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

Percentage Accurate: 79.8% → 89.6%

Time: 17.8s

Alternatives: 15

Speedup: 0.8×

• 36.7% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 79.8% 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

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;c \leq -1.45 \cdot 10^{+203} \lor \neg \left(c \leq 0.0024\right):\\ \;\;\;\;\frac{b}{c \cdot z} + \mathsf{fma}\left(9, \frac{y}{\frac{c}{\frac{x}{z}}}, -4 \cdot \left(\frac{a}{c} \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(t, -4 \cdot a, \frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z}\right)}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= c -1.45e+203) (not (<= c 0.0024)))
   (+ (/ b (* c z)) (fma 9.0 (/ y (/ c (/ x z))) (* -4.0 (* (/ a c) t))))
   (/ (fma t (* -4.0 a) (/ (fma x (* 9.0 y) 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 ((c <= -1.45e+203) || !(c <= 0.0024)) {
		tmp = (b / (c * z)) + fma(9.0, (y / (c / (x / z))), (-4.0 * ((a / c) * t)));
	} else {
		tmp = fma(t, (-4.0 * a), (fma(x, (9.0 * y), 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 ((c <= -1.45e+203) || !(c <= 0.0024))
		tmp = Float64(Float64(b / Float64(c * z)) + fma(9.0, Float64(y / Float64(c / Float64(x / z))), Float64(-4.0 * Float64(Float64(a / c) * t))));
	else
		tmp = Float64(fma(t, Float64(-4.0 * a), Float64(fma(x, Float64(9.0 * y), b) / z)) / c);
	end
	return tmp
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[c, -1.45e+203], N[Not[LessEqual[c, 0.0024]], $MachinePrecision]], N[(N[(b / N[(c * z), $MachinePrecision]), $MachinePrecision] + N[(9.0 * N[(y / N[(c / N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(-4.0 * N[(N[(a / c), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t * N[(-4.0 * a), $MachinePrecision] + N[(N[(x * N[(9.0 * y), $MachinePrecision] + b), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -1.45000000000000005e203 or 0.00239999999999999979 < c

   1. Initial program 55.2%

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

      1. associate-/r* 51.4%

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

   3. Simplified 65.3%

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

   4. Taylor expanded in t around 0 64.8%

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

      1. *-commutative 64.8%

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

      2. +-commutative 64.8%

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

      3. fma-def 64.9%

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

      4. associate-/l* 71.8%

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

      5. associate-/l* 74.2%

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

      6. associate-/l* 78.6%

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

      7. associate-/r/ 78.5%

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

   6. Simplified 78.5%

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

   if -1.45000000000000005e203 < c < 0.00239999999999999979

   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. Step-by-step derivation

      1. associate-/r* 85.9%

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

   3. Simplified 95.4%

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

4. Final simplification 89.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.45 \cdot 10^{+203} \lor \neg \left(c \leq 0.0024\right):\\ \;\;\;\;\frac{b}{c \cdot z} + \mathsf{fma}\left(9, \frac{y}{\frac{c}{\frac{x}{z}}}, -4 \cdot \left(\frac{a}{c} \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(t, -4 \cdot a, \frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z}\right)}{c}\\ \end{array} \]

Alternative 2: 89.0% accurate, 0.1× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} t_1 := y \cdot \left(9 \cdot x\right)\\ \mathbf{if}\;t_1 \leq -2 \cdot 10^{+291}:\\ \;\;\;\;\left(9 \cdot \frac{y}{z}\right) \cdot \frac{x}{c}\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{+278}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z} + t \cdot \left(-4 \cdot a\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;9 \cdot \frac{y}{\frac{c}{\frac{x}{z}}}\\ \end{array} \end{array} \]

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 (* 9.0 x))))
   (if (<= t_1 -2e+291)
     (* (* 9.0 (/ y z)) (/ x c))
     (if (<= t_1 2e+278)
       (/ (+ (/ (fma x (* 9.0 y) b) z) (* t (* -4.0 a))) c)
       (* 9.0 (/ y (/ c (/ x z))))))))

C

assert(x < y);
assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = y * (9.0 * x);
	double tmp;
	if (t_1 <= -2e+291) {
		tmp = (9.0 * (y / z)) * (x / c);
	} else if (t_1 <= 2e+278) {
		tmp = ((fma(x, (9.0 * y), b) / z) + (t * (-4.0 * a))) / c;
	} else {
		tmp = 9.0 * (y / (c / (x / z)));
	}
	return tmp;
}

Julia

x, y = sort([x, y])
t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(y * Float64(9.0 * x))
	tmp = 0.0
	if (t_1 <= -2e+291)
		tmp = Float64(Float64(9.0 * Float64(y / z)) * Float64(x / c));
	elseif (t_1 <= 2e+278)
		tmp = Float64(Float64(Float64(fma(x, Float64(9.0 * y), b) / z) + Float64(t * Float64(-4.0 * a))) / c);
	else
		tmp = Float64(9.0 * Float64(y / Float64(c / Float64(x / 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_] := Block[{t$95$1 = N[(y * N[(9.0 * x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+291], N[(N[(9.0 * N[(y / z), $MachinePrecision]), $MachinePrecision] * N[(x / c), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+278], N[(N[(N[(N[(x * N[(9.0 * y), $MachinePrecision] + b), $MachinePrecision] / z), $MachinePrecision] + N[(t * N[(-4.0 * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], N[(9.0 * N[(y / N[(c / N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 x 9) y) < -1.9999999999999999e291

   1. Initial program 60.2%

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

      1. associate-/r* 67.4%

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

   3. Simplified 71.4%

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

      1. clear-num 71.4%

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

      2. fma-udef 71.4%

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

      3. +-commutative 71.4%

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

      4. inv-pow 71.4%

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

      5. +-commutative 71.4%

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

      6. fma-udef 71.4%

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

   5. Applied egg-rr 71.4%

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

   6. Taylor expanded in x around inf 63.9%

      \[\leadsto {\color{blue}{\left(0.1111111111111111 \cdot \frac{c \cdot z}{y \cdot x}\right)}}^{-1} \]
   7. Step-by-step derivation

      1. *-commutative 63.9%

         \[\leadsto {\left(0.1111111111111111 \cdot \frac{c \cdot z}{\color{blue}{x \cdot y}}\right)}^{-1} \]

      2. times-frac 92.7%

         \[\leadsto {\left(0.1111111111111111 \cdot \color{blue}{\left(\frac{c}{x} \cdot \frac{z}{y}\right)}\right)}^{-1} \]

   8. Simplified 92.7%

      \[\leadsto {\color{blue}{\left(0.1111111111111111 \cdot \left(\frac{c}{x} \cdot \frac{z}{y}\right)\right)}}^{-1} \]
   9. Step-by-step derivation

      1. unpow-prod-down 92.5%

         \[\leadsto \color{blue}{{0.1111111111111111}^{-1} \cdot {\left(\frac{c}{x} \cdot \frac{z}{y}\right)}^{-1}} \]

      2. metadata-eval 92.5%

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

      3. unpow-prod-down 92.5%

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

      4. inv-pow 92.5%

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

      5. clear-num 92.6%

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

      6. inv-pow 92.6%

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

      7. clear-num 92.5%

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

      8. *-commutative 92.5%

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

      9. associate-*r* 92.6%

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

   10. Applied egg-rr 92.6%

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

   if -1.9999999999999999e291 < (*.f64 (*.f64 x 9) y) < 1.99999999999999993e278

   1. Initial program 77.9%

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

      1. associate-/r* 77.3%

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

   3. Simplified 90.1%

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

   if 1.99999999999999993e278 < (*.f64 (*.f64 x 9) y)

   1. Initial program 59.0%

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

      1. associate-/r* 59.4%

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

   3. Simplified 59.5%

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

   4. Taylor expanded in x around inf 59.0%

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

      1. associate-/l* 74.2%

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

      2. associate-/l* 78.6%

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

   6. Simplified 78.6%

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

4. Final simplification 89.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \left(9 \cdot x\right) \leq -2 \cdot 10^{+291}:\\ \;\;\;\;\left(9 \cdot \frac{y}{z}\right) \cdot \frac{x}{c}\\ \mathbf{elif}\;y \cdot \left(9 \cdot x\right) \leq 2 \cdot 10^{+278}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z} + t \cdot \left(-4 \cdot a\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;9 \cdot \frac{y}{\frac{c}{\frac{x}{z}}}\\ \end{array} \]

Alternative 3: 89.0% accurate, 0.2× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;c \leq -2.9 \cdot 10^{+202} \lor \neg \left(c \leq 0.0029\right):\\ \;\;\;\;\frac{b}{c \cdot z} + \mathsf{fma}\left(9, \frac{y}{\frac{c}{\frac{x}{z}}}, -4 \cdot \left(\frac{a}{c} \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z} + t \cdot \left(-4 \cdot a\right)}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= c -2.9e+202) (not (<= c 0.0029)))
   (+ (/ b (* c z)) (fma 9.0 (/ y (/ c (/ x z))) (* -4.0 (* (/ a c) t))))
   (/ (+ (/ (fma x (* 9.0 y) b) z) (* t (* -4.0 a))) c)))

C

assert(x < y);
assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((c <= -2.9e+202) || !(c <= 0.0029)) {
		tmp = (b / (c * z)) + fma(9.0, (y / (c / (x / z))), (-4.0 * ((a / c) * t)));
	} else {
		tmp = ((fma(x, (9.0 * y), b) / z) + (t * (-4.0 * a))) / c;
	}
	return tmp;
}

Julia

x, y = sort([x, y])
t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((c <= -2.9e+202) || !(c <= 0.0029))
		tmp = Float64(Float64(b / Float64(c * z)) + fma(9.0, Float64(y / Float64(c / Float64(x / z))), Float64(-4.0 * Float64(Float64(a / c) * t))));
	else
		tmp = Float64(Float64(Float64(fma(x, Float64(9.0 * y), b) / z) + Float64(t * Float64(-4.0 * a))) / c);
	end
	return tmp
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[c, -2.9e+202], N[Not[LessEqual[c, 0.0029]], $MachinePrecision]], N[(N[(b / N[(c * z), $MachinePrecision]), $MachinePrecision] + N[(9.0 * N[(y / N[(c / N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(-4.0 * N[(N[(a / c), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(x * N[(9.0 * y), $MachinePrecision] + b), $MachinePrecision] / z), $MachinePrecision] + N[(t * N[(-4.0 * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -2.8999999999999999e202 or 0.0029 < c

