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

Percentage Accurate: 79.7% → 92.4%

Time: 18.6s

Alternatives: 14

Speedup: 0.8×

• 36.7% 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: 79.7% 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: 92.4% accurate, 0.1× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -6.6 \cdot 10^{+35}:\\ \;\;\;\;\mathsf{fma}\left(-4, a \cdot t, \mathsf{fma}\left(9, \frac{x}{\frac{z}{y}}, \frac{b}{z}\right)\right) \cdot \frac{1}{c}\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-120}:\\ \;\;\;\;\frac{1}{z} \cdot \frac{\mathsf{fma}\left(x, 9 \cdot y, b + t \cdot \left(z \cdot \left(-4 \cdot a\right)\right)\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{c} \cdot \left(-4 \cdot \left(a \cdot t\right) + \left(\frac{b}{z} + 9 \cdot \frac{x \cdot y}{z}\right)\right)\\ \end{array} \end{array} \]

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 (<= z -6.6e+35)
   (* (fma -4.0 (* a t) (fma 9.0 (/ x (/ z y)) (/ b z))) (/ 1.0 c))
   (if (<= z 5e-120)
     (* (/ 1.0 z) (/ (fma x (* 9.0 y) (+ b (* t (* z (* -4.0 a))))) c))
     (* (/ 1.0 c) (+ (* -4.0 (* a t)) (+ (/ b z) (* 9.0 (/ (* x y) z))))))))

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+35) {
		tmp = fma(-4.0, (a * t), fma(9.0, (x / (z / y)), (b / z))) * (1.0 / c);
	} else if (z <= 5e-120) {
		tmp = (1.0 / z) * (fma(x, (9.0 * y), (b + (t * (z * (-4.0 * a))))) / c);
	} else {
		tmp = (1.0 / c) * ((-4.0 * (a * t)) + ((b / z) + (9.0 * ((x * y) / z))));
	}
	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+35)
		tmp = Float64(fma(-4.0, Float64(a * t), fma(9.0, Float64(x / Float64(z / y)), Float64(b / z))) * Float64(1.0 / c));
	elseif (z <= 5e-120)
		tmp = Float64(Float64(1.0 / z) * Float64(fma(x, Float64(9.0 * y), Float64(b + Float64(t * Float64(z * Float64(-4.0 * a))))) / c));
	else
		tmp = Float64(Float64(1.0 / c) * Float64(Float64(-4.0 * Float64(a * t)) + Float64(Float64(b / z) + Float64(9.0 * Float64(Float64(x * y) / z)))));
	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[LessEqual[z, -6.6e+35], N[(N[(-4.0 * N[(a * t), $MachinePrecision] + N[(9.0 * N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision] + N[(b / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(1.0 / c), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5e-120], N[(N[(1.0 / z), $MachinePrecision] * N[(N[(x * N[(9.0 * y), $MachinePrecision] + N[(b + N[(t * N[(z * N[(-4.0 * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision], N[(N[(1.0 / c), $MachinePrecision] * N[(N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision] + N[(N[(b / z), $MachinePrecision] + N[(9.0 * N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.6000000000000003e35

   1. Initial program 63.3%

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

      1. associate-/r* 70.0%

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

      2. associate-+l- 70.0%

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

      3. associate-*r* 70.0%

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

      4. associate-*r* 82.7%

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

      5. div-inv 82.5%

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

      6. associate--r- 82.5%

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

      7. fma-neg 82.5%

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

      8. associate-*r* 69.8%

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

      9. distribute-rgt-neg-in 69.8%

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

      10. associate-*l* 69.8%

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

   3. Applied egg-rr 69.8%

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

   4. Taylor expanded in x around 0 87.2%

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

      1. fma-def 87.2%

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

      2. fma-def 87.2%

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

      3. associate-/l* 91.8%

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

   6. Simplified 91.8%

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

   if -6.6000000000000003e35 < z < 5.00000000000000007e-120

   1. Initial program 96.5%

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

   3. Simplified 96.5%

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

      1. *-un-lft-identity 96.5%

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

      2. times-frac 97.9%

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

      3. +-commutative 97.9%

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

      4. fma-def 97.9%

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

   5. Applied egg-rr 97.9%

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

      1. fma-udef 97.9%

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

   7. Applied egg-rr 97.9%

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

   if 5.00000000000000007e-120 < z

   1. Initial program 66.3%

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

      1. associate-/r* 77.1%

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

      2. associate-+l- 77.1%

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

      3. associate-*r* 79.3%

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

      4. associate-*r* 83.6%

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

      5. div-inv 83.5%

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

      6. associate--r- 83.5%

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

      7. fma-neg 83.5%

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

      8. associate-*r* 79.2%

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

      9. distribute-rgt-neg-in 79.2%

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

      10. associate-*l* 79.2%

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

   3. Applied egg-rr 79.2%

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

   4. Taylor expanded in x around 0 95.3%

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

4. Final simplification 95.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.6 \cdot 10^{+35}:\\ \;\;\;\;\mathsf{fma}\left(-4, a \cdot t, \mathsf{fma}\left(9, \frac{x}{\frac{z}{y}}, \frac{b}{z}\right)\right) \cdot \frac{1}{c}\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-120}:\\ \;\;\;\;\frac{1}{z} \cdot \frac{\mathsf{fma}\left(x, 9 \cdot y, b + t \cdot \left(z \cdot \left(-4 \cdot a\right)\right)\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{c} \cdot \left(-4 \cdot \left(a \cdot t\right) + \left(\frac{b}{z} + 9 \cdot \frac{x \cdot y}{z}\right)\right)\\ \end{array} \]

Alternative 2: 88.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} t_1 := y \cdot \left(9 \cdot x\right)\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;x \cdot \frac{y \cdot \frac{9}{c}}{z}\\ \mathbf{elif}\;t_1 \leq 10^{+173}:\\ \;\;\;\;\frac{1}{c} \cdot \left(-4 \cdot \left(a \cdot t\right) + \left(\frac{b}{z} + 9 \cdot \frac{x \cdot y}{z}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{9 \cdot y}{c \cdot \frac{z}{x}}\\ \end{array} \end{array} \]

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 (* y (* 9.0 x))))
   (if (<= t_1 (- INFINITY))
     (* x (/ (* y (/ 9.0 c)) z))
     (if (<= t_1 1e+173)
       (* (/ 1.0 c) (+ (* -4.0 (* a t)) (+ (/ b z) (* 9.0 (/ (* x y) z)))))
       (/ (* 9.0 y) (* c (/ z x)))))))

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 = y * (9.0 * x);
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = x * ((y * (9.0 / c)) / z);
	} else if (t_1 <= 1e+173) {
		tmp = (1.0 / c) * ((-4.0 * (a * t)) + ((b / z) + (9.0 * ((x * y) / z))));
	} else {
		tmp = (9.0 * y) / (c * (z / x));
	}
	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 = y * (9.0 * x);
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = x * ((y * (9.0 / c)) / z);
	} else if (t_1 <= 1e+173) {
		tmp = (1.0 / c) * ((-4.0 * (a * t)) + ((b / z) + (9.0 * ((x * y) / z))));
	} else {
		tmp = (9.0 * y) / (c * (z / x));
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	t_1 = y * (9.0 * x)
	tmp = 0
	if t_1 <= -math.inf:
		tmp = x * ((y * (9.0 / c)) / z)
	elif t_1 <= 1e+173:
		tmp = (1.0 / c) * ((-4.0 * (a * t)) + ((b / z) + (9.0 * ((x * y) / z))))
	else:
		tmp = (9.0 * y) / (c * (z / x))
	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(y * Float64(9.0 * x))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(x * Float64(Float64(y * Float64(9.0 / c)) / z));
	elseif (t_1 <= 1e+173)
		tmp = Float64(Float64(1.0 / c) * Float64(Float64(-4.0 * Float64(a * t)) + Float64(Float64(b / z) + Float64(9.0 * Float64(Float64(x * y) / z)))));
	else
		tmp = Float64(Float64(9.0 * y) / Float64(c * Float64(z / x)));
	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 = y * (9.0 * x);
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = x * ((y * (9.0 / c)) / z);
	elseif (t_1 <= 1e+173)
		tmp = (1.0 / c) * ((-4.0 * (a * t)) + ((b / z) + (9.0 * ((x * y) / z))));
	else
		tmp = (9.0 * y) / (c * (z / x));
	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[(y * N[(9.0 * x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(x * N[(N[(y * N[(9.0 / c), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+173], N[(N[(1.0 / c), $MachinePrecision] * N[(N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision] + N[(N[(b / z), $MachinePrecision] + N[(9.0 * N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(9.0 * y), $MachinePrecision] / N[(c * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 x 9) y) < -inf.0

   1. Initial program 64.3%

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

   3. Simplified 74.5%

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

      1. *-un-lft-identity 74.5%

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

      2. times-frac 74.8%

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

      3. +-commutative 74.8%

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

      4. fma-def 74.8%

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

   5. Applied egg-rr 74.8%

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

   6. Taylor expanded in x around inf 79.8%

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

      1. associate-*r/ 79.8%

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

      2. *-commutative 79.8%

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

      3. associate-*l* 79.8%

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

      4. times-frac 90.1%

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

      5. associate-/l* 90.1%

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

      6. associate-*r/ 85.0%

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

      7. associate-*l/ 95.0%

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

      8. associate-/r/ 95.1%

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

   8. Simplified 95.1%

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

   if -inf.0 < (*.f64 (*.f64 x 9) y) < 1e173

   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-/r* 84.2%

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

      2. associate-+l- 84.2%

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

      3. associate-*r* 84.2%

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

      4. associate-*r* 89.1%

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

      5. div-inv 88.9%

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

      6. associate--r- 88.9%

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

      7. fma-neg 88.9%

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

      8. associate-*r* 84.1%

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

      9. distribute-rgt-neg-in 84.1%

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

      10. associate-*l* 84.1%

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

   3. Applied egg-rr 84.1%

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

   4. Taylor expanded in x around 0 95.0%

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

   if 1e173 < (*.f64 (*.f64 x 9) y)

