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

Percentage Accurate: 78.5% → 90.0%

Time: 14.2s

Alternatives: 15

Speedup: 1.1×

• 37.1% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 78.5% 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: 90.0% accurate, 0.1× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} \mathbf{if}\;c \leq -1.1 \cdot 10^{+54} \lor \neg \left(c \leq 1.3 \cdot 10^{+211}\right):\\ \;\;\;\;\frac{b}{c \cdot z} + \mathsf{fma}\left(-4, \frac{a}{\frac{c}{t}}, 9 \cdot \frac{y}{\frac{c \cdot z}{x}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(t, -4 \cdot a, \frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z}\right)}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= c -1.1e+54) (not (<= c 1.3e+211)))
   (+ (/ b (* c z)) (fma -4.0 (/ a (/ c t)) (* 9.0 (/ y (/ (* c z) x)))))
   (/ (fma t (* -4.0 a) (/ (fma x (* 9.0 y) b) z)) c)))

C

assert(x < y);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((c <= -1.1e+54) || !(c <= 1.3e+211)) {
		tmp = (b / (c * z)) + fma(-4.0, (a / (c / t)), (9.0 * (y / ((c * z) / x))));
	} else {
		tmp = fma(t, (-4.0 * a), (fma(x, (9.0 * y), b) / z)) / c;
	}
	return tmp;
}

Julia

x, y = sort([x, y])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((c <= -1.1e+54) || !(c <= 1.3e+211))
		tmp = Float64(Float64(b / Float64(c * z)) + fma(-4.0, Float64(a / Float64(c / t)), Float64(9.0 * Float64(y / Float64(Float64(c * z) / x)))));
	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.
code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[c, -1.1e+54], N[Not[LessEqual[c, 1.3e+211]], $MachinePrecision]], N[(N[(b / N[(c * z), $MachinePrecision]), $MachinePrecision] + N[(-4.0 * N[(a / N[(c / t), $MachinePrecision]), $MachinePrecision] + N[(9.0 * N[(y / N[(N[(c * z), $MachinePrecision] / x), $MachinePrecision]), $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 < -1.09999999999999995e54 or 1.2999999999999999e211 < c

   1. Initial program 57.8%

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

      1. associate-/r* 48.5%

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

   3. Simplified 66.4%

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

   4. Taylor expanded in t around 0 76.5%

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

      1. *-commutative 76.5%

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

      2. fma-def 76.5%

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

      3. associate-/l* 85.1%

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

      4. associate-/l* 87.9%

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

      5. *-commutative 87.9%

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

   6. Simplified 87.9%

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

   if -1.09999999999999995e54 < c < 1.2999999999999999e211

   1. Initial program 82.3%

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

      1. associate-/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 96.3%

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

4. Final simplification 94.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.1 \cdot 10^{+54} \lor \neg \left(c \leq 1.3 \cdot 10^{+211}\right):\\ \;\;\;\;\frac{b}{c \cdot z} + \mathsf{fma}\left(-4, \frac{a}{\frac{c}{t}}, 9 \cdot \frac{y}{\frac{c \cdot z}{x}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(t, -4 \cdot a, \frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z}\right)}{c}\\ \end{array} \]

Alternative 2: 89.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} \mathbf{if}\;c \leq -1.4 \cdot 10^{+54} \lor \neg \left(c \leq 1.75 \cdot 10^{+211}\right):\\ \;\;\;\;\frac{b}{c \cdot z} + \mathsf{fma}\left(-4, \frac{a}{\frac{c}{t}}, 9 \cdot \frac{y}{\frac{c \cdot z}{x}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(b + x \cdot \left(9 \cdot y\right)\right) \cdot \frac{1}{z} + t \cdot \left(-4 \cdot a\right)}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= c -1.4e+54) (not (<= c 1.75e+211)))
   (+ (/ b (* c z)) (fma -4.0 (/ a (/ c t)) (* 9.0 (/ y (/ (* c z) x)))))
   (/ (+ (* (+ b (* x (* 9.0 y))) (/ 1.0 z)) (* t (* -4.0 a))) c)))

C

assert(x < y);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((c <= -1.4e+54) || !(c <= 1.75e+211)) {
		tmp = (b / (c * z)) + fma(-4.0, (a / (c / t)), (9.0 * (y / ((c * z) / x))));
	} else {
		tmp = (((b + (x * (9.0 * y))) * (1.0 / z)) + (t * (-4.0 * a))) / c;
	}
	return tmp;
}

Julia

x, y = sort([x, y])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((c <= -1.4e+54) || !(c <= 1.75e+211))
		tmp = Float64(Float64(b / Float64(c * z)) + fma(-4.0, Float64(a / Float64(c / t)), Float64(9.0 * Float64(y / Float64(Float64(c * z) / x)))));
	else
		tmp = Float64(Float64(Float64(Float64(b + Float64(x * Float64(9.0 * y))) * Float64(1.0 / 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.
code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[c, -1.4e+54], N[Not[LessEqual[c, 1.75e+211]], $MachinePrecision]], N[(N[(b / N[(c * z), $MachinePrecision]), $MachinePrecision] + N[(-4.0 * N[(a / N[(c / t), $MachinePrecision]), $MachinePrecision] + N[(9.0 * N[(y / N[(N[(c * z), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(b + N[(x * N[(9.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(1.0 / z), $MachinePrecision]), $MachinePrecision] + N[(t * N[(-4.0 * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -1.40000000000000008e54 or 1.74999999999999998e211 < c

   1. Initial program 57.8%

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

      1. associate-/r* 48.5%

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

   3. Simplified 66.4%

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

   4. Taylor expanded in t around 0 76.5%

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

      1. *-commutative 76.5%

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

      2. fma-def 76.5%

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

      3. associate-/l* 85.1%

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

      4. associate-/l* 87.9%

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

      5. *-commutative 87.9%

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

   6. Simplified 87.9%

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

   if -1.40000000000000008e54 < c < 1.74999999999999998e211

   1. Initial program 82.3%

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

      1. associate-/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 95.8%

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

      1. div-inv 95.8%

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

   5. Applied egg-rr 95.8%

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

      1. fma-udef 95.8%

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

   7. Applied egg-rr 95.8%

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

4. Final simplification 93.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.4 \cdot 10^{+54} \lor \neg \left(c \leq 1.75 \cdot 10^{+211}\right):\\ \;\;\;\;\frac{b}{c \cdot z} + \mathsf{fma}\left(-4, \frac{a}{\frac{c}{t}}, 9 \cdot \frac{y}{\frac{c \cdot z}{x}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(b + x \cdot \left(9 \cdot y\right)\right) \cdot \frac{1}{z} + t \cdot \left(-4 \cdot a\right)}{c}\\ \end{array} \]

