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

Percentage Accurate: 80.2% → 89.6%

Time: 17.8s

Alternatives: 15

Speedup: 0.9×

• 38.1% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 80.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 89.6% accurate, 0.1× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;c \leq -6.7 \cdot 10^{-37}:\\ \;\;\;\;t \cdot \frac{a}{\frac{c}{-4}} + \frac{\frac{b}{c} - \frac{x \cdot \left(y \cdot -9\right)}{c}}{z}\\ \mathbf{elif}\;c \leq 8.4 \cdot 10^{-81}:\\ \;\;\;\;\frac{b + \mathsf{fma}\left(x, y \cdot 9, a \cdot \left(z \cdot \left(t \cdot \left(-4\right)\right)\right)\right)}{z} \cdot \frac{1}{c}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t \cdot \frac{a}{c}, -4, \mathsf{fma}\left(9, \frac{x}{c} \cdot \frac{y}{z}, \frac{b}{c \cdot z}\right)\right)\\ \end{array} \end{array} \]

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 (<= c -6.7e-37)
   (+ (* t (/ a (/ c -4.0))) (/ (- (/ b c) (/ (* x (* y -9.0)) c)) z))
   (if (<= c 8.4e-81)
     (* (/ (+ b (fma x (* y 9.0) (* a (* z (* t (- 4.0)))))) z) (/ 1.0 c))
     (fma (* t (/ a c)) -4.0 (fma 9.0 (* (/ x c) (/ y z)) (/ 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) {
	double tmp;
	if (c <= -6.7e-37) {
		tmp = (t * (a / (c / -4.0))) + (((b / c) - ((x * (y * -9.0)) / c)) / z);
	} else if (c <= 8.4e-81) {
		tmp = ((b + fma(x, (y * 9.0), (a * (z * (t * -4.0))))) / z) * (1.0 / c);
	} else {
		tmp = fma((t * (a / c)), -4.0, fma(9.0, ((x / c) * (y / z)), (b / (c * 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 (c <= -6.7e-37)
		tmp = Float64(Float64(t * Float64(a / Float64(c / -4.0))) + Float64(Float64(Float64(b / c) - Float64(Float64(x * Float64(y * -9.0)) / c)) / z));
	elseif (c <= 8.4e-81)
		tmp = Float64(Float64(Float64(b + fma(x, Float64(y * 9.0), Float64(a * Float64(z * Float64(t * Float64(-4.0)))))) / z) * Float64(1.0 / c));
	else
		tmp = fma(Float64(t * Float64(a / c)), -4.0, fma(9.0, Float64(Float64(x / c) * Float64(y / z)), Float64(b / Float64(c * 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[c, -6.7e-37], N[(N[(t * N[(a / N[(c / -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(b / c), $MachinePrecision] - N[(N[(x * N[(y * -9.0), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 8.4e-81], N[(N[(N[(b + N[(x * N[(y * 9.0), $MachinePrecision] + N[(a * N[(z * N[(t * (-4.0)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] * N[(1.0 / c), $MachinePrecision]), $MachinePrecision], N[(N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision] * -4.0 + N[(9.0 * N[(N[(x / c), $MachinePrecision] * N[(y / z), $MachinePrecision]), $MachinePrecision] + N[(b / N[(c * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if c < -6.70000000000000001e-37

   1. Initial program 71.5%

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

      1. associate-/r* 66.5%

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

      2. associate-+l- 66.5%

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

      3. associate-*r* 66.5%

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

      4. associate-*r* 67.9%

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

      5. div-inv 67.9%

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

      6. associate--r- 67.9%

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

      7. fma-neg 67.9%

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

      8. associate-*r* 66.6%

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

      9. distribute-rgt-neg-in 66.6%

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

      10. associate-*l* 66.6%

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

   3. Applied egg-rr 66.6%

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

   4. Taylor expanded in x around 0 79.7%

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

   5. Taylor expanded in z around -inf 90.3%

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

      1. fma-def 90.3%

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

      2. mul-1-neg 90.3%

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

      3. fma-neg 90.3%

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

      4. associate-*r/ 90.3%

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

      5. associate-*r* 90.3%

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

      6. associate-*l/ 93.0%

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

      7. *-commutative 93.0%

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

      8. *-commutative 93.0%

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

      9. associate-/l* 93.0%

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

      10. mul-1-neg 93.0%

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

      11. unsub-neg 93.0%

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

      12. associate-*r/ 93.0%

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

      13. *-commutative 93.0%

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

      14. associate-*l* 93.0%

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

   7. Simplified 93.0%

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

   if -6.70000000000000001e-37 < c < 8.3999999999999997e-81

   1. Initial program 93.8%

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

      1. associate-/r* 96.4%

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

      2. associate-+l- 96.4%

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

      3. associate-*r* 96.4%

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

      4. associate-*r* 97.2%

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

      5. div-inv 97.2%

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

      6. associate--r- 97.2%

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

      7. fma-neg 97.2%

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

      8. associate-*r* 96.3%

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

      9. distribute-rgt-neg-in 96.3%

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

      10. associate-*l* 96.3%

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

   3. Applied egg-rr 96.3%

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

   if 8.3999999999999997e-81 < c

   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 x around 0 81.8%

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

      1. cancel-sign-sub-inv 81.8%

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

      2. metadata-eval 81.8%

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

      3. +-commutative 81.8%

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

      4. *-commutative 81.8%

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

      5. fma-def 81.8%

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

      6. associate-/l* 85.2%

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

      7. associate-/r/ 87.8%

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

      8. fma-def 87.8%

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

      9. times-frac 95.7%

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

      10. *-commutative 95.7%

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

   4. Simplified 95.7%

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

4. Final simplification 95.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -6.7 \cdot 10^{-37}:\\ \;\;\;\;t \cdot \frac{a}{\frac{c}{-4}} + \frac{\frac{b}{c} - \frac{x \cdot \left(y \cdot -9\right)}{c}}{z}\\ \mathbf{elif}\;c \leq 8.4 \cdot 10^{-81}:\\ \;\;\;\;\frac{b + \mathsf{fma}\left(x, y \cdot 9, a \cdot \left(z \cdot \left(t \cdot \left(-4\right)\right)\right)\right)}{z} \cdot \frac{1}{c}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t \cdot \frac{a}{c}, -4, \mathsf{fma}\left(9, \frac{x}{c} \cdot \frac{y}{z}, \frac{b}{c \cdot z}\right)\right)\\ \end{array} \]

Alternative 2: 87.1% accurate, 0.2× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} t_1 := t \cdot \frac{a}{\frac{c}{-4}} + \frac{\frac{b}{c} - \frac{x \cdot \left(y \cdot -9\right)}{c}}{z}\\ \mathbf{if}\;c \leq -1 \cdot 10^{-35}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 1.75 \cdot 10^{+83}:\\ \;\;\;\;\frac{b + \mathsf{fma}\left(x, y \cdot 9, a \cdot \left(z \cdot \left(t \cdot \left(-4\right)\right)\right)\right)}{z} \cdot \frac{1}{c}\\ \mathbf{elif}\;c \leq 2.1 \cdot 10^{+153}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}} + \frac{y}{z} \cdot \left(9 \cdot \frac{x}{c}\right)\\ \mathbf{elif}\;c \leq 2.05 \cdot 10^{+270}:\\ \;\;\;\;\left(\frac{b}{c \cdot z} + 9 \cdot \frac{x \cdot y}{c \cdot z}\right) - 4 \cdot \frac{t \cdot a}{c}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1
         (+ (* t (/ a (/ c -4.0))) (/ (- (/ b c) (/ (* x (* y -9.0)) c)) z))))
   (if (<= c -1e-35)
     t_1
     (if (<= c 1.75e+83)
       (* (/ (+ b (fma x (* y 9.0) (* a (* z (* t (- 4.0)))))) z) (/ 1.0 c))
       (if (<= c 2.1e+153)
         (+ (* -4.0 (/ a (/ c t))) (* (/ y z) (* 9.0 (/ x c))))
         (if (<= c 2.05e+270)
           (-
            (+ (/ b (* c z)) (* 9.0 (/ (* x y) (* c z))))
            (* 4.0 (/ (* t a) c)))
           t_1))))))

C

assert(x < y);
assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (t * (a / (c / -4.0))) + (((b / c) - ((x * (y * -9.0)) / c)) / z);
	double tmp;
	if (c <= -1e-35) {
		tmp = t_1;
	} else if (c <= 1.75e+83) {
		tmp = ((b + fma(x, (y * 9.0), (a * (z * (t * -4.0))))) / z) * (1.0 / c);
	} else if (c <= 2.1e+153) {
		tmp = (-4.0 * (a / (c / t))) + ((y / z) * (9.0 * (x / c)));
	} else if (c <= 2.05e+270) {
		tmp = ((b / (c * z)) + (9.0 * ((x * y) / (c * z)))) - (4.0 * ((t * a) / c));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

x, y = sort([x, y])
t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(t * Float64(a / Float64(c / -4.0))) + Float64(Float64(Float64(b / c) - Float64(Float64(x * Float64(y * -9.0)) / c)) / z))
	tmp = 0.0
	if (c <= -1e-35)
		tmp = t_1;
	elseif (c <= 1.75e+83)
		tmp = Float64(Float64(Float64(b + fma(x, Float64(y * 9.0), Float64(a * Float64(z * Float64(t * Float64(-4.0)))))) / z) * Float64(1.0 / c));
	elseif (c <= 2.1e+153)
		tmp = Float64(Float64(-4.0 * Float64(a / Float64(c / t))) + Float64(Float64(y / z) * Float64(9.0 * Float64(x / c))));
	elseif (c <= 2.05e+270)
		tmp = Float64(Float64(Float64(b / Float64(c * z)) + Float64(9.0 * Float64(Float64(x * y) / Float64(c * z)))) - Float64(4.0 * Float64(Float64(t * a) / c)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(t * N[(a / N[(c / -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(b / c), $MachinePrecision] - N[(N[(x * N[(y * -9.0), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -1e-35], t$95$1, If[LessEqual[c, 1.75e+83], N[(N[(N[(b + N[(x * N[(y * 9.0), $MachinePrecision] + N[(a * N[(z * N[(t * (-4.0)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] * N[(1.0 / c), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 2.1e+153], N[(N[(-4.0 * N[(a / N[(c / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(y / z), $MachinePrecision] * N[(9.0 * N[(x / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 2.05e+270], N[(N[(N[(b / N[(c * z), $MachinePrecision]), $MachinePrecision] + N[(9.0 * N[(N[(x * y), $MachinePrecision] / N[(c * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * N[(N[(t * a), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if c < -1.00000000000000001e-35 or 2.04999999999999998e270 < c

