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

Percentage Accurate: 79.6% → 91.7%

Time: 16.4s

Alternatives: 17

Speedup: 1.0×

• 37.3% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 79.6% 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: 91.7% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.32 \cdot 10^{+36}:\\ \;\;\;\;\frac{\frac{x \cdot \left(9 \cdot y\right) + b}{z} + t \cdot \left(a \cdot -4\right)}{c}\\ \mathbf{elif}\;z \leq 10^{-23}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(t, a \cdot -4, \frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z}\right)}{c}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= z -1.32e+36)
   (/ (+ (/ (+ (* x (* 9.0 y)) b) z) (* t (* a -4.0))) c)
   (if (<= z 1e-23)
     (/ (+ b (- (* y (* x 9.0)) (* a (* t (* z 4.0))))) (* z c))
     (/ (fma t (* a -4.0) (/ (fma x (* 9.0 y) b) z)) c))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (z <= -1.32e+36) {
		tmp = ((((x * (9.0 * y)) + b) / z) + (t * (a * -4.0))) / c;
	} else if (z <= 1e-23) {
		tmp = (b + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (z * c);
	} else {
		tmp = fma(t, (a * -4.0), (fma(x, (9.0 * y), b) / z)) / c;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (z <= -1.32e+36)
		tmp = Float64(Float64(Float64(Float64(Float64(x * Float64(9.0 * y)) + b) / z) + Float64(t * Float64(a * -4.0))) / c);
	elseif (z <= 1e-23)
		tmp = Float64(Float64(b + Float64(Float64(y * Float64(x * 9.0)) - Float64(a * Float64(t * Float64(z * 4.0))))) / Float64(z * c));
	else
		tmp = Float64(fma(t, Float64(a * -4.0), Float64(fma(x, Float64(9.0 * y), b) / z)) / c);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[z, -1.32e+36], N[(N[(N[(N[(N[(x * N[(9.0 * y), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision] / z), $MachinePrecision] + N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[z, 1e-23], N[(N[(b + N[(N[(y * N[(x * 9.0), $MachinePrecision]), $MachinePrecision] - N[(a * N[(t * N[(z * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(N[(t * N[(a * -4.0), $MachinePrecision] + N[(N[(x * N[(9.0 * y), $MachinePrecision] + b), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.3200000000000001e36

   1. Initial program 53.7%

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

      1. associate-/r* 67.0%

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

   3. Simplified 85.0%

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

      1. fma-udef 85.0%

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

   5. Applied egg-rr 85.0%

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

   if -1.3200000000000001e36 < z < 9.9999999999999996e-24

   1. Initial program 94.9%

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

   if 9.9999999999999996e-24 < z

   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* 82.6%

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

   3. Simplified 96.8%

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

4. Final simplification 93.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.32 \cdot 10^{+36}:\\ \;\;\;\;\frac{\frac{x \cdot \left(9 \cdot y\right) + b}{z} + t \cdot \left(a \cdot -4\right)}{c}\\ \mathbf{elif}\;z \leq 10^{-23}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(t, a \cdot -4, \frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z}\right)}{c}\\ \end{array} \]

Alternative 2: 47.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 9 \cdot \left(\frac{y}{c} \cdot \frac{x}{z}\right)\\ t_2 := -4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{if}\;y \leq -2.6 \cdot 10^{-66}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -3.9 \cdot 10^{-253}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{elif}\;y \leq 6.4 \cdot 10^{-114}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 5 \cdot 10^{-42}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{+62}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 6.6 \cdot 10^{+113} \lor \neg \left(y \leq 1.85 \cdot 10^{+158}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{t \cdot a}{c}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* 9.0 (* (/ y c) (/ x z)))) (t_2 (* -4.0 (/ a (/ c t)))))
   (if (<= y -2.6e-66)
     t_1
     (if (<= y -3.9e-253)
       (/ (/ b z) c)
       (if (<= y 6.4e-114)
         t_2
         (if (<= y 5e-42)
           (/ b (* z c))
           (if (<= y 1.9e+62)
             t_2
             (if (or (<= y 6.6e+113) (not (<= y 1.85e+158)))
               t_1
               (* -4.0 (/ (* t a) c))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = 9.0 * ((y / c) * (x / z));
	double t_2 = -4.0 * (a / (c / t));
	double tmp;
	if (y <= -2.6e-66) {
		tmp = t_1;
	} else if (y <= -3.9e-253) {
		tmp = (b / z) / c;
	} else if (y <= 6.4e-114) {
		tmp = t_2;
	} else if (y <= 5e-42) {
		tmp = b / (z * c);
	} else if (y <= 1.9e+62) {
		tmp = t_2;
	} else if ((y <= 6.6e+113) || !(y <= 1.85e+158)) {
		tmp = t_1;
	} else {
		tmp = -4.0 * ((t * a) / c);
	}
	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) :: tmp
    t_1 = 9.0d0 * ((y / c) * (x / z))
    t_2 = (-4.0d0) * (a / (c / t))
    if (y <= (-2.6d-66)) then
        tmp = t_1
    else if (y <= (-3.9d-253)) then
        tmp = (b / z) / c
    else if (y <= 6.4d-114) then
        tmp = t_2
    else if (y <= 5d-42) then
        tmp = b / (z * c)
    else if (y <= 1.9d+62) then
        tmp = t_2
    else if ((y <= 6.6d+113) .or. (.not. (y <= 1.85d+158))) then
        tmp = t_1
    else
        tmp = (-4.0d0) * ((t * a) / c)
    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 = 9.0 * ((y / c) * (x / z));
	double t_2 = -4.0 * (a / (c / t));
	double tmp;
	if (y <= -2.6e-66) {
		tmp = t_1;
	} else if (y <= -3.9e-253) {
		tmp = (b / z) / c;
	} else if (y <= 6.4e-114) {
		tmp = t_2;
	} else if (y <= 5e-42) {
		tmp = b / (z * c);
	} else if (y <= 1.9e+62) {
		tmp = t_2;
	} else if ((y <= 6.6e+113) || !(y <= 1.85e+158)) {
		tmp = t_1;
	} else {
		tmp = -4.0 * ((t * a) / c);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = 9.0 * ((y / c) * (x / z))
	t_2 = -4.0 * (a / (c / t))
	tmp = 0
	if y <= -2.6e-66:
		tmp = t_1
	elif y <= -3.9e-253:
		tmp = (b / z) / c
	elif y <= 6.4e-114:
		tmp = t_2
	elif y <= 5e-42:
		tmp = b / (z * c)
	elif y <= 1.9e+62:
		tmp = t_2
	elif (y <= 6.6e+113) or not (y <= 1.85e+158):
		tmp = t_1
	else:
		tmp = -4.0 * ((t * a) / c)
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(9.0 * Float64(Float64(y / c) * Float64(x / z)))
	t_2 = Float64(-4.0 * Float64(a / Float64(c / t)))
	tmp = 0.0
	if (y <= -2.6e-66)
		tmp = t_1;
	elseif (y <= -3.9e-253)
		tmp = Float64(Float64(b / z) / c);
	elseif (y <= 6.4e-114)
		tmp = t_2;
	elseif (y <= 5e-42)
		tmp = Float64(b / Float64(z * c));
	elseif (y <= 1.9e+62)
		tmp = t_2;
	elseif ((y <= 6.6e+113) || !(y <= 1.85e+158))
		tmp = t_1;
	else
		tmp = Float64(-4.0 * Float64(Float64(t * a) / c));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = 9.0 * ((y / c) * (x / z));
	t_2 = -4.0 * (a / (c / t));
	tmp = 0.0;
	if (y <= -2.6e-66)
		tmp = t_1;
	elseif (y <= -3.9e-253)
		tmp = (b / z) / c;
	elseif (y <= 6.4e-114)
		tmp = t_2;
	elseif (y <= 5e-42)
		tmp = b / (z * c);
	elseif (y <= 1.9e+62)
		tmp = t_2;
	elseif ((y <= 6.6e+113) || ~((y <= 1.85e+158)))
		tmp = t_1;
	else
		tmp = -4.0 * ((t * a) / c);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(9.0 * N[(N[(y / c), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(-4.0 * N[(a / N[(c / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.6e-66], t$95$1, If[LessEqual[y, -3.9e-253], N[(N[(b / z), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[y, 6.4e-114], t$95$2, If[LessEqual[y, 5e-42], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.9e+62], t$95$2, If[Or[LessEqual[y, 6.6e+113], N[Not[LessEqual[y, 1.85e+158]], $MachinePrecision]], t$95$1, N[(-4.0 * N[(N[(t * a), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -2.5999999999999999e-66 or 1.89999999999999992e62 < y < 6.6000000000000006e113 or 1.85000000000000005e158 < y

   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-*l* 81.2%

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

      2. associate-*l* 78.9%

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

   3. Simplified 78.9%

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

      1. div-inv 78.9%

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

      2. associate-+l- 78.9%

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

      3. associate-*r* 78.9%

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

      4. associate-*r* 81.1%

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

      5. associate-+l- 81.1%

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

      6. +-commutative 81.1%

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

      7. associate-*r* 81.2%

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

      8. *-commutative 81.2%

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

      9. *-commutative 81.2%

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

   5. Applied egg-rr 81.2%

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

   6. Taylor expanded in x around inf 46.8%

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

      1. times-frac 53.4%

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

   8. Simplified 53.4%

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

   if -2.5999999999999999e-66 < y < -3.8999999999999999e-253

   1. Initial program 90.0%

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

      1. associate-/r* 87.0%

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

   3. Simplified 91.1%

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

   4. Taylor expanded in x around 0 82.6%

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

   5. Taylor expanded in b around inf 60.3%

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

   if -3.8999999999999999e-253 < y < 6.4000000000000003e-114 or 5.00000000000000003e-42 < y < 1.89999999999999992e62

   1. Initial program 79.5%

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

      1. associate-/r* 82.2%

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

   3. Simplified 93.5%

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

   4. Taylor expanded in t around inf 60.7%

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

      1. associate-/l* 60.7%

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

   6. Simplified 60.7%

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

   if 6.4000000000000003e-114 < y < 5.00000000000000003e-42

   1. Initial program 84.9%

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

      1. associate-/r* 92.3%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in b around inf 55.3%