   1. Initial program 73.6%

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

      1. associate-/r* 71.0%

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

      2. associate-+l- 71.0%

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

      3. associate-*r* 73.9%

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

      4. associate-*r* 70.9%

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

      5. div-inv 70.8%

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

      6. associate--r- 70.8%

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

      7. fma-neg 70.8%

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

      8. associate-*r* 73.9%

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

      9. distribute-rgt-neg-in 73.9%

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

      10. associate-*l* 73.9%

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

   3. Applied egg-rr 73.9%

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

   4. Taylor expanded in x around inf 73.7%

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

      1. *-commutative 73.7%

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

      2. *-commutative 73.7%

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

      3. times-frac 91.2%

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

      4. associate-*l* 91.1%

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

   6. Simplified 91.1%

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

      1. clear-num 91.0%

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

      2. associate-*l/ 90.9%

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

      3. *-commutative 90.9%

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

      4. frac-times 93.9%

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

      5. *-un-lft-identity 93.9%

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

   8. Applied egg-rr 93.9%

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

4. Final simplification 94.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \left(9 \cdot x\right) \leq -\infty:\\ \;\;\;\;x \cdot \frac{y \cdot \frac{9}{c}}{z}\\ \mathbf{elif}\;y \cdot \left(9 \cdot x\right) \leq 10^{+173}:\\ \;\;\;\;\frac{1}{c} \cdot \left(-4 \cdot \left(a \cdot t\right) + \left(\frac{b}{z} + 9 \cdot \frac{x \cdot y}{z}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{9 \cdot y}{c \cdot \frac{z}{x}}\\ \end{array} \]

Alternative 3: 76.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} t_1 := -4 \cdot \left(a \cdot t\right)\\ \mathbf{if}\;y \leq -2.1 \cdot 10^{+59}:\\ \;\;\;\;9 \cdot \left(\frac{x}{z} \cdot \frac{y}{c}\right)\\ \mathbf{elif}\;y \leq -1.15 \cdot 10^{-144}:\\ \;\;\;\;\frac{t_1 + 9 \cdot \frac{x \cdot y}{z}}{c}\\ \mathbf{elif}\;y \leq 6 \cdot 10^{+74}:\\ \;\;\;\;\frac{\frac{b}{z} + t_1}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{c} \cdot \left(t_1 + \left(9 \cdot y\right) \cdot \frac{x}{z}\right)\\ \end{array} \end{array} \]

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 (* -4.0 (* a t))))
   (if (<= y -2.1e+59)
     (* 9.0 (* (/ x z) (/ y c)))
     (if (<= y -1.15e-144)
       (/ (+ t_1 (* 9.0 (/ (* x y) z))) c)
       (if (<= y 6e+74)
         (/ (+ (/ b z) t_1) c)
         (* (/ 1.0 c) (+ t_1 (* (* 9.0 y) (/ x z)))))))))

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 = -4.0 * (a * t);
	double tmp;
	if (y <= -2.1e+59) {
		tmp = 9.0 * ((x / z) * (y / c));
	} else if (y <= -1.15e-144) {
		tmp = (t_1 + (9.0 * ((x * y) / z))) / c;
	} else if (y <= 6e+74) {
		tmp = ((b / z) + t_1) / c;
	} else {
		tmp = (1.0 / c) * (t_1 + ((9.0 * y) * (x / z)));
	}
	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 = (-4.0d0) * (a * t)
    if (y <= (-2.1d+59)) then
        tmp = 9.0d0 * ((x / z) * (y / c))
    else if (y <= (-1.15d-144)) then
        tmp = (t_1 + (9.0d0 * ((x * y) / z))) / c
    else if (y <= 6d+74) then
        tmp = ((b / z) + t_1) / c
    else
        tmp = (1.0d0 / c) * (t_1 + ((9.0d0 * y) * (x / z)))
    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 = -4.0 * (a * t);
	double tmp;
	if (y <= -2.1e+59) {
		tmp = 9.0 * ((x / z) * (y / c));
	} else if (y <= -1.15e-144) {
		tmp = (t_1 + (9.0 * ((x * y) / z))) / c;
	} else if (y <= 6e+74) {
		tmp = ((b / z) + t_1) / c;
	} else {
		tmp = (1.0 / c) * (t_1 + ((9.0 * y) * (x / z)));
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	t_1 = -4.0 * (a * t)
	tmp = 0
	if y <= -2.1e+59:
		tmp = 9.0 * ((x / z) * (y / c))
	elif y <= -1.15e-144:
		tmp = (t_1 + (9.0 * ((x * y) / z))) / c
	elif y <= 6e+74:
		tmp = ((b / z) + t_1) / c
	else:
		tmp = (1.0 / c) * (t_1 + ((9.0 * y) * (x / z)))
	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(-4.0 * Float64(a * t))
	tmp = 0.0
	if (y <= -2.1e+59)
		tmp = Float64(9.0 * Float64(Float64(x / z) * Float64(y / c)));
	elseif (y <= -1.15e-144)
		tmp = Float64(Float64(t_1 + Float64(9.0 * Float64(Float64(x * y) / z))) / c);
	elseif (y <= 6e+74)
		tmp = Float64(Float64(Float64(b / z) + t_1) / c);
	else
		tmp = Float64(Float64(1.0 / c) * Float64(t_1 + Float64(Float64(9.0 * y) * Float64(x / z))));
	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 = -4.0 * (a * t);
	tmp = 0.0;
	if (y <= -2.1e+59)
		tmp = 9.0 * ((x / z) * (y / c));
	elseif (y <= -1.15e-144)
		tmp = (t_1 + (9.0 * ((x * y) / z))) / c;
	elseif (y <= 6e+74)
		tmp = ((b / z) + t_1) / c;
	else
		tmp = (1.0 / c) * (t_1 + ((9.0 * y) * (x / z)));
	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[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.1e+59], N[(9.0 * N[(N[(x / z), $MachinePrecision] * N[(y / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.15e-144], N[(N[(t$95$1 + N[(9.0 * N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[y, 6e+74], N[(N[(N[(b / z), $MachinePrecision] + t$95$1), $MachinePrecision] / c), $MachinePrecision], N[(N[(1.0 / c), $MachinePrecision] * N[(t$95$1 + N[(N[(9.0 * y), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -2.09999999999999984e59

   1. Initial program 83.1%

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

   2. Taylor expanded in x around inf 53.4%

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

      1. *-commutative 53.4%

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

   4. Simplified 53.4%

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

   5. Taylor expanded in x around 0 53.4%

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

      1. *-commutative 53.4%

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

      2. times-frac 59.6%

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

   7. Simplified 59.6%

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

   if -2.09999999999999984e59 < y < -1.15e-144

   1. Initial program 76.9%

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

      1. associate-/r* 86.4%

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

      2. associate-+l- 86.4%

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

      3. associate-*r* 86.4%

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

      4. associate-*r* 88.5%

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

      5. div-inv 88.3%

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

      6. associate--r- 88.3%

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

      7. fma-neg 88.3%

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

      8. associate-*r* 86.4%

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

      9. distribute-rgt-neg-in 86.4%

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

      10. associate-*l* 86.4%

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

   3. Applied egg-rr 86.4%

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

   4. Taylor expanded in x around 0 94.0%

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

   5. Taylor expanded in b around 0 70.6%

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

   if -1.15e-144 < y < 6e74

   1. Initial program 79.2%

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

      1. associate-/r* 82.3%

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

      2. associate-+l- 82.3%

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

      3. associate-*r* 84.0%

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

      4. associate-*r* 90.3%

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

      5. div-inv 90.2%

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

      6. associate--r- 90.2%

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

      7. fma-neg 90.2%

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

      8. associate-*r* 83.9%

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

      9. distribute-rgt-neg-in 83.9%

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

      10. associate-*l* 83.9%

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

   3. Applied egg-rr 83.9%

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

   4. Taylor expanded in x around 0 94.5%

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

   5. Taylor expanded in x around 0 79.9%

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

   if 6e74 < y

   1. Initial program 72.1%

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

      1. associate-/r* 72.4%

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

      2. associate-+l- 72.4%

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

      3. associate-*r* 72.5%

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

      4. associate-*r* 78.4%

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

      5. div-inv 78.4%

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

      6. associate--r- 78.4%

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

      7. fma-neg 78.4%

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

      8. associate-*r* 72.4%

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

      9. distribute-rgt-neg-in 72.4%

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

      10. associate-*l* 72.4%

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

   3. Applied egg-rr 72.4%

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

   4. Taylor expanded in x around 0 82.3%

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

   5. Taylor expanded in x around inf 77.2%

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

      1. *-commutative 77.2%

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

      2. associate-*r/ 79.1%

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

      3. associate-*r* 79.1%

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

   7. Simplified 79.1%

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

4. Final simplification 74.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.1 \cdot 10^{+59}:\\ \;\;\;\;9 \cdot \left(\frac{x}{z} \cdot \frac{y}{c}\right)\\ \mathbf{elif}\;y \leq -1.15 \cdot 10^{-144}:\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right) + 9 \cdot \frac{x \cdot y}{z}}{c}\\ \mathbf{elif}\;y \leq 6 \cdot 10^{+74}:\\ \;\;\;\;\frac{\frac{b}{z} + -4 \cdot \left(a \cdot t\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{c} \cdot \left(-4 \cdot \left(a \cdot t\right) + \left(9 \cdot y\right) \cdot \frac{x}{z}\right)\\ \end{array} \]