   1. Initial program 71.1%

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

      1. associate-/r* 65.4%

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

      2. associate-+l- 65.4%

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

      3. associate-*r* 65.3%

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

      4. associate-*r* 66.6%

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

      5. div-inv 66.6%

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

      6. associate--r- 66.6%

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

      7. fma-neg 66.6%

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

      8. associate-*r* 65.4%

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

      9. distribute-rgt-neg-in 65.4%

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

      10. associate-*l* 65.4%

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

   3. Applied egg-rr 65.4%

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

   4. Taylor expanded in x around 0 77.5%

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

   5. Taylor expanded in z around -inf 88.6%

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

      1. fma-def 88.6%

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

      2. mul-1-neg 88.6%

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

      3. fma-neg 88.6%

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

      4. associate-*r/ 88.6%

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

      5. associate-*r* 88.6%

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

      6. associate-*l/ 92.3%

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

      7. *-commutative 92.3%

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

      8. *-commutative 92.3%

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

      9. associate-/l* 92.3%

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

      10. mul-1-neg 92.3%

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

      11. unsub-neg 92.3%

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

      12. associate-*r/ 92.3%

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

      13. *-commutative 92.3%

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

      14. associate-*l* 92.3%

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

   7. Simplified 92.3%

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

   if -1.00000000000000001e-35 < c < 1.74999999999999989e83

   1. Initial program 93.5%

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

      1. associate-/r* 94.4%

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

      2. associate-+l- 94.4%

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

      3. associate-*r* 94.4%

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

      4. associate-*r* 95.7%

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

      5. div-inv 95.7%

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

      6. associate--r- 95.7%

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

      7. fma-neg 95.7%

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

      8. associate-*r* 94.3%

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

      9. distribute-rgt-neg-in 94.3%

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

      10. associate-*l* 94.3%

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

   3. Applied egg-rr 94.3%

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

   if 1.74999999999999989e83 < c < 2.10000000000000017e153

   1. Initial program 43.2%

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

      1. associate-/r* 55.8%

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

      2. associate-+l- 55.8%

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

      3. associate-*r* 55.9%

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

      4. associate-*r* 55.9%

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

      5. div-inv 55.9%

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

      6. associate--r- 55.9%

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

      7. fma-neg 55.9%

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

      8. associate-*r* 55.9%

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

      9. distribute-rgt-neg-in 55.9%

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

      10. associate-*l* 55.9%

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

   3. Applied egg-rr 55.9%

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

   4. Taylor expanded in x around 0 61.4%

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

   5. Taylor expanded in z around -inf 61.4%

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

      1. fma-def 61.4%

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

      2. mul-1-neg 61.4%

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

      3. fma-neg 61.4%

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

      4. associate-*r/ 61.4%

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

      5. associate-*r* 61.4%

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

      6. associate-*l/ 72.1%

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

      7. *-commutative 72.1%

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

      8. *-commutative 72.1%

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

      9. associate-/l* 72.1%

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

      10. mul-1-neg 72.1%

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

      11. unsub-neg 72.1%

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

      12. associate-*r/ 72.0%

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

      13. *-commutative 72.0%

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

      14. associate-*l* 72.2%

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

   7. Simplified 72.2%

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

   8. Taylor expanded in b around 0 60.9%

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

      1. cancel-sign-sub-inv 60.9%

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

      2. metadata-eval 60.9%

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

      3. associate-/l* 71.6%

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

      4. times-frac 99.7%

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

      5. associate-*r* 99.8%

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

   10. Simplified 99.8%

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

   if 2.10000000000000017e153 < c < 2.04999999999999998e270

   1. Initial program 82.1%

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

   2. Taylor expanded in x around 0 90.9%

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

4. Final simplification 93.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1 \cdot 10^{-35}:\\ \;\;\;\;t \cdot \frac{a}{\frac{c}{-4}} + \frac{\frac{b}{c} - \frac{x \cdot \left(y \cdot -9\right)}{c}}{z}\\ \mathbf{elif}\;c \leq 1.75 \cdot 10^{+83}:\\ \;\;\;\;\frac{b + \mathsf{fma}\left(x, y \cdot 9, a \cdot \left(z \cdot \left(t \cdot \left(-4\right)\right)\right)\right)}{z} \cdot \frac{1}{c}\\ \mathbf{elif}\;c \leq 2.1 \cdot 10^{+153}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}} + \frac{y}{z} \cdot \left(9 \cdot \frac{x}{c}\right)\\ \mathbf{elif}\;c \leq 2.05 \cdot 10^{+270}:\\ \;\;\;\;\left(\frac{b}{c \cdot z} + 9 \cdot \frac{x \cdot y}{c \cdot z}\right) - 4 \cdot \frac{t \cdot a}{c}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{a}{\frac{c}{-4}} + \frac{\frac{b}{c} - \frac{x \cdot \left(y \cdot -9\right)}{c}}{z}\\ \end{array} \]

Alternative 3: 78.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} t_1 := \frac{b + 9 \cdot \left(x \cdot y\right)}{c \cdot z}\\ t_2 := \frac{-4 \cdot \left(t \cdot a\right) + \frac{b}{z}}{c}\\ t_3 := y \cdot \left(x \cdot 9\right)\\ \mathbf{if}\;t_3 \leq -5 \cdot 10^{+145}:\\ \;\;\;\;x \cdot \left(\frac{y}{c} \cdot \frac{9}{z}\right)\\ \mathbf{elif}\;t_3 \leq -2 \cdot 10^{+121}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_3 \leq -5 \cdot 10^{+53}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_3 \leq 20000000000000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_3 \leq 2 \cdot 10^{+281}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{c} \cdot \frac{x \cdot 9}{z}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (+ b (* 9.0 (* x y))) (* c z)))
        (t_2 (/ (+ (* -4.0 (* t a)) (/ b z)) c))
        (t_3 (* y (* x 9.0))))
   (if (<= t_3 -5e+145)
     (* x (* (/ y c) (/ 9.0 z)))
     (if (<= t_3 -2e+121)
       t_2
       (if (<= t_3 -5e+53)
         t_1
         (if (<= t_3 20000000000000.0)
           t_2
           (if (<= t_3 2e+281) t_1 (* (/ y c) (/ (* x 9.0) 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 = (b + (9.0 * (x * y))) / (c * z);
	double t_2 = ((-4.0 * (t * a)) + (b / z)) / c;
	double t_3 = y * (x * 9.0);
	double tmp;
	if (t_3 <= -5e+145) {
		tmp = x * ((y / c) * (9.0 / z));
	} else if (t_3 <= -2e+121) {
		tmp = t_2;
	} else if (t_3 <= -5e+53) {
		tmp = t_1;
	} else if (t_3 <= 20000000000000.0) {
		tmp = t_2;
	} else if (t_3 <= 2e+281) {
		tmp = t_1;
	} else {
		tmp = (y / c) * ((x * 9.0) / 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) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (b + (9.0d0 * (x * y))) / (c * z)
    t_2 = (((-4.0d0) * (t * a)) + (b / z)) / c
    t_3 = y * (x * 9.0d0)
    if (t_3 <= (-5d+145)) then
        tmp = x * ((y / c) * (9.0d0 / z))
    else if (t_3 <= (-2d+121)) then
        tmp = t_2
    else if (t_3 <= (-5d+53)) then
        tmp = t_1
    else if (t_3 <= 20000000000000.0d0) then
        tmp = t_2
    else if (t_3 <= 2d+281) then
        tmp = t_1
    else
        tmp = (y / c) * ((x * 9.0d0) / 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 = (b + (9.0 * (x * y))) / (c * z);
	double t_2 = ((-4.0 * (t * a)) + (b / z)) / c;
	double t_3 = y * (x * 9.0);
	double tmp;
	if (t_3 <= -5e+145) {
		tmp = x * ((y / c) * (9.0 / z));
	} else if (t_3 <= -2e+121) {
		tmp = t_2;
	} else if (t_3 <= -5e+53) {
		tmp = t_1;
	} else if (t_3 <= 20000000000000.0) {
		tmp = t_2;
	} else if (t_3 <= 2e+281) {
		tmp = t_1;
	} else {
		tmp = (y / c) * ((x * 9.0) / 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 = (b + (9.0 * (x * y))) / (c * z)
	t_2 = ((-4.0 * (t * a)) + (b / z)) / c
	t_3 = y * (x * 9.0)
	tmp = 0
	if t_3 <= -5e+145:
		tmp = x * ((y / c) * (9.0 / z))
	elif t_3 <= -2e+121:
		tmp = t_2
	elif t_3 <= -5e+53:
		tmp = t_1
	elif t_3 <= 20000000000000.0:
		tmp = t_2
	elif t_3 <= 2e+281:
		tmp = t_1
	else:
		tmp = (y / c) * ((x * 9.0) / 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(Float64(b + Float64(9.0 * Float64(x * y))) / Float64(c * z))
	t_2 = Float64(Float64(Float64(-4.0 * Float64(t * a)) + Float64(b / z)) / c)
	t_3 = Float64(y * Float64(x * 9.0))
	tmp = 0.0
	if (t_3 <= -5e+145)
		tmp = Float64(x * Float64(Float64(y / c) * Float64(9.0 / z)));
	elseif (t_3 <= -2e+121)
		tmp = t_2;
	elseif (t_3 <= -5e+53)
		tmp = t_1;
	elseif (t_3 <= 20000000000000.0)
		tmp = t_2;
	elseif (t_3 <= 2e+281)
		tmp = t_1;
	else
		tmp = Float64(Float64(y / c) * Float64(Float64(x * 9.0) / 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 = (b + (9.0 * (x * y))) / (c * z);
	t_2 = ((-4.0 * (t * a)) + (b / z)) / c;
	t_3 = y * (x * 9.0);
	tmp = 0.0;
	if (t_3 <= -5e+145)
		tmp = x * ((y / c) * (9.0 / z));
	elseif (t_3 <= -2e+121)
		tmp = t_2;
	elseif (t_3 <= -5e+53)
		tmp = t_1;
	elseif (t_3 <= 20000000000000.0)
		tmp = t_2;
	elseif (t_3 <= 2e+281)
		tmp = t_1;
	else
		tmp = (y / c) * ((x * 9.0) / 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[(N[(b + N[(9.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(c * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision] + N[(b / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]}, Block[{t$95$3 = N[(y * N[(x * 9.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$3, -5e+145], N[(x * N[(N[(y / c), $MachinePrecision] * N[(9.0 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, -2e+121], t$95$2, If[LessEqual[t$95$3, -5e+53], t$95$1, If[LessEqual[t$95$3, 20000000000000.0], t$95$2, If[LessEqual[t$95$3, 2e+281], t$95$1, N[(N[(y / c), $MachinePrecision] * N[(N[(x * 9.0), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 (*.f64 x 9) y) < -4.99999999999999967e145

