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

Percentage Accurate: 79.7% → 88.1%

Time: 18.5s

Alternatives: 18

Speedup: 0.8×

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

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 79.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 88.1% accurate, 0.2× speedup

Math

\[\begin{array}{l} [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} t_1 := \frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c}\\ t_2 := \frac{x \cdot \left(9 \cdot y\right) + \left(b - \left(a \cdot t\right) \cdot \left(z \cdot 4\right)\right)}{z \cdot c}\\ \mathbf{if}\;t_1 \leq -5 \cdot 10^{+144}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_1 \leq 10^{+68}:\\ \;\;\;\;\frac{1}{z} \cdot \left(-4 \cdot \frac{a \cdot \left(z \cdot t\right)}{c} + \left(9 \cdot \frac{x \cdot y}{c} + \frac{b}{c}\right)\right)\\ \mathbf{elif}\;t_1 \leq \infty:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(a \cdot \frac{t}{c}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (+ b (- (* y (* x 9.0)) (* a (* t (* z 4.0))))) (* z c)))
        (t_2 (/ (+ (* x (* 9.0 y)) (- b (* (* a t) (* z 4.0)))) (* z c))))
   (if (<= t_1 -5e+144)
     t_2
     (if (<= t_1 1e+68)
       (*
        (/ 1.0 z)
        (+ (* -4.0 (/ (* a (* z t)) c)) (+ (* 9.0 (/ (* x y) c)) (/ b c))))
       (if (<= t_1 INFINITY) t_2 (* -4.0 (* a (/ t c))))))))

C

assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (b + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (z * c);
	double t_2 = ((x * (9.0 * y)) + (b - ((a * t) * (z * 4.0)))) / (z * c);
	double tmp;
	if (t_1 <= -5e+144) {
		tmp = t_2;
	} else if (t_1 <= 1e+68) {
		tmp = (1.0 / z) * ((-4.0 * ((a * (z * t)) / c)) + ((9.0 * ((x * y) / c)) + (b / c)));
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = t_2;
	} else {
		tmp = -4.0 * (a * (t / c));
	}
	return tmp;
}

Java

assert t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (b + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (z * c);
	double t_2 = ((x * (9.0 * y)) + (b - ((a * t) * (z * 4.0)))) / (z * c);
	double tmp;
	if (t_1 <= -5e+144) {
		tmp = t_2;
	} else if (t_1 <= 1e+68) {
		tmp = (1.0 / z) * ((-4.0 * ((a * (z * t)) / c)) + ((9.0 * ((x * y) / c)) + (b / c)));
	} else if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = t_2;
	} else {
		tmp = -4.0 * (a * (t / c));
	}
	return tmp;
}

Python

[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	t_1 = (b + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (z * c)
	t_2 = ((x * (9.0 * y)) + (b - ((a * t) * (z * 4.0)))) / (z * c)
	tmp = 0
	if t_1 <= -5e+144:
		tmp = t_2
	elif t_1 <= 1e+68:
		tmp = (1.0 / z) * ((-4.0 * ((a * (z * t)) / c)) + ((9.0 * ((x * y) / c)) + (b / c)))
	elif t_1 <= math.inf:
		tmp = t_2
	else:
		tmp = -4.0 * (a * (t / c))
	return tmp

Julia

t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(b + Float64(Float64(y * Float64(x * 9.0)) - Float64(a * Float64(t * Float64(z * 4.0))))) / Float64(z * c))
	t_2 = Float64(Float64(Float64(x * Float64(9.0 * y)) + Float64(b - Float64(Float64(a * t) * Float64(z * 4.0)))) / Float64(z * c))
	tmp = 0.0
	if (t_1 <= -5e+144)
		tmp = t_2;
	elseif (t_1 <= 1e+68)
		tmp = Float64(Float64(1.0 / z) * Float64(Float64(-4.0 * Float64(Float64(a * Float64(z * t)) / c)) + Float64(Float64(9.0 * Float64(Float64(x * y) / c)) + Float64(b / c))));
	elseif (t_1 <= Inf)
		tmp = t_2;
	else
		tmp = Float64(-4.0 * Float64(a * Float64(t / c)));
	end
	return tmp
end