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

      1. *-commutative 55.3%

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

   6. Simplified 55.3%

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

   if 6.6000000000000006e113 < y < 1.85000000000000005e158

   1. Initial program 60.7%

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

      1. associate-/r* 70.8%

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

   3. Simplified 89.7%

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

   4. Taylor expanded in t around inf 71.2%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 57.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{-66}:\\ \;\;\;\;9 \cdot \left(\frac{y}{c} \cdot \frac{x}{z}\right)\\ \mathbf{elif}\;y \leq -3.9 \cdot 10^{-253}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{elif}\;y \leq 6.4 \cdot 10^{-114}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;y \leq 5 \cdot 10^{-42}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{+62}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;y \leq 6.6 \cdot 10^{+113} \lor \neg \left(y \leq 1.85 \cdot 10^{+158}\right):\\ \;\;\;\;9 \cdot \left(\frac{y}{c} \cdot \frac{x}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{t \cdot a}{c}\\ \end{array} \]

Alternative 3: 46.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{if}\;y \leq -2.05 \cdot 10^{-109}:\\ \;\;\;\;9 \cdot \left(\frac{x}{c} \cdot \frac{y}{z}\right)\\ \mathbf{elif}\;y \leq -1.6 \cdot 10^{-251}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{elif}\;y \leq 4.3 \cdot 10^{-113}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{-42}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;y \leq 3.7 \cdot 10^{+62}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{+114} \lor \neg \left(y \leq 7.4 \cdot 10^{+157}\right):\\ \;\;\;\;9 \cdot \left(\frac{y}{c} \cdot \frac{x}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{t \cdot a}{c}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* -4.0 (/ a (/ c t)))))
   (if (<= y -2.05e-109)
     (* 9.0 (* (/ x c) (/ y z)))
     (if (<= y -1.6e-251)
       (/ (/ b z) c)
       (if (<= y 4.3e-113)
         t_1
         (if (<= y 4.5e-42)
           (/ b (* z c))
           (if (<= y 3.7e+62)
             t_1
             (if (or (<= y 4.8e+114) (not (<= y 7.4e+157)))
               (* 9.0 (* (/ y c) (/ x z)))
               (* -4.0 (/ (* t a) c))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = -4.0 * (a / (c / t));
	double tmp;
	if (y <= -2.05e-109) {
		tmp = 9.0 * ((x / c) * (y / z));
	} else if (y <= -1.6e-251) {
		tmp = (b / z) / c;
	} else if (y <= 4.3e-113) {
		tmp = t_1;
	} else if (y <= 4.5e-42) {
		tmp = b / (z * c);
	} else if (y <= 3.7e+62) {
		tmp = t_1;
	} else if ((y <= 4.8e+114) || !(y <= 7.4e+157)) {
		tmp = 9.0 * ((y / c) * (x / z));
	} else {
		tmp = -4.0 * ((t * a) / c);
	}
	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) :: tmp
    t_1 = (-4.0d0) * (a / (c / t))
    if (y <= (-2.05d-109)) then
        tmp = 9.0d0 * ((x / c) * (y / z))
    else if (y <= (-1.6d-251)) then
        tmp = (b / z) / c
    else if (y <= 4.3d-113) then
        tmp = t_1
    else if (y <= 4.5d-42) then
        tmp = b / (z * c)
    else if (y <= 3.7d+62) then
        tmp = t_1
    else if ((y <= 4.8d+114) .or. (.not. (y <= 7.4d+157))) then
        tmp = 9.0d0 * ((y / c) * (x / z))
    else
        tmp = (-4.0d0) * ((t * a) / c)
    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 = -4.0 * (a / (c / t));
	double tmp;
	if (y <= -2.05e-109) {
		tmp = 9.0 * ((x / c) * (y / z));
	} else if (y <= -1.6e-251) {
		tmp = (b / z) / c;
	} else if (y <= 4.3e-113) {
		tmp = t_1;
	} else if (y <= 4.5e-42) {
		tmp = b / (z * c);
	} else if (y <= 3.7e+62) {
		tmp = t_1;
	} else if ((y <= 4.8e+114) || !(y <= 7.4e+157)) {
		tmp = 9.0 * ((y / c) * (x / z));
	} else {
		tmp = -4.0 * ((t * a) / c);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = -4.0 * (a / (c / t))
	tmp = 0
	if y <= -2.05e-109:
		tmp = 9.0 * ((x / c) * (y / z))
	elif y <= -1.6e-251:
		tmp = (b / z) / c
	elif y <= 4.3e-113:
		tmp = t_1
	elif y <= 4.5e-42:
		tmp = b / (z * c)
	elif y <= 3.7e+62:
		tmp = t_1
	elif (y <= 4.8e+114) or not (y <= 7.4e+157):
		tmp = 9.0 * ((y / c) * (x / z))
	else:
		tmp = -4.0 * ((t * a) / c)
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(-4.0 * Float64(a / Float64(c / t)))
	tmp = 0.0
	if (y <= -2.05e-109)
		tmp = Float64(9.0 * Float64(Float64(x / c) * Float64(y / z)));
	elseif (y <= -1.6e-251)
		tmp = Float64(Float64(b / z) / c);
	elseif (y <= 4.3e-113)
		tmp = t_1;
	elseif (y <= 4.5e-42)
		tmp = Float64(b / Float64(z * c));
	elseif (y <= 3.7e+62)
		tmp = t_1;
	elseif ((y <= 4.8e+114) || !(y <= 7.4e+157))
		tmp = Float64(9.0 * Float64(Float64(y / c) * Float64(x / z)));
	else
		tmp = Float64(-4.0 * Float64(Float64(t * a) / c));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = -4.0 * (a / (c / t));
	tmp = 0.0;
	if (y <= -2.05e-109)
		tmp = 9.0 * ((x / c) * (y / z));
	elseif (y <= -1.6e-251)
		tmp = (b / z) / c;
	elseif (y <= 4.3e-113)
		tmp = t_1;
	elseif (y <= 4.5e-42)
		tmp = b / (z * c);
	elseif (y <= 3.7e+62)
		tmp = t_1;
	elseif ((y <= 4.8e+114) || ~((y <= 7.4e+157)))
		tmp = 9.0 * ((y / c) * (x / z));
	else
		tmp = -4.0 * ((t * a) / c);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(-4.0 * N[(a / N[(c / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.05e-109], N[(9.0 * N[(N[(x / c), $MachinePrecision] * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.6e-251], N[(N[(b / z), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[y, 4.3e-113], t$95$1, If[LessEqual[y, 4.5e-42], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.7e+62], t$95$1, If[Or[LessEqual[y, 4.8e+114], N[Not[LessEqual[y, 7.4e+157]], $MachinePrecision]], N[(9.0 * N[(N[(y / c), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-4.0 * N[(N[(t * a), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if y < -2.0500000000000001e-109

   1. Initial program 80.7%

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

      1. associate-/r* 76.5%

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

   3. Simplified 82.3%

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

   4. Taylor expanded in x around inf 39.1%

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

      1. *-commutative 39.1%

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

      2. times-frac 42.3%

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

   6. Simplified 42.3%

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

   if -2.0500000000000001e-109 < y < -1.59999999999999991e-251

   1. Initial program 90.6%

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

      1. associate-/r* 86.6%

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

   3. Simplified 87.9%

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

   4. Taylor expanded in x around 0 80.3%

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

   5. Taylor expanded in b around inf 57.6%

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

   if -1.59999999999999991e-251 < y < 4.3e-113 or 4.5e-42 < y < 3.70000000000000014e62

   1. Initial program 79.5%

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

      1. associate-/r* 82.2%

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

   3. Simplified 93.5%

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

   4. Taylor expanded in t around inf 60.7%

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

      1. associate-/l* 60.7%

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

   6. Simplified 60.7%

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

   if 4.3e-113 < y < 4.5e-42

   1. Initial program 84.9%

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

      1. associate-/r* 92.3%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in b around inf 55.3%

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

      1. *-commutative 55.3%

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

   6. Simplified 55.3%

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

   if 3.70000000000000014e62 < y < 4.8e114 or 7.3999999999999997e157 < y

   1. Initial program 83.4%

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

      1. associate-*l* 83.5%

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

      2. associate-*l* 81.4%

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

   3. Simplified 81.4%

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

      1. div-inv 81.4%

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

      2. associate-+l- 81.4%

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

      3. associate-*r* 81.3%

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

      4. associate-*r* 83.3%

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

      5. associate-+l- 83.3%

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

      6. +-commutative 83.3%

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

      7. associate-*r* 83.4%

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

      8. *-commutative 83.4%

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

      9. *-commutative 83.4%

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

   5. Applied egg-rr 83.4%

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

   6. Taylor expanded in x around inf 54.9%

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

      1. times-frac 61.1%

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

   8. Simplified 61.1%

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

   if 4.8e114 < y < 7.3999999999999997e157

   1. Initial program 60.7%

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

      1. associate-/r* 70.8%

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

   3. Simplified 89.7%

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

   4. Taylor expanded in t around inf 71.2%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
3. Recombined 6 regimes into one program.

4. Final simplification 54.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.05 \cdot 10^{-109}:\\ \;\;\;\;9 \cdot \left(\frac{x}{c} \cdot \frac{y}{z}\right)\\ \mathbf{elif}\;y \leq -1.6 \cdot 10^{-251}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{elif}\;y \leq 4.3 \cdot 10^{-113}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{-42}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;y \leq 3.7 \cdot 10^{+62}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{+114} \lor \neg \left(y \leq 7.4 \cdot 10^{+157}\right):\\ \;\;\;\;9 \cdot \left(\frac{y}{c} \cdot \frac{x}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{t \cdot a}{c}\\ \end{array} \]

