3. distribute-lft-neg-in 77.5%

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

      4. *-commutative 77.5%

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

      5. associate-*r* 79.9%

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

      6. distribute-rgt-neg-in 79.9%

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

      7. metadata-eval 79.9%

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

      8. associate-*r* 79.9%

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

      9. *-commutative 79.9%

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

      10. *-commutative 79.9%

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

      11. +-commutative 79.9%

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

      12. *-un-lft-identity 79.9%

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

      13. fma-udef 80.0%

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

   5. Applied egg-rr 81.7%

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

   6. Taylor expanded in z around inf 54.7%

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

      1. associate-*l/ 63.0%

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

      2. *-commutative 63.0%

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

   8. Simplified 63.0%

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

      1. associate-*r* 63.0%

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

      2. clear-num 62.9%

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

      3. un-div-inv 63.3%

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

      4. *-commutative 63.3%

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

   10. Applied egg-rr 63.3%

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

   if -1.45999999999999999e72 < a < 8.00000000000000013e100 or 1.95e206 < a < 1.60000000000000013e219

   1. Initial program 83.0%

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

      1. associate-+l- 83.0%

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

      2. div-sub 73.1%

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

      3. *-commutative 73.1%

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

      4. associate-*r* 73.7%

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

      5. *-commutative 73.7%

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

      6. div-sub 83.6%

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

      7. associate-+l- 83.6%

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

   3. Simplified 84.2%

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

   4. Taylor expanded in x around inf 73.8%

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

   if 8.00000000000000013e100 < a < 1.95e206

   1. Initial program 80.1%

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

      1. associate-+l- 80.1%

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

      2. div-sub 80.1%

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

      3. *-commutative 80.1%

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

      4. associate-*r* 79.5%

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

      5. *-commutative 79.5%

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

      6. div-sub 79.5%

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

      7. associate-+l- 79.5%

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

   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. Taylor expanded in x around 0 76.3%

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

   5. Taylor expanded in b around 0 87.8%

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

4. Final simplification 72.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.46 \cdot 10^{+72}:\\ \;\;\;\;\frac{t \cdot -4}{\frac{c}{a}}\\ \mathbf{elif}\;a \leq 8 \cdot 10^{+100}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \mathbf{elif}\;a \leq 1.95 \cdot 10^{+206}:\\ \;\;\;\;\frac{b}{z \cdot c} + -4 \cdot \frac{t \cdot a}{c}\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{+219}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot -4}{\frac{c}{a}}\\ \end{array} \]

Alternative 13: 51.4% accurate, 1.7× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq -3.8 \cdot 10^{-80} \lor \neg \left(a \leq 4.8 \cdot 10^{-10}\right):\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= a -3.8e-80) (not (<= a 4.8e-10)))
   (* -4.0 (* t (/ a c)))
   (/ b (* z c))))

C

assert(x < y);
assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((a <= -3.8e-80) || !(a <= 4.8e-10)) {
		tmp = -4.0 * (t * (a / c));
	} else {
		tmp = b / (z * c);
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
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) :: tmp
    if ((a <= (-3.8d-80)) .or. (.not. (a <= 4.8d-10))) then
        tmp = (-4.0d0) * (t * (a / c))
    else
        tmp = b / (z * c)
    end if
    code = tmp
end function

Java

assert x < y;
assert t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((a <= -3.8e-80) || !(a <= 4.8e-10)) {
		tmp = -4.0 * (t * (a / c));
	} else {
		tmp = b / (z * c);
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if (a <= -3.8e-80) or not (a <= 4.8e-10):
		tmp = -4.0 * (t * (a / c))
	else:
		tmp = b / (z * c)
	return tmp

Julia

x, y = sort([x, y])
t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((a <= -3.8e-80) || !(a <= 4.8e-10))
		tmp = Float64(-4.0 * Float64(t * Float64(a / c)));
	else
		tmp = Float64(b / Float64(z * c));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((a <= -3.8e-80) || ~((a <= 4.8e-10)))
		tmp = -4.0 * (t * (a / c));
	else
		tmp = b / (z * c);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[a, -3.8e-80], N[Not[LessEqual[a, 4.8e-10]], $MachinePrecision]], N[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -3.79999999999999967e-80 or 4.8e-10 < a

   1. Initial program 80.6%

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

      1. associate-+l- 80.6%

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

      2. div-sub 73.3%

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

      3. *-commutative 73.3%

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

      4. associate-*r* 71.1%

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

      5. *-commutative 71.1%

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

      6. div-sub 78.3%

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

      7. associate-+l- 78.3%

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

   3. Simplified 78.0%

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

      1. sub-neg 78.0%

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

      2. associate-+l+ 78.0%

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

      3. distribute-lft-neg-in 78.0%

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

      4. *-commutative 78.0%

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

      5. associate-*r* 78.3%

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

      6. distribute-rgt-neg-in 78.3%

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

      7. metadata-eval 78.3%

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

      8. associate-*r* 78.3%

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

      9. *-commutative 78.3%

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

      10. *-commutative 78.3%

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

      11. +-commutative 78.3%

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

      12. *-un-lft-identity 78.3%

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

      13. fma-udef 78.4%

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

   5. Applied egg-rr 79.4%

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

   6. Taylor expanded in z around inf 48.5%

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

      1. associate-*l/ 51.9%

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

      2. *-commutative 51.9%

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

   8. Simplified 51.9%

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

   if -3.79999999999999967e-80 < a < 4.8e-10

   1. Initial program 84.9%

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

      1. associate-+l- 84.9%

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

      2. div-sub 76.3%

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

      3. *-commutative 76.3%

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

      4. associate-*r* 79.2%

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

      5. *-commutative 79.2%

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

      6. div-sub 87.8%

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

      7. associate-+l- 87.8%

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

   3. Simplified 87.8%

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

   4. Taylor expanded in b around inf 46.3%

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

      1. *-commutative 46.3%

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

   6. Simplified 46.3%

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

4. Final simplification 49.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.8 \cdot 10^{-80} \lor \neg \left(a \leq 4.8 \cdot 10^{-10}\right):\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \end{array} \]

Alternative 14: 51.4% accurate, 1.7× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq -7.8 \cdot 10^{-75}:\\ \;\;\;\;a \cdot \left(t \cdot \frac{-4}{c}\right)\\ \mathbf{elif}\;a \leq 1.52 \cdot 10^{-10}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= a -7.8e-75)
   (* a (* t (/ -4.0 c)))
   (if (<= a 1.52e-10) (/ b (* z c)) (* -4.0 (* t (/ a c))))))

C

assert(x < y);
assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (a <= -7.8e-75) {
		tmp = a * (t * (-4.0 / c));
	} else if (a <= 1.52e-10) {
		tmp = b / (z * c);
	} else {
		tmp = -4.0 * (t * (a / c));
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
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) :: tmp
    if (a <= (-7.8d-75)) then
        tmp = a * (t * ((-4.0d0) / c))
    else if (a <= 1.52d-10) then
        tmp = b / (z * c)
    else
        tmp = (-4.0d0) * (t * (a / c))
    end if
    code = tmp
end function

Java

assert x < y;
assert t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (a <= -7.8e-75) {
		tmp = a * (t * (-4.0 / c));
	} else if (a <= 1.52e-10) {
		tmp = b / (z * c);
	} else {
		tmp = -4.0 * (t * (a / c));
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if a <= -7.8e-75:
		tmp = a * (t * (-4.0 / c))
	elif a <= 1.52e-10:
		tmp = b / (z * c)
	else:
		tmp = -4.0 * (t * (a / c))
	return tmp

Julia

x, y = sort([x, y])
t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (a <= -7.8e-75)
		tmp = Float64(a * Float64(t * Float64(-4.0 / c)));
	elseif (a <= 1.52e-10)
		tmp = Float64(b / Float64(z * c));
	else
		tmp = Float64(-4.0 * Float64(t * Float64(a / c)));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (a <= -7.8e-75)
		tmp = a * (t * (-4.0 / c));
	elseif (a <= 1.52e-10)
		tmp = b / (z * c);
	else
		tmp = -4.0 * (t * (a / c));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[a, -7.8e-75], N[(a * N[(t * N[(-4.0 / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.52e-10], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -7.8000000000000003e-75