Alternative 3: 88.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} t_1 := y \cdot \left(9 \cdot x\right)\\ \mathbf{if}\;t_1 \leq -5 \cdot 10^{+295} \lor \neg \left(t_1 \leq 2 \cdot 10^{+287}\right):\\ \;\;\;\;9 \cdot \left(\frac{y}{z} \cdot \frac{x}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(b + x \cdot \left(9 \cdot y\right)\right) \cdot \frac{1}{z} + t \cdot \left(-4 \cdot a\right)}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* y (* 9.0 x))))
   (if (or (<= t_1 -5e+295) (not (<= t_1 2e+287)))
     (* 9.0 (* (/ y z) (/ x c)))
     (/ (+ (* (+ b (* x (* 9.0 y))) (/ 1.0 z)) (* t (* -4.0 a))) c))))

C

assert(x < y);
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 <= -5e+295) || !(t_1 <= 2e+287)) {
		tmp = 9.0 * ((y / z) * (x / c));
	} else {
		tmp = (((b + (x * (9.0 * y))) * (1.0 / z)) + (t * (-4.0 * a))) / c;
	}
	return tmp;
}

Fortran

NOTE: x and y 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 = y * (9.0d0 * x)
    if ((t_1 <= (-5d+295)) .or. (.not. (t_1 <= 2d+287))) then
        tmp = 9.0d0 * ((y / z) * (x / c))
    else
        tmp = (((b + (x * (9.0d0 * y))) * (1.0d0 / z)) + (t * ((-4.0d0) * a))) / c
    end if
    code = tmp
end function

Java

assert x < y;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = y * (9.0 * x);
	double tmp;
	if ((t_1 <= -5e+295) || !(t_1 <= 2e+287)) {
		tmp = 9.0 * ((y / z) * (x / c));
	} else {
		tmp = (((b + (x * (9.0 * y))) * (1.0 / z)) + (t * (-4.0 * a))) / c;
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y, z, t, a, b, c):
	t_1 = y * (9.0 * x)
	tmp = 0
	if (t_1 <= -5e+295) or not (t_1 <= 2e+287):
		tmp = 9.0 * ((y / z) * (x / c))
	else:
		tmp = (((b + (x * (9.0 * y))) * (1.0 / z)) + (t * (-4.0 * a))) / c
	return tmp

Julia

x, y = sort([x, y])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(y * Float64(9.0 * x))
	tmp = 0.0
	if ((t_1 <= -5e+295) || !(t_1 <= 2e+287))
		tmp = Float64(9.0 * Float64(Float64(y / z) * Float64(x / c)));
	else
		tmp = Float64(Float64(Float64(Float64(b + Float64(x * Float64(9.0 * y))) * Float64(1.0 / z)) + Float64(t * Float64(-4.0 * a))) / c);
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = y * (9.0 * x);
	tmp = 0.0;
	if ((t_1 <= -5e+295) || ~((t_1 <= 2e+287)))
		tmp = 9.0 * ((y / z) * (x / c));
	else
		tmp = (((b + (x * (9.0 * y))) * (1.0 / z)) + (t * (-4.0 * a))) / c;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y 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[Or[LessEqual[t$95$1, -5e+295], N[Not[LessEqual[t$95$1, 2e+287]], $MachinePrecision]], N[(9.0 * N[(N[(y / z), $MachinePrecision] * N[(x / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(b + N[(x * N[(9.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(1.0 / z), $MachinePrecision]), $MachinePrecision] + N[(t * N[(-4.0 * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 x 9) y) < -4.99999999999999991e295 or 2.0000000000000002e287 < (*.f64 (*.f64 x 9) y)

   1. Initial program 59.8%

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

      1. associate-/r* 58.0%

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

   3. Simplified 60.8%

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

   4. Taylor expanded in x around inf 62.5%

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

      1. *-commutative 62.5%

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

      2. times-frac 78.7%

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

   6. Simplified 78.7%

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

   if -4.99999999999999991e295 < (*.f64 (*.f64 x 9) y) < 2.0000000000000002e287

   1. Initial program 78.7%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   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 93.3%

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

      1. div-inv 93.3%

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

   5. Applied egg-rr 93.3%

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

      1. fma-udef 93.3%

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

   7. Applied egg-rr 93.3%

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

4. Final simplification 91.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \left(9 \cdot x\right) \leq -5 \cdot 10^{+295} \lor \neg \left(y \cdot \left(9 \cdot x\right) \leq 2 \cdot 10^{+287}\right):\\ \;\;\;\;9 \cdot \left(\frac{y}{z} \cdot \frac{x}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(b + x \cdot \left(9 \cdot y\right)\right) \cdot \frac{1}{z} + t \cdot \left(-4 \cdot a\right)}{c}\\ \end{array} \]

Alternative 4: 86.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} \mathbf{if}\;c \leq 3 \cdot 10^{+210}:\\ \;\;\;\;\frac{\left(b + x \cdot \left(9 \cdot y\right)\right) \cdot \frac{1}{z} + t \cdot \left(-4 \cdot a\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{c} + \frac{9 \cdot \left(y \cdot x\right)}{c}}{z} - 4 \cdot \frac{a \cdot t}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= c 3e+210)
   (/ (+ (* (+ b (* x (* 9.0 y))) (/ 1.0 z)) (* t (* -4.0 a))) c)
   (- (/ (+ (/ b c) (/ (* 9.0 (* y x)) c)) z) (* 4.0 (/ (* a t) c)))))

C

assert(x < y);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (c <= 3e+210) {
		tmp = (((b + (x * (9.0 * y))) * (1.0 / z)) + (t * (-4.0 * a))) / c;
	} else {
		tmp = (((b / c) + ((9.0 * (y * x)) / c)) / z) - (4.0 * ((a * t) / c));
	}
	return tmp;
}

Fortran

NOTE: x and y 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 (c <= 3d+210) then
        tmp = (((b + (x * (9.0d0 * y))) * (1.0d0 / z)) + (t * ((-4.0d0) * a))) / c
    else
        tmp = (((b / c) + ((9.0d0 * (y * x)) / c)) / z) - (4.0d0 * ((a * t) / c))
    end if
    code = tmp
end function