Alternative 4: 46.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{if}\;y \leq -2.45 \cdot 10^{-109}:\\ \;\;\;\;9 \cdot \left(\frac{x}{c} \cdot \frac{y}{z}\right)\\ \mathbf{elif}\;y \leq -6 \cdot 10^{-253}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{-113}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{-43}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;y \leq 4.3 \cdot 10^{+61}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{+115}:\\ \;\;\;\;9 \cdot \frac{y}{\frac{z \cdot c}{x}}\\ \mathbf{elif}\;y \leq 7.4 \cdot 10^{+157}:\\ \;\;\;\;-4 \cdot \frac{t \cdot a}{c}\\ \mathbf{else}:\\ \;\;\;\;9 \cdot \left(\frac{y}{c} \cdot \frac{x}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* -4.0 (/ a (/ c t)))))
   (if (<= y -2.45e-109)
     (* 9.0 (* (/ x c) (/ y z)))
     (if (<= y -6e-253)
       (/ (/ b z) c)
       (if (<= y 1.3e-113)
         t_1
         (if (<= y 6.2e-43)
           (/ b (* z c))
           (if (<= y 4.3e+61)
             t_1
             (if (<= y 5.5e+115)
               (* 9.0 (/ y (/ (* z c) x)))
               (if (<= y 7.4e+157)
                 (* -4.0 (/ (* t a) c))
                 (* 9.0 (* (/ y c) (/ x z))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = -4.0 * (a / (c / t));
	double tmp;
	if (y <= -2.45e-109) {
		tmp = 9.0 * ((x / c) * (y / z));
	} else if (y <= -6e-253) {
		tmp = (b / z) / c;
	} else if (y <= 1.3e-113) {
		tmp = t_1;
	} else if (y <= 6.2e-43) {
		tmp = b / (z * c);
	} else if (y <= 4.3e+61) {
		tmp = t_1;
	} else if (y <= 5.5e+115) {
		tmp = 9.0 * (y / ((z * c) / x));
	} else if (y <= 7.4e+157) {
		tmp = -4.0 * ((t * a) / c);
	} else {
		tmp = 9.0 * ((y / c) * (x / z));
	}
	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) :: tmp
    t_1 = (-4.0d0) * (a / (c / t))
    if (y <= (-2.45d-109)) then
        tmp = 9.0d0 * ((x / c) * (y / z))
    else if (y <= (-6d-253)) then
        tmp = (b / z) / c
    else if (y <= 1.3d-113) then
        tmp = t_1
    else if (y <= 6.2d-43) then
        tmp = b / (z * c)
    else if (y <= 4.3d+61) then
        tmp = t_1
    else if (y <= 5.5d+115) then
        tmp = 9.0d0 * (y / ((z * c) / x))
    else if (y <= 7.4d+157) then
        tmp = (-4.0d0) * ((t * a) / c)
    else
        tmp = 9.0d0 * ((y / c) * (x / z))
    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 = -4.0 * (a / (c / t));
	double tmp;
	if (y <= -2.45e-109) {
		tmp = 9.0 * ((x / c) * (y / z));
	} else if (y <= -6e-253) {
		tmp = (b / z) / c;
	} else if (y <= 1.3e-113) {
		tmp = t_1;
	} else if (y <= 6.2e-43) {
		tmp = b / (z * c);
	} else if (y <= 4.3e+61) {
		tmp = t_1;
	} else if (y <= 5.5e+115) {
		tmp = 9.0 * (y / ((z * c) / x));
	} else if (y <= 7.4e+157) {
		tmp = -4.0 * ((t * a) / c);
	} else {
		tmp = 9.0 * ((y / c) * (x / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = -4.0 * (a / (c / t))
	tmp = 0
	if y <= -2.45e-109:
		tmp = 9.0 * ((x / c) * (y / z))
	elif y <= -6e-253:
		tmp = (b / z) / c
	elif y <= 1.3e-113:
		tmp = t_1
	elif y <= 6.2e-43:
		tmp = b / (z * c)
	elif y <= 4.3e+61:
		tmp = t_1
	elif y <= 5.5e+115:
		tmp = 9.0 * (y / ((z * c) / x))
	elif y <= 7.4e+157:
		tmp = -4.0 * ((t * a) / c)
	else:
		tmp = 9.0 * ((y / c) * (x / z))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(-4.0 * Float64(a / Float64(c / t)))
	tmp = 0.0
	if (y <= -2.45e-109)
		tmp = Float64(9.0 * Float64(Float64(x / c) * Float64(y / z)));
	elseif (y <= -6e-253)
		tmp = Float64(Float64(b / z) / c);
	elseif (y <= 1.3e-113)
		tmp = t_1;
	elseif (y <= 6.2e-43)
		tmp = Float64(b / Float64(z * c));
	elseif (y <= 4.3e+61)
		tmp = t_1;
	elseif (y <= 5.5e+115)
		tmp = Float64(9.0 * Float64(y / Float64(Float64(z * c) / x)));
	elseif (y <= 7.4e+157)
		tmp = Float64(-4.0 * Float64(Float64(t * a) / c));
	else
		tmp = Float64(9.0 * Float64(Float64(y / c) * Float64(x / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = -4.0 * (a / (c / t));
	tmp = 0.0;
	if (y <= -2.45e-109)
		tmp = 9.0 * ((x / c) * (y / z));
	elseif (y <= -6e-253)
		tmp = (b / z) / c;
	elseif (y <= 1.3e-113)
		tmp = t_1;
	elseif (y <= 6.2e-43)
		tmp = b / (z * c);
	elseif (y <= 4.3e+61)
		tmp = t_1;
	elseif (y <= 5.5e+115)
		tmp = 9.0 * (y / ((z * c) / x));
	elseif (y <= 7.4e+157)
		tmp = -4.0 * ((t * a) / c);
	else
		tmp = 9.0 * ((y / c) * (x / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(-4.0 * N[(a / N[(c / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.45e-109], N[(9.0 * N[(N[(x / c), $MachinePrecision] * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -6e-253], N[(N[(b / z), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[y, 1.3e-113], t$95$1, If[LessEqual[y, 6.2e-43], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.3e+61], t$95$1, If[LessEqual[y, 5.5e+115], N[(9.0 * N[(y / N[(N[(z * c), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7.4e+157], N[(-4.0 * N[(N[(t * a), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision], N[(9.0 * N[(N[(y / c), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if y < -2.44999999999999999e-109

   1. Initial program 80.7%

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

      1. associate-/r* 76.5%

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

   3. Simplified 82.3%

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

   4. Taylor expanded in x around inf 39.1%

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

      1. *-commutative 39.1%

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

      2. times-frac 42.3%

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

   6. Simplified 42.3%

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

   if -2.44999999999999999e-109 < y < -6.0000000000000004e-253

   1. Initial program 90.6%

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

      1. associate-/r* 86.6%

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

   3. Simplified 87.9%

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

   4. Taylor expanded in x around 0 80.3%

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

   5. Taylor expanded in b around inf 57.6%

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

   if -6.0000000000000004e-253 < y < 1.3e-113 or 6.1999999999999999e-43 < y < 4.3000000000000001e61

   1. Initial program 79.5%

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

      1. associate-/r* 82.2%

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

   3. Simplified 93.5%

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

   4. Taylor expanded in t around inf 60.7%

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

      1. associate-/l* 60.7%

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

   6. Simplified 60.7%

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

   if 1.3e-113 < y < 6.1999999999999999e-43

   1. Initial program 84.9%

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

      1. associate-/r* 92.3%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in b around inf 55.3%

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

      1. *-commutative 55.3%

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

   6. Simplified 55.3%

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

   if 4.3000000000000001e61 < y < 5.5e115

   1. Initial program 99.9%

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

      1. associate-/r* 91.5%

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

   3. Simplified 91.6%

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

   4. Taylor expanded in x around inf 46.9%

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

      1. associate-/l* 46.9%

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

      2. *-commutative 46.9%

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

   6. Simplified 46.9%

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

   if 5.5e115 < y < 7.3999999999999997e157

   1. Initial program 60.7%

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

      1. associate-/r* 70.8%

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

   3. Simplified 89.7%

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

   4. Taylor expanded in t around inf 71.2%

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

   if 7.3999999999999997e157 < y

   1. Initial program 78.4%

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

      1. associate-*l* 78.4%

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

      2. associate-*l* 75.7%

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

   3. Simplified 75.7%

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

      1. div-inv 75.7%

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

      2. associate-+l- 75.7%

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

      3. associate-*r* 75.6%

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

      4. associate-*r* 78.3%

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

      5. associate-+l- 78.3%

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

      6. +-commutative 78.3%

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

      7. associate-*r* 78.4%

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

      8. *-commutative 78.4%

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

      9. *-commutative 78.4%

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

   5. Applied egg-rr 78.4%

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

   6. Taylor expanded in x around inf 57.3%

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

      1. times-frac 65.5%

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

   8. Simplified 65.5%

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

4. Final simplification 54.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.45 \cdot 10^{-109}:\\ \;\;\;\;9 \cdot \left(\frac{x}{c} \cdot \frac{y}{z}\right)\\ \mathbf{elif}\;y \leq -6 \cdot 10^{-253}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{-113}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{-43}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;y \leq 4.3 \cdot 10^{+61}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{+115}:\\ \;\;\;\;9 \cdot \frac{y}{\frac{z \cdot c}{x}}\\ \mathbf{elif}\;y \leq 7.4 \cdot 10^{+157}:\\ \;\;\;\;-4 \cdot \frac{t \cdot a}{c}\\ \mathbf{else}:\\ \;\;\;\;9 \cdot \left(\frac{y}{c} \cdot \frac{x}{z}\right)\\ \end{array} \]