Alternative 4: 85.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} t_1 := -4 \cdot \left(a \cdot t\right)\\ \mathbf{if}\;z \leq -4.1 \cdot 10^{+186}:\\ \;\;\;\;\frac{1}{c} \cdot \left(t_1 + \left(9 \cdot y\right) \cdot \frac{x}{z}\right)\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{+116}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(9 \cdot x\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{z} + t_1}{c}\\ \end{array} \end{array} \]

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
 (let* ((t_1 (* -4.0 (* a t))))
   (if (<= z -4.1e+186)
     (* (/ 1.0 c) (+ t_1 (* (* 9.0 y) (/ x z))))
     (if (<= z 9.5e+116)
       (/ (+ b (- (* y (* 9.0 x)) (* a (* t (* z 4.0))))) (* z c))
       (/ (+ (/ b z) t_1) 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 = -4.0 * (a * t);
	double tmp;
	if (z <= -4.1e+186) {
		tmp = (1.0 / c) * (t_1 + ((9.0 * y) * (x / z)));
	} else if (z <= 9.5e+116) {
		tmp = (b + ((y * (9.0 * x)) - (a * (t * (z * 4.0))))) / (z * c);
	} else {
		tmp = ((b / z) + t_1) / 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) :: t_1
    real(8) :: tmp
    t_1 = (-4.0d0) * (a * t)
    if (z <= (-4.1d+186)) then
        tmp = (1.0d0 / c) * (t_1 + ((9.0d0 * y) * (x / z)))
    else if (z <= 9.5d+116) then
        tmp = (b + ((y * (9.0d0 * x)) - (a * (t * (z * 4.0d0))))) / (z * c)
    else
        tmp = ((b / z) + t_1) / 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 t_1 = -4.0 * (a * t);
	double tmp;
	if (z <= -4.1e+186) {
		tmp = (1.0 / c) * (t_1 + ((9.0 * y) * (x / z)));
	} else if (z <= 9.5e+116) {
		tmp = (b + ((y * (9.0 * x)) - (a * (t * (z * 4.0))))) / (z * c);
	} else {
		tmp = ((b / z) + t_1) / c;
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	t_1 = -4.0 * (a * t)
	tmp = 0
	if z <= -4.1e+186:
		tmp = (1.0 / c) * (t_1 + ((9.0 * y) * (x / z)))
	elif z <= 9.5e+116:
		tmp = (b + ((y * (9.0 * x)) - (a * (t * (z * 4.0))))) / (z * c)
	else:
		tmp = ((b / z) + t_1) / 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(-4.0 * Float64(a * t))
	tmp = 0.0
	if (z <= -4.1e+186)
		tmp = Float64(Float64(1.0 / c) * Float64(t_1 + Float64(Float64(9.0 * y) * Float64(x / z))));
	elseif (z <= 9.5e+116)
		tmp = Float64(Float64(b + Float64(Float64(y * Float64(9.0 * x)) - Float64(a * Float64(t * Float64(z * 4.0))))) / Float64(z * c));
	else
		tmp = Float64(Float64(Float64(b / z) + t_1) / 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)
	t_1 = -4.0 * (a * t);
	tmp = 0.0;
	if (z <= -4.1e+186)
		tmp = (1.0 / c) * (t_1 + ((9.0 * y) * (x / z)));
	elseif (z <= 9.5e+116)
		tmp = (b + ((y * (9.0 * x)) - (a * (t * (z * 4.0))))) / (z * c);
	else
		tmp = ((b / z) + t_1) / 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_] := Block[{t$95$1 = N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.1e+186], N[(N[(1.0 / c), $MachinePrecision] * N[(t$95$1 + N[(N[(9.0 * y), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9.5e+116], N[(N[(b + N[(N[(y * N[(9.0 * x), $MachinePrecision]), $MachinePrecision] - N[(a * N[(t * N[(z * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(N[(N[(b / z), $MachinePrecision] + t$95$1), $MachinePrecision] / c), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.1e186

   1. Initial program 41.0%

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

      1. associate-/r* 45.1%

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

      2. associate-+l- 45.1%

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

      3. associate-*r* 45.1%

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

      4. associate-*r* 72.7%

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

      5. div-inv 72.6%

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

      6. associate--r- 72.6%

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

      7. fma-neg 72.6%

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

      8. associate-*r* 45.2%

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

      9. distribute-rgt-neg-in 45.2%

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

      10. associate-*l* 45.2%

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

   3. Applied egg-rr 45.2%

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

   4. Taylor expanded in x around 0 82.9%

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

   5. Taylor expanded in x around inf 76.2%

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

      1. *-commutative 76.2%

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

      2. associate-*r/ 86.2%

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

      3. associate-*r* 86.3%

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

   7. Simplified 86.3%

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

   if -4.1e186 < z < 9.5000000000000004e116

   1. Initial program 90.2%

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

   if 9.5000000000000004e116 < z

   1. Initial program 46.9%

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

      1. associate-/r* 66.1%

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

      2. associate-+l- 66.1%

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

      3. associate-*r* 68.6%

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

      4. associate-*r* 78.3%

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

      5. div-inv 78.0%

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

      6. associate--r- 78.0%

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

      7. fma-neg 78.0%

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

      8. associate-*r* 68.4%

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

      9. distribute-rgt-neg-in 68.4%

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

      10. associate-*l* 68.4%

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

   3. Applied egg-rr 68.4%

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

   4. Taylor expanded in x around 0 99.5%

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

   5. Taylor expanded in x around 0 86.3%

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

4. Final simplification 89.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.1 \cdot 10^{+186}:\\ \;\;\;\;\frac{1}{c} \cdot \left(-4 \cdot \left(a \cdot t\right) + \left(9 \cdot y\right) \cdot \frac{x}{z}\right)\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{+116}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(9 \cdot x\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{z} + -4 \cdot \left(a \cdot t\right)}{c}\\ \end{array} \]

Alternative 5: 51.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} t_1 := -4 \cdot \frac{a}{\frac{c}{t}}\\ t_2 := 9 \cdot \left(\frac{x}{z} \cdot \frac{y}{c}\right)\\ t_3 := \frac{\frac{b}{c}}{z}\\ \mathbf{if}\;y \leq -1.1 \cdot 10^{-113}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -4.5 \cdot 10^{-220}:\\ \;\;\;\;-4 \cdot \frac{a \cdot t}{c}\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{-307}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{-251}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{-59}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{+88}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

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 (* -4.0 (/ a (/ c t))))
        (t_2 (* 9.0 (* (/ x z) (/ y c))))
        (t_3 (/ (/ b c) z)))
   (if (<= y -1.1e-113)
     t_2
     (if (<= y -4.5e-220)
       (* -4.0 (/ (* a t) c))
       (if (<= y 1.05e-307)
         t_3
         (if (<= y 8.2e-251)
           t_1
           (if (<= y 1.1e-59) t_3 (if (<= y 2.1e+88) 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 = -4.0 * (a / (c / t));
	double t_2 = 9.0 * ((x / z) * (y / c));
	double t_3 = (b / c) / z;
	double tmp;
	if (y <= -1.1e-113) {
		tmp = t_2;
	} else if (y <= -4.5e-220) {
		tmp = -4.0 * ((a * t) / c);
	} else if (y <= 1.05e-307) {
		tmp = t_3;
	} else if (y <= 8.2e-251) {
		tmp = t_1;
	} else if (y <= 1.1e-59) {
		tmp = t_3;
	} else if (y <= 2.1e+88) {
		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) :: t_3
    real(8) :: tmp
    t_1 = (-4.0d0) * (a / (c / t))
    t_2 = 9.0d0 * ((x / z) * (y / c))
    t_3 = (b / c) / z
    if (y <= (-1.1d-113)) then
        tmp = t_2
    else if (y <= (-4.5d-220)) then
        tmp = (-4.0d0) * ((a * t) / c)
    else if (y <= 1.05d-307) then
        tmp = t_3
    else if (y <= 8.2d-251) then
        tmp = t_1
    else if (y <= 1.1d-59) then
        tmp = t_3
    else if (y <= 2.1d+88) 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 = -4.0 * (a / (c / t));
	double t_2 = 9.0 * ((x / z) * (y / c));
	double t_3 = (b / c) / z;
	double tmp;
	if (y <= -1.1e-113) {
		tmp = t_2;
	} else if (y <= -4.5e-220) {
		tmp = -4.0 * ((a * t) / c);
	} else if (y <= 1.05e-307) {
		tmp = t_3;
	} else if (y <= 8.2e-251) {
		tmp = t_1;
	} else if (y <= 1.1e-59) {
		tmp = t_3;
	} else if (y <= 2.1e+88) {
		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 = -4.0 * (a / (c / t))
	t_2 = 9.0 * ((x / z) * (y / c))
	t_3 = (b / c) / z
	tmp = 0
	if y <= -1.1e-113:
		tmp = t_2
	elif y <= -4.5e-220:
		tmp = -4.0 * ((a * t) / c)
	elif y <= 1.05e-307:
		tmp = t_3
	elif y <= 8.2e-251:
		tmp = t_1
	elif y <= 1.1e-59:
		tmp = t_3
	elif y <= 2.1e+88:
		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(-4.0 * Float64(a / Float64(c / t)))
	t_2 = Float64(9.0 * Float64(Float64(x / z) * Float64(y / c)))
	t_3 = Float64(Float64(b / c) / z)
	tmp = 0.0
	if (y <= -1.1e-113)
		tmp = t_2;
	elseif (y <= -4.5e-220)
		tmp = Float64(-4.0 * Float64(Float64(a * t) / c));
	elseif (y <= 1.05e-307)
		tmp = t_3;
	elseif (y <= 8.2e-251)
		tmp = t_1;
	elseif (y <= 1.1e-59)
		tmp = t_3;
	elseif (y <= 2.1e+88)
		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 = -4.0 * (a / (c / t));
	t_2 = 9.0 * ((x / z) * (y / c));
	t_3 = (b / c) / z;
	tmp = 0.0;
	if (y <= -1.1e-113)
		tmp = t_2;
	elseif (y <= -4.5e-220)
		tmp = -4.0 * ((a * t) / c);
	elseif (y <= 1.05e-307)
		tmp = t_3;
	elseif (y <= 8.2e-251)
		tmp = t_1;
	elseif (y <= 1.1e-59)
		tmp = t_3;
	elseif (y <= 2.1e+88)
		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[(-4.0 * N[(a / N[(c / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(9.0 * N[(N[(x / z), $MachinePrecision] * N[(y / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision]}, If[LessEqual[y, -1.1e-113], t$95$2, If[LessEqual[y, -4.5e-220], N[(-4.0 * N[(N[(a * t), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.05e-307], t$95$3, If[LessEqual[y, 8.2e-251], t$95$1, If[LessEqual[y, 1.1e-59], t$95$3, If[LessEqual[y, 2.1e+88], t$95$1, t$95$2]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.10000000000000002e-113 or 2.1e88 < y