   1. Initial program 55.2%

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

      1. associate-/r* 51.4%

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

   3. Simplified 65.3%

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

   4. Taylor expanded in t around 0 64.8%

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

      1. *-commutative 64.8%

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

      2. +-commutative 64.8%

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

      3. fma-def 64.9%

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

      4. associate-/l* 71.8%

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

      5. associate-/l* 74.2%

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

      6. associate-/l* 78.6%

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

      7. associate-/r/ 78.5%

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

   6. Simplified 78.5%

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

   if -2.8999999999999999e202 < c < 0.0029

   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. Step-by-step derivation

      1. associate-/r* 85.9%

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

   3. Simplified 94.8%

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

4. Final simplification 89.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -2.9 \cdot 10^{+202} \lor \neg \left(c \leq 0.0029\right):\\ \;\;\;\;\frac{b}{c \cdot z} + \mathsf{fma}\left(9, \frac{y}{\frac{c}{\frac{x}{z}}}, -4 \cdot \left(\frac{a}{c} \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z} + t \cdot \left(-4 \cdot a\right)}{c}\\ \end{array} \]

Alternative 4: 48.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} t_1 := \frac{1}{\frac{c}{\frac{b}{z}}}\\ t_2 := 9 \cdot \left(\frac{y}{z} \cdot \frac{x}{c}\right)\\ t_3 := -4 \cdot \left(\frac{a}{c} \cdot t\right)\\ \mathbf{if}\;x \leq -3.2 \cdot 10^{+131}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -5 \cdot 10^{+97}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -1.75 \cdot 10^{+80}:\\ \;\;\;\;\left(a \cdot t\right) \cdot \frac{-4}{c}\\ \mathbf{elif}\;x \leq -3.2 \cdot 10^{+16}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;x \leq -5.2 \cdot 10^{-39}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -1.08 \cdot 10^{-58}:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \mathbf{elif}\;x \leq -3.6 \cdot 10^{-258}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{-40}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

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 (/ 1.0 (/ c (/ b z))))
        (t_2 (* 9.0 (* (/ y z) (/ x c))))
        (t_3 (* -4.0 (* (/ a c) t))))
   (if (<= x -3.2e+131)
     t_2
     (if (<= x -5e+97)
       t_1
       (if (<= x -1.75e+80)
         (* (* a t) (/ -4.0 c))
         (if (<= x -3.2e+16)
           (/ (/ b c) z)
           (if (<= x -5.2e-39)
             t_3
             (if (<= x -1.08e-58)
               (/ b (* c z))
               (if (<= x -3.6e-258) t_3 (if (<= x 3.5e-40) 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 = 1.0 / (c / (b / z));
	double t_2 = 9.0 * ((y / z) * (x / c));
	double t_3 = -4.0 * ((a / c) * t);
	double tmp;
	if (x <= -3.2e+131) {
		tmp = t_2;
	} else if (x <= -5e+97) {
		tmp = t_1;
	} else if (x <= -1.75e+80) {
		tmp = (a * t) * (-4.0 / c);
	} else if (x <= -3.2e+16) {
		tmp = (b / c) / z;
	} else if (x <= -5.2e-39) {
		tmp = t_3;
	} else if (x <= -1.08e-58) {
		tmp = b / (c * z);
	} else if (x <= -3.6e-258) {
		tmp = t_3;
	} else if (x <= 3.5e-40) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = 1.0d0 / (c / (b / z))
    t_2 = 9.0d0 * ((y / z) * (x / c))
    t_3 = (-4.0d0) * ((a / c) * t)
    if (x <= (-3.2d+131)) then
        tmp = t_2
    else if (x <= (-5d+97)) then
        tmp = t_1
    else if (x <= (-1.75d+80)) then
        tmp = (a * t) * ((-4.0d0) / c)
    else if (x <= (-3.2d+16)) then
        tmp = (b / c) / z
    else if (x <= (-5.2d-39)) then
        tmp = t_3
    else if (x <= (-1.08d-58)) then
        tmp = b / (c * z)
    else if (x <= (-3.6d-258)) then
        tmp = t_3
    else if (x <= 3.5d-40) 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 = 1.0 / (c / (b / z));
	double t_2 = 9.0 * ((y / z) * (x / c));
	double t_3 = -4.0 * ((a / c) * t);
	double tmp;
	if (x <= -3.2e+131) {
		tmp = t_2;
	} else if (x <= -5e+97) {
		tmp = t_1;
	} else if (x <= -1.75e+80) {
		tmp = (a * t) * (-4.0 / c);
	} else if (x <= -3.2e+16) {
		tmp = (b / c) / z;
	} else if (x <= -5.2e-39) {
		tmp = t_3;
	} else if (x <= -1.08e-58) {
		tmp = b / (c * z);
	} else if (x <= -3.6e-258) {
		tmp = t_3;
	} else if (x <= 3.5e-40) {
		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 = 1.0 / (c / (b / z))
	t_2 = 9.0 * ((y / z) * (x / c))
	t_3 = -4.0 * ((a / c) * t)
	tmp = 0
	if x <= -3.2e+131:
		tmp = t_2
	elif x <= -5e+97:
		tmp = t_1
	elif x <= -1.75e+80:
		tmp = (a * t) * (-4.0 / c)
	elif x <= -3.2e+16:
		tmp = (b / c) / z
	elif x <= -5.2e-39:
		tmp = t_3
	elif x <= -1.08e-58:
		tmp = b / (c * z)
	elif x <= -3.6e-258:
		tmp = t_3
	elif x <= 3.5e-40:
		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(1.0 / Float64(c / Float64(b / z)))
	t_2 = Float64(9.0 * Float64(Float64(y / z) * Float64(x / c)))
	t_3 = Float64(-4.0 * Float64(Float64(a / c) * t))
	tmp = 0.0
	if (x <= -3.2e+131)
		tmp = t_2;
	elseif (x <= -5e+97)
		tmp = t_1;
	elseif (x <= -1.75e+80)
		tmp = Float64(Float64(a * t) * Float64(-4.0 / c));
	elseif (x <= -3.2e+16)
		tmp = Float64(Float64(b / c) / z);
	elseif (x <= -5.2e-39)
		tmp = t_3;
	elseif (x <= -1.08e-58)
		tmp = Float64(b / Float64(c * z));
	elseif (x <= -3.6e-258)
		tmp = t_3;
	elseif (x <= 3.5e-40)
		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 = 1.0 / (c / (b / z));
	t_2 = 9.0 * ((y / z) * (x / c));
	t_3 = -4.0 * ((a / c) * t);
	tmp = 0.0;
	if (x <= -3.2e+131)
		tmp = t_2;
	elseif (x <= -5e+97)
		tmp = t_1;
	elseif (x <= -1.75e+80)
		tmp = (a * t) * (-4.0 / c);
	elseif (x <= -3.2e+16)
		tmp = (b / c) / z;
	elseif (x <= -5.2e-39)
		tmp = t_3;
	elseif (x <= -1.08e-58)
		tmp = b / (c * z);
	elseif (x <= -3.6e-258)
		tmp = t_3;
	elseif (x <= 3.5e-40)
		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[(1.0 / N[(c / N[(b / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(9.0 * N[(N[(y / z), $MachinePrecision] * N[(x / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(-4.0 * N[(N[(a / c), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -3.2e+131], t$95$2, If[LessEqual[x, -5e+97], t$95$1, If[LessEqual[x, -1.75e+80], N[(N[(a * t), $MachinePrecision] * N[(-4.0 / c), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -3.2e+16], N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[x, -5.2e-39], t$95$3, If[LessEqual[x, -1.08e-58], N[(b / N[(c * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -3.6e-258], t$95$3, If[LessEqual[x, 3.5e-40], t$95$1, t$95$2]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if x < -3.2000000000000002e131 or 3.5000000000000002e-40 < x

   1. Initial program 72.0%

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

      1. associate-/r* 74.0%

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

   3. Simplified 78.9%

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

   4. Taylor expanded in x around inf 52.9%

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

      1. *-commutative 52.9%

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

   6. Simplified 52.9%

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

   7. Taylor expanded in y around 0 52.9%

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

      1. *-commutative 52.9%

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

      2. times-frac 64.5%

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

   9. Simplified 64.5%

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

   if -3.2000000000000002e131 < x < -4.99999999999999999e97 or -3.59999999999999979e-258 < x < 3.5000000000000002e-40

   1. Initial program 76.1%

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

      1. associate-/r* 77.6%

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

   3. Simplified 92.3%

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

   4. Taylor expanded in b around inf 45.2%

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

      1. *-commutative 45.2%

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

   6. Simplified 45.2%

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

      1. clear-num 45.2%

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

      2. inv-pow 45.2%

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

      3. *-commutative 45.2%

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

   8. Applied egg-rr 45.2%

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

      1. unpow-1 45.2%

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

      2. associate-/l* 46.6%

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

   10. Simplified 46.6%

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

   if -4.99999999999999999e97 < x < -1.74999999999999997e80

   1. Initial program 53.5%

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

      1. associate-/r* 53.5%

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

   3. Simplified 99.2%

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

      1. clear-num 100.0%

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

      2. fma-udef 100.0%

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

      3. +-commutative 100.0%

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

      4. inv-pow 100.0%

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

      5. +-commutative 100.0%

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

      6. fma-udef 100.0%

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

   5. Applied egg-rr 100.0%

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

   6. Taylor expanded in t around inf 100.0%

      \[\leadsto {\color{blue}{\left(-0.25 \cdot \frac{c}{a \cdot t}\right)}}^{-1} \]
   7. Step-by-step derivation

      1. associate-*r/ 100.0%

         \[\leadsto {\color{blue}{\left(\frac{-0.25 \cdot c}{a \cdot t}\right)}}^{-1} \]

   8. Simplified 100.0%

      \[\leadsto {\color{blue}{\left(\frac{-0.25 \cdot c}{a \cdot t}\right)}}^{-1} \]
   9. Step-by-step derivation

      1. div-inv 100.0%

         \[\leadsto {\color{blue}{\left(\left(-0.25 \cdot c\right) \cdot \frac{1}{a \cdot t}\right)}}^{-1} \]

      2. unpow-prod-down 98.4%

         \[\leadsto \color{blue}{{\left(-0.25 \cdot c\right)}^{-1} \cdot {\left(\frac{1}{a \cdot t}\right)}^{-1}} \]

      3. *-commutative 98.4%

         \[\leadsto {\color{blue}{\left(c \cdot -0.25\right)}}^{-1} \cdot {\left(\frac{1}{a \cdot t}\right)}^{-1} \]