   1. Initial program 82.1%

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

      1. associate-+l- 82.1%

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

      2. div-sub 76.1%

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

      3. *-commutative 76.1%

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

      4. associate-*r* 73.5%

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

      5. *-commutative 73.5%

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

      6. div-sub 79.5%

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

      7. associate-+l- 79.5%

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

   3. Simplified 81.0%

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

      1. sub-neg 81.0%

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

      2. associate-+l+ 81.0%

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

      3. distribute-lft-neg-in 81.0%

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

      4. *-commutative 81.0%

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

      5. associate-*r* 79.5%

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

      6. distribute-rgt-neg-in 79.5%

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

      7. metadata-eval 79.5%

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

      8. associate-*r* 79.5%

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

      9. *-commutative 79.5%

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

      10. *-commutative 79.5%

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

      11. +-commutative 79.5%

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

      12. *-un-lft-identity 79.5%

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

      13. fma-udef 79.6%

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

   5. Applied egg-rr 81.1%

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

   6. Taylor expanded in z around inf 48.1%

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

      1. associate-*l/ 49.7%

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

      2. *-commutative 49.7%

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

   8. Simplified 49.7%

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

      1. *-commutative 49.7%

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

      2. associate-*r/ 48.1%

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

      3. associate-*l/ 48.1%

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

   10. Applied egg-rr 48.1%

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

   11. Taylor expanded in t around 0 48.1%

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

       1. associate-/l* 51.7%

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

       2. associate-*r/ 51.7%

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

       3. *-commutative 51.7%

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

       4. associate-/l* 48.1%

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

       5. associate-*l/ 49.7%

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

       6. associate-*r/ 49.7%

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

       7. metadata-eval 49.7%

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

       8. associate-*r/ 49.7%

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

       9. associate-*l* 51.6%

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

       10. associate-*r/ 51.6%

           \[\leadsto a \cdot \left(\color{blue}{\frac{-4 \cdot 1}{c}} \cdot t\right) \]

       11. metadata-eval 51.6%

           \[\leadsto a \cdot \left(\frac{\color{blue}{-4}}{c} \cdot t\right) \]

   13. Simplified 51.6%

       \[\leadsto \color{blue}{a \cdot \left(\frac{-4}{c} \cdot t\right)} \]

   if -7.8000000000000003e-75 < a < 1.5199999999999999e-10

   1. Initial program 85.1%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 85.1%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. div-sub 76.6%

         \[\leadsto \color{blue}{\frac{\left(x \cdot 9\right) \cdot y}{z \cdot c} - \frac{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b}{z \cdot c}} \]

      3. *-commutative 76.6%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y}{z \cdot c} - \frac{\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b}{z \cdot c} \]

      4. associate-*r* 79.4%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y}{z \cdot c} - \frac{\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b}{z \cdot c} \]

      5. *-commutative 79.4%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y}{z \cdot c} - \frac{\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b}{z \cdot c} \]

      6. div-sub 87.9%

         \[\leadsto \color{blue}{\frac{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot a\right) \cdot t - b\right)}{z \cdot c}} \]

      7. associate-+l- 87.9%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

   3. Simplified 87.9%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]

   4. Taylor expanded in b around inf 45.9%

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
   5. Step-by-step derivation

      1. *-commutative 45.9%

         \[\leadsto \frac{b}{\color{blue}{z \cdot c}} \]

   6. Simplified 45.9%

      \[\leadsto \color{blue}{\frac{b}{z \cdot c}} \]

   if 1.5199999999999999e-10 < a

   1. Initial program 78.3%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 78.3%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. div-sub 69.3%

         \[\leadsto \color{blue}{\frac{\left(x \cdot 9\right) \cdot y}{z \cdot c} - \frac{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b}{z \cdot c}} \]

      3. *-commutative 69.3%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y}{z \cdot c} - \frac{\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b}{z \cdot c} \]

      4. associate-*r* 67.6%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y}{z \cdot c} - \frac{\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b}{z \cdot c} \]

      5. *-commutative 67.6%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y}{z \cdot c} - \frac{\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b}{z \cdot c} \]

      6. div-sub 76.6%

         \[\leadsto \color{blue}{\frac{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot a\right) \cdot t - b\right)}{z \cdot c}} \]

      7. associate-+l- 76.6%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

   3. Simplified 74.0%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Step-by-step derivation

      1. sub-neg 74.0%

         \[\leadsto \frac{\color{blue}{\left(x \cdot \left(9 \cdot y\right) + \left(-\left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right)\right)} + b}{z \cdot c} \]

      2. associate-+l+ 74.0%

         \[\leadsto \frac{\color{blue}{x \cdot \left(9 \cdot y\right) + \left(\left(-\left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b\right)}}{z \cdot c} \]

      3. distribute-lft-neg-in 74.0%

         \[\leadsto \frac{x \cdot \left(9 \cdot y\right) + \left(\color{blue}{\left(-z \cdot 4\right) \cdot \left(t \cdot a\right)} + b\right)}{z \cdot c} \]

      4. *-commutative 74.0%

         \[\leadsto \frac{x \cdot \left(9 \cdot y\right) + \left(\left(-z \cdot 4\right) \cdot \color{blue}{\left(a \cdot t\right)} + b\right)}{z \cdot c} \]

      5. associate-*r* 76.6%

         \[\leadsto \frac{x \cdot \left(9 \cdot y\right) + \left(\color{blue}{\left(\left(-z \cdot 4\right) \cdot a\right) \cdot t} + b\right)}{z \cdot c} \]

      6. distribute-rgt-neg-in 76.6%

         \[\leadsto \frac{x \cdot \left(9 \cdot y\right) + \left(\left(\color{blue}{\left(z \cdot \left(-4\right)\right)} \cdot a\right) \cdot t + b\right)}{z \cdot c} \]

      7. metadata-eval 76.6%

         \[\leadsto \frac{x \cdot \left(9 \cdot y\right) + \left(\left(\left(z \cdot \color{blue}{-4}\right) \cdot a\right) \cdot t + b\right)}{z \cdot c} \]

      8. associate-*r* 76.6%

         \[\leadsto \frac{x \cdot \left(9 \cdot y\right) + \left(\color{blue}{\left(z \cdot \left(-4 \cdot a\right)\right)} \cdot t + b\right)}{z \cdot c} \]

      9. *-commutative 76.6%

         \[\leadsto \frac{x \cdot \left(9 \cdot y\right) + \left(\left(z \cdot \color{blue}{\left(a \cdot -4\right)}\right) \cdot t + b\right)}{z \cdot c} \]

      10. *-commutative 76.6%

          \[\leadsto \frac{x \cdot \left(9 \cdot y\right) + \left(\color{blue}{t \cdot \left(z \cdot \left(a \cdot -4\right)\right)} + b\right)}{z \cdot c} \]

      11. +-commutative 76.6%

          \[\leadsto \frac{x \cdot \left(9 \cdot y\right) + \color{blue}{\left(b + t \cdot \left(z \cdot \left(a \cdot -4\right)\right)\right)}}{z \cdot c} \]

      12. *-un-lft-identity 76.6%

          \[\leadsto \frac{\color{blue}{1 \cdot \left(x \cdot \left(9 \cdot y\right) + \left(b + t \cdot \left(z \cdot \left(a \cdot -4\right)\right)\right)\right)}}{z \cdot c} \]

      13. fma-udef 76.6%

          \[\leadsto \frac{1 \cdot \color{blue}{\mathsf{fma}\left(x, 9 \cdot y, b + t \cdot \left(z \cdot \left(a \cdot -4\right)\right)\right)}}{z \cdot c} \]

   5. Applied egg-rr 76.9%

      \[\leadsto \color{blue}{\frac{1}{z} \cdot \frac{\mathsf{fma}\left(x, 9 \cdot y, \mathsf{fma}\left(t, z \cdot \left(a \cdot -4\right), b\right)\right)}{c}} \]

   6. Taylor expanded in z around inf 48.1%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   7. Step-by-step derivation

      1. associate-*l/ 53.9%

         \[\leadsto -4 \cdot \color{blue}{\left(\frac{a}{c} \cdot t\right)} \]

      2. *-commutative 53.9%

         \[\leadsto -4 \cdot \color{blue}{\left(t \cdot \frac{a}{c}\right)} \]

   8. Simplified 53.9%

      \[\leadsto \color{blue}{-4 \cdot \left(t \cdot \frac{a}{c}\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 49.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7.8 \cdot 10^{-75}:\\ \;\;\;\;a \cdot \left(t \cdot \frac{-4}{c}\right)\\ \mathbf{elif}\;a \leq 1.52 \cdot 10^{-10}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \end{array} \]