   1. Initial program 79.3%

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

   2. Taylor expanded in x around inf 48.7%

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

      1. *-commutative 48.7%

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

   4. Simplified 48.7%

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

   5. Taylor expanded in x around 0 48.7%

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

      1. *-commutative 48.7%

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

      2. times-frac 53.1%

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

   7. Simplified 53.1%

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

   if -1.10000000000000002e-113 < y < -4.49999999999999967e-220

   1. Initial program 60.3%

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

   2. Taylor expanded in z around inf 51.7%

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

   if -4.49999999999999967e-220 < y < 1.0500000000000001e-307 or 8.1999999999999997e-251 < y < 1.0999999999999999e-59

   1. Initial program 88.2%

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

   3. Simplified 95.7%

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

      1. *-un-lft-identity 95.7%

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

      2. times-frac 90.0%

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

      3. +-commutative 90.0%

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

      4. fma-def 90.0%

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

   5. Applied egg-rr 90.0%

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

   6. Taylor expanded in b around inf 47.2%

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

      1. associate-/r* 51.6%

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

   8. Simplified 51.6%

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

   if 1.0500000000000001e-307 < y < 8.1999999999999997e-251 or 1.0999999999999999e-59 < y < 2.1e88

   1. Initial program 76.8%

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

   2. Taylor expanded in z around inf 53.0%

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

      1. *-commutative 53.0%

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

      2. associate-/l* 48.4%

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

   4. Simplified 48.4%

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

4. Final simplification 51.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{-113}:\\ \;\;\;\;9 \cdot \left(\frac{x}{z} \cdot \frac{y}{c}\right)\\ \mathbf{elif}\;y \leq -4.5 \cdot 10^{-220}:\\ \;\;\;\;-4 \cdot \frac{a \cdot t}{c}\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{-307}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{-251}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{-59}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{+88}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{else}:\\ \;\;\;\;9 \cdot \left(\frac{x}{z} \cdot \frac{y}{c}\right)\\ \end{array} \]

Alternative 6: 51.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} t_1 := -4 \cdot \frac{a}{\frac{c}{t}}\\ t_2 := \frac{\frac{b}{c}}{z}\\ \mathbf{if}\;y \leq -1.1 \cdot 10^{-113}:\\ \;\;\;\;9 \cdot \left(\frac{x}{z} \cdot \frac{y}{c}\right)\\ \mathbf{elif}\;y \leq -3.2 \cdot 10^{-220}:\\ \;\;\;\;-4 \cdot \frac{a \cdot t}{c}\\ \mathbf{elif}\;y \leq 6.1 \cdot 10^{-307}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{-253}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{-62}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+83}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \left(9 \cdot \frac{y}{c}\right)\\ \end{array} \end{array} \]

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
 (let* ((t_1 (* -4.0 (/ a (/ c t)))) (t_2 (/ (/ b c) z)))
   (if (<= y -1.1e-113)
     (* 9.0 (* (/ x z) (/ y c)))
     (if (<= y -3.2e-220)
       (* -4.0 (/ (* a t) c))
       (if (<= y 6.1e-307)
         t_2
         (if (<= y 4.2e-253)
           t_1
           (if (<= y 4.2e-62)
             t_2
             (if (<= y 2.5e+83) t_1 (* (/ x z) (* 9.0 (/ y 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 = -4.0 * (a / (c / t));
	double t_2 = (b / c) / z;
	double tmp;
	if (y <= -1.1e-113) {
		tmp = 9.0 * ((x / z) * (y / c));
	} else if (y <= -3.2e-220) {
		tmp = -4.0 * ((a * t) / c);
	} else if (y <= 6.1e-307) {
		tmp = t_2;
	} else if (y <= 4.2e-253) {
		tmp = t_1;
	} else if (y <= 4.2e-62) {
		tmp = t_2;
	} else if (y <= 2.5e+83) {
		tmp = t_1;
	} else {
		tmp = (x / z) * (9.0 * (y / 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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (-4.0d0) * (a / (c / t))
    t_2 = (b / c) / z
    if (y <= (-1.1d-113)) then
        tmp = 9.0d0 * ((x / z) * (y / c))
    else if (y <= (-3.2d-220)) then
        tmp = (-4.0d0) * ((a * t) / c)
    else if (y <= 6.1d-307) then
        tmp = t_2
    else if (y <= 4.2d-253) then
        tmp = t_1
    else if (y <= 4.2d-62) then
        tmp = t_2
    else if (y <= 2.5d+83) then
        tmp = t_1
    else
        tmp = (x / z) * (9.0d0 * (y / 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 t_1 = -4.0 * (a / (c / t));
	double t_2 = (b / c) / z;
	double tmp;
	if (y <= -1.1e-113) {
		tmp = 9.0 * ((x / z) * (y / c));
	} else if (y <= -3.2e-220) {
		tmp = -4.0 * ((a * t) / c);
	} else if (y <= 6.1e-307) {
		tmp = t_2;
	} else if (y <= 4.2e-253) {
		tmp = t_1;
	} else if (y <= 4.2e-62) {
		tmp = t_2;
	} else if (y <= 2.5e+83) {
		tmp = t_1;
	} else {
		tmp = (x / z) * (9.0 * (y / c));
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	t_1 = -4.0 * (a / (c / t))
	t_2 = (b / c) / z
	tmp = 0
	if y <= -1.1e-113:
		tmp = 9.0 * ((x / z) * (y / c))
	elif y <= -3.2e-220:
		tmp = -4.0 * ((a * t) / c)
	elif y <= 6.1e-307:
		tmp = t_2
	elif y <= 4.2e-253:
		tmp = t_1
	elif y <= 4.2e-62:
		tmp = t_2
	elif y <= 2.5e+83:
		tmp = t_1
	else:
		tmp = (x / z) * (9.0 * (y / 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(-4.0 * Float64(a / Float64(c / t)))
	t_2 = Float64(Float64(b / c) / z)
	tmp = 0.0
	if (y <= -1.1e-113)
		tmp = Float64(9.0 * Float64(Float64(x / z) * Float64(y / c)));
	elseif (y <= -3.2e-220)
		tmp = Float64(-4.0 * Float64(Float64(a * t) / c));
	elseif (y <= 6.1e-307)
		tmp = t_2;
	elseif (y <= 4.2e-253)
		tmp = t_1;
	elseif (y <= 4.2e-62)
		tmp = t_2;
	elseif (y <= 2.5e+83)
		tmp = t_1;
	else
		tmp = Float64(Float64(x / z) * Float64(9.0 * Float64(y / 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)
	t_1 = -4.0 * (a / (c / t));
	t_2 = (b / c) / z;
	tmp = 0.0;
	if (y <= -1.1e-113)
		tmp = 9.0 * ((x / z) * (y / c));
	elseif (y <= -3.2e-220)
		tmp = -4.0 * ((a * t) / c);
	elseif (y <= 6.1e-307)
		tmp = t_2;
	elseif (y <= 4.2e-253)
		tmp = t_1;
	elseif (y <= 4.2e-62)
		tmp = t_2;
	elseif (y <= 2.5e+83)
		tmp = t_1;
	else
		tmp = (x / z) * (9.0 * (y / 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_] := Block[{t$95$1 = N[(-4.0 * N[(a / N[(c / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision]}, If[LessEqual[y, -1.1e-113], N[(9.0 * N[(N[(x / z), $MachinePrecision] * N[(y / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -3.2e-220], N[(-4.0 * N[(N[(a * t), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.1e-307], t$95$2, If[LessEqual[y, 4.2e-253], t$95$1, If[LessEqual[y, 4.2e-62], t$95$2, If[LessEqual[y, 2.5e+83], t$95$1, N[(N[(x / z), $MachinePrecision] * N[(9.0 * N[(y / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -1.10000000000000002e-113