   10. Applied egg-rr 98.4%

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

       1. *-commutative 98.4%

          \[\leadsto \color{blue}{{\left(\frac{1}{a \cdot t}\right)}^{-1} \cdot {\left(c \cdot -0.25\right)}^{-1}} \]

       2. unpow-1 98.4%

          \[\leadsto \color{blue}{\frac{1}{\frac{1}{a \cdot t}}} \cdot {\left(c \cdot -0.25\right)}^{-1} \]

       3. remove-double-div 99.2%

          \[\leadsto \color{blue}{\left(a \cdot t\right)} \cdot {\left(c \cdot -0.25\right)}^{-1} \]

       4. unpow-1 99.2%

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

       5. *-commutative 99.2%

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

       6. associate-/r* 99.2%

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

       7. metadata-eval 99.2%

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

   12. Simplified 99.2%

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

   if -1.74999999999999997e80 < x < -3.2e16

   1. Initial program 67.3%

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

      1. associate-/r* 62.9%

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

   3. Simplified 73.6%

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

      1. div-inv 73.6%

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

   5. Applied egg-rr 73.6%

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

   6. Taylor expanded in b around inf 30.7%

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

      1. associate-/r* 36.1%

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

   8. Simplified 36.1%

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

   if -3.2e16 < x < -5.2e-39 or -1.08e-58 < x < -3.59999999999999979e-258

   1. Initial program 75.9%

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

      1. associate-/r* 74.1%

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

   3. Simplified 91.4%

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

   4. Taylor expanded in t around inf 45.9%

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

      1. associate-/l* 45.8%

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

      2. associate-/r/ 52.1%

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

   6. Simplified 52.1%

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

   if -5.2e-39 < x < -1.08e-58

   1. Initial program 99.7%

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

      1. associate-/r* 80.9%

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

   3. Simplified 80.9%

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

   4. Taylor expanded in b around inf 61.3%

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

      1. *-commutative 61.3%

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

   6. Simplified 61.3%

      \[\leadsto \color{blue}{\frac{b}{z \cdot c}} \]
3. Recombined 6 regimes into one program.

4. Final simplification 54.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.2 \cdot 10^{+131}:\\ \;\;\;\;9 \cdot \left(\frac{y}{z} \cdot \frac{x}{c}\right)\\ \mathbf{elif}\;x \leq -5 \cdot 10^{+97}:\\ \;\;\;\;\frac{1}{\frac{c}{\frac{b}{z}}}\\ \mathbf{elif}\;x \leq -1.75 \cdot 10^{+80}:\\ \;\;\;\;\left(a \cdot t\right) \cdot \frac{-4}{c}\\ \mathbf{elif}\;x \leq -3.2 \cdot 10^{+16}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;x \leq -5.2 \cdot 10^{-39}:\\ \;\;\;\;-4 \cdot \left(\frac{a}{c} \cdot t\right)\\ \mathbf{elif}\;x \leq -1.08 \cdot 10^{-58}:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \mathbf{elif}\;x \leq -3.6 \cdot 10^{-258}:\\ \;\;\;\;-4 \cdot \left(\frac{a}{c} \cdot t\right)\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{-40}:\\ \;\;\;\;\frac{1}{\frac{c}{\frac{b}{z}}}\\ \mathbf{else}:\\ \;\;\;\;9 \cdot \left(\frac{y}{z} \cdot \frac{x}{c}\right)\\ \end{array} \]

Alternative 5: 48.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} t_1 := \frac{1}{\frac{c}{\frac{b}{z}}}\\ t_2 := 9 \cdot \frac{y \cdot \frac{x}{c}}{z}\\ t_3 := -4 \cdot \left(\frac{a}{c} \cdot t\right)\\ \mathbf{if}\;x \leq -3.2 \cdot 10^{+131}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -9.2 \cdot 10^{+98}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -1.55 \cdot 10^{+80}:\\ \;\;\;\;\left(a \cdot t\right) \cdot \frac{-4}{c}\\ \mathbf{elif}\;x \leq -760000000000:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;x \leq -2.75 \cdot 10^{-39}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -1.65 \cdot 10^{-58}:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \mathbf{elif}\;x \leq -1.8 \cdot 10^{-260}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq 1.9 \cdot 10^{-121}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

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 (/ 1.0 (/ c (/ b z))))
        (t_2 (* 9.0 (/ (* y (/ x c)) z)))
        (t_3 (* -4.0 (* (/ a c) t))))
   (if (<= x -3.2e+131)
     t_2
     (if (<= x -9.2e+98)
       t_1
       (if (<= x -1.55e+80)
         (* (* a t) (/ -4.0 c))
         (if (<= x -760000000000.0)
           (/ (/ b c) z)
           (if (<= x -2.75e-39)
             t_3
             (if (<= x -1.65e-58)
               (/ b (* c z))
               (if (<= x -1.8e-260) t_3 (if (<= x 1.9e-121) 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 = 1.0 / (c / (b / z));
	double t_2 = 9.0 * ((y * (x / c)) / z);
	double t_3 = -4.0 * ((a / c) * t);
	double tmp;
	if (x <= -3.2e+131) {
		tmp = t_2;
	} else if (x <= -9.2e+98) {
		tmp = t_1;
	} else if (x <= -1.55e+80) {
		tmp = (a * t) * (-4.0 / c);
	} else if (x <= -760000000000.0) {
		tmp = (b / c) / z;
	} else if (x <= -2.75e-39) {
		tmp = t_3;
	} else if (x <= -1.65e-58) {
		tmp = b / (c * z);
	} else if (x <= -1.8e-260) {
		tmp = t_3;
	} else if (x <= 1.9e-121) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = 1.0d0 / (c / (b / z))
    t_2 = 9.0d0 * ((y * (x / c)) / z)
    t_3 = (-4.0d0) * ((a / c) * t)
    if (x <= (-3.2d+131)) then
        tmp = t_2
    else if (x <= (-9.2d+98)) then
        tmp = t_1
    else if (x <= (-1.55d+80)) then
        tmp = (a * t) * ((-4.0d0) / c)
    else if (x <= (-760000000000.0d0)) then
        tmp = (b / c) / z
    else if (x <= (-2.75d-39)) then
        tmp = t_3
    else if (x <= (-1.65d-58)) then
        tmp = b / (c * z)
    else if (x <= (-1.8d-260)) then
        tmp = t_3
    else if (x <= 1.9d-121) 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 = 1.0 / (c / (b / z));
	double t_2 = 9.0 * ((y * (x / c)) / z);
	double t_3 = -4.0 * ((a / c) * t);
	double tmp;
	if (x <= -3.2e+131) {
		tmp = t_2;
	} else if (x <= -9.2e+98) {
		tmp = t_1;
	} else if (x <= -1.55e+80) {
		tmp = (a * t) * (-4.0 / c);
	} else if (x <= -760000000000.0) {
		tmp = (b / c) / z;
	} else if (x <= -2.75e-39) {
		tmp = t_3;
	} else if (x <= -1.65e-58) {
		tmp = b / (c * z);
	} else if (x <= -1.8e-260) {
		tmp = t_3;
	} else if (x <= 1.9e-121) {
		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 = 1.0 / (c / (b / z))
	t_2 = 9.0 * ((y * (x / c)) / z)
	t_3 = -4.0 * ((a / c) * t)
	tmp = 0
	if x <= -3.2e+131:
		tmp = t_2
	elif x <= -9.2e+98:
		tmp = t_1
	elif x <= -1.55e+80:
		tmp = (a * t) * (-4.0 / c)
	elif x <= -760000000000.0:
		tmp = (b / c) / z
	elif x <= -2.75e-39:
		tmp = t_3
	elif x <= -1.65e-58:
		tmp = b / (c * z)
	elif x <= -1.8e-260:
		tmp = t_3
	elif x <= 1.9e-121:
		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(1.0 / Float64(c / Float64(b / z)))
	t_2 = Float64(9.0 * Float64(Float64(y * Float64(x / c)) / z))
	t_3 = Float64(-4.0 * Float64(Float64(a / c) * t))
	tmp = 0.0
	if (x <= -3.2e+131)
		tmp = t_2;
	elseif (x <= -9.2e+98)
		tmp = t_1;
	elseif (x <= -1.55e+80)
		tmp = Float64(Float64(a * t) * Float64(-4.0 / c));
	elseif (x <= -760000000000.0)
		tmp = Float64(Float64(b / c) / z);
	elseif (x <= -2.75e-39)
		tmp = t_3;
	elseif (x <= -1.65e-58)
		tmp = Float64(b / Float64(c * z));
	elseif (x <= -1.8e-260)
		tmp = t_3;
	elseif (x <= 1.9e-121)
		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 = 1.0 / (c / (b / z));
	t_2 = 9.0 * ((y * (x / c)) / z);
	t_3 = -4.0 * ((a / c) * t);
	tmp = 0.0;
	if (x <= -3.2e+131)
		tmp = t_2;
	elseif (x <= -9.2e+98)
		tmp = t_1;
	elseif (x <= -1.55e+80)
		tmp = (a * t) * (-4.0 / c);
	elseif (x <= -760000000000.0)
		tmp = (b / c) / z;
	elseif (x <= -2.75e-39)
		tmp = t_3;
	elseif (x <= -1.65e-58)
		tmp = b / (c * z);
	elseif (x <= -1.8e-260)
		tmp = t_3;
	elseif (x <= 1.9e-121)
		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[(1.0 / N[(c / N[(b / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(9.0 * N[(N[(y * N[(x / c), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(-4.0 * N[(N[(a / c), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -3.2e+131], t$95$2, If[LessEqual[x, -9.2e+98], t$95$1, If[LessEqual[x, -1.55e+80], N[(N[(a * t), $MachinePrecision] * N[(-4.0 / c), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -760000000000.0], N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[x, -2.75e-39], t$95$3, If[LessEqual[x, -1.65e-58], N[(b / N[(c * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.8e-260], t$95$3, If[LessEqual[x, 1.9e-121], t$95$1, t$95$2]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if x < -3.2000000000000002e131 or 1.9e-121 < x

   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* 73.2%

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

   3. Simplified 79.7%

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

   4. Taylor expanded in x around inf 47.7%

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

      1. *-commutative 47.7%

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

   6. Simplified 47.7%

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

   7. Taylor expanded in y around 0 47.7%

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

      1. *-commutative 47.7%

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

      2. times-frac 56.8%

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

   9. Simplified 56.8%

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

       1. associate-*l/ 60.8%

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

   11. Applied egg-rr 60.8%

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

   if -3.2000000000000002e131 < x < -9.20000000000000053e98 or -1.8e-260 < x < 1.9e-121