Alternative 5: 46.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{if}\;y \leq -2.6 \cdot 10^{-109}:\\ \;\;\;\;9 \cdot \frac{y \cdot \frac{x}{c}}{z}\\ \mathbf{elif}\;y \leq -5.6 \cdot 10^{-252}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{elif}\;y \leq 6.4 \cdot 10^{-112}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{-43}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{+61}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{+114}:\\ \;\;\;\;9 \cdot \frac{y}{\frac{z \cdot c}{x}}\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{+158}:\\ \;\;\;\;-4 \cdot \frac{t \cdot a}{c}\\ \mathbf{else}:\\ \;\;\;\;9 \cdot \left(\frac{y}{c} \cdot \frac{x}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* -4.0 (/ a (/ c t)))))
   (if (<= y -2.6e-109)
     (* 9.0 (/ (* y (/ x c)) z))
     (if (<= y -5.6e-252)
       (/ (/ b z) c)
       (if (<= y 6.4e-112)
         t_1
         (if (<= y 5.5e-43)
           (/ b (* z c))
           (if (<= y 1.8e+61)
             t_1
             (if (<= y 3.5e+114)
               (* 9.0 (/ y (/ (* z c) x)))
               (if (<= y 2.1e+158)
                 (* -4.0 (/ (* t a) c))
                 (* 9.0 (* (/ y c) (/ x z))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = -4.0 * (a / (c / t));
	double tmp;
	if (y <= -2.6e-109) {
		tmp = 9.0 * ((y * (x / c)) / z);
	} else if (y <= -5.6e-252) {
		tmp = (b / z) / c;
	} else if (y <= 6.4e-112) {
		tmp = t_1;
	} else if (y <= 5.5e-43) {
		tmp = b / (z * c);
	} else if (y <= 1.8e+61) {
		tmp = t_1;
	} else if (y <= 3.5e+114) {
		tmp = 9.0 * (y / ((z * c) / x));
	} else if (y <= 2.1e+158) {
		tmp = -4.0 * ((t * a) / c);
	} else {
		tmp = 9.0 * ((y / c) * (x / z));
	}
	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) :: tmp
    t_1 = (-4.0d0) * (a / (c / t))
    if (y <= (-2.6d-109)) then
        tmp = 9.0d0 * ((y * (x / c)) / z)
    else if (y <= (-5.6d-252)) then
        tmp = (b / z) / c
    else if (y <= 6.4d-112) then
        tmp = t_1
    else if (y <= 5.5d-43) then
        tmp = b / (z * c)
    else if (y <= 1.8d+61) then
        tmp = t_1
    else if (y <= 3.5d+114) then
        tmp = 9.0d0 * (y / ((z * c) / x))
    else if (y <= 2.1d+158) then
        tmp = (-4.0d0) * ((t * a) / c)
    else
        tmp = 9.0d0 * ((y / c) * (x / z))
    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 = -4.0 * (a / (c / t));
	double tmp;
	if (y <= -2.6e-109) {
		tmp = 9.0 * ((y * (x / c)) / z);
	} else if (y <= -5.6e-252) {
		tmp = (b / z) / c;
	} else if (y <= 6.4e-112) {
		tmp = t_1;
	} else if (y <= 5.5e-43) {
		tmp = b / (z * c);
	} else if (y <= 1.8e+61) {
		tmp = t_1;
	} else if (y <= 3.5e+114) {
		tmp = 9.0 * (y / ((z * c) / x));
	} else if (y <= 2.1e+158) {
		tmp = -4.0 * ((t * a) / c);
	} else {
		tmp = 9.0 * ((y / c) * (x / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = -4.0 * (a / (c / t))
	tmp = 0
	if y <= -2.6e-109:
		tmp = 9.0 * ((y * (x / c)) / z)
	elif y <= -5.6e-252:
		tmp = (b / z) / c
	elif y <= 6.4e-112:
		tmp = t_1
	elif y <= 5.5e-43:
		tmp = b / (z * c)
	elif y <= 1.8e+61:
		tmp = t_1
	elif y <= 3.5e+114:
		tmp = 9.0 * (y / ((z * c) / x))
	elif y <= 2.1e+158:
		tmp = -4.0 * ((t * a) / c)
	else:
		tmp = 9.0 * ((y / c) * (x / z))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(-4.0 * Float64(a / Float64(c / t)))
	tmp = 0.0
	if (y <= -2.6e-109)
		tmp = Float64(9.0 * Float64(Float64(y * Float64(x / c)) / z));
	elseif (y <= -5.6e-252)
		tmp = Float64(Float64(b / z) / c);
	elseif (y <= 6.4e-112)
		tmp = t_1;
	elseif (y <= 5.5e-43)
		tmp = Float64(b / Float64(z * c));
	elseif (y <= 1.8e+61)
		tmp = t_1;
	elseif (y <= 3.5e+114)
		tmp = Float64(9.0 * Float64(y / Float64(Float64(z * c) / x)));
	elseif (y <= 2.1e+158)
		tmp = Float64(-4.0 * Float64(Float64(t * a) / c));
	else
		tmp = Float64(9.0 * Float64(Float64(y / c) * Float64(x / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = -4.0 * (a / (c / t));
	tmp = 0.0;
	if (y <= -2.6e-109)
		tmp = 9.0 * ((y * (x / c)) / z);
	elseif (y <= -5.6e-252)
		tmp = (b / z) / c;
	elseif (y <= 6.4e-112)
		tmp = t_1;
	elseif (y <= 5.5e-43)
		tmp = b / (z * c);
	elseif (y <= 1.8e+61)
		tmp = t_1;
	elseif (y <= 3.5e+114)
		tmp = 9.0 * (y / ((z * c) / x));
	elseif (y <= 2.1e+158)
		tmp = -4.0 * ((t * a) / c);
	else
		tmp = 9.0 * ((y / c) * (x / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(-4.0 * N[(a / N[(c / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.6e-109], N[(9.0 * N[(N[(y * N[(x / c), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -5.6e-252], N[(N[(b / z), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[y, 6.4e-112], t$95$1, If[LessEqual[y, 5.5e-43], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.8e+61], t$95$1, If[LessEqual[y, 3.5e+114], N[(9.0 * N[(y / N[(N[(z * c), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.1e+158], N[(-4.0 * N[(N[(t * a), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision], N[(9.0 * N[(N[(y / c), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if y < -2.5999999999999998e-109

   1. Initial program 80.7%

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

      1. associate-/r* 76.5%

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

   3. Simplified 82.3%

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

   4. Taylor expanded in x around inf 39.1%

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

      1. *-commutative 39.1%

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

      2. times-frac 42.3%

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

   6. Simplified 42.3%

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

      1. associate-*l/ 43.5%

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

   8. Applied egg-rr 43.5%

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

   if -2.5999999999999998e-109 < y < -5.60000000000000036e-252

   1. Initial program 90.6%

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

      1. associate-/r* 86.6%

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

   3. Simplified 87.9%

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

   4. Taylor expanded in x around 0 80.3%

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

   5. Taylor expanded in b around inf 57.6%

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

   if -5.60000000000000036e-252 < y < 6.39999999999999986e-112 or 5.50000000000000013e-43 < y < 1.80000000000000005e61

   1. Initial program 79.5%

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

      1. associate-/r* 82.2%

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

   3. Simplified 93.5%

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

   4. Taylor expanded in t around inf 60.7%

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

      1. associate-/l* 60.7%

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

   6. Simplified 60.7%

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

   if 6.39999999999999986e-112 < y < 5.50000000000000013e-43

   1. Initial program 84.9%

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

      1. associate-/r* 92.3%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in b around inf 55.3%

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

      1. *-commutative 55.3%

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

   6. Simplified 55.3%

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

   if 1.80000000000000005e61 < y < 3.5000000000000001e114

   1. Initial program 99.9%

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

      1. associate-/r* 91.5%

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

   3. Simplified 91.6%

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

   4. Taylor expanded in x around inf 46.9%

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

      1. associate-/l* 46.9%

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

      2. *-commutative 46.9%

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

   6. Simplified 46.9%

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

   if 3.5000000000000001e114 < y < 2.0999999999999999e158

   1. Initial program 60.7%

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

      1. associate-/r* 70.8%

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

   3. Simplified 89.7%

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

   4. Taylor expanded in t around inf 71.2%

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

   if 2.0999999999999999e158 < y

   1. Initial program 78.4%

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

      1. associate-*l* 78.4%

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

      2. associate-*l* 75.7%

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

   3. Simplified 75.7%

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

      1. div-inv 75.7%

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

      2. associate-+l- 75.7%

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

      3. associate-*r* 75.6%

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

      4. associate-*r* 78.3%

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

      5. associate-+l- 78.3%

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

      6. +-commutative 78.3%

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

      7. associate-*r* 78.4%

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

      8. *-commutative 78.4%

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

      9. *-commutative 78.4%

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

   5. Applied egg-rr 78.4%

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

   6. Taylor expanded in x around inf 57.3%

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

      1. times-frac 65.5%

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

   8. Simplified 65.5%

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

4. Final simplification 54.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{-109}:\\ \;\;\;\;9 \cdot \frac{y \cdot \frac{x}{c}}{z}\\ \mathbf{elif}\;y \leq -5.6 \cdot 10^{-252}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{elif}\;y \leq 6.4 \cdot 10^{-112}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{-43}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{+61}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{+114}:\\ \;\;\;\;9 \cdot \frac{y}{\frac{z \cdot c}{x}}\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{+158}:\\ \;\;\;\;-4 \cdot \frac{t \cdot a}{c}\\ \mathbf{else}:\\ \;\;\;\;9 \cdot \left(\frac{y}{c} \cdot \frac{x}{z}\right)\\ \end{array} \]

Alternative 6: 89.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(9 \cdot y\right)\\ \mathbf{if}\;z \leq -1.35 \cdot 10^{+36} \lor \neg \left(z \leq 3 \cdot 10^{-36}\right):\\ \;\;\;\;\frac{\frac{t_1 + b}{z} + t \cdot \left(a \cdot -4\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + \left(t_1 - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right)}{z \cdot c}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* x (* 9.0 y))))
   (if (or (<= z -1.35e+36) (not (<= z 3e-36)))
     (/ (+ (/ (+ t_1 b) z) (* t (* a -4.0))) c)
     (/ (+ b (- t_1 (* (* z 4.0) (* t a)))) (* z c)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = x * (9.0 * y);
	double tmp;
	if ((z <= -1.35e+36) || !(z <= 3e-36)) {
		tmp = (((t_1 + b) / z) + (t * (a * -4.0))) / c;
	} else {
		tmp = (b + (t_1 - ((z * 4.0) * (t * a)))) / (z * c);
	}
	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) :: tmp
    t_1 = x * (9.0d0 * y)
    if ((z <= (-1.35d+36)) .or. (.not. (z <= 3d-36))) then
        tmp = (((t_1 + b) / z) + (t * (a * (-4.0d0)))) / c
    else
        tmp = (b + (t_1 - ((z * 4.0d0) * (t * a)))) / (z * c)
    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 = x * (9.0 * y);
	double tmp;
	if ((z <= -1.35e+36) || !(z <= 3e-36)) {
		tmp = (((t_1 + b) / z) + (t * (a * -4.0))) / c;
	} else {
		tmp = (b + (t_1 - ((z * 4.0) * (t * a)))) / (z * c);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = x * (9.0 * y)
	tmp = 0
	if (z <= -1.35e+36) or not (z <= 3e-36):
		tmp = (((t_1 + b) / z) + (t * (a * -4.0))) / c
	else:
		tmp = (b + (t_1 - ((z * 4.0) * (t * a)))) / (z * c)
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(x * Float64(9.0 * y))
	tmp = 0.0
	if ((z <= -1.35e+36) || !(z <= 3e-36))
		tmp = Float64(Float64(Float64(Float64(t_1 + b) / z) + Float64(t * Float64(a * -4.0))) / c);
	else
		tmp = Float64(Float64(b + Float64(t_1 - Float64(Float64(z * 4.0) * Float64(t * a)))) / Float64(z * c));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = x * (9.0 * y);
	tmp = 0.0;
	if ((z <= -1.35e+36) || ~((z <= 3e-36)))
		tmp = (((t_1 + b) / z) + (t * (a * -4.0))) / c;
	else
		tmp = (b + (t_1 - ((z * 4.0) * (t * a)))) / (z * c);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(x * N[(9.0 * y), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[z, -1.35e+36], N[Not[LessEqual[z, 3e-36]], $MachinePrecision]], N[(N[(N[(N[(t$95$1 + b), $MachinePrecision] / z), $MachinePrecision] + N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], N[(N[(b + N[(t$95$1 - N[(N[(z * 4.0), $MachinePrecision] * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.35e36 or 3.0000000000000002e-36 < z