Alternative 15: 51.5% accurate, 1.7× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq -8.5 \cdot 10^{-78}:\\ \;\;\;\;a \cdot \left(t \cdot \frac{-4}{c}\right)\\ \mathbf{elif}\;a \leq 3.9 \cdot 10^{-10}:\\ \;\;\;\;b \cdot \frac{\frac{1}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= a -8.5e-78)
   (* a (* t (/ -4.0 c)))
   (if (<= a 3.9e-10) (* b (/ (/ 1.0 c) z)) (* -4.0 (* t (/ a c))))))

C

assert(x < y);
assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (a <= -8.5e-78) {
		tmp = a * (t * (-4.0 / c));
	} else if (a <= 3.9e-10) {
		tmp = b * ((1.0 / c) / z);
	} else {
		tmp = -4.0 * (t * (a / c));
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
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) :: tmp
    if (a <= (-8.5d-78)) then
        tmp = a * (t * ((-4.0d0) / c))
    else if (a <= 3.9d-10) then
        tmp = b * ((1.0d0 / c) / z)
    else
        tmp = (-4.0d0) * (t * (a / c))
    end if
    code = tmp
end function

Java

assert x < y;
assert t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (a <= -8.5e-78) {
		tmp = a * (t * (-4.0 / c));
	} else if (a <= 3.9e-10) {
		tmp = b * ((1.0 / c) / z);
	} else {
		tmp = -4.0 * (t * (a / c));
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if a <= -8.5e-78:
		tmp = a * (t * (-4.0 / c))
	elif a <= 3.9e-10:
		tmp = b * ((1.0 / c) / z)
	else:
		tmp = -4.0 * (t * (a / c))
	return tmp

Julia

x, y = sort([x, y])
t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (a <= -8.5e-78)
		tmp = Float64(a * Float64(t * Float64(-4.0 / c)));
	elseif (a <= 3.9e-10)
		tmp = Float64(b * Float64(Float64(1.0 / c) / z));
	else
		tmp = Float64(-4.0 * Float64(t * Float64(a / c)));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (a <= -8.5e-78)
		tmp = a * (t * (-4.0 / c));
	elseif (a <= 3.9e-10)
		tmp = b * ((1.0 / c) / z);
	else
		tmp = -4.0 * (t * (a / c));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[a, -8.5e-78], N[(a * N[(t * N[(-4.0 / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.9e-10], N[(b * N[(N[(1.0 / c), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -8.49999999999999957e-78

   1. Initial program 82.1%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 82.1%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. div-sub 76.1%

         \[\leadsto \color{blue}{\frac{\left(x \cdot 9\right) \cdot y}{z \cdot c} - \frac{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b}{z \cdot c}} \]

      3. *-commutative 76.1%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y}{z \cdot c} - \frac{\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b}{z \cdot c} \]

      4. associate-*r* 73.5%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y}{z \cdot c} - \frac{\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b}{z \cdot c} \]

      5. *-commutative 73.5%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y}{z \cdot c} - \frac{\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b}{z \cdot c} \]

      6. div-sub 79.5%

         \[\leadsto \color{blue}{\frac{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot a\right) \cdot t - b\right)}{z \cdot c}} \]

      7. associate-+l- 79.5%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

   3. Simplified 81.0%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Step-by-step derivation

      1. sub-neg 81.0%

         \[\leadsto \frac{\color{blue}{\left(x \cdot \left(9 \cdot y\right) + \left(-\left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right)\right)} + b}{z \cdot c} \]

      2. associate-+l+ 81.0%

         \[\leadsto \frac{\color{blue}{x \cdot \left(9 \cdot y\right) + \left(\left(-\left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b\right)}}{z \cdot c} \]

      3. distribute-lft-neg-in 81.0%

         \[\leadsto \frac{x \cdot \left(9 \cdot y\right) + \left(\color{blue}{\left(-z \cdot 4\right) \cdot \left(t \cdot a\right)} + b\right)}{z \cdot c} \]

      4. *-commutative 81.0%

         \[\leadsto \frac{x \cdot \left(9 \cdot y\right) + \left(\left(-z \cdot 4\right) \cdot \color{blue}{\left(a \cdot t\right)} + b\right)}{z \cdot c} \]

      5. associate-*r* 79.5%

         \[\leadsto \frac{x \cdot \left(9 \cdot y\right) + \left(\color{blue}{\left(\left(-z \cdot 4\right) \cdot a\right) \cdot t} + b\right)}{z \cdot c} \]

      6. distribute-rgt-neg-in 79.5%

         \[\leadsto \frac{x \cdot \left(9 \cdot y\right) + \left(\left(\color{blue}{\left(z \cdot \left(-4\right)\right)} \cdot a\right) \cdot t + b\right)}{z \cdot c} \]

      7. metadata-eval 79.5%

         \[\leadsto \frac{x \cdot \left(9 \cdot y\right) + \left(\left(\left(z \cdot \color{blue}{-4}\right) \cdot a\right) \cdot t + b\right)}{z \cdot c} \]

      8. associate-*r* 79.5%

         \[\leadsto \frac{x \cdot \left(9 \cdot y\right) + \left(\color{blue}{\left(z \cdot \left(-4 \cdot a\right)\right)} \cdot t + b\right)}{z \cdot c} \]

      9. *-commutative 79.5%

         \[\leadsto \frac{x \cdot \left(9 \cdot y\right) + \left(\left(z \cdot \color{blue}{\left(a \cdot -4\right)}\right) \cdot t + b\right)}{z \cdot c} \]

      10. *-commutative 79.5%

          \[\leadsto \frac{x \cdot \left(9 \cdot y\right) + \left(\color{blue}{t \cdot \left(z \cdot \left(a \cdot -4\right)\right)} + b\right)}{z \cdot c} \]

      11. +-commutative 79.5%

          \[\leadsto \frac{x \cdot \left(9 \cdot y\right) + \color{blue}{\left(b + t \cdot \left(z \cdot \left(a \cdot -4\right)\right)\right)}}{z \cdot c} \]

      12. *-un-lft-identity 79.5%

          \[\leadsto \frac{\color{blue}{1 \cdot \left(x \cdot \left(9 \cdot y\right) + \left(b + t \cdot \left(z \cdot \left(a \cdot -4\right)\right)\right)\right)}}{z \cdot c} \]

      13. fma-udef 79.6%

          \[\leadsto \frac{1 \cdot \color{blue}{\mathsf{fma}\left(x, 9 \cdot y, b + t \cdot \left(z \cdot \left(a \cdot -4\right)\right)\right)}}{z \cdot c} \]

   5. Applied egg-rr 81.1%

      \[\leadsto \color{blue}{\frac{1}{z} \cdot \frac{\mathsf{fma}\left(x, 9 \cdot y, \mathsf{fma}\left(t, z \cdot \left(a \cdot -4\right), b\right)\right)}{c}} \]

   6. Taylor expanded in z around inf 48.1%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   7. Step-by-step derivation

      1. associate-*l/ 49.7%

         \[\leadsto -4 \cdot \color{blue}{\left(\frac{a}{c} \cdot t\right)} \]

      2. *-commutative 49.7%

         \[\leadsto -4 \cdot \color{blue}{\left(t \cdot \frac{a}{c}\right)} \]

   8. Simplified 49.7%

      \[\leadsto \color{blue}{-4 \cdot \left(t \cdot \frac{a}{c}\right)} \]
   9. Step-by-step derivation

      1. *-commutative 49.7%

         \[\leadsto \color{blue}{\left(t \cdot \frac{a}{c}\right) \cdot -4} \]

      2. associate-*r/ 48.1%

         \[\leadsto \color{blue}{\frac{t \cdot a}{c}} \cdot -4 \]

      3. associate-*l/ 48.1%

         \[\leadsto \color{blue}{\frac{\left(t \cdot a\right) \cdot -4}{c}} \]

   10. Applied egg-rr 48.1%

       \[\leadsto \color{blue}{\frac{\left(t \cdot a\right) \cdot -4}{c}} \]

   11. Taylor expanded in t around 0 48.1%

       \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   12. Step-by-step derivation

       1. associate-/l* 51.7%

          \[\leadsto -4 \cdot \color{blue}{\frac{a}{\frac{c}{t}}} \]

       2. associate-*r/ 51.7%

          \[\leadsto \color{blue}{\frac{-4 \cdot a}{\frac{c}{t}}} \]

       3. *-commutative 51.7%

          \[\leadsto \frac{\color{blue}{a \cdot -4}}{\frac{c}{t}} \]

       4. associate-/l* 48.1%

          \[\leadsto \color{blue}{\frac{\left(a \cdot -4\right) \cdot t}{c}} \]

       5. associate-*l/ 49.7%

          \[\leadsto \color{blue}{\frac{a \cdot -4}{c} \cdot t} \]