   1. Initial program 79.1%

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

      1. associate-/r* 79.8%

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

   3. Simplified 94.4%

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

   4. Taylor expanded in b around inf 48.2%

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

      1. *-commutative 48.2%

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

   6. Simplified 48.2%

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

      1. clear-num 48.2%

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

      2. inv-pow 48.2%

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

      3. *-commutative 48.2%

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

   8. Applied egg-rr 48.2%

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

      1. unpow-1 48.2%

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

      2. associate-/l* 48.6%

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

   10. Simplified 48.6%

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

   if -9.20000000000000053e98 < x < -1.54999999999999994e80

   1. Initial program 53.5%

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

      1. associate-/r* 53.5%

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

   3. Simplified 99.2%

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

      1. clear-num 100.0%

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

      2. fma-udef 100.0%

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

      3. +-commutative 100.0%

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

      4. inv-pow 100.0%

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

      5. +-commutative 100.0%

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

      6. fma-udef 100.0%

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

   5. Applied egg-rr 100.0%

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

   6. Taylor expanded in t around inf 100.0%

      \[\leadsto {\color{blue}{\left(-0.25 \cdot \frac{c}{a \cdot t}\right)}}^{-1} \]
   7. Step-by-step derivation

      1. associate-*r/ 100.0%

         \[\leadsto {\color{blue}{\left(\frac{-0.25 \cdot c}{a \cdot t}\right)}}^{-1} \]

   8. Simplified 100.0%

      \[\leadsto {\color{blue}{\left(\frac{-0.25 \cdot c}{a \cdot t}\right)}}^{-1} \]
   9. Step-by-step derivation

      1. div-inv 100.0%

         \[\leadsto {\color{blue}{\left(\left(-0.25 \cdot c\right) \cdot \frac{1}{a \cdot t}\right)}}^{-1} \]

      2. unpow-prod-down 98.4%

         \[\leadsto \color{blue}{{\left(-0.25 \cdot c\right)}^{-1} \cdot {\left(\frac{1}{a \cdot t}\right)}^{-1}} \]

      3. *-commutative 98.4%

         \[\leadsto {\color{blue}{\left(c \cdot -0.25\right)}}^{-1} \cdot {\left(\frac{1}{a \cdot t}\right)}^{-1} \]

   10. Applied egg-rr 98.4%

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

       1. *-commutative 98.4%

          \[\leadsto \color{blue}{{\left(\frac{1}{a \cdot t}\right)}^{-1} \cdot {\left(c \cdot -0.25\right)}^{-1}} \]

       2. unpow-1 98.4%

          \[\leadsto \color{blue}{\frac{1}{\frac{1}{a \cdot t}}} \cdot {\left(c \cdot -0.25\right)}^{-1} \]

       3. remove-double-div 99.2%

          \[\leadsto \color{blue}{\left(a \cdot t\right)} \cdot {\left(c \cdot -0.25\right)}^{-1} \]

       4. unpow-1 99.2%

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

       5. *-commutative 99.2%

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

       6. associate-/r* 99.2%

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

       7. metadata-eval 99.2%

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

   12. Simplified 99.2%

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

   if -1.54999999999999994e80 < x < -7.6e11

   1. Initial program 67.3%

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

      1. associate-/r* 62.9%

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

   3. Simplified 73.6%

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

      1. div-inv 73.6%

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

   5. Applied egg-rr 73.6%

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

   6. Taylor expanded in b around inf 30.7%

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

      1. associate-/r* 36.1%

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

   8. Simplified 36.1%

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

   if -7.6e11 < x < -2.75000000000000009e-39 or -1.65000000000000013e-58 < x < -1.8e-260

   1. Initial program 74.5%

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

      1. associate-/r* 74.7%

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

   3. Simplified 91.6%

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

   4. Taylor expanded in t around inf 47.0%

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

      1. associate-/l* 45.0%

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

      2. associate-/r/ 53.1%

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

   6. Simplified 53.1%

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

   if -2.75000000000000009e-39 < x < -1.65000000000000013e-58

   1. Initial program 99.7%

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

      1. associate-/r* 80.9%

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

   3. Simplified 80.9%

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

   4. Taylor expanded in b around inf 61.3%

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

      1. *-commutative 61.3%

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

   6. Simplified 61.3%

      \[\leadsto \color{blue}{\frac{b}{z \cdot c}} \]
3. Recombined 6 regimes into one program.

4. Final simplification 54.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.2 \cdot 10^{+131}:\\ \;\;\;\;9 \cdot \frac{y \cdot \frac{x}{c}}{z}\\ \mathbf{elif}\;x \leq -9.2 \cdot 10^{+98}:\\ \;\;\;\;\frac{1}{\frac{c}{\frac{b}{z}}}\\ \mathbf{elif}\;x \leq -1.55 \cdot 10^{+80}:\\ \;\;\;\;\left(a \cdot t\right) \cdot \frac{-4}{c}\\ \mathbf{elif}\;x \leq -760000000000:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;x \leq -2.75 \cdot 10^{-39}:\\ \;\;\;\;-4 \cdot \left(\frac{a}{c} \cdot t\right)\\ \mathbf{elif}\;x \leq -1.65 \cdot 10^{-58}:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \mathbf{elif}\;x \leq -1.8 \cdot 10^{-260}:\\ \;\;\;\;-4 \cdot \left(\frac{a}{c} \cdot t\right)\\ \mathbf{elif}\;x \leq 1.9 \cdot 10^{-121}:\\ \;\;\;\;\frac{1}{\frac{c}{\frac{b}{z}}}\\ \mathbf{else}:\\ \;\;\;\;9 \cdot \frac{y \cdot \frac{x}{c}}{z}\\ \end{array} \]

Alternative 6: 48.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} t_1 := \frac{1}{\frac{c}{\frac{b}{z}}}\\ t_2 := -4 \cdot \left(\frac{a}{c} \cdot t\right)\\ \mathbf{if}\;x \leq -3.2 \cdot 10^{+131}:\\ \;\;\;\;\frac{9 \cdot \frac{y}{\frac{c}{x}}}{z}\\ \mathbf{elif}\;x \leq -4.5 \cdot 10^{+97}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -1.45 \cdot 10^{+80}:\\ \;\;\;\;\left(a \cdot t\right) \cdot \frac{-4}{c}\\ \mathbf{elif}\;x \leq -320000000000:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;x \leq -1.16 \cdot 10^{-43}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -6.6 \cdot 10^{-59}:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \mathbf{elif}\;x \leq -3.7 \cdot 10^{-256}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 1.4 \cdot 10^{-112}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;9 \cdot \frac{y \cdot \frac{x}{c}}{z}\\ \end{array} \end{array} \]

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 (/ 1.0 (/ c (/ b z)))) (t_2 (* -4.0 (* (/ a c) t))))
   (if (<= x -3.2e+131)
     (/ (* 9.0 (/ y (/ c x))) z)
     (if (<= x -4.5e+97)
       t_1
       (if (<= x -1.45e+80)
         (* (* a t) (/ -4.0 c))
         (if (<= x -320000000000.0)
           (/ (/ b c) z)
           (if (<= x -1.16e-43)
             t_2
             (if (<= x -6.6e-59)
               (/ b (* c z))
               (if (<= x -3.7e-256)
                 t_2
                 (if (<= x 1.4e-112) t_1 (* 9.0 (/ (* y (/ x 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 t_1 = 1.0 / (c / (b / z));
	double t_2 = -4.0 * ((a / c) * t);
	double tmp;
	if (x <= -3.2e+131) {
		tmp = (9.0 * (y / (c / x))) / z;
	} else if (x <= -4.5e+97) {
		tmp = t_1;
	} else if (x <= -1.45e+80) {
		tmp = (a * t) * (-4.0 / c);
	} else if (x <= -320000000000.0) {
		tmp = (b / c) / z;
	} else if (x <= -1.16e-43) {
		tmp = t_2;
	} else if (x <= -6.6e-59) {
		tmp = b / (c * z);
	} else if (x <= -3.7e-256) {
		tmp = t_2;
	} else if (x <= 1.4e-112) {
		tmp = t_1;
	} else {
		tmp = 9.0 * ((y * (x / 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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = 1.0d0 / (c / (b / z))
    t_2 = (-4.0d0) * ((a / c) * t)
    if (x <= (-3.2d+131)) then
        tmp = (9.0d0 * (y / (c / x))) / z
    else if (x <= (-4.5d+97)) then
        tmp = t_1
    else if (x <= (-1.45d+80)) then
        tmp = (a * t) * ((-4.0d0) / c)
    else if (x <= (-320000000000.0d0)) then
        tmp = (b / c) / z
    else if (x <= (-1.16d-43)) then
        tmp = t_2
    else if (x <= (-6.6d-59)) then
        tmp = b / (c * z)
    else if (x <= (-3.7d-256)) then
        tmp = t_2
    else if (x <= 1.4d-112) then
        tmp = t_1
    else
        tmp = 9.0d0 * ((y * (x / 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 t_1 = 1.0 / (c / (b / z));
	double t_2 = -4.0 * ((a / c) * t);
	double tmp;
	if (x <= -3.2e+131) {
		tmp = (9.0 * (y / (c / x))) / z;
	} else if (x <= -4.5e+97) {
		tmp = t_1;
	} else if (x <= -1.45e+80) {
		tmp = (a * t) * (-4.0 / c);
	} else if (x <= -320000000000.0) {
		tmp = (b / c) / z;
	} else if (x <= -1.16e-43) {
		tmp = t_2;
	} else if (x <= -6.6e-59) {
		tmp = b / (c * z);
	} else if (x <= -3.7e-256) {
		tmp = t_2;
	} else if (x <= 1.4e-112) {
		tmp = t_1;
	} else {
		tmp = 9.0 * ((y * (x / c)) / 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 = 1.0 / (c / (b / z))
	t_2 = -4.0 * ((a / c) * t)
	tmp = 0
	if x <= -3.2e+131:
		tmp = (9.0 * (y / (c / x))) / z
	elif x <= -4.5e+97:
		tmp = t_1
	elif x <= -1.45e+80:
		tmp = (a * t) * (-4.0 / c)
	elif x <= -320000000000.0:
		tmp = (b / c) / z
	elif x <= -1.16e-43:
		tmp = t_2
	elif x <= -6.6e-59:
		tmp = b / (c * z)
	elif x <= -3.7e-256:
		tmp = t_2
	elif x <= 1.4e-112:
		tmp = t_1
	else:
		tmp = 9.0 * ((y * (x / c)) / 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(1.0 / Float64(c / Float64(b / z)))
	t_2 = Float64(-4.0 * Float64(Float64(a / c) * t))
	tmp = 0.0
	if (x <= -3.2e+131)
		tmp = Float64(Float64(9.0 * Float64(y / Float64(c / x))) / z);
	elseif (x <= -4.5e+97)
		tmp = t_1;
	elseif (x <= -1.45e+80)
		tmp = Float64(Float64(a * t) * Float64(-4.0 / c));
	elseif (x <= -320000000000.0)
		tmp = Float64(Float64(b / c) / z);
	elseif (x <= -1.16e-43)
		tmp = t_2;
	elseif (x <= -6.6e-59)
		tmp = Float64(b / Float64(c * z));
	elseif (x <= -3.7e-256)
		tmp = t_2;
	elseif (x <= 1.4e-112)
		tmp = t_1;
	else
		tmp = Float64(9.0 * Float64(Float64(y * Float64(x / 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)
	t_1 = 1.0 / (c / (b / z));
	t_2 = -4.0 * ((a / c) * t);
	tmp = 0.0;
	if (x <= -3.2e+131)
		tmp = (9.0 * (y / (c / x))) / z;
	elseif (x <= -4.5e+97)
		tmp = t_1;
	elseif (x <= -1.45e+80)
		tmp = (a * t) * (-4.0 / c);
	elseif (x <= -320000000000.0)
		tmp = (b / c) / z;
	elseif (x <= -1.16e-43)
		tmp = t_2;
	elseif (x <= -6.6e-59)
		tmp = b / (c * z);
	elseif (x <= -3.7e-256)
		tmp = t_2;
	elseif (x <= 1.4e-112)
		tmp = t_1;
	else
		tmp = 9.0 * ((y * (x / 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_] := Block[{t$95$1 = N[(1.0 / N[(c / N[(b / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(-4.0 * N[(N[(a / c), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -3.2e+131], N[(N[(9.0 * N[(y / N[(c / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[x, -4.5e+97], t$95$1, If[LessEqual[x, -1.45e+80], N[(N[(a * t), $MachinePrecision] * N[(-4.0 / c), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -320000000000.0], N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[x, -1.16e-43], t$95$2, If[LessEqual[x, -6.6e-59], N[(b / N[(c * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -3.7e-256], t$95$2, If[LessEqual[x, 1.4e-112], t$95$1, N[(9.0 * N[(N[(y * N[(x / c), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if x < -3.2000000000000002e131