Java

assert x < y;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (c <= 3e+210) {
		tmp = (((b + (x * (9.0 * y))) * (1.0 / z)) + (t * (-4.0 * a))) / c;
	} else {
		tmp = (((b / c) + ((9.0 * (y * x)) / c)) / z) - (4.0 * ((a * t) / c));
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if c <= 3e+210:
		tmp = (((b + (x * (9.0 * y))) * (1.0 / z)) + (t * (-4.0 * a))) / c
	else:
		tmp = (((b / c) + ((9.0 * (y * x)) / c)) / z) - (4.0 * ((a * t) / c))
	return tmp

Julia

x, y = sort([x, y])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (c <= 3e+210)
		tmp = Float64(Float64(Float64(Float64(b + Float64(x * Float64(9.0 * y))) * Float64(1.0 / z)) + Float64(t * Float64(-4.0 * a))) / c);
	else
		tmp = Float64(Float64(Float64(Float64(b / c) + Float64(Float64(9.0 * Float64(y * x)) / c)) / z) - Float64(4.0 * Float64(Float64(a * t) / c)));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (c <= 3e+210)
		tmp = (((b + (x * (9.0 * y))) * (1.0 / z)) + (t * (-4.0 * a))) / c;
	else
		tmp = (((b / c) + ((9.0 * (y * x)) / c)) / z) - (4.0 * ((a * t) / c));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[c, 3e+210], N[(N[(N[(N[(b + N[(x * N[(9.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(1.0 / z), $MachinePrecision]), $MachinePrecision] + N[(t * N[(-4.0 * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], N[(N[(N[(N[(b / c), $MachinePrecision] + N[(N[(9.0 * N[(y * x), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] - N[(4.0 * N[(N[(a * t), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < 3.00000000000000022e210

   1. Initial program 76.8%

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

      1. associate-/r* 79.0%

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

   3. Simplified 91.0%

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

      1. div-inv 91.0%

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

   5. Applied egg-rr 91.0%

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

      1. fma-udef 91.0%

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

   7. Applied egg-rr 91.0%

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

   if 3.00000000000000022e210 < c

   1. Initial program 67.0%

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

      1. associate-*l* 67.0%

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

      2. associate-*l* 67.0%

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

   3. Simplified 67.0%

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

   4. Taylor expanded in x around 0 73.1%

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

   5. Taylor expanded in z around 0 83.7%

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

      1. associate-*r/ 83.8%

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

   7. Simplified 83.8%

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

4. Final simplification 90.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq 3 \cdot 10^{+210}:\\ \;\;\;\;\frac{\left(b + x \cdot \left(9 \cdot y\right)\right) \cdot \frac{1}{z} + t \cdot \left(-4 \cdot a\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{c} + \frac{9 \cdot \left(y \cdot x\right)}{c}}{z} - 4 \cdot \frac{a \cdot t}{c}\\ \end{array} \]

Alternative 5: 75.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} t_1 := t \cdot \left(-4 \cdot a\right)\\ \mathbf{if}\;b \leq -1300000 \lor \neg \left(b \leq 9 \cdot 10^{-85}\right):\\ \;\;\;\;\frac{t_1 + \frac{b}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{t_1 + \frac{9 \cdot \left(y \cdot x\right)}{z}}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y 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 (or (<= b -1300000.0) (not (<= b 9e-85)))
     (/ (+ t_1 (/ b z)) c)
     (/ (+ t_1 (/ (* 9.0 (* y x)) z)) c))))

C

assert(x < y);
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 ((b <= -1300000.0) || !(b <= 9e-85)) {
		tmp = (t_1 + (b / z)) / c;
	} else {
		tmp = (t_1 + ((9.0 * (y * x)) / z)) / c;
	}
	return tmp;
}

Fortran

NOTE: x and y 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 ((b <= (-1300000.0d0)) .or. (.not. (b <= 9d-85))) then
        tmp = (t_1 + (b / z)) / c
    else
        tmp = (t_1 + ((9.0d0 * (y * x)) / z)) / c
    end if
    code = tmp
end function

Java

assert x < y;
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 ((b <= -1300000.0) || !(b <= 9e-85)) {
		tmp = (t_1 + (b / z)) / c;
	} else {
		tmp = (t_1 + ((9.0 * (y * x)) / z)) / c;
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y, z, t, a, b, c):
	t_1 = t * (-4.0 * a)
	tmp = 0
	if (b <= -1300000.0) or not (b <= 9e-85):
		tmp = (t_1 + (b / z)) / c
	else:
		tmp = (t_1 + ((9.0 * (y * x)) / z)) / c
	return tmp

Julia

x, y = sort([x, y])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(t * Float64(-4.0 * a))
	tmp = 0.0
	if ((b <= -1300000.0) || !(b <= 9e-85))
		tmp = Float64(Float64(t_1 + Float64(b / z)) / c);
	else
		tmp = Float64(Float64(t_1 + Float64(Float64(9.0 * Float64(y * x)) / z)) / c);
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = t * (-4.0 * a);
	tmp = 0.0;
	if ((b <= -1300000.0) || ~((b <= 9e-85)))
		tmp = (t_1 + (b / z)) / c;
	else
		tmp = (t_1 + ((9.0 * (y * x)) / z)) / c;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y 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[Or[LessEqual[b, -1300000.0], N[Not[LessEqual[b, 9e-85]], $MachinePrecision]], N[(N[(t$95$1 + N[(b / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], N[(N[(t$95$1 + N[(N[(9.0 * N[(y * x), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if b < -1.3e6 or 9.00000000000000008e-85 < b

   1. Initial program 76.5%

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

      1. associate-/r* 76.8%

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

   3. Simplified 86.7%

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

   4. Taylor expanded in x around 0 74.2%

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

   if -1.3e6 < b < 9.00000000000000008e-85

   1. Initial program 75.5%

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

      1. associate-/r* 76.7%

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

   3. Simplified 90.4%

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

   4. Taylor expanded in x around inf 84.5%

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

4. Final simplification 78.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1300000 \lor \neg \left(b \leq 9 \cdot 10^{-85}\right):\\ \;\;\;\;\frac{t \cdot \left(-4 \cdot a\right) + \frac{b}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot \left(-4 \cdot a\right) + \frac{9 \cdot \left(y \cdot x\right)}{z}}{c}\\ \end{array} \]