   1. Initial program 88.9%

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

      1. div-inv 88.8%

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

      2. sub-neg 88.8%

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

      3. associate-*r* 88.8%

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

      4. fma-def 88.8%

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

      5. distribute-rgt-neg-in 88.8%

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

      6. associate-*l* 88.8%

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

   3. Applied egg-rr 88.8%

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

   4. Taylor expanded in x around inf 76.7%

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

      1. *-commutative 76.7%

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

      2. associate-/l* 82.1%

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

      3. *-commutative 82.1%

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

      4. associate-*l/ 81.9%

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

      5. associate-*r/ 82.0%

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

      6. associate-/l* 82.0%

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

      7. *-commutative 82.0%

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

      8. *-commutative 82.0%

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

      9. times-frac 84.6%

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

   6. Simplified 84.6%

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

   if -4.99999999999999967e145 < (*.f64 (*.f64 x 9) y) < -2.00000000000000007e121 or -5.0000000000000004e53 < (*.f64 (*.f64 x 9) y) < 2e13

   1. Initial program 81.6%

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

      1. associate-/r* 83.2%

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

      2. associate-+l- 83.2%

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

      3. associate-*r* 83.2%

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

      4. associate-*r* 84.5%

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

      5. div-inv 84.4%

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

      6. associate--r- 84.4%

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

      7. fma-neg 84.4%

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

      8. associate-*r* 83.2%

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

      9. distribute-rgt-neg-in 83.2%

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

      10. associate-*l* 83.2%

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

   3. Applied egg-rr 83.2%

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

   4. Taylor expanded in x around 0 90.8%

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

   5. Taylor expanded in x around 0 85.2%

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

   if -2.00000000000000007e121 < (*.f64 (*.f64 x 9) y) < -5.0000000000000004e53 or 2e13 < (*.f64 (*.f64 x 9) y) < 2.0000000000000001e281

   1. Initial program 93.3%

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

   2. Taylor expanded in z around 0 84.5%

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

   if 2.0000000000000001e281 < (*.f64 (*.f64 x 9) y)

   1. Initial program 54.0%

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

   2. Taylor expanded in x around inf 58.1%

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

      1. associate-*r/ 54.0%

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

      2. associate-*r* 54.0%

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

      3. *-commutative 54.0%

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

      4. associate-*r* 54.0%

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

      5. *-commutative 54.0%

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

   4. Simplified 54.0%

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

      1. associate-*r* 54.0%

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

      2. times-frac 87.5%

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

   6. Applied egg-rr 87.5%

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

4. Final simplification 85.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \left(x \cdot 9\right) \leq -5 \cdot 10^{+145}:\\ \;\;\;\;x \cdot \left(\frac{y}{c} \cdot \frac{9}{z}\right)\\ \mathbf{elif}\;y \cdot \left(x \cdot 9\right) \leq -2 \cdot 10^{+121}:\\ \;\;\;\;\frac{-4 \cdot \left(t \cdot a\right) + \frac{b}{z}}{c}\\ \mathbf{elif}\;y \cdot \left(x \cdot 9\right) \leq -5 \cdot 10^{+53}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{c \cdot z}\\ \mathbf{elif}\;y \cdot \left(x \cdot 9\right) \leq 20000000000000:\\ \;\;\;\;\frac{-4 \cdot \left(t \cdot a\right) + \frac{b}{z}}{c}\\ \mathbf{elif}\;y \cdot \left(x \cdot 9\right) \leq 2 \cdot 10^{+281}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{c} \cdot \frac{x \cdot 9}{z}\\ \end{array} \]

Alternative 4: 78.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot 9\right)\\ t_2 := -4 \cdot \left(t \cdot a\right)\\ t_3 := \frac{t_2 + \frac{b}{z}}{c}\\ \mathbf{if}\;t_1 \leq -5 \cdot 10^{+145}:\\ \;\;\;\;x \cdot \left(\frac{y}{c} \cdot \frac{9}{z}\right)\\ \mathbf{elif}\;t_1 \leq -2 \cdot 10^{+121}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t_1 \leq -1 \cdot 10^{+70}:\\ \;\;\;\;\frac{t_2 + 9 \cdot \frac{x \cdot y}{z}}{c}\\ \mathbf{elif}\;t_1 \leq 20000000000000:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{+281}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{c} \cdot \frac{x \cdot 9}{z}\\ \end{array} \end{array} \]

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 (* x 9.0)))
        (t_2 (* -4.0 (* t a)))
        (t_3 (/ (+ t_2 (/ b z)) c)))
   (if (<= t_1 -5e+145)
     (* x (* (/ y c) (/ 9.0 z)))
     (if (<= t_1 -2e+121)
       t_3
       (if (<= t_1 -1e+70)
         (/ (+ t_2 (* 9.0 (/ (* x y) z))) c)
         (if (<= t_1 20000000000000.0)
           t_3
           (if (<= t_1 2e+281)
             (/ (+ b (* 9.0 (* x y))) (* c z))
             (* (/ y c) (/ (* x 9.0) 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 = y * (x * 9.0);
	double t_2 = -4.0 * (t * a);
	double t_3 = (t_2 + (b / z)) / c;
	double tmp;
	if (t_1 <= -5e+145) {
		tmp = x * ((y / c) * (9.0 / z));
	} else if (t_1 <= -2e+121) {
		tmp = t_3;
	} else if (t_1 <= -1e+70) {
		tmp = (t_2 + (9.0 * ((x * y) / z))) / c;
	} else if (t_1 <= 20000000000000.0) {
		tmp = t_3;
	} else if (t_1 <= 2e+281) {
		tmp = (b + (9.0 * (x * y))) / (c * z);
	} else {
		tmp = (y / c) * ((x * 9.0) / 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) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = y * (x * 9.0d0)
    t_2 = (-4.0d0) * (t * a)
    t_3 = (t_2 + (b / z)) / c
    if (t_1 <= (-5d+145)) then
        tmp = x * ((y / c) * (9.0d0 / z))
    else if (t_1 <= (-2d+121)) then
        tmp = t_3
    else if (t_1 <= (-1d+70)) then
        tmp = (t_2 + (9.0d0 * ((x * y) / z))) / c
    else if (t_1 <= 20000000000000.0d0) then
        tmp = t_3
    else if (t_1 <= 2d+281) then
        tmp = (b + (9.0d0 * (x * y))) / (c * z)
    else
        tmp = (y / c) * ((x * 9.0d0) / 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 = y * (x * 9.0);
	double t_2 = -4.0 * (t * a);
	double t_3 = (t_2 + (b / z)) / c;
	double tmp;
	if (t_1 <= -5e+145) {
		tmp = x * ((y / c) * (9.0 / z));
	} else if (t_1 <= -2e+121) {
		tmp = t_3;
	} else if (t_1 <= -1e+70) {
		tmp = (t_2 + (9.0 * ((x * y) / z))) / c;
	} else if (t_1 <= 20000000000000.0) {
		tmp = t_3;
	} else if (t_1 <= 2e+281) {
		tmp = (b + (9.0 * (x * y))) / (c * z);
	} else {
		tmp = (y / c) * ((x * 9.0) / 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 = y * (x * 9.0)
	t_2 = -4.0 * (t * a)
	t_3 = (t_2 + (b / z)) / c
	tmp = 0
	if t_1 <= -5e+145:
		tmp = x * ((y / c) * (9.0 / z))
	elif t_1 <= -2e+121:
		tmp = t_3
	elif t_1 <= -1e+70:
		tmp = (t_2 + (9.0 * ((x * y) / z))) / c
	elif t_1 <= 20000000000000.0:
		tmp = t_3
	elif t_1 <= 2e+281:
		tmp = (b + (9.0 * (x * y))) / (c * z)
	else:
		tmp = (y / c) * ((x * 9.0) / 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(y * Float64(x * 9.0))
	t_2 = Float64(-4.0 * Float64(t * a))
	t_3 = Float64(Float64(t_2 + Float64(b / z)) / c)
	tmp = 0.0
	if (t_1 <= -5e+145)
		tmp = Float64(x * Float64(Float64(y / c) * Float64(9.0 / z)));
	elseif (t_1 <= -2e+121)
		tmp = t_3;
	elseif (t_1 <= -1e+70)
		tmp = Float64(Float64(t_2 + Float64(9.0 * Float64(Float64(x * y) / z))) / c);
	elseif (t_1 <= 20000000000000.0)
		tmp = t_3;
	elseif (t_1 <= 2e+281)
		tmp = Float64(Float64(b + Float64(9.0 * Float64(x * y))) / Float64(c * z));
	else
		tmp = Float64(Float64(y / c) * Float64(Float64(x * 9.0) / 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 = y * (x * 9.0);
	t_2 = -4.0 * (t * a);
	t_3 = (t_2 + (b / z)) / c;
	tmp = 0.0;
	if (t_1 <= -5e+145)
		tmp = x * ((y / c) * (9.0 / z));
	elseif (t_1 <= -2e+121)
		tmp = t_3;
	elseif (t_1 <= -1e+70)
		tmp = (t_2 + (9.0 * ((x * y) / z))) / c;
	elseif (t_1 <= 20000000000000.0)
		tmp = t_3;
	elseif (t_1 <= 2e+281)
		tmp = (b + (9.0 * (x * y))) / (c * z);
	else
		tmp = (y / c) * ((x * 9.0) / 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[(y * N[(x * 9.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(t$95$2 + N[(b / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+145], N[(x * N[(N[(y / c), $MachinePrecision] * N[(9.0 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -2e+121], t$95$3, If[LessEqual[t$95$1, -1e+70], N[(N[(t$95$2 + N[(9.0 * N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[t$95$1, 20000000000000.0], t$95$3, If[LessEqual[t$95$1, 2e+281], N[(N[(b + N[(9.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(c * z), $MachinePrecision]), $MachinePrecision], N[(N[(y / c), $MachinePrecision] * N[(N[(x * 9.0), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if (*.f64 (*.f64 x 9) y) < -4.99999999999999967e145

   1. Initial program 88.9%

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

      1. div-inv 88.8%

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

      2. sub-neg 88.8%

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

      3. associate-*r* 88.8%

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

      4. fma-def 88.8%

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

      5. distribute-rgt-neg-in 88.8%

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

      6. associate-*l* 88.8%

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

   3. Applied egg-rr 88.8%

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

   4. Taylor expanded in x around inf 76.7%

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

      1. *-commutative 76.7%

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

      2. associate-/l* 82.1%

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

      3. *-commutative 82.1%

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

      4. associate-*l/ 81.9%

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

      5. associate-*r/ 82.0%

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

      6. associate-/l* 82.0%

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

      7. *-commutative 82.0%

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

      8. *-commutative 82.0%

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

      9. times-frac 84.6%

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

   6. Simplified 84.6%

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

   if -4.99999999999999967e145 < (*.f64 (*.f64 x 9) y) < -2.00000000000000007e121 or -1.00000000000000007e70 < (*.f64 (*.f64 x 9) y) < 2e13