   1. Initial program 81.9%

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

   2. Taylor expanded in x around inf 43.4%

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

      1. *-commutative 43.4%

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

   4. Simplified 43.4%

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

   5. Taylor expanded in x around 0 43.4%

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

      1. *-commutative 43.4%

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

      2. times-frac 44.6%

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

   7. Simplified 44.6%

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

   if -1.10000000000000002e-113 < y < -3.20000000000000005e-220

   1. Initial program 60.3%

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

   2. Taylor expanded in z around inf 51.7%

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

   if -3.20000000000000005e-220 < y < 6.09999999999999974e-307 or 4.1999999999999998e-253 < y < 4.1999999999999998e-62

   1. Initial program 88.2%

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

   3. Simplified 95.7%

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

      1. *-un-lft-identity 95.7%

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

      2. times-frac 90.0%

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

      3. +-commutative 90.0%

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

      4. fma-def 90.0%

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

   5. Applied egg-rr 90.0%

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

   6. Taylor expanded in b around inf 49.2%

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

      1. associate-/r* 53.7%

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

   8. Simplified 53.7%

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

   if 6.09999999999999974e-307 < y < 4.1999999999999998e-253 or 4.1999999999999998e-62 < y < 2.50000000000000014e83

   1. Initial program 76.8%

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

   2. Taylor expanded in z around inf 50.6%

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

      1. *-commutative 50.6%

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

      2. associate-/l* 46.0%

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

   4. Simplified 46.0%

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

   if 2.50000000000000014e83 < y

   1. Initial program 74.5%

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

      1. associate-/r* 74.8%

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

      2. associate-+l- 74.8%

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

      3. associate-*r* 74.9%

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

      4. associate-*r* 79.1%

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

      5. div-inv 79.0%

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

      6. associate--r- 79.0%

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

      7. fma-neg 79.0%

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

      8. associate-*r* 74.8%

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

      9. distribute-rgt-neg-in 74.8%

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

      10. associate-*l* 74.8%

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

   3. Applied egg-rr 74.8%

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

   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. *-commutative 58.5%

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

      2. *-commutative 58.5%

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

      3. times-frac 69.0%

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

      4. associate-*l* 69.0%

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

   6. Simplified 69.0%

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

4. Final simplification 51.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{-113}:\\ \;\;\;\;9 \cdot \left(\frac{x}{z} \cdot \frac{y}{c}\right)\\ \mathbf{elif}\;y \leq -3.2 \cdot 10^{-220}:\\ \;\;\;\;-4 \cdot \frac{a \cdot t}{c}\\ \mathbf{elif}\;y \leq 6.1 \cdot 10^{-307}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{-253}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{-62}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+83}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \left(9 \cdot \frac{y}{c}\right)\\ \end{array} \]

Alternative 7: 51.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} t_1 := -4 \cdot \frac{a}{\frac{c}{t}}\\ t_2 := \frac{\frac{b}{c}}{z}\\ \mathbf{if}\;y \leq -1.1 \cdot 10^{-113}:\\ \;\;\;\;x \cdot \frac{y \cdot \frac{9}{c}}{z}\\ \mathbf{elif}\;y \leq -2.45 \cdot 10^{-220}:\\ \;\;\;\;-4 \cdot \frac{a \cdot t}{c}\\ \mathbf{elif}\;y \leq -2.05 \cdot 10^{-307}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{-251}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{-59}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 7.3 \cdot 10^{+84}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \left(9 \cdot \frac{y}{c}\right)\\ \end{array} \end{array} \]

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
 (let* ((t_1 (* -4.0 (/ a (/ c t)))) (t_2 (/ (/ b c) z)))
   (if (<= y -1.1e-113)
     (* x (/ (* y (/ 9.0 c)) z))
     (if (<= y -2.45e-220)
       (* -4.0 (/ (* a t) c))
       (if (<= y -2.05e-307)
         t_2
         (if (<= y 2.4e-251)
           t_1
           (if (<= y 1.45e-59)
             t_2
             (if (<= y 7.3e+84) t_1 (* (/ x z) (* 9.0 (/ y 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 = -4.0 * (a / (c / t));
	double t_2 = (b / c) / z;
	double tmp;
	if (y <= -1.1e-113) {
		tmp = x * ((y * (9.0 / c)) / z);
	} else if (y <= -2.45e-220) {
		tmp = -4.0 * ((a * t) / c);
	} else if (y <= -2.05e-307) {
		tmp = t_2;
	} else if (y <= 2.4e-251) {
		tmp = t_1;
	} else if (y <= 1.45e-59) {
		tmp = t_2;
	} else if (y <= 7.3e+84) {
		tmp = t_1;
	} else {
		tmp = (x / z) * (9.0 * (y / 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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (-4.0d0) * (a / (c / t))
    t_2 = (b / c) / z
    if (y <= (-1.1d-113)) then
        tmp = x * ((y * (9.0d0 / c)) / z)
    else if (y <= (-2.45d-220)) then
        tmp = (-4.0d0) * ((a * t) / c)
    else if (y <= (-2.05d-307)) then
        tmp = t_2
    else if (y <= 2.4d-251) then
        tmp = t_1
    else if (y <= 1.45d-59) then
        tmp = t_2
    else if (y <= 7.3d+84) then
        tmp = t_1
    else
        tmp = (x / z) * (9.0d0 * (y / 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 t_1 = -4.0 * (a / (c / t));
	double t_2 = (b / c) / z;
	double tmp;
	if (y <= -1.1e-113) {
		tmp = x * ((y * (9.0 / c)) / z);
	} else if (y <= -2.45e-220) {
		tmp = -4.0 * ((a * t) / c);
	} else if (y <= -2.05e-307) {
		tmp = t_2;
	} else if (y <= 2.4e-251) {
		tmp = t_1;
	} else if (y <= 1.45e-59) {
		tmp = t_2;
	} else if (y <= 7.3e+84) {
		tmp = t_1;
	} else {
		tmp = (x / z) * (9.0 * (y / c));
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	t_1 = -4.0 * (a / (c / t))
	t_2 = (b / c) / z
	tmp = 0
	if y <= -1.1e-113:
		tmp = x * ((y * (9.0 / c)) / z)
	elif y <= -2.45e-220:
		tmp = -4.0 * ((a * t) / c)
	elif y <= -2.05e-307:
		tmp = t_2
	elif y <= 2.4e-251:
		tmp = t_1
	elif y <= 1.45e-59:
		tmp = t_2
	elif y <= 7.3e+84:
		tmp = t_1
	else:
		tmp = (x / z) * (9.0 * (y / 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(-4.0 * Float64(a / Float64(c / t)))
	t_2 = Float64(Float64(b / c) / z)
	tmp = 0.0
	if (y <= -1.1e-113)
		tmp = Float64(x * Float64(Float64(y * Float64(9.0 / c)) / z));
	elseif (y <= -2.45e-220)
		tmp = Float64(-4.0 * Float64(Float64(a * t) / c));
	elseif (y <= -2.05e-307)
		tmp = t_2;
	elseif (y <= 2.4e-251)
		tmp = t_1;
	elseif (y <= 1.45e-59)
		tmp = t_2;
	elseif (y <= 7.3e+84)
		tmp = t_1;
	else
		tmp = Float64(Float64(x / z) * Float64(9.0 * Float64(y / 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)
	t_1 = -4.0 * (a / (c / t));
	t_2 = (b / c) / z;
	tmp = 0.0;
	if (y <= -1.1e-113)
		tmp = x * ((y * (9.0 / c)) / z);
	elseif (y <= -2.45e-220)
		tmp = -4.0 * ((a * t) / c);
	elseif (y <= -2.05e-307)
		tmp = t_2;
	elseif (y <= 2.4e-251)
		tmp = t_1;
	elseif (y <= 1.45e-59)
		tmp = t_2;
	elseif (y <= 7.3e+84)
		tmp = t_1;
	else
		tmp = (x / z) * (9.0 * (y / 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_] := Block[{t$95$1 = N[(-4.0 * N[(a / N[(c / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision]}, If[LessEqual[y, -1.1e-113], N[(x * N[(N[(y * N[(9.0 / c), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2.45e-220], N[(-4.0 * N[(N[(a * t), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2.05e-307], t$95$2, If[LessEqual[y, 2.4e-251], t$95$1, If[LessEqual[y, 1.45e-59], t$95$2, If[LessEqual[y, 7.3e+84], t$95$1, N[(N[(x / z), $MachinePrecision] * N[(9.0 * N[(y / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -1.10000000000000002e-113

   1. Initial program 81.9%

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

   3. Simplified 78.4%

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

      1. *-un-lft-identity 78.4%

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

      2. times-frac 77.6%

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

      3. +-commutative 77.6%

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

      4. fma-def 77.6%

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

   5. Applied egg-rr 77.6%

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

   6. Taylor expanded in x around inf 43.4%

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

      1. associate-*r/ 43.4%

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

      2. *-commutative 43.4%

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

      3. associate-*l* 43.4%

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

      4. times-frac 43.4%

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

      5. associate-/l* 43.4%

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

      6. associate-*r/ 44.6%

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

      7. associate-*l/ 44.4%

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

      8. associate-/r/ 44.4%

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

   8. Simplified 44.4%

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

   if -1.10000000000000002e-113 < y < -2.4500000000000001e-220

   1. Initial program 60.3%

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

   2. Taylor expanded in z around inf 51.7%

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

   if -2.4500000000000001e-220 < y < -2.05000000000000016e-307 or 2.39999999999999996e-251 < y < 1.45000000000000008e-59

   1. Initial program 88.4%

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

   3. Simplified 95.8%

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

      1. *-un-lft-identity 95.8%

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

      2. times-frac 90.2%

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

      3. +-commutative 90.2%

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

      4. fma-def 90.2%

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

   5. Applied egg-rr 90.2%

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

   6. Taylor expanded in b around inf 48.2%

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

      1. associate-/r* 52.6%

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

   8. Simplified 52.6%

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

   if -2.05000000000000016e-307 < y < 2.39999999999999996e-251 or 1.45000000000000008e-59 < y < 7.3e84