       6. associate-*r/ 49.7%

          \[\leadsto \color{blue}{\left(a \cdot \frac{-4}{c}\right)} \cdot t \]

       7. metadata-eval 49.7%

          \[\leadsto \left(a \cdot \frac{\color{blue}{-4 \cdot 1}}{c}\right) \cdot t \]

       8. associate-*r/ 49.7%

          \[\leadsto \left(a \cdot \color{blue}{\left(-4 \cdot \frac{1}{c}\right)}\right) \cdot t \]

       9. associate-*l* 51.6%

          \[\leadsto \color{blue}{a \cdot \left(\left(-4 \cdot \frac{1}{c}\right) \cdot t\right)} \]

       10. associate-*r/ 51.6%

           \[\leadsto a \cdot \left(\color{blue}{\frac{-4 \cdot 1}{c}} \cdot t\right) \]

       11. metadata-eval 51.6%

           \[\leadsto a \cdot \left(\frac{\color{blue}{-4}}{c} \cdot t\right) \]

   13. Simplified 51.6%

       \[\leadsto \color{blue}{a \cdot \left(\frac{-4}{c} \cdot t\right)} \]

   if -8.49999999999999957e-78 < a < 3.9e-10

   1. Initial program 85.1%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 85.1%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. div-sub 76.6%

         \[\leadsto \color{blue}{\frac{\left(x \cdot 9\right) \cdot y}{z \cdot c} - \frac{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b}{z \cdot c}} \]

      3. *-commutative 76.6%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y}{z \cdot c} - \frac{\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b}{z \cdot c} \]

      4. associate-*r* 79.4%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y}{z \cdot c} - \frac{\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b}{z \cdot c} \]

      5. *-commutative 79.4%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y}{z \cdot c} - \frac{\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b}{z \cdot c} \]

      6. div-sub 87.9%

         \[\leadsto \color{blue}{\frac{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot a\right) \cdot t - b\right)}{z \cdot c}} \]

      7. associate-+l- 87.9%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

   3. Simplified 87.9%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Step-by-step derivation

      1. sub-neg 87.9%

         \[\leadsto \frac{\color{blue}{\left(x \cdot \left(9 \cdot y\right) + \left(-\left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right)\right)} + b}{z \cdot c} \]

      2. associate-+l+ 87.9%

         \[\leadsto \frac{\color{blue}{x \cdot \left(9 \cdot y\right) + \left(\left(-\left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b\right)}}{z \cdot c} \]

      3. distribute-lft-neg-in 87.9%

         \[\leadsto \frac{x \cdot \left(9 \cdot y\right) + \left(\color{blue}{\left(-z \cdot 4\right) \cdot \left(t \cdot a\right)} + b\right)}{z \cdot c} \]

      4. *-commutative 87.9%

         \[\leadsto \frac{x \cdot \left(9 \cdot y\right) + \left(\left(-z \cdot 4\right) \cdot \color{blue}{\left(a \cdot t\right)} + b\right)}{z \cdot c} \]

      5. associate-*r* 87.9%

         \[\leadsto \frac{x \cdot \left(9 \cdot y\right) + \left(\color{blue}{\left(\left(-z \cdot 4\right) \cdot a\right) \cdot t} + b\right)}{z \cdot c} \]

      6. distribute-rgt-neg-in 87.9%

         \[\leadsto \frac{x \cdot \left(9 \cdot y\right) + \left(\left(\color{blue}{\left(z \cdot \left(-4\right)\right)} \cdot a\right) \cdot t + b\right)}{z \cdot c} \]

      7. metadata-eval 87.9%

         \[\leadsto \frac{x \cdot \left(9 \cdot y\right) + \left(\left(\left(z \cdot \color{blue}{-4}\right) \cdot a\right) \cdot t + b\right)}{z \cdot c} \]

      8. associate-*r* 87.9%

         \[\leadsto \frac{x \cdot \left(9 \cdot y\right) + \left(\color{blue}{\left(z \cdot \left(-4 \cdot a\right)\right)} \cdot t + b\right)}{z \cdot c} \]

      9. *-commutative 87.9%

         \[\leadsto \frac{x \cdot \left(9 \cdot y\right) + \left(\left(z \cdot \color{blue}{\left(a \cdot -4\right)}\right) \cdot t + b\right)}{z \cdot c} \]

      10. *-commutative 87.9%

          \[\leadsto \frac{x \cdot \left(9 \cdot y\right) + \left(\color{blue}{t \cdot \left(z \cdot \left(a \cdot -4\right)\right)} + b\right)}{z \cdot c} \]

      11. +-commutative 87.9%

          \[\leadsto \frac{x \cdot \left(9 \cdot y\right) + \color{blue}{\left(b + t \cdot \left(z \cdot \left(a \cdot -4\right)\right)\right)}}{z \cdot c} \]

      12. *-un-lft-identity 87.9%

          \[\leadsto \frac{\color{blue}{1 \cdot \left(x \cdot \left(9 \cdot y\right) + \left(b + t \cdot \left(z \cdot \left(a \cdot -4\right)\right)\right)\right)}}{z \cdot c} \]

      13. fma-udef 87.9%

          \[\leadsto \frac{1 \cdot \color{blue}{\mathsf{fma}\left(x, 9 \cdot y, b + t \cdot \left(z \cdot \left(a \cdot -4\right)\right)\right)}}{z \cdot c} \]

   5. Applied egg-rr 89.8%

      \[\leadsto \color{blue}{\frac{1}{z} \cdot \frac{\mathsf{fma}\left(x, 9 \cdot y, \mathsf{fma}\left(t, z \cdot \left(a \cdot -4\right), b\right)\right)}{c}} \]
   6. Step-by-step derivation

      1. clear-num 89.7%

         \[\leadsto \frac{1}{z} \cdot \color{blue}{\frac{1}{\frac{c}{\mathsf{fma}\left(x, 9 \cdot y, \mathsf{fma}\left(t, z \cdot \left(a \cdot -4\right), b\right)\right)}}} \]

      2. un-div-inv 90.3%

         \[\leadsto \color{blue}{\frac{\frac{1}{z}}{\frac{c}{\mathsf{fma}\left(x, 9 \cdot y, \mathsf{fma}\left(t, z \cdot \left(a \cdot -4\right), b\right)\right)}}} \]

   7. Applied egg-rr 90.3%

      \[\leadsto \color{blue}{\frac{\frac{1}{z}}{\frac{c}{\mathsf{fma}\left(x, 9 \cdot y, \mathsf{fma}\left(t, z \cdot \left(a \cdot -4\right), b\right)\right)}}} \]

   8. Taylor expanded in b around inf 45.9%

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
   9. Step-by-step derivation

      1. associate-/l/ 44.0%

         \[\leadsto \color{blue}{\frac{\frac{b}{z}}{c}} \]

   10. Simplified 44.0%

       \[\leadsto \color{blue}{\frac{\frac{b}{z}}{c}} \]
   11. Step-by-step derivation

       1. associate-/r* 45.9%

          \[\leadsto \color{blue}{\frac{b}{z \cdot c}} \]

       2. div-inv 46.7%

          \[\leadsto \color{blue}{b \cdot \frac{1}{z \cdot c}} \]

       3. *-commutative 46.7%

          \[\leadsto b \cdot \frac{1}{\color{blue}{c \cdot z}} \]

       4. associate-/r* 46.8%

          \[\leadsto b \cdot \color{blue}{\frac{\frac{1}{c}}{z}} \]

   12. Applied egg-rr 46.8%

       \[\leadsto \color{blue}{b \cdot \frac{\frac{1}{c}}{z}} \]

   if 3.9e-10 < a

   1. Initial program 78.3%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 78.3%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. div-sub 69.3%

         \[\leadsto \color{blue}{\frac{\left(x \cdot 9\right) \cdot y}{z \cdot c} - \frac{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b}{z \cdot c}} \]

      3. *-commutative 69.3%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y}{z \cdot c} - \frac{\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b}{z \cdot c} \]

      4. associate-*r* 67.6%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y}{z \cdot c} - \frac{\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b}{z \cdot c} \]

      5. *-commutative 67.6%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y}{z \cdot c} - \frac{\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b}{z \cdot c} \]

      6. div-sub 76.6%

         \[\leadsto \color{blue}{\frac{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot a\right) \cdot t - b\right)}{z \cdot c}} \]