   1. Initial program 81.4%

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

      1. associate-/r* 83.5%

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

      2. associate-+l- 83.5%

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

      3. associate-*r* 83.5%

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

      4. associate-*r* 84.8%

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

      5. div-inv 84.7%

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

      6. associate--r- 84.7%

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

      7. fma-neg 84.7%

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

      8. associate-*r* 83.5%

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

      9. distribute-rgt-neg-in 83.5%

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

      10. associate-*l* 83.5%

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

   3. Applied egg-rr 83.5%

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

   4. Taylor expanded in x around 0 91.0%

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

   5. Taylor expanded in x around 0 84.9%

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

   if -2.00000000000000007e121 < (*.f64 (*.f64 x 9) y) < -1.00000000000000007e70

   1. Initial program 99.4%

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

      1. associate-/r* 99.5%

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

      2. associate-+l- 99.5%

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

      3. associate-*r* 99.5%

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

      4. associate-*r* 99.4%

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

      5. div-inv 99.7%

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

      6. associate--r- 99.7%

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

      7. fma-neg 99.7%

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

      8. associate-*r* 99.5%

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

      9. distribute-rgt-neg-in 99.5%

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

      10. associate-*l* 99.5%

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

   3. Applied egg-rr 99.5%

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

   4. Taylor expanded in x around 0 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 b around 0 99.7%

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

   if 2e13 < (*.f64 (*.f64 x 9) y) < 2.0000000000000001e281

   1. Initial program 93.7%

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

   2. Taylor expanded in z around 0 85.0%

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

   if 2.0000000000000001e281 < (*.f64 (*.f64 x 9) y)

   1. Initial program 54.0%

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

   2. Taylor expanded in x around inf 58.1%

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

      1. associate-*r/ 54.0%

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

      2. associate-*r* 54.0%

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

      3. *-commutative 54.0%

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

      4. associate-*r* 54.0%

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

      5. *-commutative 54.0%

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

   4. Simplified 54.0%

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

      1. associate-*r* 54.0%

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

      2. times-frac 87.5%

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

   6. Applied egg-rr 87.5%

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

4. Final simplification 85.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \left(x \cdot 9\right) \leq -5 \cdot 10^{+145}:\\ \;\;\;\;x \cdot \left(\frac{y}{c} \cdot \frac{9}{z}\right)\\ \mathbf{elif}\;y \cdot \left(x \cdot 9\right) \leq -2 \cdot 10^{+121}:\\ \;\;\;\;\frac{-4 \cdot \left(t \cdot a\right) + \frac{b}{z}}{c}\\ \mathbf{elif}\;y \cdot \left(x \cdot 9\right) \leq -1 \cdot 10^{+70}:\\ \;\;\;\;\frac{-4 \cdot \left(t \cdot a\right) + 9 \cdot \frac{x \cdot y}{z}}{c}\\ \mathbf{elif}\;y \cdot \left(x \cdot 9\right) \leq 20000000000000:\\ \;\;\;\;\frac{-4 \cdot \left(t \cdot a\right) + \frac{b}{z}}{c}\\ \mathbf{elif}\;y \cdot \left(x \cdot 9\right) \leq 2 \cdot 10^{+281}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{c} \cdot \frac{x \cdot 9}{z}\\ \end{array} \]

Alternative 5: 54.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} t_1 := \left(a \cdot -4\right) \cdot \frac{1}{\frac{c}{t}}\\ t_2 := y \cdot \left(x \cdot 9\right)\\ \mathbf{if}\;t_2 \leq -5 \cdot 10^{-12}:\\ \;\;\;\;\frac{y}{c} \cdot \frac{x \cdot 9}{z}\\ \mathbf{elif}\;t_2 \leq -4 \cdot 10^{-223}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_2 \leq 10^{-124}:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \mathbf{elif}\;t_2 \leq 2 \cdot 10^{+17}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{c} \cdot \frac{9}{z}\right)\\ \end{array} \end{array} \]

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 (* (* a -4.0) (/ 1.0 (/ c t)))) (t_2 (* y (* x 9.0))))
   (if (<= t_2 -5e-12)
     (* (/ y c) (/ (* x 9.0) z))
     (if (<= t_2 -4e-223)
       t_1
       (if (<= t_2 1e-124)
         (/ b (* c z))
         (if (<= t_2 2e+17) t_1 (* x (* (/ y c) (/ 9.0 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 = (a * -4.0) * (1.0 / (c / t));
	double t_2 = y * (x * 9.0);
	double tmp;
	if (t_2 <= -5e-12) {
		tmp = (y / c) * ((x * 9.0) / z);
	} else if (t_2 <= -4e-223) {
		tmp = t_1;
	} else if (t_2 <= 1e-124) {
		tmp = b / (c * z);
	} else if (t_2 <= 2e+17) {
		tmp = t_1;
	} else {
		tmp = x * ((y / c) * (9.0 / 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) :: t_2
    real(8) :: tmp
    t_1 = (a * (-4.0d0)) * (1.0d0 / (c / t))
    t_2 = y * (x * 9.0d0)
    if (t_2 <= (-5d-12)) then
        tmp = (y / c) * ((x * 9.0d0) / z)
    else if (t_2 <= (-4d-223)) then
        tmp = t_1
    else if (t_2 <= 1d-124) then
        tmp = b / (c * z)
    else if (t_2 <= 2d+17) then
        tmp = t_1
    else
        tmp = x * ((y / c) * (9.0d0 / 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 = (a * -4.0) * (1.0 / (c / t));
	double t_2 = y * (x * 9.0);
	double tmp;
	if (t_2 <= -5e-12) {
		tmp = (y / c) * ((x * 9.0) / z);
	} else if (t_2 <= -4e-223) {
		tmp = t_1;
	} else if (t_2 <= 1e-124) {
		tmp = b / (c * z);
	} else if (t_2 <= 2e+17) {
		tmp = t_1;
	} else {
		tmp = x * ((y / c) * (9.0 / 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 = (a * -4.0) * (1.0 / (c / t))
	t_2 = y * (x * 9.0)
	tmp = 0
	if t_2 <= -5e-12:
		tmp = (y / c) * ((x * 9.0) / z)
	elif t_2 <= -4e-223:
		tmp = t_1
	elif t_2 <= 1e-124:
		tmp = b / (c * z)
	elif t_2 <= 2e+17:
		tmp = t_1
	else:
		tmp = x * ((y / c) * (9.0 / 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(Float64(a * -4.0) * Float64(1.0 / Float64(c / t)))
	t_2 = Float64(y * Float64(x * 9.0))
	tmp = 0.0
	if (t_2 <= -5e-12)
		tmp = Float64(Float64(y / c) * Float64(Float64(x * 9.0) / z));
	elseif (t_2 <= -4e-223)
		tmp = t_1;
	elseif (t_2 <= 1e-124)
		tmp = Float64(b / Float64(c * z));
	elseif (t_2 <= 2e+17)
		tmp = t_1;
	else
		tmp = Float64(x * Float64(Float64(y / c) * Float64(9.0 / 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 = (a * -4.0) * (1.0 / (c / t));
	t_2 = y * (x * 9.0);
	tmp = 0.0;
	if (t_2 <= -5e-12)
		tmp = (y / c) * ((x * 9.0) / z);
	elseif (t_2 <= -4e-223)
		tmp = t_1;
	elseif (t_2 <= 1e-124)
		tmp = b / (c * z);
	elseif (t_2 <= 2e+17)
		tmp = t_1;
	else
		tmp = x * ((y / c) * (9.0 / 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[(N[(a * -4.0), $MachinePrecision] * N[(1.0 / N[(c / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(x * 9.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -5e-12], N[(N[(y / c), $MachinePrecision] * N[(N[(x * 9.0), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, -4e-223], t$95$1, If[LessEqual[t$95$2, 1e-124], N[(b / N[(c * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 2e+17], t$95$1, N[(x * N[(N[(y / c), $MachinePrecision] * N[(9.0 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 (*.f64 x 9) y) < -4.9999999999999997e-12

   1. Initial program 84.9%

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

   2. Taylor expanded in x around inf 64.0%

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

      1. associate-*r/ 63.9%

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

      2. associate-*r* 64.0%

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

      3. *-commutative 64.0%

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

      4. associate-*r* 63.9%

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

      5. *-commutative 63.9%

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

   4. Simplified 63.9%

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

      1. associate-*r* 64.0%

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

      2. times-frac 65.7%

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

   6. Applied egg-rr 65.7%

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

   if -4.9999999999999997e-12 < (*.f64 (*.f64 x 9) y) < -3.9999999999999999e-223 or 9.99999999999999933e-125 < (*.f64 (*.f64 x 9) y) < 2e17

   1. Initial program 78.8%

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

   2. Taylor expanded in z around inf 54.6%

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

      1. associate-/l* 62.8%

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

      2. associate-*r/ 62.8%

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

      3. *-commutative 62.8%

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

   4. Simplified 62.8%

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

      1. div-inv 62.8%

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

      2. *-commutative 62.8%

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

   6. Applied egg-rr 62.8%

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

   if -3.9999999999999999e-223 < (*.f64 (*.f64 x 9) y) < 9.99999999999999933e-125

   1. Initial program 87.5%

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

   2. Taylor expanded in b around inf 65.7%

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

      1. *-commutative 65.7%

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

   4. Simplified 65.7%

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

   if 2e17 < (*.f64 (*.f64 x 9) y)

   1. Initial program 77.6%

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

      1. div-inv 77.6%

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

      2. sub-neg 77.6%

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

      3. associate-*r* 77.6%

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

      4. fma-def 77.6%

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

      5. distribute-rgt-neg-in 77.6%

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

      6. associate-*l* 77.6%

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

   3. Applied egg-rr 77.6%

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

   4. Taylor expanded in x around inf 62.0%

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

      1. *-commutative 62.0%

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

      2. associate-/l* 70.3%

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

      3. *-commutative 70.3%

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

      4. associate-*l/ 70.4%

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

      5. associate-*r/ 68.7%

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

      6. associate-/l* 68.8%

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

      7. *-commutative 68.8%

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

      8. *-commutative 68.8%

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

      9. times-frac 65.5%

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

   6. Simplified 65.5%

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

4. Final simplification 64.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \left(x \cdot 9\right) \leq -5 \cdot 10^{-12}:\\ \;\;\;\;\frac{y}{c} \cdot \frac{x \cdot 9}{z}\\ \mathbf{elif}\;y \cdot \left(x \cdot 9\right) \leq -4 \cdot 10^{-223}:\\ \;\;\;\;\left(a \cdot -4\right) \cdot \frac{1}{\frac{c}{t}}\\ \mathbf{elif}\;y \cdot \left(x \cdot 9\right) \leq 10^{-124}:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \mathbf{elif}\;y \cdot \left(x \cdot 9\right) \leq 2 \cdot 10^{+17}:\\ \;\;\;\;\left(a \cdot -4\right) \cdot \frac{1}{\frac{c}{t}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{c} \cdot \frac{9}{z}\right)\\ \end{array} \]