Alternative 6: 85.8% accurate, 1.1× speedup

Math

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

FPCore

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

C

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

Fortran

NOTE: x and y 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 = ((t * ((-4.0d0) * a)) + ((b + (x * (9.0d0 * y))) / z)) / c
end function

Java

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

Python

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

Julia

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

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp = code(x, y, z, t, a, b, c)
	tmp = ((t * (-4.0 * a)) + ((b + (x * (9.0 * y))) / z)) / c;
end

Wolfram

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

Derivation

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* 76.8%

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

3. Simplified 88.3%

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

   1. fma-udef 88.3%

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

5. Applied egg-rr 88.3%

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

6. Final simplification 88.3%

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

Alternative 7: 49.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} t_1 := -4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{if}\;b \leq -2.2 \cdot 10^{+154}:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \mathbf{elif}\;b \leq -3.5 \cdot 10^{-139}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -1.5 \cdot 10^{-184}:\\ \;\;\;\;9 \cdot \left(\frac{y}{z} \cdot \frac{x}{c}\right)\\ \mathbf{elif}\;b \leq 2.3 \cdot 10^{-16}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* -4.0 (* t (/ a c)))))
   (if (<= b -2.2e+154)
     (/ b (* c z))
     (if (<= b -3.5e-139)
       t_1
       (if (<= b -1.5e-184)
         (* 9.0 (* (/ y z) (/ x c)))
         (if (<= b 2.3e-16) t_1 (/ (/ b c) z)))))))

C

assert(x < y);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = -4.0 * (t * (a / c));
	double tmp;
	if (b <= -2.2e+154) {
		tmp = b / (c * z);
	} else if (b <= -3.5e-139) {
		tmp = t_1;
	} else if (b <= -1.5e-184) {
		tmp = 9.0 * ((y / z) * (x / c));
	} else if (b <= 2.3e-16) {
		tmp = t_1;
	} else {
		tmp = (b / c) / z;
	}
	return tmp;
}

Fortran

NOTE: x and y 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) * (t * (a / c))
    if (b <= (-2.2d+154)) then
        tmp = b / (c * z)
    else if (b <= (-3.5d-139)) then
        tmp = t_1
    else if (b <= (-1.5d-184)) then
        tmp = 9.0d0 * ((y / z) * (x / c))
    else if (b <= 2.3d-16) then
        tmp = t_1
    else
        tmp = (b / c) / z
    end if
    code = tmp
end function

Java

assert x < y;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = -4.0 * (t * (a / c));
	double tmp;
	if (b <= -2.2e+154) {
		tmp = b / (c * z);
	} else if (b <= -3.5e-139) {
		tmp = t_1;
	} else if (b <= -1.5e-184) {
		tmp = 9.0 * ((y / z) * (x / c));
	} else if (b <= 2.3e-16) {
		tmp = t_1;
	} else {
		tmp = (b / c) / z;
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y, z, t, a, b, c):
	t_1 = -4.0 * (t * (a / c))
	tmp = 0
	if b <= -2.2e+154:
		tmp = b / (c * z)
	elif b <= -3.5e-139:
		tmp = t_1
	elif b <= -1.5e-184:
		tmp = 9.0 * ((y / z) * (x / c))
	elif b <= 2.3e-16:
		tmp = t_1
	else:
		tmp = (b / c) / z
	return tmp

Julia

x, y = sort([x, y])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(-4.0 * Float64(t * Float64(a / c)))
	tmp = 0.0
	if (b <= -2.2e+154)
		tmp = Float64(b / Float64(c * z));
	elseif (b <= -3.5e-139)
		tmp = t_1;
	elseif (b <= -1.5e-184)
		tmp = Float64(9.0 * Float64(Float64(y / z) * Float64(x / c)));
	elseif (b <= 2.3e-16)
		tmp = t_1;
	else
		tmp = Float64(Float64(b / c) / z);
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = -4.0 * (t * (a / c));
	tmp = 0.0;
	if (b <= -2.2e+154)
		tmp = b / (c * z);
	elseif (b <= -3.5e-139)
		tmp = t_1;
	elseif (b <= -1.5e-184)
		tmp = 9.0 * ((y / z) * (x / c));
	elseif (b <= 2.3e-16)
		tmp = t_1;
	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.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2.2e+154], N[(b / N[(c * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -3.5e-139], t$95$1, If[LessEqual[b, -1.5e-184], N[(9.0 * N[(N[(y / z), $MachinePrecision] * N[(x / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.3e-16], t$95$1, N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -2.2000000000000001e154

   1. Initial program 77.4%

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

      1. associate-/r* 66.2%

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

   3. Simplified 77.7%

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

   4. Taylor expanded in b around inf 65.6%

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

      1. *-commutative 65.6%

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

   6. Simplified 65.6%

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

   if -2.2000000000000001e154 < b < -3.50000000000000001e-139 or -1.49999999999999996e-184 < b < 2.2999999999999999e-16

   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* 74.8%

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

   3. Simplified 92.4%

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

   4. Taylor expanded in t around inf 57.1%

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

      1. associate-/l* 57.7%

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

      2. associate-/r/ 58.2%

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

   6. Simplified 58.2%

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

   if -3.50000000000000001e-139 < b < -1.49999999999999996e-184

   1. Initial program 91.9%

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

      1. associate-/r* 84.0%

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

   3. Simplified 84.1%

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

   4. Taylor expanded in x around inf 68.5%

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

      1. *-commutative 68.5%

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

      2. times-frac 76.3%

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

   6. Simplified 76.3%

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

   if 2.2999999999999999e-16 < b

   1. Initial program 81.2%

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

      1. associate-/r* 82.7%

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

   3. Simplified 86.3%

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

      1. div-inv 86.3%

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

   5. Applied egg-rr 86.3%

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

   6. Taylor expanded in b around inf 57.1%

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

      1. associate-/r* 60.1%

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

   8. Simplified 60.1%

      \[\leadsto \color{blue}{\frac{\frac{b}{c}}{z}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 60.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.2 \cdot 10^{+154}:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \mathbf{elif}\;b \leq -3.5 \cdot 10^{-139}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;b \leq -1.5 \cdot 10^{-184}:\\ \;\;\;\;9 \cdot \left(\frac{y}{z} \cdot \frac{x}{c}\right)\\ \mathbf{elif}\;b \leq 2.3 \cdot 10^{-16}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \end{array} \]