   1. Initial program 66.7%

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

      1. associate-/r* 75.1%

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

   3. Simplified 89.8%

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

      1. fma-udef 89.8%

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

   5. Applied egg-rr 89.8%

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

   if -1.35e36 < z < 3.0000000000000002e-36

   1. Initial program 95.4%

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

      1. associate-*l* 95.4%

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

      2. associate-*l* 91.0%

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

   3. Simplified 91.0%

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

4. Final simplification 90.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{+36} \lor \neg \left(z \leq 3 \cdot 10^{-36}\right):\\ \;\;\;\;\frac{\frac{x \cdot \left(9 \cdot y\right) + b}{z} + t \cdot \left(a \cdot -4\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + \left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right)}{z \cdot c}\\ \end{array} \]

Alternative 7: 91.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{+36} \lor \neg \left(z \leq 1.4 \cdot 10^{-35}\right):\\ \;\;\;\;\frac{\frac{x \cdot \left(9 \cdot y\right) + b}{z} + t \cdot \left(a \cdot -4\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= z -3e+36) (not (<= z 1.4e-35)))
   (/ (+ (/ (+ (* x (* 9.0 y)) b) z) (* t (* a -4.0))) c)
   (/ (+ b (- (* y (* x 9.0)) (* a (* t (* z 4.0))))) (* z c))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((z <= -3e+36) || !(z <= 1.4e-35)) {
		tmp = ((((x * (9.0 * y)) + b) / z) + (t * (a * -4.0))) / c;
	} else {
		tmp = (b + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (z * c);
	}
	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) :: tmp
    if ((z <= (-3d+36)) .or. (.not. (z <= 1.4d-35))) then
        tmp = ((((x * (9.0d0 * y)) + b) / z) + (t * (a * (-4.0d0)))) / c
    else
        tmp = (b + ((y * (x * 9.0d0)) - (a * (t * (z * 4.0d0))))) / (z * c)
    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 tmp;
	if ((z <= -3e+36) || !(z <= 1.4e-35)) {
		tmp = ((((x * (9.0 * y)) + b) / z) + (t * (a * -4.0))) / c;
	} else {
		tmp = (b + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (z * c);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if (z <= -3e+36) or not (z <= 1.4e-35):
		tmp = ((((x * (9.0 * y)) + b) / z) + (t * (a * -4.0))) / c
	else:
		tmp = (b + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (z * c)
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((z <= -3e+36) || !(z <= 1.4e-35))
		tmp = Float64(Float64(Float64(Float64(Float64(x * Float64(9.0 * y)) + b) / z) + Float64(t * Float64(a * -4.0))) / c);
	else
		tmp = Float64(Float64(b + Float64(Float64(y * Float64(x * 9.0)) - Float64(a * Float64(t * Float64(z * 4.0))))) / Float64(z * c));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((z <= -3e+36) || ~((z <= 1.4e-35)))
		tmp = ((((x * (9.0 * y)) + b) / z) + (t * (a * -4.0))) / c;
	else
		tmp = (b + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (z * c);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[z, -3e+36], N[Not[LessEqual[z, 1.4e-35]], $MachinePrecision]], N[(N[(N[(N[(N[(x * N[(9.0 * y), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision] / z), $MachinePrecision] + N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], N[(N[(b + N[(N[(y * N[(x * 9.0), $MachinePrecision]), $MachinePrecision] - N[(a * N[(t * N[(z * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3e36 or 1.4e-35 < z

   1. Initial program 66.7%

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

      1. associate-/r* 75.1%

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

   3. Simplified 89.8%

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

      1. fma-udef 89.8%

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

   5. Applied egg-rr 89.8%

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

   if -3e36 < z < 1.4e-35

   1. Initial program 95.4%

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

4. Final simplification 92.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{+36} \lor \neg \left(z \leq 1.4 \cdot 10^{-35}\right):\\ \;\;\;\;\frac{\frac{x \cdot \left(9 \cdot y\right) + b}{z} + t \cdot \left(a \cdot -4\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c}\\ \end{array} \]

Alternative 8: 67.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t \cdot \left(a \cdot -4\right) + \frac{b}{z}}{c}\\ t_2 := \frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \mathbf{if}\;y \leq -2.45 \cdot 10^{-154}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{+61}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 4 \cdot 10^{+114}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{+158}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{z} + 9 \cdot \frac{y}{\frac{z}{x}}}{c}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (+ (* t (* a -4.0)) (/ b z)) c))
        (t_2 (/ (+ b (* 9.0 (* x y))) (* z c))))
   (if (<= y -2.45e-154)
     t_2
     (if (<= y 1.8e+61)
       t_1
       (if (<= y 4e+114)
         t_2
         (if (<= y 4.5e+158) t_1 (/ (+ (/ b z) (* 9.0 (/ y (/ z x)))) c)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = ((t * (a * -4.0)) + (b / z)) / c;
	double t_2 = (b + (9.0 * (x * y))) / (z * c);
	double tmp;
	if (y <= -2.45e-154) {
		tmp = t_2;
	} else if (y <= 1.8e+61) {
		tmp = t_1;
	} else if (y <= 4e+114) {
		tmp = t_2;
	} else if (y <= 4.5e+158) {
		tmp = t_1;
	} else {
		tmp = ((b / z) + (9.0 * (y / (z / x)))) / c;
	}
	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) :: tmp
    t_1 = ((t * (a * (-4.0d0))) + (b / z)) / c
    t_2 = (b + (9.0d0 * (x * y))) / (z * c)
    if (y <= (-2.45d-154)) then
        tmp = t_2
    else if (y <= 1.8d+61) then
        tmp = t_1
    else if (y <= 4d+114) then
        tmp = t_2
    else if (y <= 4.5d+158) then
        tmp = t_1
    else
        tmp = ((b / z) + (9.0d0 * (y / (z / x)))) / c
    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 = ((t * (a * -4.0)) + (b / z)) / c;
	double t_2 = (b + (9.0 * (x * y))) / (z * c);
	double tmp;
	if (y <= -2.45e-154) {
		tmp = t_2;
	} else if (y <= 1.8e+61) {
		tmp = t_1;
	} else if (y <= 4e+114) {
		tmp = t_2;
	} else if (y <= 4.5e+158) {
		tmp = t_1;
	} else {
		tmp = ((b / z) + (9.0 * (y / (z / x)))) / c;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = ((t * (a * -4.0)) + (b / z)) / c
	t_2 = (b + (9.0 * (x * y))) / (z * c)
	tmp = 0
	if y <= -2.45e-154:
		tmp = t_2
	elif y <= 1.8e+61:
		tmp = t_1
	elif y <= 4e+114:
		tmp = t_2
	elif y <= 4.5e+158:
		tmp = t_1
	else:
		tmp = ((b / z) + (9.0 * (y / (z / x)))) / c
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(Float64(t * Float64(a * -4.0)) + Float64(b / z)) / c)
	t_2 = Float64(Float64(b + Float64(9.0 * Float64(x * y))) / Float64(z * c))
	tmp = 0.0
	if (y <= -2.45e-154)
		tmp = t_2;
	elseif (y <= 1.8e+61)
		tmp = t_1;
	elseif (y <= 4e+114)
		tmp = t_2;
	elseif (y <= 4.5e+158)
		tmp = t_1;
	else
		tmp = Float64(Float64(Float64(b / z) + Float64(9.0 * Float64(y / Float64(z / x)))) / c);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = ((t * (a * -4.0)) + (b / z)) / c;
	t_2 = (b + (9.0 * (x * y))) / (z * c);
	tmp = 0.0;
	if (y <= -2.45e-154)
		tmp = t_2;
	elseif (y <= 1.8e+61)
		tmp = t_1;
	elseif (y <= 4e+114)
		tmp = t_2;
	elseif (y <= 4.5e+158)
		tmp = t_1;
	else
		tmp = ((b / z) + (9.0 * (y / (z / x)))) / c;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision] + N[(b / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b + N[(9.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.45e-154], t$95$2, If[LessEqual[y, 1.8e+61], t$95$1, If[LessEqual[y, 4e+114], t$95$2, If[LessEqual[y, 4.5e+158], t$95$1, N[(N[(N[(b / z), $MachinePrecision] + N[(9.0 * N[(y / N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.44999999999999998e-154 or 1.80000000000000005e61 < y < 4e114

   1. Initial program 83.5%

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

      1. associate-/r* 78.4%

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

   3. Simplified 83.3%

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

   4. Taylor expanded in z around 0 61.3%

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

   if -2.44999999999999998e-154 < y < 1.80000000000000005e61 or 4e114 < y < 4.50000000000000046e158

   1. Initial program 79.9%

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

      1. associate-/r* 83.5%

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

   3. Simplified 92.9%

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

   4. Taylor expanded in x around 0 84.9%

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

   if 4.50000000000000046e158 < y

   1. Initial program 78.4%

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

      1. associate-/r* 78.5%

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

   3. Simplified 81.6%

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

   4. Taylor expanded in t around 0 73.2%

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

      1. associate-/l* 76.0%

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

   6. Simplified 76.0%

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

4. Final simplification 73.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.45 \cdot 10^{-154}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{+61}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + \frac{b}{z}}{c}\\ \mathbf{elif}\;y \leq 4 \cdot 10^{+114}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{+158}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + \frac{b}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{z} + 9 \cdot \frac{y}{\frac{z}{x}}}{c}\\ \end{array} \]