MATLAB

t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (b + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (z * c);
	t_2 = ((x * (9.0 * y)) + (b - ((a * t) * (z * 4.0)))) / (z * c);
	tmp = 0.0;
	if (t_1 <= -5e+144)
		tmp = t_2;
	elseif (t_1 <= 1e+68)
		tmp = (1.0 / z) * ((-4.0 * ((a * (z * t)) / c)) + ((9.0 * ((x * y) / c)) + (b / c)));
	elseif (t_1 <= Inf)
		tmp = t_2;
	else
		tmp = -4.0 * (a * (t / c));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(b + N[(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]}, Block[{t$95$2 = N[(N[(N[(x * N[(9.0 * y), $MachinePrecision]), $MachinePrecision] + N[(b - N[(N[(a * t), $MachinePrecision] * N[(z * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+144], t$95$2, If[LessEqual[t$95$1, 1e+68], N[(N[(1.0 / z), $MachinePrecision] * N[(N[(-4.0 * N[(N[(a * N[(z * t), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision] + N[(N[(9.0 * N[(N[(x * y), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision] + N[(b / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, Infinity], t$95$2, N[(-4.0 * N[(a * N[(t / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)) b) (*.f64 z c)) < -4.9999999999999999e144 or 9.99999999999999953e67 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)) b) (*.f64 z c)) < +inf.0

   1. Initial program 83.1%

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

      1. associate-+l- 83.1%

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

      2. associate-*l* 83.1%

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

      3. associate-*l* 87.3%

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

   3. Simplified 87.3%

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

   if -4.9999999999999999e144 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)) b) (*.f64 z c)) < 9.99999999999999953e67

   1. Initial program 87.5%

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

      1. associate-+l- 87.5%

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

      2. associate-*r* 87.6%

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

      3. associate-*r* 85.2%

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

      4. *-un-lft-identity 85.2%

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

      5. times-frac 96.3%

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

      6. associate--r- 96.3%

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

      7. fma-neg 96.3%

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

      8. associate-*r* 98.6%

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

      9. distribute-rgt-neg-in 98.6%

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

      10. associate-*l* 98.6%

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

   3. Applied egg-rr 98.6%

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

   4. Taylor expanded in x around 0 98.7%

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

   if +inf.0 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)) b) (*.f64 z c))

   1. Initial program 0.0%

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

      1. associate-+l- 0.0%

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

      2. associate-*l* 0.0%

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

      3. associate-*l* 1.3%

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

   3. Simplified 1.3%

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

   4. Taylor expanded in x around 0 6.2%

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

   5. Taylor expanded in b around 0 60.5%

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

   6. Taylor expanded in a around inf 60.5%

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

      1. associate-*r/ 86.9%

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

   8. Simplified 86.9%

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

4. Final simplification 90.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c} \leq -5 \cdot 10^{+144}:\\ \;\;\;\;\frac{x \cdot \left(9 \cdot y\right) + \left(b - \left(a \cdot t\right) \cdot \left(z \cdot 4\right)\right)}{z \cdot c}\\ \mathbf{elif}\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c} \leq 10^{+68}:\\ \;\;\;\;\frac{1}{z} \cdot \left(-4 \cdot \frac{a \cdot \left(z \cdot t\right)}{c} + \left(9 \cdot \frac{x \cdot y}{c} + \frac{b}{c}\right)\right)\\ \mathbf{elif}\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c} \leq \infty:\\ \;\;\;\;\frac{x \cdot \left(9 \cdot y\right) + \left(b - \left(a \cdot t\right) \cdot \left(z \cdot 4\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(a \cdot \frac{t}{c}\right)\\ \end{array} \]