Alternative 8: 49.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} t_1 := -4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{if}\;b \leq -1.45 \cdot 10^{+161}:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \mathbf{elif}\;b \leq -6 \cdot 10^{-142}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -3.6 \cdot 10^{-184}:\\ \;\;\;\;9 \cdot \frac{y}{\frac{z}{\frac{x}{c}}}\\ \mathbf{elif}\;b \leq 1.05 \cdot 10^{-13}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* -4.0 (* t (/ a c)))))
   (if (<= b -1.45e+161)
     (/ b (* c z))
     (if (<= b -6e-142)
       t_1
       (if (<= b -3.6e-184)
         (* 9.0 (/ y (/ z (/ x c))))
         (if (<= b 1.05e-13) t_1 (/ (/ b c) z)))))))

C

assert(x < y);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = -4.0 * (t * (a / c));
	double tmp;
	if (b <= -1.45e+161) {
		tmp = b / (c * z);
	} else if (b <= -6e-142) {
		tmp = t_1;
	} else if (b <= -3.6e-184) {
		tmp = 9.0 * (y / (z / (x / c)));
	} else if (b <= 1.05e-13) {
		tmp = t_1;
	} else {
		tmp = (b / c) / z;
	}
	return tmp;
}

Fortran

NOTE: x and y 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) * (t * (a / c))
    if (b <= (-1.45d+161)) then
        tmp = b / (c * z)
    else if (b <= (-6d-142)) then
        tmp = t_1
    else if (b <= (-3.6d-184)) then
        tmp = 9.0d0 * (y / (z / (x / c)))
    else if (b <= 1.05d-13) then
        tmp = t_1
    else
        tmp = (b / c) / z
    end if
    code = tmp
end function

Java

assert x < y;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = -4.0 * (t * (a / c));
	double tmp;
	if (b <= -1.45e+161) {
		tmp = b / (c * z);
	} else if (b <= -6e-142) {
		tmp = t_1;
	} else if (b <= -3.6e-184) {
		tmp = 9.0 * (y / (z / (x / c)));
	} else if (b <= 1.05e-13) {
		tmp = t_1;
	} else {
		tmp = (b / c) / z;
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y, z, t, a, b, c):
	t_1 = -4.0 * (t * (a / c))
	tmp = 0
	if b <= -1.45e+161:
		tmp = b / (c * z)
	elif b <= -6e-142:
		tmp = t_1
	elif b <= -3.6e-184:
		tmp = 9.0 * (y / (z / (x / c)))
	elif b <= 1.05e-13:
		tmp = t_1
	else:
		tmp = (b / c) / z
	return tmp

Julia

x, y = sort([x, y])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(-4.0 * Float64(t * Float64(a / c)))
	tmp = 0.0
	if (b <= -1.45e+161)
		tmp = Float64(b / Float64(c * z));
	elseif (b <= -6e-142)
		tmp = t_1;
	elseif (b <= -3.6e-184)
		tmp = Float64(9.0 * Float64(y / Float64(z / Float64(x / c))));
	elseif (b <= 1.05e-13)
		tmp = t_1;
	else
		tmp = Float64(Float64(b / c) / z);
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = -4.0 * (t * (a / c));
	tmp = 0.0;
	if (b <= -1.45e+161)
		tmp = b / (c * z);
	elseif (b <= -6e-142)
		tmp = t_1;
	elseif (b <= -3.6e-184)
		tmp = 9.0 * (y / (z / (x / c)));
	elseif (b <= 1.05e-13)
		tmp = t_1;
	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.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.45e+161], N[(b / N[(c * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -6e-142], t$95$1, If[LessEqual[b, -3.6e-184], N[(9.0 * N[(y / N[(z / N[(x / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.05e-13], t$95$1, N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -1.45000000000000008e161

   1. Initial program 77.4%

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

      1. associate-/r* 66.2%

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

   3. Simplified 77.7%

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

   4. Taylor expanded in b around inf 65.6%

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

      1. *-commutative 65.6%

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

   6. Simplified 65.6%

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

   if -1.45000000000000008e161 < b < -6.0000000000000002e-142 or -3.6000000000000001e-184 < b < 1.04999999999999994e-13

   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* 74.8%

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

   3. Simplified 92.4%

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

   4. Taylor expanded in t around inf 57.1%

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

      1. associate-/l* 57.7%

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

      2. associate-/r/ 58.2%

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

   6. Simplified 58.2%

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

   if -6.0000000000000002e-142 < b < -3.6000000000000001e-184

   1. Initial program 91.9%

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

      1. associate-/r* 84.0%

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

   3. Simplified 84.1%

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

   4. Taylor expanded in x around inf 68.5%

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

      1. associate-/l* 75.9%

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

      2. *-commutative 75.9%

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

   6. Simplified 75.9%

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

      1. expm1-log1p-u 50.5%

         \[\leadsto 9 \cdot \frac{y}{\color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{z \cdot c}{x}\right)\right)}} \]

      2. expm1-udef 18.1%

         \[\leadsto 9 \cdot \frac{y}{\color{blue}{e^{\mathsf{log1p}\left(\frac{z \cdot c}{x}\right)} - 1}} \]

      3. associate-/l* 18.0%

         \[\leadsto 9 \cdot \frac{y}{e^{\mathsf{log1p}\left(\color{blue}{\frac{z}{\frac{x}{c}}}\right)} - 1} \]

   8. Applied egg-rr 18.0%

      \[\leadsto 9 \cdot \frac{y}{\color{blue}{e^{\mathsf{log1p}\left(\frac{z}{\frac{x}{c}}\right)} - 1}} \]
   9. Step-by-step derivation

      1. expm1-def 50.6%

         \[\leadsto 9 \cdot \frac{y}{\color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{z}{\frac{x}{c}}\right)\right)}} \]

      2. expm1-log1p 76.0%

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

   10. Simplified 76.0%

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

   if 1.04999999999999994e-13 < b

   1. Initial program 81.2%

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

      1. associate-/r* 82.7%

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

   3. Simplified 86.3%

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

      1. div-inv 86.3%

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

   5. Applied egg-rr 86.3%

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

   6. Taylor expanded in b around inf 57.1%

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

      1. associate-/r* 60.1%

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

   8. Simplified 60.1%

      \[\leadsto \color{blue}{\frac{\frac{b}{c}}{z}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 60.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.45 \cdot 10^{+161}:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \mathbf{elif}\;b \leq -6 \cdot 10^{-142}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;b \leq -3.6 \cdot 10^{-184}:\\ \;\;\;\;9 \cdot \frac{y}{\frac{z}{\frac{x}{c}}}\\ \mathbf{elif}\;b \leq 1.05 \cdot 10^{-13}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \end{array} \]