   1. Initial program 74.6%

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

      1. associate-/r* 80.3%

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

   3. Simplified 83.3%

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

      1. clear-num 83.2%

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

      2. fma-udef 83.2%

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

      3. +-commutative 83.2%

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

      4. inv-pow 83.2%

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

      5. +-commutative 83.2%

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

      6. fma-udef 83.2%

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

   5. Applied egg-rr 83.2%

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

   6. Taylor expanded in x around inf 69.4%

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

      1. associate-*r/ 69.3%

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

      2. *-commutative 69.3%

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

      3. associate-/r* 72.8%

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

      4. *-commutative 72.8%

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

   8. Simplified 72.8%

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

   9. Taylor expanded in y around 0 72.8%

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

       1. associate-/l* 89.3%

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

   11. Simplified 89.3%

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

   if -3.2000000000000002e131 < x < -4.49999999999999976e97 or -3.70000000000000029e-256 < x < 1.40000000000000011e-112

   1. Initial program 78.1%

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

      1. associate-/r* 80.1%

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

   3. Simplified 94.5%

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

   4. Taylor expanded in b around inf 47.5%

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

      1. *-commutative 47.5%

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

   6. Simplified 47.5%

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

      1. clear-num 47.5%

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

      2. inv-pow 47.5%

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

      3. *-commutative 47.5%

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

   8. Applied egg-rr 47.5%

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

      1. unpow-1 47.5%

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

      2. associate-/l* 47.9%

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

   10. Simplified 47.9%

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

   if -4.49999999999999976e97 < x < -1.44999999999999993e80

   1. Initial program 53.5%

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

      1. associate-/r* 53.5%

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

   3. Simplified 99.2%

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

      1. clear-num 100.0%

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

      2. fma-udef 100.0%

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

      3. +-commutative 100.0%

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

      4. inv-pow 100.0%

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

      5. +-commutative 100.0%

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

      6. fma-udef 100.0%

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

   5. Applied egg-rr 100.0%

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

   6. Taylor expanded in t around inf 100.0%

      \[\leadsto {\color{blue}{\left(-0.25 \cdot \frac{c}{a \cdot t}\right)}}^{-1} \]
   7. Step-by-step derivation

      1. associate-*r/ 100.0%

         \[\leadsto {\color{blue}{\left(\frac{-0.25 \cdot c}{a \cdot t}\right)}}^{-1} \]

   8. Simplified 100.0%

      \[\leadsto {\color{blue}{\left(\frac{-0.25 \cdot c}{a \cdot t}\right)}}^{-1} \]
   9. Step-by-step derivation

      1. div-inv 100.0%

         \[\leadsto {\color{blue}{\left(\left(-0.25 \cdot c\right) \cdot \frac{1}{a \cdot t}\right)}}^{-1} \]

      2. unpow-prod-down 98.4%

         \[\leadsto \color{blue}{{\left(-0.25 \cdot c\right)}^{-1} \cdot {\left(\frac{1}{a \cdot t}\right)}^{-1}} \]

      3. *-commutative 98.4%

         \[\leadsto {\color{blue}{\left(c \cdot -0.25\right)}}^{-1} \cdot {\left(\frac{1}{a \cdot t}\right)}^{-1} \]

   10. Applied egg-rr 98.4%

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

       1. *-commutative 98.4%

          \[\leadsto \color{blue}{{\left(\frac{1}{a \cdot t}\right)}^{-1} \cdot {\left(c \cdot -0.25\right)}^{-1}} \]

       2. unpow-1 98.4%

          \[\leadsto \color{blue}{\frac{1}{\frac{1}{a \cdot t}}} \cdot {\left(c \cdot -0.25\right)}^{-1} \]

       3. remove-double-div 99.2%

          \[\leadsto \color{blue}{\left(a \cdot t\right)} \cdot {\left(c \cdot -0.25\right)}^{-1} \]

       4. unpow-1 99.2%

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

       5. *-commutative 99.2%

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

       6. associate-/r* 99.2%

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

       7. metadata-eval 99.2%

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

   12. Simplified 99.2%

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

   if -1.44999999999999993e80 < x < -3.2e11

   1. Initial program 67.3%

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

      1. associate-/r* 62.9%

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

   3. Simplified 73.6%

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

      1. div-inv 73.6%

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

   5. Applied egg-rr 73.6%

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

   6. Taylor expanded in b around inf 30.7%

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

      1. associate-/r* 36.1%

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

   8. Simplified 36.1%

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

   if -3.2e11 < x < -1.1600000000000001e-43 or -6.59999999999999964e-59 < x < -3.70000000000000029e-256

   1. Initial program 75.9%

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

      1. associate-/r* 74.1%

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

   3. Simplified 91.4%

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

   4. Taylor expanded in t around inf 45.9%

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

      1. associate-/l* 45.8%

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

      2. associate-/r/ 52.1%

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

   6. Simplified 52.1%

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

   if -1.1600000000000001e-43 < x < -6.59999999999999964e-59

   1. Initial program 99.7%

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

      1. associate-/r* 80.9%

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

   3. Simplified 80.9%

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

   4. Taylor expanded in b around inf 61.3%

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

      1. *-commutative 61.3%

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

   6. Simplified 61.3%

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

   if 1.40000000000000011e-112 < x

   1. Initial program 70.2%

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

      1. associate-/r* 70.2%

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

   3. Simplified 78.2%

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

   4. Taylor expanded in x around inf 38.7%

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

      1. *-commutative 38.7%

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

   6. Simplified 38.7%

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

   7. Taylor expanded in y around 0 38.7%

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

      1. *-commutative 38.7%

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

      2. times-frac 44.5%

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

   9. Simplified 44.5%

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

       1. associate-*l/ 49.0%

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

   11. Applied egg-rr 49.0%

       \[\leadsto 9 \cdot \color{blue}{\frac{y \cdot \frac{x}{c}}{z}} \]
3. Recombined 7 regimes into one program.

4. Final simplification 54.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.2 \cdot 10^{+131}:\\ \;\;\;\;\frac{9 \cdot \frac{y}{\frac{c}{x}}}{z}\\ \mathbf{elif}\;x \leq -4.5 \cdot 10^{+97}:\\ \;\;\;\;\frac{1}{\frac{c}{\frac{b}{z}}}\\ \mathbf{elif}\;x \leq -1.45 \cdot 10^{+80}:\\ \;\;\;\;\left(a \cdot t\right) \cdot \frac{-4}{c}\\ \mathbf{elif}\;x \leq -320000000000:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;x \leq -1.16 \cdot 10^{-43}:\\ \;\;\;\;-4 \cdot \left(\frac{a}{c} \cdot t\right)\\ \mathbf{elif}\;x \leq -6.6 \cdot 10^{-59}:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \mathbf{elif}\;x \leq -3.7 \cdot 10^{-256}:\\ \;\;\;\;-4 \cdot \left(\frac{a}{c} \cdot t\right)\\ \mathbf{elif}\;x \leq 1.4 \cdot 10^{-112}:\\ \;\;\;\;\frac{1}{\frac{c}{\frac{b}{z}}}\\ \mathbf{else}:\\ \;\;\;\;9 \cdot \frac{y \cdot \frac{x}{c}}{z}\\ \end{array} \]

Alternative 7: 84.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} t_1 := t \cdot \left(-4 \cdot a\right)\\ \mathbf{if}\;z \leq -7 \cdot 10^{+99}:\\ \;\;\;\;\frac{t_1 + 9 \cdot \frac{y \cdot x}{z}}{c}\\ \mathbf{elif}\;z \leq 1.42 \cdot 10^{+206}:\\ \;\;\;\;\frac{b + \left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(a \cdot t\right)\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t_1 + \frac{b}{z}}{c}\\ \end{array} \end{array} \]

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
 (let* ((t_1 (* t (* -4.0 a))))
   (if (<= z -7e+99)
     (/ (+ t_1 (* 9.0 (/ (* y x) z))) c)
     (if (<= z 1.42e+206)
       (/ (+ b (- (* x (* 9.0 y)) (* (* z 4.0) (* a t)))) (* c z))
       (/ (+ t_1 (/ b z)) c)))))