      7. associate-+l- 76.6%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

   3. Simplified 74.0%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Step-by-step derivation

      1. sub-neg 74.0%

         \[\leadsto \frac{\color{blue}{\left(x \cdot \left(9 \cdot y\right) + \left(-\left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right)\right)} + b}{z \cdot c} \]

      2. associate-+l+ 74.0%

         \[\leadsto \frac{\color{blue}{x \cdot \left(9 \cdot y\right) + \left(\left(-\left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b\right)}}{z \cdot c} \]

      3. distribute-lft-neg-in 74.0%

         \[\leadsto \frac{x \cdot \left(9 \cdot y\right) + \left(\color{blue}{\left(-z \cdot 4\right) \cdot \left(t \cdot a\right)} + b\right)}{z \cdot c} \]

      4. *-commutative 74.0%

         \[\leadsto \frac{x \cdot \left(9 \cdot y\right) + \left(\left(-z \cdot 4\right) \cdot \color{blue}{\left(a \cdot t\right)} + b\right)}{z \cdot c} \]

      5. associate-*r* 76.6%

         \[\leadsto \frac{x \cdot \left(9 \cdot y\right) + \left(\color{blue}{\left(\left(-z \cdot 4\right) \cdot a\right) \cdot t} + b\right)}{z \cdot c} \]

      6. distribute-rgt-neg-in 76.6%

         \[\leadsto \frac{x \cdot \left(9 \cdot y\right) + \left(\left(\color{blue}{\left(z \cdot \left(-4\right)\right)} \cdot a\right) \cdot t + b\right)}{z \cdot c} \]

      7. metadata-eval 76.6%

         \[\leadsto \frac{x \cdot \left(9 \cdot y\right) + \left(\left(\left(z \cdot \color{blue}{-4}\right) \cdot a\right) \cdot t + b\right)}{z \cdot c} \]

      8. associate-*r* 76.6%

         \[\leadsto \frac{x \cdot \left(9 \cdot y\right) + \left(\color{blue}{\left(z \cdot \left(-4 \cdot a\right)\right)} \cdot t + b\right)}{z \cdot c} \]

      9. *-commutative 76.6%

         \[\leadsto \frac{x \cdot \left(9 \cdot y\right) + \left(\left(z \cdot \color{blue}{\left(a \cdot -4\right)}\right) \cdot t + b\right)}{z \cdot c} \]

      10. *-commutative 76.6%

          \[\leadsto \frac{x \cdot \left(9 \cdot y\right) + \left(\color{blue}{t \cdot \left(z \cdot \left(a \cdot -4\right)\right)} + b\right)}{z \cdot c} \]

      11. +-commutative 76.6%

          \[\leadsto \frac{x \cdot \left(9 \cdot y\right) + \color{blue}{\left(b + t \cdot \left(z \cdot \left(a \cdot -4\right)\right)\right)}}{z \cdot c} \]

      12. *-un-lft-identity 76.6%

          \[\leadsto \frac{\color{blue}{1 \cdot \left(x \cdot \left(9 \cdot y\right) + \left(b + t \cdot \left(z \cdot \left(a \cdot -4\right)\right)\right)\right)}}{z \cdot c} \]

      13. fma-udef 76.6%

          \[\leadsto \frac{1 \cdot \color{blue}{\mathsf{fma}\left(x, 9 \cdot y, b + t \cdot \left(z \cdot \left(a \cdot -4\right)\right)\right)}}{z \cdot c} \]

   5. Applied egg-rr 76.9%

      \[\leadsto \color{blue}{\frac{1}{z} \cdot \frac{\mathsf{fma}\left(x, 9 \cdot y, \mathsf{fma}\left(t, z \cdot \left(a \cdot -4\right), b\right)\right)}{c}} \]

   6. Taylor expanded in z around inf 48.1%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   7. Step-by-step derivation

      1. associate-*l/ 53.9%

         \[\leadsto -4 \cdot \color{blue}{\left(\frac{a}{c} \cdot t\right)} \]

      2. *-commutative 53.9%

         \[\leadsto -4 \cdot \color{blue}{\left(t \cdot \frac{a}{c}\right)} \]

   8. Simplified 53.9%

      \[\leadsto \color{blue}{-4 \cdot \left(t \cdot \frac{a}{c}\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 50.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -8.5 \cdot 10^{-78}:\\ \;\;\;\;a \cdot \left(t \cdot \frac{-4}{c}\right)\\ \mathbf{elif}\;a \leq 3.9 \cdot 10^{-10}:\\ \;\;\;\;b \cdot \frac{\frac{1}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \end{array} \]

Alternative 16: 51.5% accurate, 1.7× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq -1.9 \cdot 10^{-75}:\\ \;\;\;\;a \cdot \left(t \cdot \frac{-4}{c}\right)\\ \mathbf{elif}\;a \leq 2.25 \cdot 10^{-10}:\\ \;\;\;\;b \cdot \frac{\frac{1}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot -4}{\frac{c}{a}}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= a -1.9e-75)
   (* a (* t (/ -4.0 c)))
   (if (<= a 2.25e-10) (* b (/ (/ 1.0 c) z)) (/ (* t -4.0) (/ c a)))))

C

assert(x < y);
assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (a <= -1.9e-75) {
		tmp = a * (t * (-4.0 / c));
	} else if (a <= 2.25e-10) {
		tmp = b * ((1.0 / c) / z);
	} else {
		tmp = (t * -4.0) / (c / a);
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
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) :: tmp
    if (a <= (-1.9d-75)) then
        tmp = a * (t * ((-4.0d0) / c))
    else if (a <= 2.25d-10) then
        tmp = b * ((1.0d0 / c) / z)
    else
        tmp = (t * (-4.0d0)) / (c / a)
    end if
    code = tmp
end function

Java

assert x < y;
assert t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (a <= -1.9e-75) {
		tmp = a * (t * (-4.0 / c));
	} else if (a <= 2.25e-10) {
		tmp = b * ((1.0 / c) / z);
	} else {
		tmp = (t * -4.0) / (c / a);
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if a <= -1.9e-75:
		tmp = a * (t * (-4.0 / c))
	elif a <= 2.25e-10:
		tmp = b * ((1.0 / c) / z)
	else:
		tmp = (t * -4.0) / (c / a)
	return tmp

Julia

x, y = sort([x, y])
t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (a <= -1.9e-75)
		tmp = Float64(a * Float64(t * Float64(-4.0 / c)));
	elseif (a <= 2.25e-10)
		tmp = Float64(b * Float64(Float64(1.0 / c) / z));
	else
		tmp = Float64(Float64(t * -4.0) / Float64(c / a));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (a <= -1.9e-75)
		tmp = a * (t * (-4.0 / c));
	elseif (a <= 2.25e-10)
		tmp = b * ((1.0 / c) / z);
	else
		tmp = (t * -4.0) / (c / a);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[a, -1.9e-75], N[(a * N[(t * N[(-4.0 / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.25e-10], N[(b * N[(N[(1.0 / c), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(N[(t * -4.0), $MachinePrecision] / N[(c / a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.89999999999999997e-75

   1. Initial program 82.1%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 82.1%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. div-sub 76.1%

         \[\leadsto \color{blue}{\frac{\left(x \cdot 9\right) \cdot y}{z \cdot c} - \frac{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b}{z \cdot c}} \]

      3. *-commutative 76.1%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y}{z \cdot c} - \frac{\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b}{z \cdot c} \]

      4. associate-*r* 73.5%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y}{z \cdot c} - \frac{\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b}{z \cdot c} \]

      5. *-commutative 73.5%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y}{z \cdot c} - \frac{\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b}{z \cdot c} \]

      6. div-sub 79.5%

         \[\leadsto \color{blue}{\frac{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot a\right) \cdot t - b\right)}{z \cdot c}} \]

      7. associate-+l- 79.5%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

   3. Simplified 81.0%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Step-by-step derivation

      1. sub-neg 81.0%

         \[\leadsto \frac{\color{blue}{\left(x \cdot \left(9 \cdot y\right) + \left(-\left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right)\right)} + b}{z \cdot c} \]

      2. associate-+l+ 81.0%

         \[\leadsto \frac{\color{blue}{x \cdot \left(9 \cdot y\right) + \left(\left(-\left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b\right)}}{z \cdot c} \]

      3. distribute-lft-neg-in 81.0%

         \[\leadsto \frac{x \cdot \left(9 \cdot y\right) + \left(\color{blue}{\left(-z \cdot 4\right) \cdot \left(t \cdot a\right)} + b\right)}{z \cdot c} \]