Alternative 9: 49.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} t_1 := -4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{if}\;b \leq -1.25 \cdot 10^{+161}:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \mathbf{elif}\;b \leq -3.8 \cdot 10^{-143}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -1.62 \cdot 10^{-183}:\\ \;\;\;\;9 \cdot \frac{y}{\frac{c \cdot z}{x}}\\ \mathbf{elif}\;b \leq 5.2 \cdot 10^{-13}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* -4.0 (* t (/ a c)))))
   (if (<= b -1.25e+161)
     (/ b (* c z))
     (if (<= b -3.8e-143)
       t_1
       (if (<= b -1.62e-183)
         (* 9.0 (/ y (/ (* c z) x)))
         (if (<= b 5.2e-13) t_1 (/ (/ b c) z)))))))

C

assert(x < y);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = -4.0 * (t * (a / c));
	double tmp;
	if (b <= -1.25e+161) {
		tmp = b / (c * z);
	} else if (b <= -3.8e-143) {
		tmp = t_1;
	} else if (b <= -1.62e-183) {
		tmp = 9.0 * (y / ((c * z) / x));
	} else if (b <= 5.2e-13) {
		tmp = t_1;
	} else {
		tmp = (b / c) / z;
	}
	return tmp;
}

Fortran

NOTE: x and y 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) * (t * (a / c))
    if (b <= (-1.25d+161)) then
        tmp = b / (c * z)
    else if (b <= (-3.8d-143)) then
        tmp = t_1
    else if (b <= (-1.62d-183)) then
        tmp = 9.0d0 * (y / ((c * z) / x))
    else if (b <= 5.2d-13) then
        tmp = t_1
    else
        tmp = (b / c) / z
    end if
    code = tmp
end function

Java

assert x < y;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = -4.0 * (t * (a / c));
	double tmp;
	if (b <= -1.25e+161) {
		tmp = b / (c * z);
	} else if (b <= -3.8e-143) {
		tmp = t_1;
	} else if (b <= -1.62e-183) {
		tmp = 9.0 * (y / ((c * z) / x));
	} else if (b <= 5.2e-13) {
		tmp = t_1;
	} else {
		tmp = (b / c) / z;
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y, z, t, a, b, c):
	t_1 = -4.0 * (t * (a / c))
	tmp = 0
	if b <= -1.25e+161:
		tmp = b / (c * z)
	elif b <= -3.8e-143:
		tmp = t_1
	elif b <= -1.62e-183:
		tmp = 9.0 * (y / ((c * z) / x))
	elif b <= 5.2e-13:
		tmp = t_1
	else:
		tmp = (b / c) / z
	return tmp

Julia

x, y = sort([x, y])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(-4.0 * Float64(t * Float64(a / c)))
	tmp = 0.0
	if (b <= -1.25e+161)
		tmp = Float64(b / Float64(c * z));
	elseif (b <= -3.8e-143)
		tmp = t_1;
	elseif (b <= -1.62e-183)
		tmp = Float64(9.0 * Float64(y / Float64(Float64(c * z) / x)));
	elseif (b <= 5.2e-13)
		tmp = t_1;
	else
		tmp = Float64(Float64(b / c) / z);
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = -4.0 * (t * (a / c));
	tmp = 0.0;
	if (b <= -1.25e+161)
		tmp = b / (c * z);
	elseif (b <= -3.8e-143)
		tmp = t_1;
	elseif (b <= -1.62e-183)
		tmp = 9.0 * (y / ((c * z) / x));
	elseif (b <= 5.2e-13)
		tmp = t_1;
	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.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.25e+161], N[(b / N[(c * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -3.8e-143], t$95$1, If[LessEqual[b, -1.62e-183], N[(9.0 * N[(y / N[(N[(c * z), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 5.2e-13], t$95$1, N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -1.2499999999999999e161

   1. Initial program 77.4%

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

      1. associate-/r* 66.2%

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

   3. Simplified 77.7%

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

   4. Taylor expanded in b around inf 65.6%

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

      1. *-commutative 65.6%

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

   6. Simplified 65.6%

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

   if -1.2499999999999999e161 < b < -3.79999999999999981e-143 or -1.62e-183 < b < 5.2000000000000001e-13

   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* 74.8%

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

   3. Simplified 92.4%

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

   4. Taylor expanded in t around inf 57.1%

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

      1. associate-/l* 57.7%

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

      2. associate-/r/ 58.2%

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

   6. Simplified 58.2%

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

   if -3.79999999999999981e-143 < b < -1.62e-183

   1. Initial program 91.9%

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

      1. associate-/r* 84.0%

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

   3. Simplified 84.1%

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

   4. Taylor expanded in x around inf 68.5%

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

      1. associate-/l* 75.9%

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

      2. *-commutative 75.9%

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

   6. Simplified 75.9%

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

   if 5.2000000000000001e-13 < b

   1. Initial program 81.2%

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

      1. associate-/r* 82.7%

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

   3. Simplified 86.3%

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

      1. div-inv 86.3%

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

   5. Applied egg-rr 86.3%

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

   6. Taylor expanded in b around inf 57.1%

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

      1. associate-/r* 60.1%

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

   8. Simplified 60.1%

      \[\leadsto \color{blue}{\frac{\frac{b}{c}}{z}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 60.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.25 \cdot 10^{+161}:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \mathbf{elif}\;b \leq -3.8 \cdot 10^{-143}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;b \leq -1.62 \cdot 10^{-183}:\\ \;\;\;\;9 \cdot \frac{y}{\frac{c \cdot z}{x}}\\ \mathbf{elif}\;b \leq 5.2 \cdot 10^{-13}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \end{array} \]

Alternative 10: 68.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{+119} \lor \neg \left(z \leq 2.45 \cdot 10^{+36}\right):\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{b + 9 \cdot \left(y \cdot x\right)}{c \cdot z}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= z -3.1e+119) (not (<= z 2.45e+36)))
   (* -4.0 (* t (/ a c)))
   (/ (+ b (* 9.0 (* y x))) (* c z))))