   1. Initial program 76.2%

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

   2. Taylor expanded in z around inf 51.8%

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

      1. *-commutative 51.8%

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

      2. associate-/l* 47.1%

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

   4. Simplified 47.1%

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

   if 7.3e84 < y

   1. Initial program 74.5%

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

      1. associate-/r* 74.8%

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

      2. associate-+l- 74.8%

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

      3. associate-*r* 74.9%

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

      4. associate-*r* 79.1%

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

      5. div-inv 79.0%

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

      6. associate--r- 79.0%

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

      7. fma-neg 79.0%

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

      8. associate-*r* 74.8%

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

      9. distribute-rgt-neg-in 74.8%

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

      10. associate-*l* 74.8%

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

   3. Applied egg-rr 74.8%

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

   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. *-commutative 58.5%

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

      2. *-commutative 58.5%

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

      3. times-frac 69.0%

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

      4. associate-*l* 69.0%

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

   6. Simplified 69.0%

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

4. Final simplification 51.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{-113}:\\ \;\;\;\;x \cdot \frac{y \cdot \frac{9}{c}}{z}\\ \mathbf{elif}\;y \leq -2.45 \cdot 10^{-220}:\\ \;\;\;\;-4 \cdot \frac{a \cdot t}{c}\\ \mathbf{elif}\;y \leq -2.05 \cdot 10^{-307}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{-251}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{-59}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;y \leq 7.3 \cdot 10^{+84}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \left(9 \cdot \frac{y}{c}\right)\\ \end{array} \]

Alternative 8: 51.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} t_1 := -4 \cdot \frac{a}{\frac{c}{t}}\\ t_2 := \frac{\frac{b}{c}}{z}\\ \mathbf{if}\;y \leq -1.75 \cdot 10^{-133}:\\ \;\;\;\;\frac{9 \cdot y}{c \cdot \frac{z}{x}}\\ \mathbf{elif}\;y \leq -2.8 \cdot 10^{-220}:\\ \;\;\;\;-4 \cdot \frac{a \cdot t}{c}\\ \mathbf{elif}\;y \leq -3.05 \cdot 10^{-307}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 9.8 \cdot 10^{-253}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.25 \cdot 10^{-63}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{+83}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \left(9 \cdot \frac{y}{c}\right)\\ \end{array} \end{array} \]

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
 (let* ((t_1 (* -4.0 (/ a (/ c t)))) (t_2 (/ (/ b c) z)))
   (if (<= y -1.75e-133)
     (/ (* 9.0 y) (* c (/ z x)))
     (if (<= y -2.8e-220)
       (* -4.0 (/ (* a t) c))
       (if (<= y -3.05e-307)
         t_2
         (if (<= y 9.8e-253)
           t_1
           (if (<= y 2.25e-63)
             t_2
             (if (<= y 6.2e+83) t_1 (* (/ x z) (* 9.0 (/ y 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 = -4.0 * (a / (c / t));
	double t_2 = (b / c) / z;
	double tmp;
	if (y <= -1.75e-133) {
		tmp = (9.0 * y) / (c * (z / x));
	} else if (y <= -2.8e-220) {
		tmp = -4.0 * ((a * t) / c);
	} else if (y <= -3.05e-307) {
		tmp = t_2;
	} else if (y <= 9.8e-253) {
		tmp = t_1;
	} else if (y <= 2.25e-63) {
		tmp = t_2;
	} else if (y <= 6.2e+83) {
		tmp = t_1;
	} else {
		tmp = (x / z) * (9.0 * (y / 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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (-4.0d0) * (a / (c / t))
    t_2 = (b / c) / z
    if (y <= (-1.75d-133)) then
        tmp = (9.0d0 * y) / (c * (z / x))
    else if (y <= (-2.8d-220)) then
        tmp = (-4.0d0) * ((a * t) / c)
    else if (y <= (-3.05d-307)) then
        tmp = t_2
    else if (y <= 9.8d-253) then
        tmp = t_1
    else if (y <= 2.25d-63) then
        tmp = t_2
    else if (y <= 6.2d+83) then
        tmp = t_1
    else
        tmp = (x / z) * (9.0d0 * (y / 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 t_1 = -4.0 * (a / (c / t));
	double t_2 = (b / c) / z;
	double tmp;
	if (y <= -1.75e-133) {
		tmp = (9.0 * y) / (c * (z / x));
	} else if (y <= -2.8e-220) {
		tmp = -4.0 * ((a * t) / c);
	} else if (y <= -3.05e-307) {
		tmp = t_2;
	} else if (y <= 9.8e-253) {
		tmp = t_1;
	} else if (y <= 2.25e-63) {
		tmp = t_2;
	} else if (y <= 6.2e+83) {
		tmp = t_1;
	} else {
		tmp = (x / z) * (9.0 * (y / c));
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	t_1 = -4.0 * (a / (c / t))
	t_2 = (b / c) / z
	tmp = 0
	if y <= -1.75e-133:
		tmp = (9.0 * y) / (c * (z / x))
	elif y <= -2.8e-220:
		tmp = -4.0 * ((a * t) / c)
	elif y <= -3.05e-307:
		tmp = t_2
	elif y <= 9.8e-253:
		tmp = t_1
	elif y <= 2.25e-63:
		tmp = t_2
	elif y <= 6.2e+83:
		tmp = t_1
	else:
		tmp = (x / z) * (9.0 * (y / 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(-4.0 * Float64(a / Float64(c / t)))
	t_2 = Float64(Float64(b / c) / z)
	tmp = 0.0
	if (y <= -1.75e-133)
		tmp = Float64(Float64(9.0 * y) / Float64(c * Float64(z / x)));
	elseif (y <= -2.8e-220)
		tmp = Float64(-4.0 * Float64(Float64(a * t) / c));
	elseif (y <= -3.05e-307)
		tmp = t_2;
	elseif (y <= 9.8e-253)
		tmp = t_1;
	elseif (y <= 2.25e-63)
		tmp = t_2;
	elseif (y <= 6.2e+83)
		tmp = t_1;
	else
		tmp = Float64(Float64(x / z) * Float64(9.0 * Float64(y / 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)
	t_1 = -4.0 * (a / (c / t));
	t_2 = (b / c) / z;
	tmp = 0.0;
	if (y <= -1.75e-133)
		tmp = (9.0 * y) / (c * (z / x));
	elseif (y <= -2.8e-220)
		tmp = -4.0 * ((a * t) / c);
	elseif (y <= -3.05e-307)
		tmp = t_2;
	elseif (y <= 9.8e-253)
		tmp = t_1;
	elseif (y <= 2.25e-63)
		tmp = t_2;
	elseif (y <= 6.2e+83)
		tmp = t_1;
	else
		tmp = (x / z) * (9.0 * (y / 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_] := Block[{t$95$1 = N[(-4.0 * N[(a / N[(c / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision]}, If[LessEqual[y, -1.75e-133], N[(N[(9.0 * y), $MachinePrecision] / N[(c * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2.8e-220], N[(-4.0 * N[(N[(a * t), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -3.05e-307], t$95$2, If[LessEqual[y, 9.8e-253], t$95$1, If[LessEqual[y, 2.25e-63], t$95$2, If[LessEqual[y, 6.2e+83], t$95$1, N[(N[(x / z), $MachinePrecision] * N[(9.0 * N[(y / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -1.75000000000000001e-133

   1. Initial program 80.2%

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

      1. associate-/r* 84.5%

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

      2. associate-+l- 84.5%

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

      3. associate-*r* 84.5%

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

      4. associate-*r* 83.4%

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

      5. div-inv 83.3%

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

      6. associate--r- 83.3%

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

      7. fma-neg 83.3%

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

      8. associate-*r* 84.4%

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

      9. distribute-rgt-neg-in 84.4%

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

      10. associate-*l* 84.4%

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

   3. Applied egg-rr 84.4%

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

   4. Taylor expanded in x around inf 41.4%

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

      1. *-commutative 41.4%

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

      2. *-commutative 41.4%

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

      3. times-frac 42.5%

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

      4. associate-*l* 41.4%

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

   6. Simplified 41.4%

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

      1. clear-num 41.4%

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

      2. associate-*l/ 41.4%

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

      3. *-commutative 41.4%

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

      4. frac-times 44.4%

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

      5. *-un-lft-identity 44.4%

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

   8. Applied egg-rr 44.4%

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

   if -1.75000000000000001e-133 < y < -2.7999999999999999e-220

   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. Taylor expanded in z around inf 46.5%

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

   if -2.7999999999999999e-220 < y < -3.04999999999999987e-307 or 9.7999999999999999e-253 < y < 2.25e-63

   1. Initial program 88.2%

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

   3. Simplified 95.7%

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

      1. *-un-lft-identity 95.7%

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

      2. times-frac 90.0%

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

      3. +-commutative 90.0%

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

      4. fma-def 90.0%

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

   5. Applied egg-rr 90.0%

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

   6. Taylor expanded in b around inf 49.2%

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

      1. associate-/r* 53.7%

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

   8. Simplified 53.7%

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

   if -3.04999999999999987e-307 < y < 9.7999999999999999e-253 or 2.25e-63 < y < 6.19999999999999984e83