Alternative 6: 87.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} t_1 := t \cdot \frac{a}{\frac{c}{-4}} + \frac{\frac{b}{c} - \frac{x \cdot \left(y \cdot -9\right)}{c}}{z}\\ \mathbf{if}\;c \leq -2.9 \cdot 10^{-37}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 1.75 \cdot 10^{+83}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{c \cdot z}\\ \mathbf{elif}\;c \leq 2.2 \cdot 10^{+175}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}} + \frac{y}{z} \cdot \left(9 \cdot \frac{x}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1
         (+ (* t (/ a (/ c -4.0))) (/ (- (/ b c) (/ (* x (* y -9.0)) c)) z))))
   (if (<= c -2.9e-37)
     t_1
     (if (<= c 1.75e+83)
       (/ (+ b (- (* y (* x 9.0)) (* a (* t (* z 4.0))))) (* c z))
       (if (<= c 2.2e+175)
         (+ (* -4.0 (/ a (/ c t))) (* (/ y z) (* 9.0 (/ x c))))
         t_1)))))

C

assert(x < y);
assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (t * (a / (c / -4.0))) + (((b / c) - ((x * (y * -9.0)) / c)) / z);
	double tmp;
	if (c <= -2.9e-37) {
		tmp = t_1;
	} else if (c <= 1.75e+83) {
		tmp = (b + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (c * z);
	} else if (c <= 2.2e+175) {
		tmp = (-4.0 * (a / (c / t))) + ((y / z) * (9.0 * (x / c)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (t * (a / (c / (-4.0d0)))) + (((b / c) - ((x * (y * (-9.0d0))) / c)) / z)
    if (c <= (-2.9d-37)) then
        tmp = t_1
    else if (c <= 1.75d+83) then
        tmp = (b + ((y * (x * 9.0d0)) - (a * (t * (z * 4.0d0))))) / (c * z)
    else if (c <= 2.2d+175) then
        tmp = ((-4.0d0) * (a / (c / t))) + ((y / z) * (9.0d0 * (x / c)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y;
assert t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (t * (a / (c / -4.0))) + (((b / c) - ((x * (y * -9.0)) / c)) / z);
	double tmp;
	if (c <= -2.9e-37) {
		tmp = t_1;
	} else if (c <= 1.75e+83) {
		tmp = (b + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (c * z);
	} else if (c <= 2.2e+175) {
		tmp = (-4.0 * (a / (c / t))) + ((y / z) * (9.0 * (x / c)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	t_1 = (t * (a / (c / -4.0))) + (((b / c) - ((x * (y * -9.0)) / c)) / z)
	tmp = 0
	if c <= -2.9e-37:
		tmp = t_1
	elif c <= 1.75e+83:
		tmp = (b + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (c * z)
	elif c <= 2.2e+175:
		tmp = (-4.0 * (a / (c / t))) + ((y / z) * (9.0 * (x / c)))
	else:
		tmp = t_1
	return tmp

Julia

x, y = sort([x, y])
t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(t * Float64(a / Float64(c / -4.0))) + Float64(Float64(Float64(b / c) - Float64(Float64(x * Float64(y * -9.0)) / c)) / z))
	tmp = 0.0
	if (c <= -2.9e-37)
		tmp = t_1;
	elseif (c <= 1.75e+83)
		tmp = Float64(Float64(b + Float64(Float64(y * Float64(x * 9.0)) - Float64(a * Float64(t * Float64(z * 4.0))))) / Float64(c * z));
	elseif (c <= 2.2e+175)
		tmp = Float64(Float64(-4.0 * Float64(a / Float64(c / t))) + Float64(Float64(y / z) * Float64(9.0 * Float64(x / c))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (t * (a / (c / -4.0))) + (((b / c) - ((x * (y * -9.0)) / c)) / z);
	tmp = 0.0;
	if (c <= -2.9e-37)
		tmp = t_1;
	elseif (c <= 1.75e+83)
		tmp = (b + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (c * z);
	elseif (c <= 2.2e+175)
		tmp = (-4.0 * (a / (c / t))) + ((y / z) * (9.0 * (x / c)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(t * N[(a / N[(c / -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(b / c), $MachinePrecision] - N[(N[(x * N[(y * -9.0), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -2.9e-37], t$95$1, If[LessEqual[c, 1.75e+83], N[(N[(b + N[(N[(y * N[(x * 9.0), $MachinePrecision]), $MachinePrecision] - N[(a * N[(t * N[(z * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(c * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 2.2e+175], N[(N[(-4.0 * N[(a / N[(c / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(y / z), $MachinePrecision] * N[(9.0 * N[(x / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if c < -2.90000000000000005e-37 or 2.1999999999999999e175 < c

   1. Initial program 74.7%

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

      1. associate-/r* 67.2%

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

      2. associate-+l- 67.2%

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

      3. associate-*r* 67.2%

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

      4. associate-*r* 68.2%

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

      5. div-inv 68.2%

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

      6. associate--r- 68.2%

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

      7. fma-neg 68.2%

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

      8. associate-*r* 67.2%

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

      9. distribute-rgt-neg-in 67.2%

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

      10. associate-*l* 67.2%

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

   3. Applied egg-rr 67.2%

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

   4. Taylor expanded in x around 0 77.9%

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

   5. Taylor expanded in z around -inf 88.8%

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

      1. fma-def 88.8%

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

      2. mul-1-neg 88.8%

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

      3. fma-neg 88.8%

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

      4. associate-*r/ 88.8%

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

      5. associate-*r* 88.8%

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

      6. associate-*l/ 91.8%

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

      7. *-commutative 91.8%

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

      8. *-commutative 91.8%

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

      9. associate-/l* 91.8%

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

      10. mul-1-neg 91.8%

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

      11. unsub-neg 91.8%

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

      12. associate-*r/ 91.8%

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

      13. *-commutative 91.8%

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

      14. associate-*l* 91.7%

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

   7. Simplified 91.7%

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

   if -2.90000000000000005e-37 < c < 1.74999999999999989e83

   1. Initial program 93.5%

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

   if 1.74999999999999989e83 < c < 2.1999999999999999e175

   1. Initial program 44.8%

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

      1. associate-/r* 55.0%

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

      2. associate-+l- 55.0%

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

      3. associate-*r* 55.1%

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

      4. associate-*r* 55.1%

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

      5. div-inv 55.1%

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

      6. associate--r- 55.1%

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

      7. fma-neg 55.1%

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

      8. associate-*r* 55.1%

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

      9. distribute-rgt-neg-in 55.1%

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

      10. associate-*l* 55.1%

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

   3. Applied egg-rr 55.1%

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

   4. Taylor expanded in x around 0 59.5%

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

   5. Taylor expanded in z around -inf 59.5%

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

      1. fma-def 59.5%

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

      2. mul-1-neg 59.5%

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

      3. fma-neg 59.5%

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

      4. associate-*r/ 59.5%

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

      5. associate-*r* 59.5%

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

      6. associate-*l/ 68.1%

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

      7. *-commutative 68.1%

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

      8. *-commutative 68.1%

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

      9. associate-/l* 68.1%

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

      10. mul-1-neg 68.1%

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

      11. unsub-neg 68.1%

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

      12. associate-*r/ 63.6%

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

      13. *-commutative 63.6%

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

      14. associate-*l* 63.7%

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

   7. Simplified 63.7%

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

   8. Taylor expanded in b around 0 54.4%

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

      1. cancel-sign-sub-inv 54.4%

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

      2. metadata-eval 54.4%

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

      3. associate-/l* 63.0%

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

      4. times-frac 90.5%

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

      5. associate-*r* 90.7%

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

   10. Simplified 90.7%

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

4. Final simplification 92.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -2.9 \cdot 10^{-37}:\\ \;\;\;\;t \cdot \frac{a}{\frac{c}{-4}} + \frac{\frac{b}{c} - \frac{x \cdot \left(y \cdot -9\right)}{c}}{z}\\ \mathbf{elif}\;c \leq 1.75 \cdot 10^{+83}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{c \cdot z}\\ \mathbf{elif}\;c \leq 2.2 \cdot 10^{+175}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}} + \frac{y}{z} \cdot \left(9 \cdot \frac{x}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{a}{\frac{c}{-4}} + \frac{\frac{b}{c} - \frac{x \cdot \left(y \cdot -9\right)}{c}}{z}\\ \end{array} \]

Alternative 7: 91.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{+29} \lor \neg \left(z \leq 3.2 \cdot 10^{-73}\right):\\ \;\;\;\;\frac{1}{c} \cdot \left(-4 \cdot \left(t \cdot a\right) + \left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{c \cdot z}\\ \end{array} \end{array} \]

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 -5e+29) (not (<= z 3.2e-73)))
   (* (/ 1.0 c) (+ (* -4.0 (* t a)) (+ (* 9.0 (/ (* x y) z)) (/ b z))))
   (/ (+ b (- (* y (* x 9.0)) (* a (* t (* z 4.0))))) (* 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) {
	double tmp;
	if ((z <= -5e+29) || !(z <= 3.2e-73)) {
		tmp = (1.0 / c) * ((-4.0 * (t * a)) + ((9.0 * ((x * y) / z)) + (b / z)));
	} else {
		tmp = (b + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (c * 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) :: tmp
    if ((z <= (-5d+29)) .or. (.not. (z <= 3.2d-73))) then
        tmp = (1.0d0 / c) * (((-4.0d0) * (t * a)) + ((9.0d0 * ((x * y) / z)) + (b / z)))
    else
        tmp = (b + ((y * (x * 9.0d0)) - (a * (t * (z * 4.0d0))))) / (c * 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 tmp;
	if ((z <= -5e+29) || !(z <= 3.2e-73)) {
		tmp = (1.0 / c) * ((-4.0 * (t * a)) + ((9.0 * ((x * y) / z)) + (b / z)));
	} else {
		tmp = (b + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (c * z);
	}
	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 <= -5e+29) or not (z <= 3.2e-73):
		tmp = (1.0 / c) * ((-4.0 * (t * a)) + ((9.0 * ((x * y) / z)) + (b / z)))
	else:
		tmp = (b + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (c * 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 <= -5e+29) || !(z <= 3.2e-73))
		tmp = Float64(Float64(1.0 / c) * Float64(Float64(-4.0 * Float64(t * a)) + Float64(Float64(9.0 * Float64(Float64(x * y) / z)) + Float64(b / z))));
	else
		tmp = Float64(Float64(b + Float64(Float64(y * Float64(x * 9.0)) - Float64(a * Float64(t * Float64(z * 4.0))))) / Float64(c * 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)
	tmp = 0.0;
	if ((z <= -5e+29) || ~((z <= 3.2e-73)))
		tmp = (1.0 / c) * ((-4.0 * (t * a)) + ((9.0 * ((x * y) / z)) + (b / z)));
	else
		tmp = (b + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (c * 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_] := If[Or[LessEqual[z, -5e+29], N[Not[LessEqual[z, 3.2e-73]], $MachinePrecision]], N[(N[(1.0 / c), $MachinePrecision] * N[(N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision] + N[(N[(9.0 * N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] + N[(b / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b + N[(N[(y * N[(x * 9.0), $MachinePrecision]), $MachinePrecision] - N[(a * N[(t * N[(z * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(c * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.0000000000000001e29 or 3.19999999999999986e-73 < z