C

assert(x < y);
assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = t * (-4.0 * a);
	double tmp;
	if (z <= -7e+99) {
		tmp = (t_1 + (9.0 * ((y * x) / z))) / c;
	} else if (z <= 1.42e+206) {
		tmp = (b + ((x * (9.0 * y)) - ((z * 4.0) * (a * t)))) / (c * z);
	} else {
		tmp = (t_1 + (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) :: t_1
    real(8) :: tmp
    t_1 = t * ((-4.0d0) * a)
    if (z <= (-7d+99)) then
        tmp = (t_1 + (9.0d0 * ((y * x) / z))) / c
    else if (z <= 1.42d+206) then
        tmp = (b + ((x * (9.0d0 * y)) - ((z * 4.0d0) * (a * t)))) / (c * z)
    else
        tmp = (t_1 + (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 t_1 = t * (-4.0 * a);
	double tmp;
	if (z <= -7e+99) {
		tmp = (t_1 + (9.0 * ((y * x) / z))) / c;
	} else if (z <= 1.42e+206) {
		tmp = (b + ((x * (9.0 * y)) - ((z * 4.0) * (a * t)))) / (c * z);
	} else {
		tmp = (t_1 + (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):
	t_1 = t * (-4.0 * a)
	tmp = 0
	if z <= -7e+99:
		tmp = (t_1 + (9.0 * ((y * x) / z))) / c
	elif z <= 1.42e+206:
		tmp = (b + ((x * (9.0 * y)) - ((z * 4.0) * (a * t)))) / (c * z)
	else:
		tmp = (t_1 + (b / z)) / c
	return tmp

Julia

x, y = sort([x, y])
t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(t * Float64(-4.0 * a))
	tmp = 0.0
	if (z <= -7e+99)
		tmp = Float64(Float64(t_1 + Float64(9.0 * Float64(Float64(y * x) / z))) / c);
	elseif (z <= 1.42e+206)
		tmp = Float64(Float64(b + Float64(Float64(x * Float64(9.0 * y)) - Float64(Float64(z * 4.0) * Float64(a * t)))) / Float64(c * z));
	else
		tmp = Float64(Float64(t_1 + 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)
	t_1 = t * (-4.0 * a);
	tmp = 0.0;
	if (z <= -7e+99)
		tmp = (t_1 + (9.0 * ((y * x) / z))) / c;
	elseif (z <= 1.42e+206)
		tmp = (b + ((x * (9.0 * y)) - ((z * 4.0) * (a * t)))) / (c * z);
	else
		tmp = (t_1 + (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_] := Block[{t$95$1 = N[(t * N[(-4.0 * a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -7e+99], N[(N[(t$95$1 + N[(9.0 * N[(N[(y * x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[z, 1.42e+206], N[(N[(b + N[(N[(x * N[(9.0 * y), $MachinePrecision]), $MachinePrecision] - N[(N[(z * 4.0), $MachinePrecision] * N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(c * z), $MachinePrecision]), $MachinePrecision], N[(N[(t$95$1 + N[(b / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.9999999999999995e99

   1. Initial program 35.3%

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

      1. associate-/r* 47.3%

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

   3. Simplified 83.6%

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

   4. Taylor expanded in x around inf 72.6%

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

   if -6.9999999999999995e99 < z < 1.42000000000000005e206

   1. Initial program 89.4%

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

      1. associate-*l* 89.4%

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

      2. associate-*l* 87.9%

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

   3. Simplified 87.9%

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

   if 1.42000000000000005e206 < z

   1. Initial program 29.1%

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

      1. associate-/r* 47.5%

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

   3. Simplified 82.0%

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

   4. Taylor expanded in x around 0 86.7%

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

4. Final simplification 84.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{+99}:\\ \;\;\;\;\frac{t \cdot \left(-4 \cdot a\right) + 9 \cdot \frac{y \cdot x}{z}}{c}\\ \mathbf{elif}\;z \leq 1.42 \cdot 10^{+206}:\\ \;\;\;\;\frac{b + \left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(a \cdot t\right)\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot \left(-4 \cdot a\right) + \frac{b}{z}}{c}\\ \end{array} \]

Alternative 8: 85.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} t_1 := t \cdot \left(-4 \cdot a\right)\\ \mathbf{if}\;z \leq -1.25 \cdot 10^{+101}:\\ \;\;\;\;\frac{t_1 + 9 \cdot \frac{y \cdot x}{z}}{c}\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{+206}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(9 \cdot x\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t_1 + \frac{b}{z}}{c}\\ \end{array} \end{array} \]

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
 (let* ((t_1 (* t (* -4.0 a))))
   (if (<= z -1.25e+101)
     (/ (+ t_1 (* 9.0 (/ (* y x) z))) c)
     (if (<= z 1.45e+206)
       (/ (+ b (- (* y (* 9.0 x)) (* a (* t (* z 4.0))))) (* c z))
       (/ (+ t_1 (/ b z)) c)))))

C

assert(x < y);
assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = t * (-4.0 * a);
	double tmp;
	if (z <= -1.25e+101) {
		tmp = (t_1 + (9.0 * ((y * x) / z))) / c;
	} else if (z <= 1.45e+206) {
		tmp = (b + ((y * (9.0 * x)) - (a * (t * (z * 4.0))))) / (c * z);
	} else {
		tmp = (t_1 + (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) :: t_1
    real(8) :: tmp
    t_1 = t * ((-4.0d0) * a)
    if (z <= (-1.25d+101)) then
        tmp = (t_1 + (9.0d0 * ((y * x) / z))) / c
    else if (z <= 1.45d+206) then
        tmp = (b + ((y * (9.0d0 * x)) - (a * (t * (z * 4.0d0))))) / (c * z)
    else
        tmp = (t_1 + (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 t_1 = t * (-4.0 * a);
	double tmp;
	if (z <= -1.25e+101) {
		tmp = (t_1 + (9.0 * ((y * x) / z))) / c;
	} else if (z <= 1.45e+206) {
		tmp = (b + ((y * (9.0 * x)) - (a * (t * (z * 4.0))))) / (c * z);
	} else {
		tmp = (t_1 + (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):
	t_1 = t * (-4.0 * a)
	tmp = 0
	if z <= -1.25e+101:
		tmp = (t_1 + (9.0 * ((y * x) / z))) / c
	elif z <= 1.45e+206:
		tmp = (b + ((y * (9.0 * x)) - (a * (t * (z * 4.0))))) / (c * z)
	else:
		tmp = (t_1 + (b / z)) / c
	return tmp

Julia

x, y = sort([x, y])
t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(t * Float64(-4.0 * a))
	tmp = 0.0
	if (z <= -1.25e+101)
		tmp = Float64(Float64(t_1 + Float64(9.0 * Float64(Float64(y * x) / z))) / c);
	elseif (z <= 1.45e+206)
		tmp = Float64(Float64(b + Float64(Float64(y * Float64(9.0 * x)) - Float64(a * Float64(t * Float64(z * 4.0))))) / Float64(c * z));
	else
		tmp = Float64(Float64(t_1 + 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)
	t_1 = t * (-4.0 * a);
	tmp = 0.0;
	if (z <= -1.25e+101)
		tmp = (t_1 + (9.0 * ((y * x) / z))) / c;
	elseif (z <= 1.45e+206)
		tmp = (b + ((y * (9.0 * x)) - (a * (t * (z * 4.0))))) / (c * z);
	else
		tmp = (t_1 + (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_] := Block[{t$95$1 = N[(t * N[(-4.0 * a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.25e+101], N[(N[(t$95$1 + N[(9.0 * N[(N[(y * x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[z, 1.45e+206], N[(N[(b + N[(N[(y * N[(9.0 * x), $MachinePrecision]), $MachinePrecision] - N[(a * N[(t * N[(z * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(c * z), $MachinePrecision]), $MachinePrecision], N[(N[(t$95$1 + N[(b / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.24999999999999997e101

   1. Initial program 35.3%

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

      1. associate-/r* 47.3%

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

   3. Simplified 83.6%

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

   4. Taylor expanded in x around inf 72.6%

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

   if -1.24999999999999997e101 < z < 1.45e206

   1. Initial program 89.4%

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

   if 1.45e206 < z

   1. Initial program 29.1%

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

      1. associate-/r* 47.5%

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

   3. Simplified 82.0%

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

   4. Taylor expanded in x around 0 86.7%

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

4. Final simplification 86.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{+101}:\\ \;\;\;\;\frac{t \cdot \left(-4 \cdot a\right) + 9 \cdot \frac{y \cdot x}{z}}{c}\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{+206}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(9 \cdot x\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot \left(-4 \cdot a\right) + \frac{b}{z}}{c}\\ \end{array} \]

Alternative 9: 68.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} t_1 := \frac{b + 9 \cdot \left(y \cdot x\right)}{c \cdot z}\\ t_2 := \frac{t \cdot \left(-4 \cdot a\right)}{c}\\ \mathbf{if}\;z \leq -1.8 \cdot 10^{+120}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{+59}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{+180}:\\ \;\;\;\;\frac{1}{\frac{-0.25}{a} \cdot \frac{c}{t}}\\ \mathbf{elif}\;z \leq 1.42 \cdot 10^{+206}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