C

assert(x < y);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((z <= -3.1e+119) || !(z <= 2.45e+36)) {
		tmp = -4.0 * (t * (a / 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.
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 <= (-3.1d+119)) .or. (.not. (z <= 2.45d+36))) then
        tmp = (-4.0d0) * (t * (a / c))
    else
        tmp = (b + (9.0d0 * (y * x))) / (c * z)
    end if
    code = tmp
end function

Java

assert x < y;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((z <= -3.1e+119) || !(z <= 2.45e+36)) {
		tmp = -4.0 * (t * (a / c));
	} else {
		tmp = (b + (9.0 * (y * x))) / (c * z);
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if (z <= -3.1e+119) or not (z <= 2.45e+36):
		tmp = -4.0 * (t * (a / c))
	else:
		tmp = (b + (9.0 * (y * x))) / (c * z)
	return tmp

Julia

x, y = sort([x, y])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((z <= -3.1e+119) || !(z <= 2.45e+36))
		tmp = Float64(-4.0 * Float64(t * Float64(a / 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])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((z <= -3.1e+119) || ~((z <= 2.45e+36)))
		tmp = -4.0 * (t * (a / 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.
code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[z, -3.1e+119], N[Not[LessEqual[z, 2.45e+36]], $MachinePrecision]], N[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision]), $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 < -3.09999999999999995e119 or 2.4499999999999999e36 < z

   1. Initial program 53.9%

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

      1. associate-/r* 62.0%

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

   3. Simplified 90.4%

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

   4. Taylor expanded in t around inf 61.7%

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

      1. associate-/l* 64.9%

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

      2. associate-/r/ 65.0%

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

   6. Simplified 65.0%

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

   if -3.09999999999999995e119 < z < 2.4499999999999999e36

   1. Initial program 90.5%

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

      1. associate-/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 75.8%

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

4. Final simplification 71.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{+119} \lor \neg \left(z \leq 2.45 \cdot 10^{+36}\right):\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{b + 9 \cdot \left(y \cdot x\right)}{c \cdot z}\\ \end{array} \]

Alternative 11: 75.5% accurate, 1.3× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -0.8 \lor \neg \left(z \leq 3 \cdot 10^{-42}\right):\\ \;\;\;\;\frac{t \cdot \left(-4 \cdot a\right) + \frac{b}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + 9 \cdot \left(y \cdot x\right)}{c \cdot z}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= z -0.8) (not (<= z 3e-42)))
   (/ (+ (* t (* -4.0 a)) (/ b z)) c)
   (/ (+ b (* 9.0 (* y x))) (* c z))))

C

assert(x < y);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((z <= -0.8) || !(z <= 3e-42)) {
		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.
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 <= (-0.8d0)) .or. (.not. (z <= 3d-42))) 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;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((z <= -0.8) || !(z <= 3e-42)) {
		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])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if (z <= -0.8) or not (z <= 3e-42):
		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])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((z <= -0.8) || !(z <= 3e-42))
		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])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((z <= -0.8) || ~((z <= 3e-42)))
		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.
code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[z, -0.8], N[Not[LessEqual[z, 3e-42]], $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 < -0.80000000000000004 or 3.00000000000000027e-42 < z

   1. Initial program 59.9%

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

      1. associate-/r* 67.3%

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

   3. Simplified 88.7%

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

   4. Taylor expanded in x around 0 77.0%

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

   if -0.80000000000000004 < z < 3.00000000000000027e-42

   1. Initial program 95.0%

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

      1. associate-/r* 87.8%

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

   3. Simplified 87.9%

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

   4. Taylor expanded in z around 0 82.0%

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

4. Final simplification 79.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.8 \lor \neg \left(z \leq 3 \cdot 10^{-42}\right):\\ \;\;\;\;\frac{t \cdot \left(-4 \cdot a\right) + \frac{b}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + 9 \cdot \left(y \cdot x\right)}{c \cdot z}\\ \end{array} \]

Alternative 12: 75.5% accurate, 1.3× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} t_1 := t \cdot \left(-4 \cdot a\right)\\ \mathbf{if}\;z \leq -0.85:\\ \;\;\;\;\frac{t_1 + b \cdot \frac{1}{z}}{c}\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-37}:\\ \;\;\;\;\frac{b + 9 \cdot \left(y \cdot x\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t_1 + \frac{b}{z}}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* t (* -4.0 a))))
   (if (<= z -0.85)
     (/ (+ t_1 (* b (/ 1.0 z))) c)
     (if (<= z 1.4e-37)
       (/ (+ b (* 9.0 (* y x))) (* c z))
       (/ (+ t_1 (/ b z)) c)))))

C

assert(x < y);
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 <= -0.85) {
		tmp = (t_1 + (b * (1.0 / z))) / c;
	} else if (z <= 1.4e-37) {
		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.
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 <= (-0.85d0)) then
        tmp = (t_1 + (b * (1.0d0 / z))) / c
    else if (z <= 1.4d-37) 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;
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 <= -0.85) {
		tmp = (t_1 + (b * (1.0 / z))) / c;
	} else if (z <= 1.4e-37) {
		tmp = (b + (9.0 * (y * x))) / (c * z);
	} else {
		tmp = (t_1 + (b / z)) / c;
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y, z, t, a, b, c):
	t_1 = t * (-4.0 * a)
	tmp = 0
	if z <= -0.85:
		tmp = (t_1 + (b * (1.0 / z))) / c
	elif z <= 1.4e-37:
		tmp = (b + (9.0 * (y * x))) / (c * z)
	else:
		tmp = (t_1 + (b / z)) / c
	return tmp

Julia

x, y = sort([x, y])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(t * Float64(-4.0 * a))
	tmp = 0.0
	if (z <= -0.85)
		tmp = Float64(Float64(t_1 + Float64(b * Float64(1.0 / z))) / c);
	elseif (z <= 1.4e-37)
		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])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = t * (-4.0 * a);
	tmp = 0.0;
	if (z <= -0.85)
		tmp = (t_1 + (b * (1.0 / z))) / c;
	elseif (z <= 1.4e-37)
		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.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(t * N[(-4.0 * a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -0.85], N[(N[(t$95$1 + N[(b * N[(1.0 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[z, 1.4e-37], 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 < -0.849999999999999978