Alternative 2: 86.9% accurate, 0.2× speedup

Math

\[\begin{array}{l} [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{+115}:\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right) + \frac{b}{z}}{c}\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{+91}:\\ \;\;\;\;\frac{1}{z} \cdot \frac{b + \mathsf{fma}\left(x, 9 \cdot y, a \cdot \left(z \cdot \left(t \cdot \left(-4\right)\right)\right)\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{b}{z \cdot c} + 9 \cdot \frac{x \cdot y}{z \cdot c}\right) - 4 \cdot \frac{a \cdot t}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= z -3e+115)
   (/ (+ (* -4.0 (* a t)) (/ b z)) c)
   (if (<= z 8.2e+91)
     (* (/ 1.0 z) (/ (+ b (fma x (* 9.0 y) (* a (* z (* t (- 4.0)))))) c))
     (- (+ (/ b (* z c)) (* 9.0 (/ (* x y) (* z c)))) (* 4.0 (/ (* a t) c))))))

C

assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (z <= -3e+115) {
		tmp = ((-4.0 * (a * t)) + (b / z)) / c;
	} else if (z <= 8.2e+91) {
		tmp = (1.0 / z) * ((b + fma(x, (9.0 * y), (a * (z * (t * -4.0))))) / c);
	} else {
		tmp = ((b / (z * c)) + (9.0 * ((x * y) / (z * c)))) - (4.0 * ((a * t) / c));
	}
	return tmp;
}

Julia

t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (z <= -3e+115)
		tmp = Float64(Float64(Float64(-4.0 * Float64(a * t)) + Float64(b / z)) / c);
	elseif (z <= 8.2e+91)
		tmp = Float64(Float64(1.0 / z) * Float64(Float64(b + fma(x, Float64(9.0 * y), Float64(a * Float64(z * Float64(t * Float64(-4.0)))))) / c));
	else
		tmp = Float64(Float64(Float64(b / Float64(z * c)) + Float64(9.0 * Float64(Float64(x * y) / Float64(z * c)))) - Float64(4.0 * Float64(Float64(a * t) / c)));
	end
	return tmp
end

Wolfram

NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[z, -3e+115], N[(N[(N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision] + N[(b / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[z, 8.2e+91], N[(N[(1.0 / z), $MachinePrecision] * N[(N[(b + N[(x * N[(9.0 * y), $MachinePrecision] + N[(a * N[(z * N[(t * (-4.0)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision], N[(N[(N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision] + N[(9.0 * N[(N[(x * y), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * N[(N[(a * t), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -3e115

   1. Initial program 50.0%

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

      1. associate-+l- 50.0%

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

      2. associate-*l* 50.0%

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

      3. associate-*l* 62.2%

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

   3. Simplified 62.2%

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

   4. Taylor expanded in x around 0 47.5%

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

   5. Taylor expanded in b around 0 87.0%

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

   6. Taylor expanded in c around 0 92.4%

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

   if -3e115 < z < 8.2000000000000005e91

   1. Initial program 92.5%

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

      1. associate-+l- 92.5%

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

      2. associate-*r* 92.6%

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

      3. associate-*r* 91.5%

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

      4. *-un-lft-identity 91.5%

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

      5. times-frac 93.3%

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

      6. associate--r- 93.3%

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

      7. fma-neg 93.3%

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

      8. associate-*r* 94.4%

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

      9. distribute-rgt-neg-in 94.4%

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

      10. associate-*l* 94.4%

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

   3. Applied egg-rr 94.4%

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

   if 8.2000000000000005e91 < z

   1. Initial program 51.3%

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

   2. Taylor expanded in x around 0 75.8%

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

4. Final simplification 90.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{+115}:\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right) + \frac{b}{z}}{c}\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{+91}:\\ \;\;\;\;\frac{1}{z} \cdot \frac{b + \mathsf{fma}\left(x, 9 \cdot y, a \cdot \left(z \cdot \left(t \cdot \left(-4\right)\right)\right)\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{b}{z \cdot c} + 9 \cdot \frac{x \cdot y}{z \cdot c}\right) - 4 \cdot \frac{a \cdot t}{c}\\ \end{array} \]