Alternative 9: 74.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{+69} \lor \neg \left(z \leq -5 \cdot 10^{-20}\right) \land \left(z \leq -3.3 \cdot 10^{-93} \lor \neg \left(z \leq 2.7 \cdot 10^{-50}\right)\right):\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + \frac{b}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= z -1.9e+69)
         (and (not (<= z -5e-20)) (or (<= z -3.3e-93) (not (<= z 2.7e-50)))))
   (/ (+ (* t (* a -4.0)) (/ b z)) c)
   (/ (+ b (* 9.0 (* x y))) (* z c))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((z <= -1.9e+69) || (!(z <= -5e-20) && ((z <= -3.3e-93) || !(z <= 2.7e-50)))) {
		tmp = ((t * (a * -4.0)) + (b / z)) / c;
	} else {
		tmp = (b + (9.0 * (x * y))) / (z * c);
	}
	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) :: tmp
    if ((z <= (-1.9d+69)) .or. (.not. (z <= (-5d-20))) .and. (z <= (-3.3d-93)) .or. (.not. (z <= 2.7d-50))) then
        tmp = ((t * (a * (-4.0d0))) + (b / z)) / c
    else
        tmp = (b + (9.0d0 * (x * y))) / (z * c)
    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 tmp;
	if ((z <= -1.9e+69) || (!(z <= -5e-20) && ((z <= -3.3e-93) || !(z <= 2.7e-50)))) {
		tmp = ((t * (a * -4.0)) + (b / z)) / c;
	} else {
		tmp = (b + (9.0 * (x * y))) / (z * c);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if (z <= -1.9e+69) or (not (z <= -5e-20) and ((z <= -3.3e-93) or not (z <= 2.7e-50))):
		tmp = ((t * (a * -4.0)) + (b / z)) / c
	else:
		tmp = (b + (9.0 * (x * y))) / (z * c)
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((z <= -1.9e+69) || (!(z <= -5e-20) && ((z <= -3.3e-93) || !(z <= 2.7e-50))))
		tmp = Float64(Float64(Float64(t * Float64(a * -4.0)) + Float64(b / z)) / c);
	else
		tmp = Float64(Float64(b + Float64(9.0 * Float64(x * y))) / Float64(z * c));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((z <= -1.9e+69) || (~((z <= -5e-20)) && ((z <= -3.3e-93) || ~((z <= 2.7e-50)))))
		tmp = ((t * (a * -4.0)) + (b / z)) / c;
	else
		tmp = (b + (9.0 * (x * y))) / (z * c);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[z, -1.9e+69], And[N[Not[LessEqual[z, -5e-20]], $MachinePrecision], Or[LessEqual[z, -3.3e-93], N[Not[LessEqual[z, 2.7e-50]], $MachinePrecision]]]], N[(N[(N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision] + N[(b / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], N[(N[(b + N[(9.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.90000000000000014e69 or -4.9999999999999999e-20 < z < -3.3000000000000001e-93 or 2.7e-50 < z

   1. Initial program 70.6%

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

      1. associate-/r* 77.7%

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

   3. Simplified 90.6%

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

   4. Taylor expanded in x around 0 80.5%

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

   if -1.90000000000000014e69 < z < -4.9999999999999999e-20 or -3.3000000000000001e-93 < z < 2.7e-50

   1. Initial program 93.4%

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

      1. associate-/r* 84.1%

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

   3. Simplified 83.3%

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

   4. Taylor expanded in 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 81.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{+69} \lor \neg \left(z \leq -5 \cdot 10^{-20}\right) \land \left(z \leq -3.3 \cdot 10^{-93} \lor \neg \left(z \leq 2.7 \cdot 10^{-50}\right)\right):\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + \frac{b}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \end{array} \]

Alternative 10: 67.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t \cdot \left(a \cdot -4\right) + \frac{b}{z}}{c}\\ t_2 := b + 9 \cdot \left(x \cdot y\right)\\ t_3 := \frac{t_2}{z \cdot c}\\ \mathbf{if}\;y \leq -1.1 \cdot 10^{-153}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{+61}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{+115}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{+158}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{t_2}{z}}{c}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (+ (* t (* a -4.0)) (/ b z)) c))
        (t_2 (+ b (* 9.0 (* x y))))
        (t_3 (/ t_2 (* z c))))
   (if (<= y -1.1e-153)
     t_3
     (if (<= y 7.2e+61)
       t_1
       (if (<= y 2.9e+115) t_3 (if (<= y 1.9e+158) t_1 (/ (/ t_2 z) c)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = ((t * (a * -4.0)) + (b / z)) / c;
	double t_2 = b + (9.0 * (x * y));
	double t_3 = t_2 / (z * c);
	double tmp;
	if (y <= -1.1e-153) {
		tmp = t_3;
	} else if (y <= 7.2e+61) {
		tmp = t_1;
	} else if (y <= 2.9e+115) {
		tmp = t_3;
	} else if (y <= 1.9e+158) {
		tmp = t_1;
	} else {
		tmp = (t_2 / z) / c;
	}
	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) :: tmp
    t_1 = ((t * (a * (-4.0d0))) + (b / z)) / c
    t_2 = b + (9.0d0 * (x * y))
    t_3 = t_2 / (z * c)
    if (y <= (-1.1d-153)) then
        tmp = t_3
    else if (y <= 7.2d+61) then
        tmp = t_1
    else if (y <= 2.9d+115) then
        tmp = t_3
    else if (y <= 1.9d+158) then
        tmp = t_1
    else
        tmp = (t_2 / z) / c
    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 = ((t * (a * -4.0)) + (b / z)) / c;
	double t_2 = b + (9.0 * (x * y));
	double t_3 = t_2 / (z * c);
	double tmp;
	if (y <= -1.1e-153) {
		tmp = t_3;
	} else if (y <= 7.2e+61) {
		tmp = t_1;
	} else if (y <= 2.9e+115) {
		tmp = t_3;
	} else if (y <= 1.9e+158) {
		tmp = t_1;
	} else {
		tmp = (t_2 / z) / c;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = ((t * (a * -4.0)) + (b / z)) / c
	t_2 = b + (9.0 * (x * y))
	t_3 = t_2 / (z * c)
	tmp = 0
	if y <= -1.1e-153:
		tmp = t_3
	elif y <= 7.2e+61:
		tmp = t_1
	elif y <= 2.9e+115:
		tmp = t_3
	elif y <= 1.9e+158:
		tmp = t_1
	else:
		tmp = (t_2 / z) / c
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(Float64(t * Float64(a * -4.0)) + Float64(b / z)) / c)
	t_2 = Float64(b + Float64(9.0 * Float64(x * y)))
	t_3 = Float64(t_2 / Float64(z * c))
	tmp = 0.0
	if (y <= -1.1e-153)
		tmp = t_3;
	elseif (y <= 7.2e+61)
		tmp = t_1;
	elseif (y <= 2.9e+115)
		tmp = t_3;
	elseif (y <= 1.9e+158)
		tmp = t_1;
	else
		tmp = Float64(Float64(t_2 / z) / c);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = ((t * (a * -4.0)) + (b / z)) / c;
	t_2 = b + (9.0 * (x * y));
	t_3 = t_2 / (z * c);
	tmp = 0.0;
	if (y <= -1.1e-153)
		tmp = t_3;
	elseif (y <= 7.2e+61)
		tmp = t_1;
	elseif (y <= 2.9e+115)
		tmp = t_3;
	elseif (y <= 1.9e+158)
		tmp = t_1;
	else
		tmp = (t_2 / z) / c;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision] + N[(b / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]}, Block[{t$95$2 = N[(b + N[(9.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 / N[(z * c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.1e-153], t$95$3, If[LessEqual[y, 7.2e+61], t$95$1, If[LessEqual[y, 2.9e+115], t$95$3, If[LessEqual[y, 1.9e+158], t$95$1, N[(N[(t$95$2 / z), $MachinePrecision] / c), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.1e-153 or 7.20000000000000021e61 < y < 2.90000000000000005e115

   1. Initial program 83.5%

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

      1. associate-/r* 78.4%

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

   3. Simplified 83.3%

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

   4. Taylor expanded in z around 0 61.3%

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

   if -1.1e-153 < y < 7.20000000000000021e61 or 2.90000000000000005e115 < y < 1.8999999999999999e158

   1. Initial program 79.9%

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

      1. associate-/r* 83.5%

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

   3. Simplified 92.9%

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

   4. Taylor expanded in x around 0 84.9%

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

   if 1.8999999999999999e158 < y

   1. Initial program 78.4%

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

      1. associate-/r* 78.5%

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

   3. Simplified 73.3%

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

      1. fma-udef 73.3%

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

   5. Applied egg-rr 73.3%

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

   6. Taylor expanded in z around 0 76.1%

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

4. Final simplification 73.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{-153}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{+61}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + \frac{b}{z}}{c}\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{+115}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{+158}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + \frac{b}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b + 9 \cdot \left(x \cdot y\right)}{z}}{c}\\ \end{array} \]