   1. Initial program 52.6%

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

      1. associate-/r* 58.8%

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

   3. Simplified 84.7%

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

      1. div-inv 84.8%

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

   5. Applied egg-rr 84.8%

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

   6. Taylor expanded in x around 0 74.1%

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

   if -0.849999999999999978 < z < 1.4000000000000001e-37

   1. Initial program 95.0%

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

      1. associate-/r* 87.8%

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

   3. Simplified 87.9%

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

   4. Taylor expanded in z around 0 82.0%

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

   if 1.4000000000000001e-37 < z

   1. Initial program 67.5%

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

      1. associate-/r* 76.1%

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

   3. Simplified 92.8%

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

   4. Taylor expanded in x around 0 80.0%

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

4. Final simplification 79.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.85:\\ \;\;\;\;\frac{t \cdot \left(-4 \cdot a\right) + b \cdot \frac{1}{z}}{c}\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-37}:\\ \;\;\;\;\frac{b + 9 \cdot \left(y \cdot x\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot \left(-4 \cdot a\right) + \frac{b}{z}}{c}\\ \end{array} \]

Alternative 13: 49.6% accurate, 1.7× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} \mathbf{if}\;b \leq -1.5 \cdot 10^{+154}:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \mathbf{elif}\;b \leq 9.5 \cdot 10^{-14}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= b -1.5e+154)
   (/ b (* c z))
   (if (<= b 9.5e-14) (* -4.0 (* t (/ a c))) (/ (/ b c) z))))

C

assert(x < y);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (b <= -1.5e+154) {
		tmp = b / (c * z);
	} else if (b <= 9.5e-14) {
		tmp = -4.0 * (t * (a / c));
	} else {
		tmp = (b / c) / z;
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (b <= (-1.5d+154)) then
        tmp = b / (c * z)
    else if (b <= 9.5d-14) then
        tmp = (-4.0d0) * (t * (a / c))
    else
        tmp = (b / c) / z
    end if
    code = tmp
end function

Java

assert x < y;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (b <= -1.5e+154) {
		tmp = b / (c * z);
	} else if (b <= 9.5e-14) {
		tmp = -4.0 * (t * (a / c));
	} else {
		tmp = (b / c) / z;
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if b <= -1.5e+154:
		tmp = b / (c * z)
	elif b <= 9.5e-14:
		tmp = -4.0 * (t * (a / c))
	else:
		tmp = (b / c) / z
	return tmp

Julia

x, y = sort([x, y])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (b <= -1.5e+154)
		tmp = Float64(b / Float64(c * z));
	elseif (b <= 9.5e-14)
		tmp = Float64(-4.0 * Float64(t * Float64(a / c)));
	else
		tmp = Float64(Float64(b / c) / z);
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (b <= -1.5e+154)
		tmp = b / (c * z);
	elseif (b <= 9.5e-14)
		tmp = -4.0 * (t * (a / c));
	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.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[b, -1.5e+154], N[(b / N[(c * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 9.5e-14], N[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.50000000000000013e154

   1. Initial program 77.4%

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

      1. associate-/r* 66.2%

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

   3. Simplified 77.7%

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

   4. Taylor expanded in b around inf 65.6%

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

      1. *-commutative 65.6%

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

   6. Simplified 65.6%

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

   if -1.50000000000000013e154 < b < 9.4999999999999999e-14

   1. Initial program 73.3%

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

      1. associate-/r* 75.5%

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

   3. Simplified 91.8%

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

   4. Taylor expanded in t around inf 56.0%

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

      1. associate-/l* 56.5%

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

      2. associate-/r/ 56.4%

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

   6. Simplified 56.4%

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

   if 9.4999999999999999e-14 < b

   1. Initial program 81.2%

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

      1. associate-/r* 82.7%

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

   3. Simplified 86.3%

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

      1. div-inv 86.3%

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

   5. Applied egg-rr 86.3%

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

   6. Taylor expanded in b around inf 57.1%

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

      1. associate-/r* 60.1%

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

   8. Simplified 60.1%

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

4. Final simplification 58.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.5 \cdot 10^{+154}:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \mathbf{elif}\;b \leq 9.5 \cdot 10^{-14}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \end{array} \]

Alternative 14: 34.5% accurate, 2.7× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq 4 \cdot 10^{-177}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= y 4e-177) (/ (/ b c) z) (/ b (* c z))))

C

assert(x < y);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (y <= 4e-177) {
		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.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (y <= 4d-177) then
        tmp = (b / c) / z
    else
        tmp = b / (c * z)
    end if
    code = tmp
end function

Java

assert x < y;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (y <= 4e-177) {
		tmp = (b / c) / z;
	} else {
		tmp = b / (c * z);
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if y <= 4e-177:
		tmp = (b / c) / z
	else:
		tmp = b / (c * z)
	return tmp

Julia

x, y = sort([x, y])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (y <= 4e-177)
		tmp = Float64(Float64(b / c) / z);
	else
		tmp = Float64(b / Float64(c * z));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (y <= 4e-177)
		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.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[y, 4e-177], N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision], N[(b / N[(c * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 3.99999999999999981e-177

   1. Initial program 78.2%

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

      1. associate-/r* 78.0%

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

   3. Simplified 89.5%

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

      1. div-inv 89.5%

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

   5. Applied egg-rr 89.5%

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

   6. Taylor expanded in b around inf 39.8%

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

      1. associate-/r* 41.0%

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

   8. Simplified 41.0%

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

   if 3.99999999999999981e-177 < y

   1. Initial program 72.7%

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

      1. associate-/r* 74.8%

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

   3. Simplified 86.4%

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

   4. Taylor expanded in b around inf 33.3%

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

      1. *-commutative 33.3%

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

   6. Simplified 33.3%

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

4. Final simplification 38.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 4 \cdot 10^{-177}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \end{array} \]

Alternative 15: 34.5% accurate, 3.8× speedup

Math

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

FPCore

NOTE: x and y 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);
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.
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;
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])
def code(x, y, z, t, a, b, c):
	return b / (c * z)

Julia

x, y = sort([x, y])
function code(x, y, z, t, a, b, c)
	return Float64(b / Float64(c * z))
end

MATLAB

x, y = num2cell(sort([x, y])){:}
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.
code[x_, y_, z_, t_, a_, b_, c_] := N[(b / N[(c * z), $MachinePrecision]), $MachinePrecision]

Derivation

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* 76.8%

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

3. Simplified 88.7%

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

4. Taylor expanded in b around inf 37.3%

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

   1. *-commutative 37.3%

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

6. Simplified 37.3%

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

7. Final simplification 37.3%

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

Developer target: 79.8% 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 2023229 
(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)))