Alternative 3: 86.8% accurate, 0.2× speedup

Math

\[\begin{array}{l} [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{+119}:\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right) + \frac{b}{z}}{c}\\ \mathbf{elif}\;z \leq 1.42 \cdot 10^{+91}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, 9 \cdot y, b + t \cdot \left(z \cdot \left(-4 \cdot a\right)\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{b}{z \cdot c} + 9 \cdot \frac{x \cdot y}{z \cdot c}\right) - 4 \cdot \frac{a \cdot t}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= z -3.1e+119)
   (/ (+ (* -4.0 (* a t)) (/ b z)) c)
   (if (<= z 1.42e+91)
     (/ (fma x (* 9.0 y) (+ b (* t (* z (* -4.0 a))))) (* z c))
     (- (+ (/ b (* z c)) (* 9.0 (/ (* x y) (* z c)))) (* 4.0 (/ (* a t) c))))))

C

assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (z <= -3.1e+119) {
		tmp = ((-4.0 * (a * t)) + (b / z)) / c;
	} else if (z <= 1.42e+91) {
		tmp = fma(x, (9.0 * y), (b + (t * (z * (-4.0 * a))))) / (z * c);
	} else {
		tmp = ((b / (z * c)) + (9.0 * ((x * y) / (z * c)))) - (4.0 * ((a * t) / c));
	}
	return tmp;
}

Julia

t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (z <= -3.1e+119)
		tmp = Float64(Float64(Float64(-4.0 * Float64(a * t)) + Float64(b / z)) / c);
	elseif (z <= 1.42e+91)
		tmp = Float64(fma(x, Float64(9.0 * y), Float64(b + Float64(t * Float64(z * Float64(-4.0 * a))))) / Float64(z * c));
	else
		tmp = Float64(Float64(Float64(b / Float64(z * c)) + Float64(9.0 * Float64(Float64(x * y) / Float64(z * c)))) - Float64(4.0 * Float64(Float64(a * t) / c)));
	end
	return tmp
end

Wolfram

NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[z, -3.1e+119], N[(N[(N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision] + N[(b / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[z, 1.42e+91], N[(N[(x * N[(9.0 * y), $MachinePrecision] + N[(b + N[(t * N[(z * N[(-4.0 * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(N[(N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision] + N[(9.0 * N[(N[(x * y), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * N[(N[(a * t), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.09999999999999995e119

   1. Initial program 48.8%

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

      1. associate-+l- 48.8%

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

      2. associate-*l* 48.8%

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

      3. associate-*l* 61.3%

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

   3. Simplified 61.3%

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

   4. Taylor expanded in x around 0 46.2%

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

   5. Taylor expanded in b around 0 86.7%

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

   6. Taylor expanded in c around 0 92.3%

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

   if -3.09999999999999995e119 < z < 1.41999999999999995e91

   1. Initial program 92.5%

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

   3. Simplified 92.1%

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

   if 1.41999999999999995e91 < z

   1. Initial program 51.3%

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

   2. Taylor expanded in x around 0 75.8%

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

4. Final simplification 89.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{+119}:\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right) + \frac{b}{z}}{c}\\ \mathbf{elif}\;z \leq 1.42 \cdot 10^{+91}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, 9 \cdot y, b + t \cdot \left(z \cdot \left(-4 \cdot a\right)\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{b}{z \cdot c} + 9 \cdot \frac{x \cdot y}{z \cdot c}\right) - 4 \cdot \frac{a \cdot t}{c}\\ \end{array} \]

Alternative 4: 86.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{+118}:\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right) + \frac{b}{z}}{c}\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{+90}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{b}{z \cdot c} + 9 \cdot \frac{x \cdot y}{z \cdot c}\right) - 4 \cdot \frac{a \cdot t}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= z -1.6e+118)
   (/ (+ (* -4.0 (* a t)) (/ b z)) c)
   (if (<= z 8.5e+90)
     (/ (+ b (- (* y (* x 9.0)) (* a (* t (* z 4.0))))) (* z c))
     (- (+ (/ b (* z c)) (* 9.0 (/ (* x y) (* z c)))) (* 4.0 (/ (* a t) c))))))