Alternative 11: 74.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ t_2 := \frac{t \cdot \left(a \cdot -4\right) + \frac{b}{z}}{c}\\ \mathbf{if}\;z \leq -2.3 \cdot 10^{+69}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -6 \cdot 10^{-20}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.85 \cdot 10^{-93}:\\ \;\;\;\;\frac{-4 \cdot \left(t \cdot a\right)}{c} + \frac{b}{z \cdot c}\\ \mathbf{elif}\;z \leq 2.45 \cdot 10^{-48}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (+ b (* 9.0 (* x y))) (* z c)))
        (t_2 (/ (+ (* t (* a -4.0)) (/ b z)) c)))
   (if (<= z -2.3e+69)
     t_2
     (if (<= z -6e-20)
       t_1
       (if (<= z -1.85e-93)
         (+ (/ (* -4.0 (* t a)) c) (/ b (* z c)))
         (if (<= z 2.45e-48) 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 + (9.0 * (x * y))) / (z * c);
	double t_2 = ((t * (a * -4.0)) + (b / z)) / c;
	double tmp;
	if (z <= -2.3e+69) {
		tmp = t_2;
	} else if (z <= -6e-20) {
		tmp = t_1;
	} else if (z <= -1.85e-93) {
		tmp = ((-4.0 * (t * a)) / c) + (b / (z * c));
	} else if (z <= 2.45e-48) {
		tmp = t_1;
	} else {
		tmp = 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) :: tmp
    t_1 = (b + (9.0d0 * (x * y))) / (z * c)
    t_2 = ((t * (a * (-4.0d0))) + (b / z)) / c
    if (z <= (-2.3d+69)) then
        tmp = t_2
    else if (z <= (-6d-20)) then
        tmp = t_1
    else if (z <= (-1.85d-93)) then
        tmp = (((-4.0d0) * (t * a)) / c) + (b / (z * c))
    else if (z <= 2.45d-48) then
        tmp = t_1
    else
        tmp = 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 + (9.0 * (x * y))) / (z * c);
	double t_2 = ((t * (a * -4.0)) + (b / z)) / c;
	double tmp;
	if (z <= -2.3e+69) {
		tmp = t_2;
	} else if (z <= -6e-20) {
		tmp = t_1;
	} else if (z <= -1.85e-93) {
		tmp = ((-4.0 * (t * a)) / c) + (b / (z * c));
	} else if (z <= 2.45e-48) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = (b + (9.0 * (x * y))) / (z * c)
	t_2 = ((t * (a * -4.0)) + (b / z)) / c
	tmp = 0
	if z <= -2.3e+69:
		tmp = t_2
	elif z <= -6e-20:
		tmp = t_1
	elif z <= -1.85e-93:
		tmp = ((-4.0 * (t * a)) / c) + (b / (z * c))
	elif z <= 2.45e-48:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(b + Float64(9.0 * Float64(x * y))) / Float64(z * c))
	t_2 = Float64(Float64(Float64(t * Float64(a * -4.0)) + Float64(b / z)) / c)
	tmp = 0.0
	if (z <= -2.3e+69)
		tmp = t_2;
	elseif (z <= -6e-20)
		tmp = t_1;
	elseif (z <= -1.85e-93)
		tmp = Float64(Float64(Float64(-4.0 * Float64(t * a)) / c) + Float64(b / Float64(z * c)));
	elseif (z <= 2.45e-48)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (b + (9.0 * (x * y))) / (z * c);
	t_2 = ((t * (a * -4.0)) + (b / z)) / c;
	tmp = 0.0;
	if (z <= -2.3e+69)
		tmp = t_2;
	elseif (z <= -6e-20)
		tmp = t_1;
	elseif (z <= -1.85e-93)
		tmp = ((-4.0 * (t * a)) / c) + (b / (z * c));
	elseif (z <= 2.45e-48)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(b + N[(9.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision] + N[(b / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]}, If[LessEqual[z, -2.3e+69], t$95$2, If[LessEqual[z, -6e-20], t$95$1, If[LessEqual[z, -1.85e-93], N[(N[(N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision] + N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.45e-48], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.30000000000000017e69 or 2.4500000000000001e-48 < z

   1. Initial program 67.3%

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

      1. associate-/r* 75.9%

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

   3. Simplified 90.3%

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

   4. Taylor expanded in x around 0 79.9%

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

   if -2.30000000000000017e69 < z < -6.00000000000000057e-20 or -1.85000000000000001e-93 < z < 2.4500000000000001e-48

   1. Initial program 93.4%

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

      1. associate-/r* 84.1%

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

   3. Simplified 83.3%

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

   4. Taylor expanded in z around 0 82.0%

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

   if -6.00000000000000057e-20 < z < -1.85000000000000001e-93

   1. Initial program 99.8%

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

      1. associate-/r* 92.9%

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

   3. Simplified 93.0%

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

   4. Taylor expanded in x around 0 86.2%

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

   5. Taylor expanded in b around 0 93.0%

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

      1. associate-*r/ 93.0%

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

   7. Simplified 93.0%

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

4. Final simplification 81.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{+69}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + \frac{b}{z}}{c}\\ \mathbf{elif}\;z \leq -6 \cdot 10^{-20}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \mathbf{elif}\;z \leq -1.85 \cdot 10^{-93}:\\ \;\;\;\;\frac{-4 \cdot \left(t \cdot a\right)}{c} + \frac{b}{z \cdot c}\\ \mathbf{elif}\;z \leq 2.45 \cdot 10^{-48}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + \frac{b}{z}}{c}\\ \end{array} \]

Alternative 12: 74.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ t_2 := \frac{t \cdot \left(a \cdot -4\right) + \frac{b}{z}}{c}\\ \mathbf{if}\;z \leq -2.5 \cdot 10^{+69}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -5 \cdot 10^{-20}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{-132}:\\ \;\;\;\;\frac{b - 4 \cdot \left(a \cdot \left(z \cdot t\right)\right)}{z \cdot c}\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-54}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (+ b (* 9.0 (* x y))) (* z c)))
        (t_2 (/ (+ (* t (* a -4.0)) (/ b z)) c)))
   (if (<= z -2.5e+69)
     t_2
     (if (<= z -5e-20)
       t_1
       (if (<= z -3.8e-132)
         (/ (- b (* 4.0 (* a (* z t)))) (* z c))
         (if (<= z 4.2e-54) 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 + (9.0 * (x * y))) / (z * c);
	double t_2 = ((t * (a * -4.0)) + (b / z)) / c;
	double tmp;
	if (z <= -2.5e+69) {
		tmp = t_2;
	} else if (z <= -5e-20) {
		tmp = t_1;
	} else if (z <= -3.8e-132) {
		tmp = (b - (4.0 * (a * (z * t)))) / (z * c);
	} else if (z <= 4.2e-54) {
		tmp = t_1;
	} else {
		tmp = 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) :: tmp
    t_1 = (b + (9.0d0 * (x * y))) / (z * c)
    t_2 = ((t * (a * (-4.0d0))) + (b / z)) / c
    if (z <= (-2.5d+69)) then
        tmp = t_2
    else if (z <= (-5d-20)) then
        tmp = t_1
    else if (z <= (-3.8d-132)) then
        tmp = (b - (4.0d0 * (a * (z * t)))) / (z * c)
    else if (z <= 4.2d-54) then
        tmp = t_1
    else
        tmp = 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 + (9.0 * (x * y))) / (z * c);
	double t_2 = ((t * (a * -4.0)) + (b / z)) / c;
	double tmp;
	if (z <= -2.5e+69) {
		tmp = t_2;
	} else if (z <= -5e-20) {
		tmp = t_1;
	} else if (z <= -3.8e-132) {
		tmp = (b - (4.0 * (a * (z * t)))) / (z * c);
	} else if (z <= 4.2e-54) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = (b + (9.0 * (x * y))) / (z * c)
	t_2 = ((t * (a * -4.0)) + (b / z)) / c
	tmp = 0
	if z <= -2.5e+69:
		tmp = t_2
	elif z <= -5e-20:
		tmp = t_1
	elif z <= -3.8e-132:
		tmp = (b - (4.0 * (a * (z * t)))) / (z * c)
	elif z <= 4.2e-54:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(b + Float64(9.0 * Float64(x * y))) / Float64(z * c))
	t_2 = Float64(Float64(Float64(t * Float64(a * -4.0)) + Float64(b / z)) / c)
	tmp = 0.0
	if (z <= -2.5e+69)
		tmp = t_2;
	elseif (z <= -5e-20)
		tmp = t_1;
	elseif (z <= -3.8e-132)
		tmp = Float64(Float64(b - Float64(4.0 * Float64(a * Float64(z * t)))) / Float64(z * c));
	elseif (z <= 4.2e-54)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (b + (9.0 * (x * y))) / (z * c);
	t_2 = ((t * (a * -4.0)) + (b / z)) / c;
	tmp = 0.0;
	if (z <= -2.5e+69)
		tmp = t_2;
	elseif (z <= -5e-20)
		tmp = t_1;
	elseif (z <= -3.8e-132)
		tmp = (b - (4.0 * (a * (z * t)))) / (z * c);
	elseif (z <= 4.2e-54)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(b + N[(9.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision] + N[(b / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]}, If[LessEqual[z, -2.5e+69], t$95$2, If[LessEqual[z, -5e-20], t$95$1, If[LessEqual[z, -3.8e-132], N[(N[(b - N[(4.0 * N[(a * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.2e-54], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.50000000000000018e69 or 4.2e-54 < z

   1. Initial program 67.3%

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

      1. associate-/r* 75.9%

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

   3. Simplified 90.3%

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

   4. Taylor expanded in x around 0 79.9%

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

   if -2.50000000000000018e69 < z < -4.9999999999999999e-20 or -3.7999999999999997e-132 < z < 4.2e-54

   1. Initial program 93.0%

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

      1. associate-/r* 83.9%

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

   3. Simplified 83.1%

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

   4. Taylor expanded in z around 0 82.6%

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

   if -4.9999999999999999e-20 < z < -3.7999999999999997e-132

   1. Initial program 99.7%

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

      1. associate-*l* 99.8%

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

      2. associate-*l* 90.6%

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

   3. Simplified 90.6%

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

   4. Taylor expanded in x around 0 90.6%

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

4. Final simplification 82.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+69}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + \frac{b}{z}}{c}\\ \mathbf{elif}\;z \leq -5 \cdot 10^{-20}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{-132}:\\ \;\;\;\;\frac{b - 4 \cdot \left(a \cdot \left(z \cdot t\right)\right)}{z \cdot c}\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-54}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + \frac{b}{z}}{c}\\ \end{array} \]

Alternative 13: 84.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.3 \cdot 10^{+213}:\\ \;\;\;\;\frac{\frac{x \cdot \left(9 \cdot y\right) + b}{z} + t \cdot \left(a \cdot -4\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;9 \cdot \frac{x}{c \cdot \frac{z}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= y 1.3e+213)
   (/ (+ (/ (+ (* x (* 9.0 y)) b) z) (* t (* a -4.0))) c)
   (* 9.0 (/ x (* c (/ z y))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (y <= 1.3e+213) {
		tmp = ((((x * (9.0 * y)) + b) / z) + (t * (a * -4.0))) / c;
	} else {
		tmp = 9.0 * (x / (c * (z / y)));
	}
	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) :: tmp
    if (y <= 1.3d+213) then
        tmp = ((((x * (9.0d0 * y)) + b) / z) + (t * (a * (-4.0d0)))) / c
    else
        tmp = 9.0d0 * (x / (c * (z / y)))
    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 tmp;
	if (y <= 1.3e+213) {
		tmp = ((((x * (9.0 * y)) + b) / z) + (t * (a * -4.0))) / c;
	} else {
		tmp = 9.0 * (x / (c * (z / y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if y <= 1.3e+213:
		tmp = ((((x * (9.0 * y)) + b) / z) + (t * (a * -4.0))) / c
	else:
		tmp = 9.0 * (x / (c * (z / y)))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (y <= 1.3e+213)
		tmp = Float64(Float64(Float64(Float64(Float64(x * Float64(9.0 * y)) + b) / z) + Float64(t * Float64(a * -4.0))) / c);
	else
		tmp = Float64(9.0 * Float64(x / Float64(c * Float64(z / y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (y <= 1.3e+213)
		tmp = ((((x * (9.0 * y)) + b) / z) + (t * (a * -4.0))) / c;
	else
		tmp = 9.0 * (x / (c * (z / y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[y, 1.3e+213], N[(N[(N[(N[(N[(x * N[(9.0 * y), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision] / z), $MachinePrecision] + N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], N[(9.0 * N[(x / N[(c * N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 1.29999999999999999e213