   1. Initial program 71.1%

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

      1. associate-/r* 76.4%

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

      2. associate-+l- 76.4%

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

      3. associate-*r* 76.4%

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

      4. associate-*r* 78.5%

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

      5. div-inv 78.5%

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

      6. associate--r- 78.5%

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

      7. fma-neg 78.5%

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

      8. associate-*r* 76.4%

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

      9. distribute-rgt-neg-in 76.4%

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

      10. associate-*l* 76.4%

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

   3. Applied egg-rr 76.4%

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

   4. Taylor expanded in x around 0 87.0%

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

   if -5.0000000000000001e29 < z < 3.19999999999999986e-73

   1. Initial program 94.9%

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

4. Final simplification 90.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{+29} \lor \neg \left(z \leq 3.2 \cdot 10^{-73}\right):\\ \;\;\;\;\frac{1}{c} \cdot \left(-4 \cdot \left(t \cdot a\right) + \left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{c \cdot z}\\ \end{array} \]

Alternative 8: 83.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq 1.4 \cdot 10^{+179}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}} + \frac{y}{z} \cdot \left(9 \cdot \frac{x}{c}\right)\\ \end{array} \end{array} \]

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 (<= z 1.4e+179)
   (/ (+ b (- (* y (* x 9.0)) (* a (* t (* z 4.0))))) (* c z))
   (+ (* -4.0 (/ a (/ c t))) (* (/ y z) (* 9.0 (/ x 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 <= 1.4e+179) {
		tmp = (b + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (c * z);
	} else {
		tmp = (-4.0 * (a / (c / t))) + ((y / z) * (9.0 * (x / 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 <= 1.4d+179) then
        tmp = (b + ((y * (x * 9.0d0)) - (a * (t * (z * 4.0d0))))) / (c * z)
    else
        tmp = ((-4.0d0) * (a / (c / t))) + ((y / z) * (9.0d0 * (x / 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 <= 1.4e+179) {
		tmp = (b + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (c * z);
	} else {
		tmp = (-4.0 * (a / (c / t))) + ((y / z) * (9.0 * (x / 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 <= 1.4e+179:
		tmp = (b + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (c * z)
	else:
		tmp = (-4.0 * (a / (c / t))) + ((y / z) * (9.0 * (x / 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 <= 1.4e+179)
		tmp = Float64(Float64(b + Float64(Float64(y * Float64(x * 9.0)) - Float64(a * Float64(t * Float64(z * 4.0))))) / Float64(c * z));
	else
		tmp = Float64(Float64(-4.0 * Float64(a / Float64(c / t))) + Float64(Float64(y / z) * Float64(9.0 * Float64(x / 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 <= 1.4e+179)
		tmp = (b + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (c * z);
	else
		tmp = (-4.0 * (a / (c / t))) + ((y / z) * (9.0 * (x / c)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[z, 1.4e+179], N[(N[(b + N[(N[(y * N[(x * 9.0), $MachinePrecision]), $MachinePrecision] - N[(a * N[(t * N[(z * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(c * z), $MachinePrecision]), $MachinePrecision], N[(N[(-4.0 * N[(a / N[(c / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(y / z), $MachinePrecision] * N[(9.0 * N[(x / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 1.4e179

   1. Initial program 87.4%

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

   if 1.4e179 < z

   1. Initial program 41.1%

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

      1. associate-/r* 52.0%

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

      2. associate-+l- 52.0%

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

      3. associate-*r* 52.0%

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

      4. associate-*r* 51.9%

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

      5. div-inv 52.0%

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

      6. associate--r- 52.0%

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

      7. fma-neg 52.0%

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

      8. associate-*r* 52.1%

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

      9. distribute-rgt-neg-in 52.1%

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

      10. associate-*l* 52.1%

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

   3. Applied egg-rr 52.1%

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

   4. Taylor expanded in x around 0 79.3%

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

   5. Taylor expanded in z around -inf 75.6%

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

      1. fma-def 75.6%

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

      2. mul-1-neg 75.6%

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

      3. fma-neg 75.6%

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

      4. associate-*r/ 75.6%

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

      5. associate-*r* 75.6%

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

      6. associate-*l/ 75.7%

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

      7. *-commutative 75.7%

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

      8. *-commutative 75.7%

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

      9. associate-/l* 75.7%

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

      10. mul-1-neg 75.7%

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

      11. unsub-neg 75.7%

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

      12. associate-*r/ 75.7%

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

      13. *-commutative 75.7%

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

      14. associate-*l* 75.6%

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

   7. Simplified 75.6%

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

   8. Taylor expanded in b around 0 78.8%

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

      1. cancel-sign-sub-inv 78.8%

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

      2. metadata-eval 78.8%

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

      3. associate-/l* 65.8%

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

      4. times-frac 79.6%

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

      5. associate-*r* 79.6%

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

   10. Simplified 79.6%

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

4. Final simplification 86.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 1.4 \cdot 10^{+179}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}} + \frac{y}{z} \cdot \left(9 \cdot \frac{x}{c}\right)\\ \end{array} \]

Alternative 9: 68.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} t_1 := \frac{b + 9 \cdot \left(x \cdot y\right)}{c \cdot z}\\ t_2 := t \cdot \frac{a \cdot -4}{c}\\ \mathbf{if}\;a \leq -3.3 \cdot 10^{+37}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 5 \cdot 10^{+170}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.75 \cdot 10^{+182}:\\ \;\;\;\;-4 \cdot \frac{t \cdot a}{c}\\ \mathbf{elif}\;a \leq 1.4 \cdot 10^{+192}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (+ b (* 9.0 (* x y))) (* c z))) (t_2 (* t (/ (* a -4.0) c))))
   (if (<= a -3.3e+37)
     t_2
     (if (<= a 5e+170)
       t_1
       (if (<= a 1.75e+182)
         (* -4.0 (/ (* t a) c))
         (if (<= a 1.4e+192) t_1 t_2))))))

C

assert(x < y);
assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (b + (9.0 * (x * y))) / (c * z);
	double t_2 = t * ((a * -4.0) / c);
	double tmp;
	if (a <= -3.3e+37) {
		tmp = t_2;
	} else if (a <= 5e+170) {
		tmp = t_1;
	} else if (a <= 1.75e+182) {
		tmp = -4.0 * ((t * a) / c);
	} else if (a <= 1.4e+192) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (b + (9.0d0 * (x * y))) / (c * z)
    t_2 = t * ((a * (-4.0d0)) / c)
    if (a <= (-3.3d+37)) then
        tmp = t_2
    else if (a <= 5d+170) then
        tmp = t_1
    else if (a <= 1.75d+182) then
        tmp = (-4.0d0) * ((t * a) / c)
    else if (a <= 1.4d+192) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

assert x < y;
assert t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (b + (9.0 * (x * y))) / (c * z);
	double t_2 = t * ((a * -4.0) / c);
	double tmp;
	if (a <= -3.3e+37) {
		tmp = t_2;
	} else if (a <= 5e+170) {
		tmp = t_1;
	} else if (a <= 1.75e+182) {
		tmp = -4.0 * ((t * a) / c);
	} else if (a <= 1.4e+192) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	t_1 = (b + (9.0 * (x * y))) / (c * z)
	t_2 = t * ((a * -4.0) / c)
	tmp = 0
	if a <= -3.3e+37:
		tmp = t_2
	elif a <= 5e+170:
		tmp = t_1
	elif a <= 1.75e+182:
		tmp = -4.0 * ((t * a) / c)
	elif a <= 1.4e+192:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

x, y = sort([x, y])
t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(b + Float64(9.0 * Float64(x * y))) / Float64(c * z))
	t_2 = Float64(t * Float64(Float64(a * -4.0) / c))
	tmp = 0.0
	if (a <= -3.3e+37)
		tmp = t_2;
	elseif (a <= 5e+170)
		tmp = t_1;
	elseif (a <= 1.75e+182)
		tmp = Float64(-4.0 * Float64(Float64(t * a) / c));
	elseif (a <= 1.4e+192)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (b + (9.0 * (x * y))) / (c * z);
	t_2 = t * ((a * -4.0) / c);
	tmp = 0.0;
	if (a <= -3.3e+37)
		tmp = t_2;
	elseif (a <= 5e+170)
		tmp = t_1;
	elseif (a <= 1.75e+182)
		tmp = -4.0 * ((t * a) / c);
	elseif (a <= 1.4e+192)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(b + N[(9.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(c * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(N[(a * -4.0), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -3.3e+37], t$95$2, If[LessEqual[a, 5e+170], t$95$1, If[LessEqual[a, 1.75e+182], N[(-4.0 * N[(N[(t * a), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.4e+192], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -3.3000000000000001e37 or 1.39999999999999988e192 < a

   1. Initial program 81.2%

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

   2. Taylor expanded in z around inf 57.3%

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

      1. associate-/l* 65.0%

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

      2. associate-*r/ 65.0%

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

      3. *-commutative 65.0%

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

   4. Simplified 65.0%

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

      1. associate-/r/ 68.9%

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

      2. *-commutative 68.9%

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

   6. Applied egg-rr 68.9%

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

   if -3.3000000000000001e37 < a < 4.99999999999999977e170 or 1.75000000000000011e182 < a < 1.39999999999999988e192

   1. Initial program 83.5%

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

   2. Taylor expanded in z around 0 71.5%

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

   if 4.99999999999999977e170 < a < 1.75000000000000011e182

   1. Initial program 60.0%

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

   2. Taylor expanded in z around inf 99.7%

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

4. Final simplification 71.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.3 \cdot 10^{+37}:\\ \;\;\;\;t \cdot \frac{a \cdot -4}{c}\\ \mathbf{elif}\;a \leq 5 \cdot 10^{+170}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{c \cdot z}\\ \mathbf{elif}\;a \leq 1.75 \cdot 10^{+182}:\\ \;\;\;\;-4 \cdot \frac{t \cdot a}{c}\\ \mathbf{elif}\;a \leq 1.4 \cdot 10^{+192}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{a \cdot -4}{c}\\ \end{array} \]

Alternative 10: 68.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} t_1 := t \cdot \frac{a \cdot -4}{c}\\ \mathbf{if}\;a \leq -3.3 \cdot 10^{+37}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2.5 \cdot 10^{+171}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{c \cdot z}\\ \mathbf{elif}\;a \leq 1.9 \cdot 10^{+182}:\\ \;\;\;\;-4 \cdot \frac{t \cdot a}{c}\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{+189}:\\ \;\;\;\;\frac{b + y \cdot \left(x \cdot 9\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* t (/ (* a -4.0) c))))
   (if (<= a -3.3e+37)
     t_1
     (if (<= a 2.5e+171)
       (/ (+ b (* 9.0 (* x y))) (* c z))
       (if (<= a 1.9e+182)
         (* -4.0 (/ (* t a) c))
         (if (<= a 1.25e+189) (/ (+ b (* y (* x 9.0))) (* c z)) t_1))))))