   1. Initial program 76.8%

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

   2. Taylor expanded in z around inf 50.6%

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

      1. *-commutative 50.6%

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

      2. associate-/l* 46.0%

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

   4. Simplified 46.0%

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

   if 6.19999999999999984e83 < y

   1. Initial program 74.5%

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

      1. associate-/r* 74.8%

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

      2. associate-+l- 74.8%

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

      3. associate-*r* 74.9%

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

      4. associate-*r* 79.1%

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

      5. div-inv 79.0%

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

      6. associate--r- 79.0%

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

      7. fma-neg 79.0%

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

      8. associate-*r* 74.8%

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

      9. distribute-rgt-neg-in 74.8%

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

      10. associate-*l* 74.8%

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

   3. Applied egg-rr 74.8%

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

   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. *-commutative 58.5%

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

      2. *-commutative 58.5%

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

      3. times-frac 69.0%

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

      4. associate-*l* 69.0%

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

   6. Simplified 69.0%

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

4. Final simplification 51.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.75 \cdot 10^{-133}:\\ \;\;\;\;\frac{9 \cdot y}{c \cdot \frac{z}{x}}\\ \mathbf{elif}\;y \leq -2.8 \cdot 10^{-220}:\\ \;\;\;\;-4 \cdot \frac{a \cdot t}{c}\\ \mathbf{elif}\;y \leq -3.05 \cdot 10^{-307}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;y \leq 9.8 \cdot 10^{-253}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;y \leq 2.25 \cdot 10^{-63}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{+83}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \left(9 \cdot \frac{y}{c}\right)\\ \end{array} \]

Alternative 9: 75.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} t_1 := -4 \cdot \left(a \cdot t\right)\\ \mathbf{if}\;y \leq -2.1 \cdot 10^{+59}:\\ \;\;\;\;9 \cdot \left(\frac{x}{z} \cdot \frac{y}{c}\right)\\ \mathbf{elif}\;y \leq -7.5 \cdot 10^{-145} \lor \neg \left(y \leq 5.1 \cdot 10^{+74}\right):\\ \;\;\;\;\frac{t_1 + 9 \cdot \frac{x \cdot y}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{z} + t_1}{c}\\ \end{array} \end{array} \]

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
 (let* ((t_1 (* -4.0 (* a t))))
   (if (<= y -2.1e+59)
     (* 9.0 (* (/ x z) (/ y c)))
     (if (or (<= y -7.5e-145) (not (<= y 5.1e+74)))
       (/ (+ t_1 (* 9.0 (/ (* x y) z))) c)
       (/ (+ (/ b z) t_1) 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 = -4.0 * (a * t);
	double tmp;
	if (y <= -2.1e+59) {
		tmp = 9.0 * ((x / z) * (y / c));
	} else if ((y <= -7.5e-145) || !(y <= 5.1e+74)) {
		tmp = (t_1 + (9.0 * ((x * y) / z))) / c;
	} else {
		tmp = ((b / z) + t_1) / 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) :: t_1
    real(8) :: tmp
    t_1 = (-4.0d0) * (a * t)
    if (y <= (-2.1d+59)) then
        tmp = 9.0d0 * ((x / z) * (y / c))
    else if ((y <= (-7.5d-145)) .or. (.not. (y <= 5.1d+74))) then
        tmp = (t_1 + (9.0d0 * ((x * y) / z))) / c
    else
        tmp = ((b / z) + t_1) / 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 t_1 = -4.0 * (a * t);
	double tmp;
	if (y <= -2.1e+59) {
		tmp = 9.0 * ((x / z) * (y / c));
	} else if ((y <= -7.5e-145) || !(y <= 5.1e+74)) {
		tmp = (t_1 + (9.0 * ((x * y) / z))) / c;
	} else {
		tmp = ((b / z) + t_1) / c;
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	t_1 = -4.0 * (a * t)
	tmp = 0
	if y <= -2.1e+59:
		tmp = 9.0 * ((x / z) * (y / c))
	elif (y <= -7.5e-145) or not (y <= 5.1e+74):
		tmp = (t_1 + (9.0 * ((x * y) / z))) / c
	else:
		tmp = ((b / z) + t_1) / 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(-4.0 * Float64(a * t))
	tmp = 0.0
	if (y <= -2.1e+59)
		tmp = Float64(9.0 * Float64(Float64(x / z) * Float64(y / c)));
	elseif ((y <= -7.5e-145) || !(y <= 5.1e+74))
		tmp = Float64(Float64(t_1 + Float64(9.0 * Float64(Float64(x * y) / z))) / c);
	else
		tmp = Float64(Float64(Float64(b / z) + t_1) / 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)
	t_1 = -4.0 * (a * t);
	tmp = 0.0;
	if (y <= -2.1e+59)
		tmp = 9.0 * ((x / z) * (y / c));
	elseif ((y <= -7.5e-145) || ~((y <= 5.1e+74)))
		tmp = (t_1 + (9.0 * ((x * y) / z))) / c;
	else
		tmp = ((b / z) + t_1) / 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_] := Block[{t$95$1 = N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.1e+59], N[(9.0 * N[(N[(x / z), $MachinePrecision] * N[(y / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, -7.5e-145], N[Not[LessEqual[y, 5.1e+74]], $MachinePrecision]], N[(N[(t$95$1 + N[(9.0 * N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], N[(N[(N[(b / z), $MachinePrecision] + t$95$1), $MachinePrecision] / c), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.09999999999999984e59

   1. Initial program 83.1%

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

   2. Taylor expanded in x around inf 53.4%

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

      1. *-commutative 53.4%

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

   4. Simplified 53.4%

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

   5. Taylor expanded in x around 0 53.4%

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

      1. *-commutative 53.4%

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

      2. times-frac 59.6%

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

   7. Simplified 59.6%

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

   if -2.09999999999999984e59 < y < -7.4999999999999996e-145 or 5.1000000000000004e74 < y

   1. Initial program 74.5%

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

      1. associate-/r* 79.5%

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

      2. associate-+l- 79.5%

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

      3. associate-*r* 79.5%

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

      4. associate-*r* 83.5%

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

      5. div-inv 83.4%

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

      6. associate--r- 83.4%

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

      7. fma-neg 83.4%

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

      8. associate-*r* 79.5%

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

      9. distribute-rgt-neg-in 79.5%

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

      10. associate-*l* 79.5%

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

   3. Applied egg-rr 79.5%

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

   4. Taylor expanded in x around 0 88.2%

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

   5. Taylor expanded in b around 0 73.9%

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

   if -7.4999999999999996e-145 < y < 5.1000000000000004e74

   1. Initial program 79.2%

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

      1. associate-/r* 82.3%

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

      2. associate-+l- 82.3%

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

      3. associate-*r* 84.0%

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

      4. associate-*r* 90.3%

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

      5. div-inv 90.2%

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

      6. associate--r- 90.2%

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

      7. fma-neg 90.2%

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

      8. associate-*r* 83.9%

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

      9. distribute-rgt-neg-in 83.9%

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

      10. associate-*l* 83.9%

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

   3. Applied egg-rr 83.9%

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

   4. Taylor expanded in x around 0 94.5%

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

   5. Taylor expanded in x around 0 79.9%

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

4. Final simplification 73.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.1 \cdot 10^{+59}:\\ \;\;\;\;9 \cdot \left(\frac{x}{z} \cdot \frac{y}{c}\right)\\ \mathbf{elif}\;y \leq -7.5 \cdot 10^{-145} \lor \neg \left(y \leq 5.1 \cdot 10^{+74}\right):\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right) + 9 \cdot \frac{x \cdot y}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{z} + -4 \cdot \left(a \cdot t\right)}{c}\\ \end{array} \]

Alternative 10: 72.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -3.5 \cdot 10^{+270}:\\ \;\;\;\;x \cdot \frac{y \cdot \frac{9}{c}}{z}\\ \mathbf{elif}\;x \leq -2.4 \cdot 10^{+111}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \mathbf{elif}\;x \leq 1.12 \cdot 10^{-69}:\\ \;\;\;\;\frac{\frac{b}{z} + -4 \cdot \left(a \cdot t\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;9 \cdot \left(\frac{x}{z} \cdot \frac{y}{c}\right)\\ \end{array} \end{array} \]

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 (<= x -3.5e+270)
   (* x (/ (* y (/ 9.0 c)) z))
   (if (<= x -2.4e+111)
     (/ (+ b (* 9.0 (* x y))) (* z c))
     (if (<= x 1.12e-69)
       (/ (+ (/ b z) (* -4.0 (* a t))) c)
       (* 9.0 (* (/ x z) (/ y 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 (x <= -3.5e+270) {
		tmp = x * ((y * (9.0 / c)) / z);
	} else if (x <= -2.4e+111) {
		tmp = (b + (9.0 * (x * y))) / (z * c);
	} else if (x <= 1.12e-69) {
		tmp = ((b / z) + (-4.0 * (a * t))) / c;
	} else {
		tmp = 9.0 * ((x / z) * (y / 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 (x <= (-3.5d+270)) then
        tmp = x * ((y * (9.0d0 / c)) / z)
    else if (x <= (-2.4d+111)) then
        tmp = (b + (9.0d0 * (x * y))) / (z * c)
    else if (x <= 1.12d-69) then
        tmp = ((b / z) + ((-4.0d0) * (a * t))) / c
    else
        tmp = 9.0d0 * ((x / z) * (y / 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 (x <= -3.5e+270) {
		tmp = x * ((y * (9.0 / c)) / z);
	} else if (x <= -2.4e+111) {
		tmp = (b + (9.0 * (x * y))) / (z * c);
	} else if (x <= 1.12e-69) {
		tmp = ((b / z) + (-4.0 * (a * t))) / c;
	} else {
		tmp = 9.0 * ((x / z) * (y / 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 x <= -3.5e+270:
		tmp = x * ((y * (9.0 / c)) / z)
	elif x <= -2.4e+111:
		tmp = (b + (9.0 * (x * y))) / (z * c)
	elif x <= 1.12e-69:
		tmp = ((b / z) + (-4.0 * (a * t))) / c
	else:
		tmp = 9.0 * ((x / z) * (y / 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 (x <= -3.5e+270)
		tmp = Float64(x * Float64(Float64(y * Float64(9.0 / c)) / z));
	elseif (x <= -2.4e+111)
		tmp = Float64(Float64(b + Float64(9.0 * Float64(x * y))) / Float64(z * c));
	elseif (x <= 1.12e-69)
		tmp = Float64(Float64(Float64(b / z) + Float64(-4.0 * Float64(a * t))) / c);
	else
		tmp = Float64(9.0 * Float64(Float64(x / z) * Float64(y / 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 (x <= -3.5e+270)
		tmp = x * ((y * (9.0 / c)) / z);
	elseif (x <= -2.4e+111)
		tmp = (b + (9.0 * (x * y))) / (z * c);
	elseif (x <= 1.12e-69)
		tmp = ((b / z) + (-4.0 * (a * t))) / c;
	else
		tmp = 9.0 * ((x / z) * (y / 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[x, -3.5e+270], N[(x * N[(N[(y * N[(9.0 / c), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -2.4e+111], N[(N[(b + N[(9.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.12e-69], N[(N[(N[(b / z), $MachinePrecision] + N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], N[(9.0 * N[(N[(x / z), $MachinePrecision] * N[(y / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x < -3.4999999999999999e270