   1. Initial program 82.1%

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

      1. associate-/r* 81.8%

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

   3. Simplified 88.0%

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

      1. fma-udef 88.0%

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

   5. Applied egg-rr 88.0%

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

   if 1.29999999999999999e213 < y

   1. Initial program 71.0%

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

      1. associate-/r* 66.7%

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

   3. Simplified 72.0%

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

   4. Taylor expanded in x around inf 61.4%

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

      1. *-commutative 61.4%

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

      2. times-frac 61.9%

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

   6. Simplified 61.9%

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

      1. clear-num 61.9%

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

      2. frac-times 66.5%

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

      3. *-un-lft-identity 66.5%

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

   8. Applied egg-rr 66.5%

      \[\leadsto 9 \cdot \color{blue}{\frac{x}{\frac{z}{y} \cdot c}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 86.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.3 \cdot 10^{+213}:\\ \;\;\;\;\frac{\frac{x \cdot \left(9 \cdot y\right) + b}{z} + t \cdot \left(a \cdot -4\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;9 \cdot \frac{x}{c \cdot \frac{z}{y}}\\ \end{array} \]

Alternative 14: 68.7% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.25 \cdot 10^{+70}:\\ \;\;\;\;-4 \cdot \frac{t \cdot a}{c}\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{+110}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= z -2.25e+70)
   (* -4.0 (/ (* t a) c))
   (if (<= z 2.5e+110)
     (/ (+ b (* 9.0 (* x y))) (* z c))
     (* -4.0 (/ a (/ c t))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (z <= -2.25e+70) {
		tmp = -4.0 * ((t * a) / c);
	} else if (z <= 2.5e+110) {
		tmp = (b + (9.0 * (x * y))) / (z * c);
	} else {
		tmp = -4.0 * (a / (c / t));
	}
	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) :: tmp
    if (z <= (-2.25d+70)) then
        tmp = (-4.0d0) * ((t * a) / c)
    else if (z <= 2.5d+110) then
        tmp = (b + (9.0d0 * (x * y))) / (z * c)
    else
        tmp = (-4.0d0) * (a / (c / t))
    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 tmp;
	if (z <= -2.25e+70) {
		tmp = -4.0 * ((t * a) / c);
	} else if (z <= 2.5e+110) {
		tmp = (b + (9.0 * (x * y))) / (z * c);
	} else {
		tmp = -4.0 * (a / (c / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if z <= -2.25e+70:
		tmp = -4.0 * ((t * a) / c)
	elif z <= 2.5e+110:
		tmp = (b + (9.0 * (x * y))) / (z * c)
	else:
		tmp = -4.0 * (a / (c / t))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (z <= -2.25e+70)
		tmp = Float64(-4.0 * Float64(Float64(t * a) / c));
	elseif (z <= 2.5e+110)
		tmp = Float64(Float64(b + Float64(9.0 * Float64(x * y))) / Float64(z * c));
	else
		tmp = Float64(-4.0 * Float64(a / Float64(c / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (z <= -2.25e+70)
		tmp = -4.0 * ((t * a) / c);
	elseif (z <= 2.5e+110)
		tmp = (b + (9.0 * (x * y))) / (z * c);
	else
		tmp = -4.0 * (a / (c / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[z, -2.25e+70], N[(-4.0 * N[(N[(t * a), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.5e+110], N[(N[(b + N[(9.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(-4.0 * N[(a / N[(c / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.25e70

   1. Initial program 54.0%

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

      1. associate-/r* 68.7%

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

   3. Simplified 86.9%

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

   4. Taylor expanded in t around inf 70.9%

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

   if -2.25e70 < z < 2.49999999999999989e110

   1. Initial program 92.3%

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

      1. associate-/r* 85.8%

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

   3. Simplified 86.1%

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

   4. Taylor expanded in z around 0 74.2%

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

   if 2.49999999999999989e110 < z

   1. Initial program 66.6%

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

      1. associate-/r* 72.8%

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

   3. Simplified 96.8%

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

   4. Taylor expanded in t around inf 65.4%

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

      1. associate-/l* 65.4%

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

   6. Simplified 65.4%

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

4. Final simplification 72.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.25 \cdot 10^{+70}:\\ \;\;\;\;-4 \cdot \frac{t \cdot a}{c}\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{+110}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \end{array} \]

Alternative 15: 49.3% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2.7 \cdot 10^{+77}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;b \leq 6.7 \cdot 10^{-43}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= b -2.7e+77)
   (/ b (* z c))
   (if (<= b 6.7e-43) (* -4.0 (* t (/ a c))) (/ (/ b z) c))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (b <= -2.7e+77) {
		tmp = b / (z * c);
	} else if (b <= 6.7e-43) {
		tmp = -4.0 * (t * (a / c));
	} else {
		tmp = (b / z) / c;
	}
	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) :: tmp
    if (b <= (-2.7d+77)) then
        tmp = b / (z * c)
    else if (b <= 6.7d-43) then
        tmp = (-4.0d0) * (t * (a / c))
    else
        tmp = (b / z) / c
    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 tmp;
	if (b <= -2.7e+77) {
		tmp = b / (z * c);
	} else if (b <= 6.7e-43) {
		tmp = -4.0 * (t * (a / c));
	} else {
		tmp = (b / z) / c;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if b <= -2.7e+77:
		tmp = b / (z * c)
	elif b <= 6.7e-43:
		tmp = -4.0 * (t * (a / c))
	else:
		tmp = (b / z) / c
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (b <= -2.7e+77)
		tmp = Float64(b / Float64(z * c));
	elseif (b <= 6.7e-43)
		tmp = Float64(-4.0 * Float64(t * Float64(a / c)));
	else
		tmp = Float64(Float64(b / z) / c);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (b <= -2.7e+77)
		tmp = b / (z * c);
	elseif (b <= 6.7e-43)
		tmp = -4.0 * (t * (a / c));
	else
		tmp = (b / z) / c;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[b, -2.7e+77], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 6.7e-43], N[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b / z), $MachinePrecision] / c), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -2.6999999999999998e77

   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* 70.5%

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

   3. Simplified 81.7%

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

   4. Taylor expanded in b around inf 51.4%

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

      1. *-commutative 51.4%

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

   6. Simplified 51.4%

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

   if -2.6999999999999998e77 < b < 6.6999999999999998e-43

   1. Initial program 81.9%

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

      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 89.2%

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

   4. Taylor expanded in t around inf 49.5%

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

      1. associate-/l* 51.8%

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

      2. associate-/r/ 49.6%

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

   6. Simplified 49.6%

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

   if 6.6999999999999998e-43 < b

   1. Initial program 83.6%

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

      1. associate-/r* 85.3%

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

   3. Simplified 89.4%

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

   4. Taylor expanded in x around 0 79.9%

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

   5. Taylor expanded in b around inf 59.7%

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

4. Final simplification 52.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.7 \cdot 10^{+77}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;b \leq 6.7 \cdot 10^{-43}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \end{array} \]

Alternative 16: 50.1% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -6.6 \cdot 10^{+78}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;b \leq 4.4 \cdot 10^{+52}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= b -6.6e+78)
   (/ b (* z c))
   (if (<= b 4.4e+52) (* -4.0 (/ a (/ c t))) (/ (/ b z) c))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (b <= -6.6e+78) {
		tmp = b / (z * c);
	} else if (b <= 4.4e+52) {
		tmp = -4.0 * (a / (c / t));
	} else {
		tmp = (b / z) / c;
	}
	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) :: tmp
    if (b <= (-6.6d+78)) then
        tmp = b / (z * c)
    else if (b <= 4.4d+52) then
        tmp = (-4.0d0) * (a / (c / t))
    else
        tmp = (b / z) / c
    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 tmp;
	if (b <= -6.6e+78) {
		tmp = b / (z * c);
	} else if (b <= 4.4e+52) {
		tmp = -4.0 * (a / (c / t));
	} else {
		tmp = (b / z) / c;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if b <= -6.6e+78:
		tmp = b / (z * c)
	elif b <= 4.4e+52:
		tmp = -4.0 * (a / (c / t))
	else:
		tmp = (b / z) / c
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (b <= -6.6e+78)
		tmp = Float64(b / Float64(z * c));
	elseif (b <= 4.4e+52)
		tmp = Float64(-4.0 * Float64(a / Float64(c / t)));
	else
		tmp = Float64(Float64(b / z) / c);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (b <= -6.6e+78)
		tmp = b / (z * c);
	elseif (b <= 4.4e+52)
		tmp = -4.0 * (a / (c / t));
	else
		tmp = (b / z) / c;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[b, -6.6e+78], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 4.4e+52], N[(-4.0 * N[(a / N[(c / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b / z), $MachinePrecision] / c), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -6.6e78

   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* 70.5%

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

   3. Simplified 81.7%

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

   4. Taylor expanded in b around inf 51.4%

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

      1. *-commutative 51.4%

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

   6. Simplified 51.4%

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

   if -6.6e78 < b < 4.4e52

   1. Initial program 83.0%

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

      1. associate-/r* 83.1%

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

   3. Simplified 89.0%

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

   4. Taylor expanded in t around inf 48.4%

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

      1. associate-/l* 50.4%

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

   6. Simplified 50.4%

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

   if 4.4e52 < b

   1. Initial program 81.3%

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

      1. associate-/r* 84.9%

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

   3. Simplified 90.0%

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

   4. Taylor expanded in x around 0 84.8%

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

   5. Taylor expanded in b around inf 66.5%

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

4. Final simplification 54.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -6.6 \cdot 10^{+78}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;b \leq 4.4 \cdot 10^{+52}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \end{array} \]

Alternative 17: 34.5% accurate, 3.8× speedup

Math

\[\begin{array}{l} \\ \frac{b}{z \cdot c} \end{array} \]

FPCore

(FPCore (x y z t a b c) :precision binary64 (/ b (* z c)))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	return 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 = 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 b / (z * c);
}

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision]

Derivation

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* 80.6%

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

3. Simplified 87.6%

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

4. Taylor expanded in b around inf 36.1%

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

   1. *-commutative 36.1%

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

6. Simplified 36.1%

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

7. Final simplification 36.1%

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

Developer target: 80.0% 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 2023215 
(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)))