      4. *-commutative 81.0%

         \[\leadsto \frac{x \cdot \left(9 \cdot y\right) + \left(\left(-z \cdot 4\right) \cdot \color{blue}{\left(a \cdot t\right)} + b\right)}{z \cdot c} \]

      5. associate-*r* 79.5%

         \[\leadsto \frac{x \cdot \left(9 \cdot y\right) + \left(\color{blue}{\left(\left(-z \cdot 4\right) \cdot a\right) \cdot t} + b\right)}{z \cdot c} \]

      6. distribute-rgt-neg-in 79.5%

         \[\leadsto \frac{x \cdot \left(9 \cdot y\right) + \left(\left(\color{blue}{\left(z \cdot \left(-4\right)\right)} \cdot a\right) \cdot t + b\right)}{z \cdot c} \]

      7. metadata-eval 79.5%

         \[\leadsto \frac{x \cdot \left(9 \cdot y\right) + \left(\left(\left(z \cdot \color{blue}{-4}\right) \cdot a\right) \cdot t + b\right)}{z \cdot c} \]

      8. associate-*r* 79.5%

         \[\leadsto \frac{x \cdot \left(9 \cdot y\right) + \left(\color{blue}{\left(z \cdot \left(-4 \cdot a\right)\right)} \cdot t + b\right)}{z \cdot c} \]

      9. *-commutative 79.5%

         \[\leadsto \frac{x \cdot \left(9 \cdot y\right) + \left(\left(z \cdot \color{blue}{\left(a \cdot -4\right)}\right) \cdot t + b\right)}{z \cdot c} \]

      10. *-commutative 79.5%

          \[\leadsto \frac{x \cdot \left(9 \cdot y\right) + \left(\color{blue}{t \cdot \left(z \cdot \left(a \cdot -4\right)\right)} + b\right)}{z \cdot c} \]

      11. +-commutative 79.5%

          \[\leadsto \frac{x \cdot \left(9 \cdot y\right) + \color{blue}{\left(b + t \cdot \left(z \cdot \left(a \cdot -4\right)\right)\right)}}{z \cdot c} \]

      12. *-un-lft-identity 79.5%

          \[\leadsto \frac{\color{blue}{1 \cdot \left(x \cdot \left(9 \cdot y\right) + \left(b + t \cdot \left(z \cdot \left(a \cdot -4\right)\right)\right)\right)}}{z \cdot c} \]

      13. fma-udef 79.6%

          \[\leadsto \frac{1 \cdot \color{blue}{\mathsf{fma}\left(x, 9 \cdot y, b + t \cdot \left(z \cdot \left(a \cdot -4\right)\right)\right)}}{z \cdot c} \]

   5. Applied egg-rr 81.1%

      \[\leadsto \color{blue}{\frac{1}{z} \cdot \frac{\mathsf{fma}\left(x, 9 \cdot y, \mathsf{fma}\left(t, z \cdot \left(a \cdot -4\right), b\right)\right)}{c}} \]

   6. Taylor expanded in z around inf 48.1%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   7. Step-by-step derivation

      1. associate-*l/ 49.7%

         \[\leadsto -4 \cdot \color{blue}{\left(\frac{a}{c} \cdot t\right)} \]

      2. *-commutative 49.7%

         \[\leadsto -4 \cdot \color{blue}{\left(t \cdot \frac{a}{c}\right)} \]

   8. Simplified 49.7%

      \[\leadsto \color{blue}{-4 \cdot \left(t \cdot \frac{a}{c}\right)} \]
   9. Step-by-step derivation

      1. *-commutative 49.7%

         \[\leadsto \color{blue}{\left(t \cdot \frac{a}{c}\right) \cdot -4} \]

      2. associate-*r/ 48.1%

         \[\leadsto \color{blue}{\frac{t \cdot a}{c}} \cdot -4 \]

      3. associate-*l/ 48.1%

         \[\leadsto \color{blue}{\frac{\left(t \cdot a\right) \cdot -4}{c}} \]

   10. Applied egg-rr 48.1%

       \[\leadsto \color{blue}{\frac{\left(t \cdot a\right) \cdot -4}{c}} \]

   11. Taylor expanded in t around 0 48.1%

       \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   12. Step-by-step derivation

       1. associate-/l* 51.7%

          \[\leadsto -4 \cdot \color{blue}{\frac{a}{\frac{c}{t}}} \]

       2. associate-*r/ 51.7%

          \[\leadsto \color{blue}{\frac{-4 \cdot a}{\frac{c}{t}}} \]

       3. *-commutative 51.7%

          \[\leadsto \frac{\color{blue}{a \cdot -4}}{\frac{c}{t}} \]

       4. associate-/l* 48.1%

          \[\leadsto \color{blue}{\frac{\left(a \cdot -4\right) \cdot t}{c}} \]

       5. associate-*l/ 49.7%

          \[\leadsto \color{blue}{\frac{a \cdot -4}{c} \cdot t} \]

       6. associate-*r/ 49.7%

          \[\leadsto \color{blue}{\left(a \cdot \frac{-4}{c}\right)} \cdot t \]

       7. metadata-eval 49.7%

          \[\leadsto \left(a \cdot \frac{\color{blue}{-4 \cdot 1}}{c}\right) \cdot t \]

       8. associate-*r/ 49.7%

          \[\leadsto \left(a \cdot \color{blue}{\left(-4 \cdot \frac{1}{c}\right)}\right) \cdot t \]

       9. associate-*l* 51.6%

          \[\leadsto \color{blue}{a \cdot \left(\left(-4 \cdot \frac{1}{c}\right) \cdot t\right)} \]

       10. associate-*r/ 51.6%

           \[\leadsto a \cdot \left(\color{blue}{\frac{-4 \cdot 1}{c}} \cdot t\right) \]

       11. metadata-eval 51.6%

           \[\leadsto a \cdot \left(\frac{\color{blue}{-4}}{c} \cdot t\right) \]

   13. Simplified 51.6%

       \[\leadsto \color{blue}{a \cdot \left(\frac{-4}{c} \cdot t\right)} \]

   if -1.89999999999999997e-75 < a < 2.25e-10

   1. Initial program 85.1%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 85.1%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. div-sub 76.6%

         \[\leadsto \color{blue}{\frac{\left(x \cdot 9\right) \cdot y}{z \cdot c} - \frac{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b}{z \cdot c}} \]

      3. *-commutative 76.6%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y}{z \cdot c} - \frac{\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b}{z \cdot c} \]

      4. associate-*r* 79.4%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y}{z \cdot c} - \frac{\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b}{z \cdot c} \]

      5. *-commutative 79.4%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y}{z \cdot c} - \frac{\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b}{z \cdot c} \]

      6. div-sub 87.9%

         \[\leadsto \color{blue}{\frac{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot a\right) \cdot t - b\right)}{z \cdot c}} \]

      7. associate-+l- 87.9%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

   3. Simplified 87.9%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Step-by-step derivation

      1. sub-neg 87.9%

         \[\leadsto \frac{\color{blue}{\left(x \cdot \left(9 \cdot y\right) + \left(-\left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right)\right)} + b}{z \cdot c} \]

      2. associate-+l+ 87.9%

         \[\leadsto \frac{\color{blue}{x \cdot \left(9 \cdot y\right) + \left(\left(-\left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b\right)}}{z \cdot c} \]

      3. distribute-lft-neg-in 87.9%

         \[\leadsto \frac{x \cdot \left(9 \cdot y\right) + \left(\color{blue}{\left(-z \cdot 4\right) \cdot \left(t \cdot a\right)} + b\right)}{z \cdot c} \]

      4. *-commutative 87.9%

         \[\leadsto \frac{x \cdot \left(9 \cdot y\right) + \left(\left(-z \cdot 4\right) \cdot \color{blue}{\left(a \cdot t\right)} + b\right)}{z \cdot c} \]

      5. associate-*r* 87.9%

         \[\leadsto \frac{x \cdot \left(9 \cdot y\right) + \left(\color{blue}{\left(\left(-z \cdot 4\right) \cdot a\right) \cdot t} + b\right)}{z \cdot c} \]

      6. distribute-rgt-neg-in 87.9%

         \[\leadsto \frac{x \cdot \left(9 \cdot y\right) + \left(\left(\color{blue}{\left(z \cdot \left(-4\right)\right)} \cdot a\right) \cdot t + b\right)}{z \cdot c} \]

      7. metadata-eval 87.9%

         \[\leadsto \frac{x \cdot \left(9 \cdot y\right) + \left(\left(\left(z \cdot \color{blue}{-4}\right) \cdot a\right) \cdot t + b\right)}{z \cdot c} \]