   1. Initial program 43.7%

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

   3. Simplified 59.8%

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

      1. *-un-lft-identity 59.8%

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

      2. times-frac 60.3%

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

      3. +-commutative 60.3%

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

      4. fma-def 60.3%

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

   5. Applied egg-rr 60.3%

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

   6. Taylor expanded in x around inf 51.8%

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

      1. associate-*r/ 51.8%

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

      2. *-commutative 51.8%

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

      3. associate-*l* 51.8%

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

      4. times-frac 76.0%

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

      5. associate-/l* 75.8%

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

      6. associate-*r/ 75.9%

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

      7. associate-*l/ 83.2%

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

      8. associate-/r/ 83.4%

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

   8. Simplified 83.4%

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

   if -3.4999999999999999e270 < x < -2.40000000000000006e111

   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. associate-*l* 80.1%

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

      3. associate-*l* 77.7%

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

   3. Simplified 77.7%

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

   4. Taylor expanded in z around 0 71.4%

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

   if -2.40000000000000006e111 < x < 1.12e-69

   1. Initial program 79.0%

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

      1. associate-/r* 85.5%

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

      2. associate-+l- 85.5%

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

      3. associate-*r* 85.6%

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

      4. associate-*r* 89.7%

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

      5. div-inv 89.6%

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

      6. associate--r- 89.6%

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

      7. fma-neg 89.6%

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

      8. associate-*r* 85.5%

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

      9. distribute-rgt-neg-in 85.5%

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

      10. associate-*l* 85.5%

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

   3. Applied egg-rr 85.5%

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

   4. Taylor expanded in x around 0 96.6%

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

   5. Taylor expanded in x around 0 84.7%

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

   if 1.12e-69 < x

   1. Initial program 80.8%

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

   2. Taylor expanded in x around inf 38.5%

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

      1. *-commutative 38.5%

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

   4. Simplified 38.5%

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

   5. Taylor expanded in x around 0 38.5%

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

      1. *-commutative 38.5%

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

      2. times-frac 38.6%

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

   7. Simplified 38.6%

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

4. Final simplification 68.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.5 \cdot 10^{+270}:\\ \;\;\;\;x \cdot \frac{y \cdot \frac{9}{c}}{z}\\ \mathbf{elif}\;x \leq -2.4 \cdot 10^{+111}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \mathbf{elif}\;x \leq 1.12 \cdot 10^{-69}:\\ \;\;\;\;\frac{\frac{b}{z} + -4 \cdot \left(a \cdot t\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;9 \cdot \left(\frac{x}{z} \cdot \frac{y}{c}\right)\\ \end{array} \]

Alternative 11: 68.1% accurate, 1.3× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{+172} \lor \neg \left(z \leq 1.85 \cdot 10^{+117}\right):\\ \;\;\;\;-4 \cdot \frac{a \cdot t}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \end{array} \end{array} \]

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 (<= z -1.3e+172) (not (<= z 1.85e+117)))
   (* -4.0 (/ (* a t) c))
   (/ (+ 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 ((z <= -1.3e+172) || !(z <= 1.85e+117)) {
		tmp = -4.0 * ((a * t) / c);
	} 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 ((z <= (-1.3d+172)) .or. (.not. (z <= 1.85d+117))) then
        tmp = (-4.0d0) * ((a * t) / c)
    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 ((z <= -1.3e+172) || !(z <= 1.85e+117)) {
		tmp = -4.0 * ((a * t) / c);
	} 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 (z <= -1.3e+172) or not (z <= 1.85e+117):
		tmp = -4.0 * ((a * t) / c)
	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 ((z <= -1.3e+172) || !(z <= 1.85e+117))
		tmp = Float64(-4.0 * Float64(Float64(a * t) / c));
	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 ((z <= -1.3e+172) || ~((z <= 1.85e+117)))
		tmp = -4.0 * ((a * t) / c);
	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[z, -1.3e+172], N[Not[LessEqual[z, 1.85e+117]], $MachinePrecision]], N[(-4.0 * N[(N[(a * t), $MachinePrecision] / c), $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 z < -1.3e172 or 1.8499999999999999e117 < z

   1. Initial program 46.9%

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

   2. Taylor expanded in z around inf 67.8%

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

   if -1.3e172 < z < 1.8499999999999999e117

   1. Initial program 90.5%

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

      1. associate-+l- 90.5%

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

      2. associate-*l* 91.0%

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

      3. associate-*l* 88.9%

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

   3. Simplified 88.9%

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

   4. Taylor expanded in z around 0 71.0%

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

4. Final simplification 70.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{+172} \lor \neg \left(z \leq 1.85 \cdot 10^{+117}\right):\\ \;\;\;\;-4 \cdot \frac{a \cdot t}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \end{array} \]

Alternative 12: 48.6% accurate, 1.7× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;b \leq -2.3 \cdot 10^{+66} \lor \neg \left(b \leq 2.9 \cdot 10^{+141}\right):\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{a \cdot t}{c}\\ \end{array} \end{array} \]

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 (<= b -2.3e+66) (not (<= b 2.9e+141)))
   (/ (/ b c) z)
   (* -4.0 (/ (* a t) 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 ((b <= -2.3e+66) || !(b <= 2.9e+141)) {
		tmp = (b / c) / z;
	} else {
		tmp = -4.0 * ((a * t) / 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 ((b <= (-2.3d+66)) .or. (.not. (b <= 2.9d+141))) then
        tmp = (b / c) / z
    else
        tmp = (-4.0d0) * ((a * t) / 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 ((b <= -2.3e+66) || !(b <= 2.9e+141)) {
		tmp = (b / c) / z;
	} else {
		tmp = -4.0 * ((a * t) / 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 (b <= -2.3e+66) or not (b <= 2.9e+141):
		tmp = (b / c) / z
	else:
		tmp = -4.0 * ((a * t) / 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 ((b <= -2.3e+66) || !(b <= 2.9e+141))
		tmp = Float64(Float64(b / c) / z);
	else
		tmp = Float64(-4.0 * Float64(Float64(a * t) / 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 ((b <= -2.3e+66) || ~((b <= 2.9e+141)))
		tmp = (b / c) / z;
	else
		tmp = -4.0 * ((a * t) / 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[b, -2.3e+66], N[Not[LessEqual[b, 2.9e+141]], $MachinePrecision]], N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision], N[(-4.0 * N[(N[(a * t), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -2.3e66 or 2.90000000000000007e141 < b

   1. Initial program 76.4%

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

   3. Simplified 79.7%

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

      1. *-un-lft-identity 79.7%

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

      2. times-frac 83.2%

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

      3. +-commutative 83.2%

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

      4. fma-def 83.2%

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

   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 b around inf 58.6%

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

      1. associate-/r* 67.7%

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

   8. Simplified 67.7%

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

   if -2.3e66 < b < 2.90000000000000007e141

   1. Initial program 78.9%

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

   2. Taylor expanded in z around inf 48.7%

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

4. Final simplification 55.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.3 \cdot 10^{+66} \lor \neg \left(b \leq 2.9 \cdot 10^{+141}\right):\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{a \cdot t}{c}\\ \end{array} \]

Alternative 13: 35.1% 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 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. Taylor expanded in b around inf 34.1%

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

   1. *-commutative 34.1%

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

4. Simplified 34.1%

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

5. Final simplification 34.1%

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

Alternative 14: 34.4% accurate, 3.8× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \frac{\frac{b}{c}}{z} \end{array} \]

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 c) z))

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 / c) / z;
}

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 / c) / z
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 / c) / z;
}

Python

[x, y] = sort([x, y])
[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	return (b / c) / z

Julia

x, y = sort([x, y])
t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	return Float64(Float64(b / c) / z)
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 / c) / z;
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[(N[(b / c), $MachinePrecision] / z), $MachinePrecision]

Derivation

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

3. Simplified 79.6%

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

   1. *-un-lft-identity 79.6%

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

   2. times-frac 81.0%

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

   3. +-commutative 81.0%

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

   4. fma-def 81.0%

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

5. Applied egg-rr 81.0%

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

6. Taylor expanded in b around inf 34.1%

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

   1. associate-/r* 36.4%

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

8. Simplified 36.4%

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

9. Final simplification 36.4%

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

Developer target: 81.2% 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 2023308 
(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)))