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 (* y x))) (* c z))) (t_2 (/ (* t (* -4.0 a)) c)))
   (if (<= z -1.8e+120)
     t_2
     (if (<= z 7.2e+59)
       t_1
       (if (<= z 1.65e+180)
         (/ 1.0 (* (/ -0.25 a) (/ c t)))
         (if (<= z 1.42e+206) 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 * (y * x))) / (c * z);
	double t_2 = (t * (-4.0 * a)) / c;
	double tmp;
	if (z <= -1.8e+120) {
		tmp = t_2;
	} else if (z <= 7.2e+59) {
		tmp = t_1;
	} else if (z <= 1.65e+180) {
		tmp = 1.0 / ((-0.25 / a) * (c / t));
	} else if (z <= 1.42e+206) {
		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 * (y * x))) / (c * z)
    t_2 = (t * ((-4.0d0) * a)) / c
    if (z <= (-1.8d+120)) then
        tmp = t_2
    else if (z <= 7.2d+59) then
        tmp = t_1
    else if (z <= 1.65d+180) then
        tmp = 1.0d0 / (((-0.25d0) / a) * (c / t))
    else if (z <= 1.42d+206) 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 * (y * x))) / (c * z);
	double t_2 = (t * (-4.0 * a)) / c;
	double tmp;
	if (z <= -1.8e+120) {
		tmp = t_2;
	} else if (z <= 7.2e+59) {
		tmp = t_1;
	} else if (z <= 1.65e+180) {
		tmp = 1.0 / ((-0.25 / a) * (c / t));
	} else if (z <= 1.42e+206) {
		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 * (y * x))) / (c * z)
	t_2 = (t * (-4.0 * a)) / c
	tmp = 0
	if z <= -1.8e+120:
		tmp = t_2
	elif z <= 7.2e+59:
		tmp = t_1
	elif z <= 1.65e+180:
		tmp = 1.0 / ((-0.25 / a) * (c / t))
	elif z <= 1.42e+206:
		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(y * x))) / Float64(c * z))
	t_2 = Float64(Float64(t * Float64(-4.0 * a)) / c)
	tmp = 0.0
	if (z <= -1.8e+120)
		tmp = t_2;
	elseif (z <= 7.2e+59)
		tmp = t_1;
	elseif (z <= 1.65e+180)
		tmp = Float64(1.0 / Float64(Float64(-0.25 / a) * Float64(c / t)));
	elseif (z <= 1.42e+206)
		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 * (y * x))) / (c * z);
	t_2 = (t * (-4.0 * a)) / c;
	tmp = 0.0;
	if (z <= -1.8e+120)
		tmp = t_2;
	elseif (z <= 7.2e+59)
		tmp = t_1;
	elseif (z <= 1.65e+180)
		tmp = 1.0 / ((-0.25 / a) * (c / t));
	elseif (z <= 1.42e+206)
		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[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(c * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t * N[(-4.0 * a), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]}, If[LessEqual[z, -1.8e+120], t$95$2, If[LessEqual[z, 7.2e+59], t$95$1, If[LessEqual[z, 1.65e+180], N[(1.0 / N[(N[(-0.25 / a), $MachinePrecision] * N[(c / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.42e+206], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.80000000000000008e120 or 1.42000000000000005e206 < z

   1. Initial program 32.8%

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

      1. associate-/r* 47.3%

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

   3. Simplified 82.6%

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

   4. Taylor expanded in t around inf 65.7%

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

      1. associate-*r* 65.7%

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

      2. *-commutative 65.7%

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

      3. *-commutative 65.7%

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

      4. *-commutative 65.7%

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

   6. Simplified 65.7%

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

   if -1.80000000000000008e120 < z < 7.1999999999999997e59 or 1.64999999999999995e180 < z < 1.42000000000000005e206

   1. Initial program 92.4%

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

      1. associate-/r* 85.4%

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

   3. Simplified 87.2%

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

   4. Taylor expanded in z around 0 80.0%

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

   if 7.1999999999999997e59 < z < 1.64999999999999995e180

   1. Initial program 56.9%

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

      1. associate-/r* 72.9%

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

   3. Simplified 78.6%

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

      1. clear-num 78.8%

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

      2. fma-udef 78.8%

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

      3. +-commutative 78.8%

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

      4. inv-pow 78.8%

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

      5. +-commutative 78.8%

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

      6. fma-udef 78.8%

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

   5. Applied egg-rr 78.8%

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

   6. Taylor expanded in t around inf 46.9%

      \[\leadsto {\color{blue}{\left(-0.25 \cdot \frac{c}{a \cdot t}\right)}}^{-1} \]
   7. Step-by-step derivation

      1. associate-*r/ 46.9%

         \[\leadsto {\color{blue}{\left(\frac{-0.25 \cdot c}{a \cdot t}\right)}}^{-1} \]

   8. Simplified 46.9%

      \[\leadsto {\color{blue}{\left(\frac{-0.25 \cdot c}{a \cdot t}\right)}}^{-1} \]
   9. Step-by-step derivation

      1. unpow-1 46.9%

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

      2. times-frac 51.8%

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

   10. Applied egg-rr 51.8%

       \[\leadsto \color{blue}{\frac{1}{\frac{-0.25}{a} \cdot \frac{c}{t}}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 74.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+120}:\\ \;\;\;\;\frac{t \cdot \left(-4 \cdot a\right)}{c}\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{+59}:\\ \;\;\;\;\frac{b + 9 \cdot \left(y \cdot x\right)}{c \cdot z}\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{+180}:\\ \;\;\;\;\frac{1}{\frac{-0.25}{a} \cdot \frac{c}{t}}\\ \mathbf{elif}\;z \leq 1.42 \cdot 10^{+206}:\\ \;\;\;\;\frac{b + 9 \cdot \left(y \cdot x\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot \left(-4 \cdot a\right)}{c}\\ \end{array} \]

Alternative 10: 74.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} t_1 := t \cdot \left(-4 \cdot a\right)\\ \mathbf{if}\;z \leq -1.6 \cdot 10^{+70}:\\ \;\;\;\;\frac{t_1 + 9 \cdot \frac{y \cdot x}{z}}{c}\\ \mathbf{elif}\;z \leq 62000000000:\\ \;\;\;\;\frac{b + 9 \cdot \left(y \cdot x\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t_1 + \frac{b}{z}}{c}\\ \end{array} \end{array} \]

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
 (let* ((t_1 (* t (* -4.0 a))))
   (if (<= z -1.6e+70)
     (/ (+ t_1 (* 9.0 (/ (* y x) z))) c)
     (if (<= z 62000000000.0)
       (/ (+ b (* 9.0 (* y x))) (* c z))
       (/ (+ t_1 (/ b z)) c)))))

C

assert(x < y);
assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = t * (-4.0 * a);
	double tmp;
	if (z <= -1.6e+70) {
		tmp = (t_1 + (9.0 * ((y * x) / z))) / c;
	} else if (z <= 62000000000.0) {
		tmp = (b + (9.0 * (y * x))) / (c * z);
	} else {
		tmp = (t_1 + (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) :: t_1
    real(8) :: tmp
    t_1 = t * ((-4.0d0) * a)
    if (z <= (-1.6d+70)) then
        tmp = (t_1 + (9.0d0 * ((y * x) / z))) / c
    else if (z <= 62000000000.0d0) then
        tmp = (b + (9.0d0 * (y * x))) / (c * z)
    else
        tmp = (t_1 + (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 t_1 = t * (-4.0 * a);
	double tmp;
	if (z <= -1.6e+70) {
		tmp = (t_1 + (9.0 * ((y * x) / z))) / c;
	} else if (z <= 62000000000.0) {
		tmp = (b + (9.0 * (y * x))) / (c * z);
	} else {
		tmp = (t_1 + (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):
	t_1 = t * (-4.0 * a)
	tmp = 0
	if z <= -1.6e+70:
		tmp = (t_1 + (9.0 * ((y * x) / z))) / c
	elif z <= 62000000000.0:
		tmp = (b + (9.0 * (y * x))) / (c * z)
	else:
		tmp = (t_1 + (b / z)) / c
	return tmp

Julia

x, y = sort([x, y])
t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(t * Float64(-4.0 * a))
	tmp = 0.0
	if (z <= -1.6e+70)
		tmp = Float64(Float64(t_1 + Float64(9.0 * Float64(Float64(y * x) / z))) / c);
	elseif (z <= 62000000000.0)
		tmp = Float64(Float64(b + Float64(9.0 * Float64(y * x))) / Float64(c * z));
	else
		tmp = Float64(Float64(t_1 + 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)
	t_1 = t * (-4.0 * a);
	tmp = 0.0;
	if (z <= -1.6e+70)
		tmp = (t_1 + (9.0 * ((y * x) / z))) / c;
	elseif (z <= 62000000000.0)
		tmp = (b + (9.0 * (y * x))) / (c * z);
	else
		tmp = (t_1 + (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_] := Block[{t$95$1 = N[(t * N[(-4.0 * a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.6e+70], N[(N[(t$95$1 + N[(9.0 * N[(N[(y * x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[z, 62000000000.0], N[(N[(b + N[(9.0 * N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(c * z), $MachinePrecision]), $MachinePrecision], N[(N[(t$95$1 + N[(b / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.6000000000000001e70

   1. Initial program 40.6%

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

      1. associate-/r* 51.4%

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

   3. Simplified 83.7%

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

   4. Taylor expanded in x around inf 72.9%

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

   if -1.6000000000000001e70 < z < 6.2e10

   1. Initial program 94.5%

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

      1. associate-/r* 86.9%

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

   3. Simplified 87.7%

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

   4. Taylor expanded in z around 0 83.5%

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

   if 6.2e10 < z

   1. Initial program 53.8%

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

      1. associate-/r* 64.3%

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

   3. Simplified 81.2%

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

   4. Taylor expanded in x around 0 74.4%

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

4. Final simplification 79.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{+70}:\\ \;\;\;\;\frac{t \cdot \left(-4 \cdot a\right) + 9 \cdot \frac{y \cdot x}{z}}{c}\\ \mathbf{elif}\;z \leq 62000000000:\\ \;\;\;\;\frac{b + 9 \cdot \left(y \cdot x\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot \left(-4 \cdot a\right) + \frac{b}{z}}{c}\\ \end{array} \]

Alternative 11: 74.7% accurate, 1.3× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{+116} \lor \neg \left(z \leq 960000000000\right):\\ \;\;\;\;\frac{t \cdot \left(-4 \cdot a\right) + \frac{b}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + 9 \cdot \left(y \cdot x\right)}{c \cdot z}\\ \end{array} \end{array} \]

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 -1.45e+116) (not (<= z 960000000000.0)))
   (/ (+ (* t (* -4.0 a)) (/ b z)) c)
   (/ (+ b (* 9.0 (* y x))) (* 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 <= -1.45e+116) || !(z <= 960000000000.0)) {
		tmp = ((t * (-4.0 * a)) + (b / z)) / c;
	} else {
		tmp = (b + (9.0 * (y * x))) / (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 <= (-1.45d+116)) .or. (.not. (z <= 960000000000.0d0))) then
        tmp = ((t * ((-4.0d0) * a)) + (b / z)) / c
    else
        tmp = (b + (9.0d0 * (y * x))) / (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 <= -1.45e+116) || !(z <= 960000000000.0)) {
		tmp = ((t * (-4.0 * a)) + (b / z)) / c;
	} else {
		tmp = (b + (9.0 * (y * x))) / (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 <= -1.45e+116) or not (z <= 960000000000.0):
		tmp = ((t * (-4.0 * a)) + (b / z)) / c
	else:
		tmp = (b + (9.0 * (y * x))) / (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 <= -1.45e+116) || !(z <= 960000000000.0))
		tmp = Float64(Float64(Float64(t * Float64(-4.0 * a)) + Float64(b / z)) / c);
	else
		tmp = Float64(Float64(b + Float64(9.0 * Float64(y * x))) / 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 <= -1.45e+116) || ~((z <= 960000000000.0)))
		tmp = ((t * (-4.0 * a)) + (b / z)) / c;
	else
		tmp = (b + (9.0 * (y * x))) / (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, -1.45e+116], N[Not[LessEqual[z, 960000000000.0]], $MachinePrecision]], N[(N[(N[(t * N[(-4.0 * a), $MachinePrecision]), $MachinePrecision] + N[(b / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], N[(N[(b + N[(9.0 * N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(c * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.4500000000000001e116 or 9.6e11 < z