C

assert(x < y);
assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = t * ((a * -4.0) / c);
	double tmp;
	if (a <= -3.3e+37) {
		tmp = t_1;
	} else if (a <= 2.5e+171) {
		tmp = (b + (9.0 * (x * y))) / (c * z);
	} else if (a <= 1.9e+182) {
		tmp = -4.0 * ((t * a) / c);
	} else if (a <= 1.25e+189) {
		tmp = (b + (y * (x * 9.0))) / (c * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * ((a * (-4.0d0)) / c)
    if (a <= (-3.3d+37)) then
        tmp = t_1
    else if (a <= 2.5d+171) then
        tmp = (b + (9.0d0 * (x * y))) / (c * z)
    else if (a <= 1.9d+182) then
        tmp = (-4.0d0) * ((t * a) / c)
    else if (a <= 1.25d+189) then
        tmp = (b + (y * (x * 9.0d0))) / (c * z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y;
assert t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = t * ((a * -4.0) / c);
	double tmp;
	if (a <= -3.3e+37) {
		tmp = t_1;
	} else if (a <= 2.5e+171) {
		tmp = (b + (9.0 * (x * y))) / (c * z);
	} else if (a <= 1.9e+182) {
		tmp = -4.0 * ((t * a) / c);
	} else if (a <= 1.25e+189) {
		tmp = (b + (y * (x * 9.0))) / (c * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	t_1 = t * ((a * -4.0) / c)
	tmp = 0
	if a <= -3.3e+37:
		tmp = t_1
	elif a <= 2.5e+171:
		tmp = (b + (9.0 * (x * y))) / (c * z)
	elif a <= 1.9e+182:
		tmp = -4.0 * ((t * a) / c)
	elif a <= 1.25e+189:
		tmp = (b + (y * (x * 9.0))) / (c * z)
	else:
		tmp = t_1
	return tmp

Julia

x, y = sort([x, y])
t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(t * Float64(Float64(a * -4.0) / c))
	tmp = 0.0
	if (a <= -3.3e+37)
		tmp = t_1;
	elseif (a <= 2.5e+171)
		tmp = Float64(Float64(b + Float64(9.0 * Float64(x * y))) / Float64(c * z));
	elseif (a <= 1.9e+182)
		tmp = Float64(-4.0 * Float64(Float64(t * a) / c));
	elseif (a <= 1.25e+189)
		tmp = Float64(Float64(b + Float64(y * Float64(x * 9.0))) / Float64(c * z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = t * ((a * -4.0) / c);
	tmp = 0.0;
	if (a <= -3.3e+37)
		tmp = t_1;
	elseif (a <= 2.5e+171)
		tmp = (b + (9.0 * (x * y))) / (c * z);
	elseif (a <= 1.9e+182)
		tmp = -4.0 * ((t * a) / c);
	elseif (a <= 1.25e+189)
		tmp = (b + (y * (x * 9.0))) / (c * z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(t * N[(N[(a * -4.0), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -3.3e+37], t$95$1, If[LessEqual[a, 2.5e+171], N[(N[(b + N[(9.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(c * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.9e+182], N[(-4.0 * N[(N[(t * a), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.25e+189], N[(N[(b + N[(y * N[(x * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(c * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -3.3000000000000001e37 or 1.2500000000000001e189 < a

   1. Initial program 81.2%

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

   2. Taylor expanded in z around inf 57.3%

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

      1. associate-/l* 65.0%

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

      2. associate-*r/ 65.0%

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

      3. *-commutative 65.0%

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

   4. Simplified 65.0%

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

      1. associate-/r/ 68.9%

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

      2. *-commutative 68.9%

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

   6. Applied egg-rr 68.9%

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

   if -3.3000000000000001e37 < a < 2.5000000000000002e171

   1. Initial program 83.4%

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

   2. Taylor expanded in z around 0 71.3%

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

   if 2.5000000000000002e171 < a < 1.90000000000000006e182

   1. Initial program 60.0%

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

   2. Taylor expanded in z around inf 99.7%

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

   if 1.90000000000000006e182 < a < 1.2500000000000001e189

   1. Initial program 87.9%

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

      1. associate-/r* 99.2%

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

      2. associate-+l- 99.2%

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

      3. associate-*r* 98.8%

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

      4. associate-*r* 98.8%

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

      5. div-inv 98.8%

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

      6. associate--r- 98.8%

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

      7. fma-neg 98.8%

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

      8. associate-*r* 98.8%

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

      9. distribute-rgt-neg-in 98.8%

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

      10. associate-*l* 98.8%

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

   3. Applied egg-rr 98.8%

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

   4. Taylor expanded in x around 0 100.0%

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

   5. Taylor expanded in z around 0 87.9%

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

      1. associate-*r* 87.9%

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

      2. *-commutative 87.9%

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

      3. *-commutative 87.9%

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

      4. *-commutative 87.9%

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

      5. *-commutative 87.9%

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

   7. Simplified 87.9%

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

4. Final simplification 71.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.3 \cdot 10^{+37}:\\ \;\;\;\;t \cdot \frac{a \cdot -4}{c}\\ \mathbf{elif}\;a \leq 2.5 \cdot 10^{+171}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{c \cdot z}\\ \mathbf{elif}\;a \leq 1.9 \cdot 10^{+182}:\\ \;\;\;\;-4 \cdot \frac{t \cdot a}{c}\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{+189}:\\ \;\;\;\;\frac{b + y \cdot \left(x \cdot 9\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{a \cdot -4}{c}\\ \end{array} \]

Alternative 11: 48.7% accurate, 1.4× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} t_1 := t \cdot \frac{a \cdot -4}{c}\\ \mathbf{if}\;t \leq -3.2 \cdot 10^{+51}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -2 \cdot 10^{-99}:\\ \;\;\;\;9 \cdot \frac{x \cdot y}{c \cdot z}\\ \mathbf{elif}\;t \leq 3.7 \cdot 10^{-202}:\\ \;\;\;\;\frac{b}{c} \cdot \frac{1}{z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* t (/ (* a -4.0) c))))
   (if (<= t -3.2e+51)
     t_1
     (if (<= t -2e-99)
       (* 9.0 (/ (* x y) (* c z)))
       (if (<= t 3.7e-202) (* (/ b c) (/ 1.0 z)) t_1)))))

C

assert(x < y);
assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = t * ((a * -4.0) / c);
	double tmp;
	if (t <= -3.2e+51) {
		tmp = t_1;
	} else if (t <= -2e-99) {
		tmp = 9.0 * ((x * y) / (c * z));
	} else if (t <= 3.7e-202) {
		tmp = (b / c) * (1.0 / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * ((a * (-4.0d0)) / c)
    if (t <= (-3.2d+51)) then
        tmp = t_1
    else if (t <= (-2d-99)) then
        tmp = 9.0d0 * ((x * y) / (c * z))
    else if (t <= 3.7d-202) then
        tmp = (b / c) * (1.0d0 / z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y;
assert t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = t * ((a * -4.0) / c);
	double tmp;
	if (t <= -3.2e+51) {
		tmp = t_1;
	} else if (t <= -2e-99) {
		tmp = 9.0 * ((x * y) / (c * z));
	} else if (t <= 3.7e-202) {
		tmp = (b / c) * (1.0 / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	t_1 = t * ((a * -4.0) / c)
	tmp = 0
	if t <= -3.2e+51:
		tmp = t_1
	elif t <= -2e-99:
		tmp = 9.0 * ((x * y) / (c * z))
	elif t <= 3.7e-202:
		tmp = (b / c) * (1.0 / z)
	else:
		tmp = t_1
	return tmp

Julia

x, y = sort([x, y])
t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(t * Float64(Float64(a * -4.0) / c))
	tmp = 0.0
	if (t <= -3.2e+51)
		tmp = t_1;
	elseif (t <= -2e-99)
		tmp = Float64(9.0 * Float64(Float64(x * y) / Float64(c * z)));
	elseif (t <= 3.7e-202)
		tmp = Float64(Float64(b / c) * Float64(1.0 / z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = t * ((a * -4.0) / c);
	tmp = 0.0;
	if (t <= -3.2e+51)
		tmp = t_1;
	elseif (t <= -2e-99)
		tmp = 9.0 * ((x * y) / (c * z));
	elseif (t <= 3.7e-202)
		tmp = (b / c) * (1.0 / z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(t * N[(N[(a * -4.0), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.2e+51], t$95$1, If[LessEqual[t, -2e-99], N[(9.0 * N[(N[(x * y), $MachinePrecision] / N[(c * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.7e-202], N[(N[(b / c), $MachinePrecision] * N[(1.0 / z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.2000000000000002e51 or 3.69999999999999991e-202 < t

   1. Initial program 77.1%

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

   2. Taylor expanded in z around inf 45.7%

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

      1. associate-/l* 49.9%

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

      2. associate-*r/ 49.9%

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

      3. *-commutative 49.9%

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

   4. Simplified 49.9%

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

      1. associate-/r/ 50.2%

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

      2. *-commutative 50.2%

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

   6. Applied egg-rr 50.2%

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

   if -3.2000000000000002e51 < t < -2e-99

   1. Initial program 96.2%

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

   2. Taylor expanded in x around inf 58.7%

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

   if -2e-99 < t < 3.69999999999999991e-202

   1. Initial program 86.3%

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

   2. Taylor expanded in b around inf 49.6%

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

      1. *-commutative 49.6%

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

   4. Simplified 49.6%

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

      1. *-un-lft-identity 49.6%

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

      2. times-frac 51.7%

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

   6. Applied egg-rr 51.7%

      \[\leadsto \color{blue}{\frac{1}{z} \cdot \frac{b}{c}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 51.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.2 \cdot 10^{+51}:\\ \;\;\;\;t \cdot \frac{a \cdot -4}{c}\\ \mathbf{elif}\;t \leq -2 \cdot 10^{-99}:\\ \;\;\;\;9 \cdot \frac{x \cdot y}{c \cdot z}\\ \mathbf{elif}\;t \leq 3.7 \cdot 10^{-202}:\\ \;\;\;\;\frac{b}{c} \cdot \frac{1}{z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{a \cdot -4}{c}\\ \end{array} \]

Alternative 12: 48.7% accurate, 1.4× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} t_1 := t \cdot \frac{a \cdot -4}{c}\\ \mathbf{if}\;t \leq -1.25 \cdot 10^{+53}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -4.8 \cdot 10^{-98}:\\ \;\;\;\;\frac{x}{c} \cdot \frac{y \cdot 9}{z}\\ \mathbf{elif}\;t \leq 3.8 \cdot 10^{-202}:\\ \;\;\;\;\frac{b}{c} \cdot \frac{1}{z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* t (/ (* a -4.0) c))))
   (if (<= t -1.25e+53)
     t_1
     (if (<= t -4.8e-98)
       (* (/ x c) (/ (* y 9.0) z))
       (if (<= t 3.8e-202) (* (/ b c) (/ 1.0 z)) t_1)))))