      8. associate-*r* 87.9%

         \[\leadsto \frac{x \cdot \left(9 \cdot y\right) + \left(\color{blue}{\left(z \cdot \left(-4 \cdot a\right)\right)} \cdot t + b\right)}{z \cdot c} \]

      9. *-commutative 87.9%

         \[\leadsto \frac{x \cdot \left(9 \cdot y\right) + \left(\left(z \cdot \color{blue}{\left(a \cdot -4\right)}\right) \cdot t + b\right)}{z \cdot c} \]

      10. *-commutative 87.9%

          \[\leadsto \frac{x \cdot \left(9 \cdot y\right) + \left(\color{blue}{t \cdot \left(z \cdot \left(a \cdot -4\right)\right)} + b\right)}{z \cdot c} \]

      11. +-commutative 87.9%

          \[\leadsto \frac{x \cdot \left(9 \cdot y\right) + \color{blue}{\left(b + t \cdot \left(z \cdot \left(a \cdot -4\right)\right)\right)}}{z \cdot c} \]

      12. *-un-lft-identity 87.9%

          \[\leadsto \frac{\color{blue}{1 \cdot \left(x \cdot \left(9 \cdot y\right) + \left(b + t \cdot \left(z \cdot \left(a \cdot -4\right)\right)\right)\right)}}{z \cdot c} \]

      13. fma-udef 87.9%

          \[\leadsto \frac{1 \cdot \color{blue}{\mathsf{fma}\left(x, 9 \cdot y, b + t \cdot \left(z \cdot \left(a \cdot -4\right)\right)\right)}}{z \cdot c} \]

   5. Applied egg-rr 89.8%

      \[\leadsto \color{blue}{\frac{1}{z} \cdot \frac{\mathsf{fma}\left(x, 9 \cdot y, \mathsf{fma}\left(t, z \cdot \left(a \cdot -4\right), b\right)\right)}{c}} \]
   6. Step-by-step derivation

      1. clear-num 89.7%

         \[\leadsto \frac{1}{z} \cdot \color{blue}{\frac{1}{\frac{c}{\mathsf{fma}\left(x, 9 \cdot y, \mathsf{fma}\left(t, z \cdot \left(a \cdot -4\right), b\right)\right)}}} \]

      2. un-div-inv 90.3%

         \[\leadsto \color{blue}{\frac{\frac{1}{z}}{\frac{c}{\mathsf{fma}\left(x, 9 \cdot y, \mathsf{fma}\left(t, z \cdot \left(a \cdot -4\right), b\right)\right)}}} \]

   7. Applied egg-rr 90.3%

      \[\leadsto \color{blue}{\frac{\frac{1}{z}}{\frac{c}{\mathsf{fma}\left(x, 9 \cdot y, \mathsf{fma}\left(t, z \cdot \left(a \cdot -4\right), b\right)\right)}}} \]

   8. Taylor expanded in b around inf 45.9%

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
   9. Step-by-step derivation

      1. associate-/l/ 44.0%

         \[\leadsto \color{blue}{\frac{\frac{b}{z}}{c}} \]

   10. Simplified 44.0%

       \[\leadsto \color{blue}{\frac{\frac{b}{z}}{c}} \]
   11. Step-by-step derivation

       1. associate-/r* 45.9%

          \[\leadsto \color{blue}{\frac{b}{z \cdot c}} \]

       2. div-inv 46.7%

          \[\leadsto \color{blue}{b \cdot \frac{1}{z \cdot c}} \]

       3. *-commutative 46.7%

          \[\leadsto b \cdot \frac{1}{\color{blue}{c \cdot z}} \]

       4. associate-/r* 46.8%

          \[\leadsto b \cdot \color{blue}{\frac{\frac{1}{c}}{z}} \]

   12. Applied egg-rr 46.8%

       \[\leadsto \color{blue}{b \cdot \frac{\frac{1}{c}}{z}} \]

   if 2.25e-10 < a

   1. Initial program 78.3%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 78.3%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. div-sub 69.3%

         \[\leadsto \color{blue}{\frac{\left(x \cdot 9\right) \cdot y}{z \cdot c} - \frac{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b}{z \cdot c}} \]

      3. *-commutative 69.3%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y}{z \cdot c} - \frac{\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b}{z \cdot c} \]

      4. associate-*r* 67.6%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y}{z \cdot c} - \frac{\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b}{z \cdot c} \]

      5. *-commutative 67.6%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y}{z \cdot c} - \frac{\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b}{z \cdot c} \]

      6. div-sub 76.6%

         \[\leadsto \color{blue}{\frac{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot a\right) \cdot t - b\right)}{z \cdot c}} \]

      7. associate-+l- 76.6%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

   3. Simplified 74.0%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Step-by-step derivation

      1. sub-neg 74.0%

         \[\leadsto \frac{\color{blue}{\left(x \cdot \left(9 \cdot y\right) + \left(-\left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right)\right)} + b}{z \cdot c} \]

      2. associate-+l+ 74.0%

         \[\leadsto \frac{\color{blue}{x \cdot \left(9 \cdot y\right) + \left(\left(-\left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b\right)}}{z \cdot c} \]

      3. distribute-lft-neg-in 74.0%

         \[\leadsto \frac{x \cdot \left(9 \cdot y\right) + \left(\color{blue}{\left(-z \cdot 4\right) \cdot \left(t \cdot a\right)} + b\right)}{z \cdot c} \]

      4. *-commutative 74.0%

         \[\leadsto \frac{x \cdot \left(9 \cdot y\right) + \left(\left(-z \cdot 4\right) \cdot \color{blue}{\left(a \cdot t\right)} + b\right)}{z \cdot c} \]

      5. associate-*r* 76.6%

         \[\leadsto \frac{x \cdot \left(9 \cdot y\right) + \left(\color{blue}{\left(\left(-z \cdot 4\right) \cdot a\right) \cdot t} + b\right)}{z \cdot c} \]

      6. distribute-rgt-neg-in 76.6%

         \[\leadsto \frac{x \cdot \left(9 \cdot y\right) + \left(\left(\color{blue}{\left(z \cdot \left(-4\right)\right)} \cdot a\right) \cdot t + b\right)}{z \cdot c} \]

      7. metadata-eval 76.6%

         \[\leadsto \frac{x \cdot \left(9 \cdot y\right) + \left(\left(\left(z \cdot \color{blue}{-4}\right) \cdot a\right) \cdot t + b\right)}{z \cdot c} \]

      8. associate-*r* 76.6%

         \[\leadsto \frac{x \cdot \left(9 \cdot y\right) + \left(\color{blue}{\left(z \cdot \left(-4 \cdot a\right)\right)} \cdot t + b\right)}{z \cdot c} \]

      9. *-commutative 76.6%

         \[\leadsto \frac{x \cdot \left(9 \cdot y\right) + \left(\left(z \cdot \color{blue}{\left(a \cdot -4\right)}\right) \cdot t + b\right)}{z \cdot c} \]

      10. *-commutative 76.6%

          \[\leadsto \frac{x \cdot \left(9 \cdot y\right) + \left(\color{blue}{t \cdot \left(z \cdot \left(a \cdot -4\right)\right)} + b\right)}{z \cdot c} \]

      11. +-commutative 76.6%

          \[\leadsto \frac{x \cdot \left(9 \cdot y\right) + \color{blue}{\left(b + t \cdot \left(z \cdot \left(a \cdot -4\right)\right)\right)}}{z \cdot c} \]

      12. *-un-lft-identity 76.6%

          \[\leadsto \frac{\color{blue}{1 \cdot \left(x \cdot \left(9 \cdot y\right) + \left(b + t \cdot \left(z \cdot \left(a \cdot -4\right)\right)\right)\right)}}{z \cdot c} \]

      13. fma-udef 76.6%

          \[\leadsto \frac{1 \cdot \color{blue}{\mathsf{fma}\left(x, 9 \cdot y, b + t \cdot \left(z \cdot \left(a \cdot -4\right)\right)\right)}}{z \cdot c} \]

   5. Applied egg-rr 76.9%

      \[\leadsto \color{blue}{\frac{1}{z} \cdot \frac{\mathsf{fma}\left(x, 9 \cdot y, \mathsf{fma}\left(t, z \cdot \left(a \cdot -4\right), b\right)\right)}{c}} \]

   6. Taylor expanded in z around inf 48.1%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   7. Step-by-step derivation

      1. associate-*l/ 53.9%

         \[\leadsto -4 \cdot \color{blue}{\left(\frac{a}{c} \cdot t\right)} \]