   1. Initial program 45.2%

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

      1. associate-/r* 56.6%

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

   3. Simplified 81.9%

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

   4. Taylor expanded in x around 0 73.9%

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

   if -1.4500000000000001e116 < z < 9.6e11

   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* 86.4%

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

   3. Simplified 87.7%

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

   4. Taylor expanded in z around 0 81.8%

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

4. Final simplification 78.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{+116} \lor \neg \left(z \leq 960000000000\right):\\ \;\;\;\;\frac{t \cdot \left(-4 \cdot a\right) + \frac{b}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + 9 \cdot \left(y \cdot x\right)}{c \cdot z}\\ \end{array} \]

Alternative 12: 48.8% accurate, 1.4× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} t_1 := -4 \cdot \left(\frac{a}{c} \cdot t\right)\\ \mathbf{if}\;a \leq -1.65 \cdot 10^{-162}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.3 \cdot 10^{-132}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;a \leq 1.45 \cdot 10^{+111}:\\ \;\;\;\;\frac{1}{\frac{c}{\frac{b}{z}}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

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 (* -4.0 (* (/ a c) t))))
   (if (<= a -1.65e-162)
     t_1
     (if (<= a 1.3e-132)
       (/ (/ b c) z)
       (if (<= a 1.45e+111) (/ 1.0 (/ c (/ b 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 = -4.0 * ((a / c) * t);
	double tmp;
	if (a <= -1.65e-162) {
		tmp = t_1;
	} else if (a <= 1.3e-132) {
		tmp = (b / c) / z;
	} else if (a <= 1.45e+111) {
		tmp = 1.0 / (c / (b / 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 = (-4.0d0) * ((a / c) * t)
    if (a <= (-1.65d-162)) then
        tmp = t_1
    else if (a <= 1.3d-132) then
        tmp = (b / c) / z
    else if (a <= 1.45d+111) then
        tmp = 1.0d0 / (c / (b / 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 = -4.0 * ((a / c) * t);
	double tmp;
	if (a <= -1.65e-162) {
		tmp = t_1;
	} else if (a <= 1.3e-132) {
		tmp = (b / c) / z;
	} else if (a <= 1.45e+111) {
		tmp = 1.0 / (c / (b / 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 = -4.0 * ((a / c) * t)
	tmp = 0
	if a <= -1.65e-162:
		tmp = t_1
	elif a <= 1.3e-132:
		tmp = (b / c) / z
	elif a <= 1.45e+111:
		tmp = 1.0 / (c / (b / 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(-4.0 * Float64(Float64(a / c) * t))
	tmp = 0.0
	if (a <= -1.65e-162)
		tmp = t_1;
	elseif (a <= 1.3e-132)
		tmp = Float64(Float64(b / c) / z);
	elseif (a <= 1.45e+111)
		tmp = Float64(1.0 / Float64(c / Float64(b / 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 = -4.0 * ((a / c) * t);
	tmp = 0.0;
	if (a <= -1.65e-162)
		tmp = t_1;
	elseif (a <= 1.3e-132)
		tmp = (b / c) / z;
	elseif (a <= 1.45e+111)
		tmp = 1.0 / (c / (b / 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[(-4.0 * N[(N[(a / c), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.65e-162], t$95$1, If[LessEqual[a, 1.3e-132], N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[a, 1.45e+111], N[(1.0 / N[(c / N[(b / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.65000000000000007e-162 or 1.45e111 < a

   1. Initial program 71.7%

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

      1. associate-/r* 72.9%

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

   3. Simplified 83.4%

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

   4. Taylor expanded in t around inf 47.0%

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

      1. associate-/l* 48.9%

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

      2. associate-/r/ 52.3%

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

   6. Simplified 52.3%

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

   if -1.65000000000000007e-162 < a < 1.3e-132

   1. Initial program 73.1%

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

      1. associate-/r* 74.4%

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

   3. Simplified 89.0%

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

      1. div-inv 88.9%

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

   5. Applied egg-rr 88.9%

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

   6. Taylor expanded in b around inf 41.3%

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

      1. associate-/r* 41.4%

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

   8. Simplified 41.4%

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

   if 1.3e-132 < a < 1.45e111

   1. Initial program 84.7%

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

      1. associate-/r* 79.9%

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

   3. Simplified 85.0%

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

   4. Taylor expanded in b around inf 41.6%

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

      1. *-commutative 41.6%

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

   6. Simplified 41.6%

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

      1. clear-num 41.6%

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

      2. inv-pow 41.6%

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

      3. *-commutative 41.6%

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

   8. Applied egg-rr 41.6%

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

      1. unpow-1 41.6%

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

      2. associate-/l* 42.0%

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

   10. Simplified 42.0%

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

4. Final simplification 47.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.65 \cdot 10^{-162}:\\ \;\;\;\;-4 \cdot \left(\frac{a}{c} \cdot t\right)\\ \mathbf{elif}\;a \leq 1.3 \cdot 10^{-132}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;a \leq 1.45 \cdot 10^{+111}:\\ \;\;\;\;\frac{1}{\frac{c}{\frac{b}{z}}}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(\frac{a}{c} \cdot t\right)\\ \end{array} \]

Alternative 13: 49.1% accurate, 1.7× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq -1.65 \cdot 10^{-162} \lor \neg \left(a \leq 5.5 \cdot 10^{+112}\right):\\ \;\;\;\;-4 \cdot \left(\frac{a}{c} \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \end{array} \end{array} \]

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 (<= a -1.65e-162) (not (<= a 5.5e+112)))
   (* -4.0 (* (/ a c) t))
   (/ (/ 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 ((a <= -1.65e-162) || !(a <= 5.5e+112)) {
		tmp = -4.0 * ((a / c) * t);
	} else {
		tmp = (b / 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 ((a <= (-1.65d-162)) .or. (.not. (a <= 5.5d+112))) then
        tmp = (-4.0d0) * ((a / c) * t)
    else
        tmp = (b / 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 ((a <= -1.65e-162) || !(a <= 5.5e+112)) {
		tmp = -4.0 * ((a / c) * t);
	} else {
		tmp = (b / 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 (a <= -1.65e-162) or not (a <= 5.5e+112):
		tmp = -4.0 * ((a / c) * t)
	else:
		tmp = (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 ((a <= -1.65e-162) || !(a <= 5.5e+112))
		tmp = Float64(-4.0 * Float64(Float64(a / c) * t));
	else
		tmp = Float64(Float64(b / 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 ((a <= -1.65e-162) || ~((a <= 5.5e+112)))
		tmp = -4.0 * ((a / c) * t);
	else
		tmp = (b / 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[a, -1.65e-162], N[Not[LessEqual[a, 5.5e+112]], $MachinePrecision]], N[(-4.0 * N[(N[(a / c), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.65000000000000007e-162 or 5.50000000000000026e112 < a

   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* 72.7%

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

   3. Simplified 83.3%

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

   4. Taylor expanded in t around inf 47.3%

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

      1. associate-/l* 49.3%

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

      2. associate-/r/ 52.7%

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

   6. Simplified 52.7%

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

   if -1.65000000000000007e-162 < a < 5.50000000000000026e112

   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. Step-by-step derivation

      1. associate-/r* 76.3%

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

   3. Simplified 86.9%

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

      1. div-inv 86.9%

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

   5. Applied egg-rr 86.9%

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

   6. Taylor expanded in b around inf 41.0%

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

      1. associate-/r* 40.3%

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

   8. Simplified 40.3%

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

4. Final simplification 46.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.65 \cdot 10^{-162} \lor \neg \left(a \leq 5.5 \cdot 10^{+112}\right):\\ \;\;\;\;-4 \cdot \left(\frac{a}{c} \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \end{array} \]

Alternative 14: 35.1% accurate, 2.7× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -2.4 \cdot 10^{-279}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \end{array} \end{array} \]

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 (<= t -2.4e-279) (/ (/ b c) 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 (t <= -2.4e-279) {
		tmp = (b / c) / z;
	} else {
		tmp = b / (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 (t <= (-2.4d-279)) then
        tmp = (b / c) / z
    else
        tmp = b / (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 (t <= -2.4e-279) {
		tmp = (b / c) / z;
	} else {
		tmp = b / (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 t <= -2.4e-279:
		tmp = (b / c) / z
	else:
		tmp = 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 (t <= -2.4e-279)
		tmp = Float64(Float64(b / c) / z);
	else
		tmp = Float64(b / 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 (t <= -2.4e-279)
		tmp = (b / c) / z;
	else
		tmp = b / (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[LessEqual[t, -2.4e-279], N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision], N[(b / N[(c * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.3999999999999999e-279

   1. Initial program 74.8%

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

      1. associate-/r* 73.6%

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

   3. Simplified 83.4%

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

      1. div-inv 83.4%

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

   5. Applied egg-rr 83.4%

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

   6. Taylor expanded in b around inf 32.0%

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

      1. associate-/r* 33.6%

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

   8. Simplified 33.6%

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

   if -2.3999999999999999e-279 < t

   1. Initial program 73.5%

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

      1. associate-/r* 75.1%

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

   3. Simplified 86.3%

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

   4. Taylor expanded in b around inf 35.4%

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

      1. *-commutative 35.4%

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

   6. Simplified 35.4%

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

4. Final simplification 34.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.4 \cdot 10^{-279}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \end{array} \]

Alternative 15: 35.9% 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 74.1%

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

   1. associate-/r* 74.4%

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

3. Simplified 85.4%

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

4. Taylor expanded in b around inf 33.8%

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

   1. *-commutative 33.8%

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

6. Simplified 33.8%

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

7. Final simplification 33.8%

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

Developer target: 81.1% 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 2023252 
(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)))