C

assert(x < y);
assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = t * ((a * -4.0) / c);
	double tmp;
	if (t <= -1.25e+53) {
		tmp = t_1;
	} else if (t <= -4.8e-98) {
		tmp = (x / c) * ((y * 9.0) / z);
	} else if (t <= 3.8e-202) {
		tmp = (b / c) * (1.0 / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * ((a * (-4.0d0)) / c)
    if (t <= (-1.25d+53)) then
        tmp = t_1
    else if (t <= (-4.8d-98)) then
        tmp = (x / c) * ((y * 9.0d0) / z)
    else if (t <= 3.8d-202) then
        tmp = (b / c) * (1.0d0 / z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y;
assert t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = t * ((a * -4.0) / c);
	double tmp;
	if (t <= -1.25e+53) {
		tmp = t_1;
	} else if (t <= -4.8e-98) {
		tmp = (x / c) * ((y * 9.0) / z);
	} else if (t <= 3.8e-202) {
		tmp = (b / c) * (1.0 / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	t_1 = t * ((a * -4.0) / c)
	tmp = 0
	if t <= -1.25e+53:
		tmp = t_1
	elif t <= -4.8e-98:
		tmp = (x / c) * ((y * 9.0) / z)
	elif t <= 3.8e-202:
		tmp = (b / c) * (1.0 / z)
	else:
		tmp = t_1
	return tmp

Julia

x, y = sort([x, y])
t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(t * Float64(Float64(a * -4.0) / c))
	tmp = 0.0
	if (t <= -1.25e+53)
		tmp = t_1;
	elseif (t <= -4.8e-98)
		tmp = Float64(Float64(x / c) * Float64(Float64(y * 9.0) / z));
	elseif (t <= 3.8e-202)
		tmp = Float64(Float64(b / c) * Float64(1.0 / z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = t * ((a * -4.0) / c);
	tmp = 0.0;
	if (t <= -1.25e+53)
		tmp = t_1;
	elseif (t <= -4.8e-98)
		tmp = (x / c) * ((y * 9.0) / z);
	elseif (t <= 3.8e-202)
		tmp = (b / c) * (1.0 / z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(t * N[(N[(a * -4.0), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.25e+53], t$95$1, If[LessEqual[t, -4.8e-98], N[(N[(x / c), $MachinePrecision] * N[(N[(y * 9.0), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.8e-202], N[(N[(b / c), $MachinePrecision] * N[(1.0 / z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.2500000000000001e53 or 3.80000000000000014e-202 < t

   1. Initial program 77.1%

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

   2. Taylor expanded in z around inf 45.7%

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

      1. associate-/l* 49.9%

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

      2. associate-*r/ 49.9%

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

      3. *-commutative 49.9%

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

   4. Simplified 49.9%

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

      1. associate-/r/ 50.2%

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

      2. *-commutative 50.2%

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

   6. Applied egg-rr 50.2%

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

   if -1.2500000000000001e53 < t < -4.8000000000000001e-98

   1. Initial program 96.2%

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

   2. Taylor expanded in x around inf 58.7%

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

      1. associate-*r/ 58.7%

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

      2. associate-*r* 58.6%

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

      3. *-commutative 58.6%

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

      4. associate-*r* 58.6%

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

      5. *-commutative 58.6%

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

   4. Simplified 58.6%

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

      1. *-commutative 58.6%

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

      2. times-frac 49.9%

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

   6. Applied egg-rr 49.9%

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

   if -4.8000000000000001e-98 < t < 3.80000000000000014e-202

   1. Initial program 86.3%

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

   2. Taylor expanded in b around inf 49.6%

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

      1. *-commutative 49.6%

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

   4. Simplified 49.6%

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

      1. *-un-lft-identity 49.6%

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

      2. times-frac 51.7%

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

   6. Applied egg-rr 51.7%

      \[\leadsto \color{blue}{\frac{1}{z} \cdot \frac{b}{c}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 50.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.25 \cdot 10^{+53}:\\ \;\;\;\;t \cdot \frac{a \cdot -4}{c}\\ \mathbf{elif}\;t \leq -4.8 \cdot 10^{-98}:\\ \;\;\;\;\frac{x}{c} \cdot \frac{y \cdot 9}{z}\\ \mathbf{elif}\;t \leq 3.8 \cdot 10^{-202}:\\ \;\;\;\;\frac{b}{c} \cdot \frac{1}{z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{a \cdot -4}{c}\\ \end{array} \]

Alternative 13: 46.8% accurate, 1.7× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq -5.8 \cdot 10^{-69} \lor \neg \left(a \leq 4.6 \cdot 10^{+115}\right):\\ \;\;\;\;-4 \cdot \frac{t \cdot a}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= a -5.8e-69) (not (<= a 4.6e+115)))
   (* -4.0 (/ (* t a) c))
   (/ (/ b z) c)))

C

assert(x < y);
assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((a <= -5.8e-69) || !(a <= 4.6e+115)) {
		tmp = -4.0 * ((t * a) / c);
	} else {
		tmp = (b / z) / c;
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if ((a <= (-5.8d-69)) .or. (.not. (a <= 4.6d+115))) then
        tmp = (-4.0d0) * ((t * a) / c)
    else
        tmp = (b / z) / c
    end if
    code = tmp
end function

Java

assert x < y;
assert t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((a <= -5.8e-69) || !(a <= 4.6e+115)) {
		tmp = -4.0 * ((t * a) / c);
	} else {
		tmp = (b / z) / c;
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if (a <= -5.8e-69) or not (a <= 4.6e+115):
		tmp = -4.0 * ((t * a) / c)
	else:
		tmp = (b / z) / c
	return tmp

Julia

x, y = sort([x, y])
t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((a <= -5.8e-69) || !(a <= 4.6e+115))
		tmp = Float64(-4.0 * Float64(Float64(t * a) / c));
	else
		tmp = Float64(Float64(b / z) / c);
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((a <= -5.8e-69) || ~((a <= 4.6e+115)))
		tmp = -4.0 * ((t * a) / c);
	else
		tmp = (b / z) / c;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[a, -5.8e-69], N[Not[LessEqual[a, 4.6e+115]], $MachinePrecision]], N[(-4.0 * N[(N[(t * a), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision], N[(N[(b / z), $MachinePrecision] / c), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -5.7999999999999997e-69 or 4.60000000000000007e115 < a

   1. Initial program 79.8%

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

   2. Taylor expanded in z around inf 50.1%

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

   if -5.7999999999999997e-69 < a < 4.60000000000000007e115

   1. Initial program 84.9%

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

      1. associate-/r* 82.2%

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

      2. associate-+l- 82.2%

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

      3. associate-*r* 82.2%

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

      4. associate-*r* 84.4%

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

      5. div-inv 84.3%

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

      6. associate--r- 84.3%

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

      7. fma-neg 84.3%

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

      8. associate-*r* 82.1%

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

      9. distribute-rgt-neg-in 82.1%

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

      10. associate-*l* 82.1%

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

   3. Applied egg-rr 82.1%

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

   4. Taylor expanded in x around 0 84.2%

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

   5. Taylor expanded in b around inf 44.5%

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

      1. associate-/l/ 43.7%

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

   7. Simplified 43.7%

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

4. Final simplification 46.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.8 \cdot 10^{-69} \lor \neg \left(a \leq 4.6 \cdot 10^{+115}\right):\\ \;\;\;\;-4 \cdot \frac{t \cdot a}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \end{array} \]

Alternative 14: 49.4% accurate, 1.7× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq -1.95 \cdot 10^{-69} \lor \neg \left(a \leq 4.6 \cdot 10^{+115}\right):\\ \;\;\;\;t \cdot \frac{a \cdot -4}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= a -1.95e-69) (not (<= a 4.6e+115)))
   (* t (/ (* a -4.0) c))
   (/ (/ b z) c)))

C

assert(x < y);
assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((a <= -1.95e-69) || !(a <= 4.6e+115)) {
		tmp = t * ((a * -4.0) / c);
	} else {
		tmp = (b / z) / c;
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if ((a <= (-1.95d-69)) .or. (.not. (a <= 4.6d+115))) then
        tmp = t * ((a * (-4.0d0)) / c)
    else
        tmp = (b / z) / c
    end if
    code = tmp
end function

Java

assert x < y;
assert t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((a <= -1.95e-69) || !(a <= 4.6e+115)) {
		tmp = t * ((a * -4.0) / c);
	} else {
		tmp = (b / z) / c;
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if (a <= -1.95e-69) or not (a <= 4.6e+115):
		tmp = t * ((a * -4.0) / c)
	else:
		tmp = (b / z) / c
	return tmp

Julia

x, y = sort([x, y])
t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((a <= -1.95e-69) || !(a <= 4.6e+115))
		tmp = Float64(t * Float64(Float64(a * -4.0) / c));
	else
		tmp = Float64(Float64(b / z) / c);
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((a <= -1.95e-69) || ~((a <= 4.6e+115)))
		tmp = t * ((a * -4.0) / c);
	else
		tmp = (b / z) / c;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[a, -1.95e-69], N[Not[LessEqual[a, 4.6e+115]], $MachinePrecision]], N[(t * N[(N[(a * -4.0), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision], N[(N[(b / z), $MachinePrecision] / c), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.9499999999999999e-69 or 4.60000000000000007e115 < a

   1. Initial program 79.8%

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

   2. Taylor expanded in z around inf 50.1%

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

      1. associate-/l* 53.0%

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

      2. associate-*r/ 53.0%

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

      3. *-commutative 53.0%

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

   4. Simplified 53.0%

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

      1. associate-/r/ 54.6%

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

      2. *-commutative 54.6%

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

   6. Applied egg-rr 54.6%

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

   if -1.9499999999999999e-69 < a < 4.60000000000000007e115

   1. Initial program 84.9%

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

      1. associate-/r* 82.2%

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

      2. associate-+l- 82.2%

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

      3. associate-*r* 82.2%

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

      4. associate-*r* 84.4%

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

      5. div-inv 84.3%

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

      6. associate--r- 84.3%

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

      7. fma-neg 84.3%

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

      8. associate-*r* 82.1%

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

      9. distribute-rgt-neg-in 82.1%

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

      10. associate-*l* 82.1%

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

   3. Applied egg-rr 82.1%

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

   4. Taylor expanded in x around 0 84.2%

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

   5. Taylor expanded in b around inf 44.5%

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

      1. associate-/l/ 43.7%

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

   7. Simplified 43.7%

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

4. Final simplification 49.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.95 \cdot 10^{-69} \lor \neg \left(a \leq 4.6 \cdot 10^{+115}\right):\\ \;\;\;\;t \cdot \frac{a \cdot -4}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \end{array} \]

Alternative 15: 34.9% accurate, 3.8× speedup

Math

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

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(b / Float64(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[(b / N[(c * z), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 82.4%

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

2. Taylor expanded in b around inf 37.7%

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

   1. *-commutative 37.7%

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

4. Simplified 37.7%

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

5. Final simplification 37.7%

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

Developer target: 80.4% 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 2023320 
(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)))