      2. *-commutative 53.9%

         \[\leadsto -4 \cdot \color{blue}{\left(t \cdot \frac{a}{c}\right)} \]

   8. Simplified 53.9%

      \[\leadsto \color{blue}{-4 \cdot \left(t \cdot \frac{a}{c}\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 53.9%

         \[\leadsto \color{blue}{\left(-4 \cdot t\right) \cdot \frac{a}{c}} \]

      2. clear-num 53.8%

         \[\leadsto \left(-4 \cdot t\right) \cdot \color{blue}{\frac{1}{\frac{c}{a}}} \]

      3. un-div-inv 53.9%

         \[\leadsto \color{blue}{\frac{-4 \cdot t}{\frac{c}{a}}} \]

      4. *-commutative 53.9%

         \[\leadsto \frac{\color{blue}{t \cdot -4}}{\frac{c}{a}} \]

   10. Applied egg-rr 53.9%

       \[\leadsto \color{blue}{\frac{t \cdot -4}{\frac{c}{a}}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 50.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.9 \cdot 10^{-75}:\\ \;\;\;\;a \cdot \left(t \cdot \frac{-4}{c}\right)\\ \mathbf{elif}\;a \leq 2.25 \cdot 10^{-10}:\\ \;\;\;\;b \cdot \frac{\frac{1}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot -4}{\frac{c}{a}}\\ \end{array} \]

Alternative 17: 34.9% accurate, 2.7× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq 1.9 \cdot 10^{-210}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= y 1.9e-210) (/ (/ b c) z) (/ b (* z c))))

C

assert(x < y);
assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (y <= 1.9e-210) {
		tmp = (b / c) / z;
	} else {
		tmp = b / (z * c);
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
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) :: tmp
    if (y <= 1.9d-210) then
        tmp = (b / c) / z
    else
        tmp = b / (z * c)
    end if
    code = tmp
end function

Java

assert x < y;
assert t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (y <= 1.9e-210) {
		tmp = (b / c) / z;
	} else {
		tmp = b / (z * c);
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if y <= 1.9e-210:
		tmp = (b / c) / z
	else:
		tmp = b / (z * c)
	return tmp

Julia

x, y = sort([x, y])
t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (y <= 1.9e-210)
		tmp = Float64(Float64(b / c) / z);
	else
		tmp = Float64(b / Float64(z * c));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (y <= 1.9e-210)
		tmp = (b / c) / z;
	else
		tmp = b / (z * c);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[y, 1.9e-210], N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 1.90000000000000002e-210

   1. Initial program 85.6%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 85.6%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. div-sub 78.0%

         \[\leadsto \color{blue}{\frac{\left(x \cdot 9\right) \cdot y}{z \cdot c} - \frac{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b}{z \cdot c}} \]

      3. *-commutative 78.0%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y}{z \cdot c} - \frac{\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b}{z \cdot c} \]

      4. associate-*r* 77.8%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y}{z \cdot c} - \frac{\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b}{z \cdot c} \]

      5. *-commutative 77.8%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y}{z \cdot c} - \frac{\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b}{z \cdot c} \]

      6. div-sub 85.4%

         \[\leadsto \color{blue}{\frac{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot a\right) \cdot t - b\right)}{z \cdot c}} \]

      7. associate-+l- 85.4%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

   3. Simplified 84.4%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]

   4. Taylor expanded in x around inf 64.2%

      \[\leadsto \frac{\color{blue}{9 \cdot \left(x \cdot y\right)} + b}{z \cdot c} \]
   5. Step-by-step derivation

      1. associate-*r* 64.2%

         \[\leadsto \frac{\color{blue}{\left(9 \cdot x\right) \cdot y} + b}{z \cdot c} \]

   6. Simplified 64.2%

      \[\leadsto \frac{\color{blue}{\left(9 \cdot x\right) \cdot y} + b}{z \cdot c} \]

   7. Taylor expanded in x around 0 38.5%

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
   8. Step-by-step derivation

      1. associate-/r* 39.8%

         \[\leadsto \color{blue}{\frac{\frac{b}{c}}{z}} \]

   9. Simplified 39.8%

      \[\leadsto \color{blue}{\frac{\frac{b}{c}}{z}} \]

   if 1.90000000000000002e-210 < y

   1. Initial program 78.1%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 78.1%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. div-sub 70.1%

         \[\leadsto \color{blue}{\frac{\left(x \cdot 9\right) \cdot y}{z \cdot c} - \frac{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b}{z \cdot c}} \]

      3. *-commutative 70.1%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y}{z \cdot c} - \frac{\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b}{z \cdot c} \]

      4. associate-*r* 70.0%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y}{z \cdot c} - \frac{\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b}{z \cdot c} \]

      5. *-commutative 70.0%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y}{z \cdot c} - \frac{\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b}{z \cdot c} \]

      6. div-sub 78.1%

         \[\leadsto \color{blue}{\frac{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot a\right) \cdot t - b\right)}{z \cdot c}} \]

      7. associate-+l- 78.1%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

   3. Simplified 79.0%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]

   4. Taylor expanded in b around inf 34.3%

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
   5. Step-by-step derivation

      1. *-commutative 34.3%

         \[\leadsto \frac{b}{\color{blue}{z \cdot c}} \]

   6. Simplified 34.3%

      \[\leadsto \color{blue}{\frac{b}{z \cdot c}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 37.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.9 \cdot 10^{-210}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \end{array} \]

Alternative 18: 35.0% accurate, 3.8× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \frac{b}{z \cdot c} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c) :precision binary64 (/ b (* z c)))

C

assert(x < y);
assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	return b / (z * c);
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
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 = b / (z * c)
end function

Java

assert x < y;
assert t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	return b / (z * c);
}

Python

[x, y] = sort([x, y])
[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	return b / (z * c)

Julia

x, y = sort([x, y])
t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	return Float64(b / Float64(z * c))
end

MATLAB

x, y = num2cell(sort([x, y])){:}
t, a = num2cell(sort([t, a])){:}
function tmp = code(x, y, z, t, a, b, c)
	tmp = b / (z * c);
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 82.3%

   \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
2. Step-by-step derivation

   1. associate-+l- 82.3%

      \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

   2. div-sub 74.5%

      \[\leadsto \color{blue}{\frac{\left(x \cdot 9\right) \cdot y}{z \cdot c} - \frac{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b}{z \cdot c}} \]

   3. *-commutative 74.5%

      \[\leadsto \frac{\left(x \cdot 9\right) \cdot y}{z \cdot c} - \frac{\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b}{z \cdot c} \]

   4. associate-*r* 74.4%

      \[\leadsto \frac{\left(x \cdot 9\right) \cdot y}{z \cdot c} - \frac{\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b}{z \cdot c} \]

   5. *-commutative 74.4%

      \[\leadsto \frac{\left(x \cdot 9\right) \cdot y}{z \cdot c} - \frac{\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b}{z \cdot c} \]

   6. div-sub 82.2%

      \[\leadsto \color{blue}{\frac{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot a\right) \cdot t - b\right)}{z \cdot c}} \]

   7. associate-+l- 82.2%

      \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

3. Simplified 82.0%

   \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]

4. Taylor expanded in b around inf 36.6%

   \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
5. Step-by-step derivation

   1. *-commutative 36.6%

      \[\leadsto \frac{b}{\color{blue}{z \cdot c}} \]

6. Simplified 36.6%

   \[\leadsto \color{blue}{\frac{b}{z \cdot c}} \]

7. Final simplification 36.6%

   \[\leadsto \frac{b}{z \cdot c} \]

Developer target: 80.7% accurate, 0.2× 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 2023301 
(FPCore (x y z t a b c)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, J"
  :precision binary64

  :herbie-target
  (if (< (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)) -1.100156740804105e-171) (/ (+ (- (* (* x 9.0) y) (* (* z 4.0) (* t a))) b) (* z c)) (if (< (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)) 0.0) (/ (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) z) c) (if (< (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)) 1.1708877911747488e-53) (/ (+ (- (* (* x 9.0) y) (* (* z 4.0) (* t a))) b) (* z c)) (if (< (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)) 2.876823679546137e+130) (- (+ (* (* 9.0 (/ y c)) (/ x z)) (/ b (* c z))) (* 4.0 (/ (* a t) c))) (if (< (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)) 1.3838515042456319e+158) (/ (+ (- (* (* x 9.0) y) (* (* z 4.0) (* t a))) b) (* z c)) (- (+ (* 9.0 (* (/ y (* c z)) x)) (/ b (* c z))) (* 4.0 (/ (* a t) c))))))))

  (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)))