C

assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (z <= -1.6e+118) {
		tmp = ((-4.0 * (a * t)) + (b / z)) / c;
	} else if (z <= 8.5e+90) {
		tmp = (b + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (z * c);
	} else {
		tmp = ((b / (z * c)) + (9.0 * ((x * y) / (z * c)))) - (4.0 * ((a * t) / c));
	}
	return tmp;
}

Fortran

NOTE: t and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (z <= (-1.6d+118)) then
        tmp = (((-4.0d0) * (a * t)) + (b / z)) / c
    else if (z <= 8.5d+90) then
        tmp = (b + ((y * (x * 9.0d0)) - (a * (t * (z * 4.0d0))))) / (z * c)
    else
        tmp = ((b / (z * c)) + (9.0d0 * ((x * y) / (z * c)))) - (4.0d0 * ((a * t) / c))
    end if
    code = tmp
end function

Java

assert t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (z <= -1.6e+118) {
		tmp = ((-4.0 * (a * t)) + (b / z)) / c;
	} else if (z <= 8.5e+90) {
		tmp = (b + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (z * c);
	} else {
		tmp = ((b / (z * c)) + (9.0 * ((x * y) / (z * c)))) - (4.0 * ((a * t) / c));
	}
	return tmp;
}

Python

[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if z <= -1.6e+118:
		tmp = ((-4.0 * (a * t)) + (b / z)) / c
	elif z <= 8.5e+90:
		tmp = (b + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (z * c)
	else:
		tmp = ((b / (z * c)) + (9.0 * ((x * y) / (z * c)))) - (4.0 * ((a * t) / c))
	return tmp

Julia

t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (z <= -1.6e+118)
		tmp = Float64(Float64(Float64(-4.0 * Float64(a * t)) + Float64(b / z)) / c);
	elseif (z <= 8.5e+90)
		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(Float64(Float64(b / Float64(z * c)) + Float64(9.0 * Float64(Float64(x * y) / Float64(z * c)))) - Float64(4.0 * Float64(Float64(a * t) / c)));
	end
	return tmp
end

MATLAB

t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (z <= -1.6e+118)
		tmp = ((-4.0 * (a * t)) + (b / z)) / c;
	elseif (z <= 8.5e+90)
		tmp = (b + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (z * c);
	else
		tmp = ((b / (z * c)) + (9.0 * ((x * y) / (z * c)))) - (4.0 * ((a * t) / c));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[z, -1.6e+118], N[(N[(N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision] + N[(b / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[z, 8.5e+90], 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[(N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision] + N[(9.0 * N[(N[(x * y), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * N[(N[(a * t), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.60000000000000008e118

   1. Initial program 48.8%

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

      1. associate-+l- 48.8%

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

      2. associate-*l* 48.8%

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

      3. associate-*l* 61.3%

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

   3. Simplified 61.3%

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

   4. Taylor expanded in x around 0 46.2%

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

   5. Taylor expanded in b around 0 86.7%

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

   6. Taylor expanded in c around 0 92.3%

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

   if -1.60000000000000008e118 < z < 8.5000000000000002e90

   1. Initial program 92.5%

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

   if 8.5000000000000002e90 < z

   1. Initial program 51.3%

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

   2. Taylor expanded in x around 0 75.8%

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

4. Final simplification 89.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{+118}:\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right) + \frac{b}{z}}{c}\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{+90}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{b}{z \cdot c} + 9 \cdot \frac{x \cdot y}{z \cdot c}\right) - 4 \cdot \frac{a \cdot t}{c}\\ \end{array} \]

Alternative 5: 49.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} t_1 := 9 \cdot \left(\frac{x}{c} \cdot \frac{y}{z}\right)\\ t_2 := \frac{\frac{b}{c}}{z}\\ \mathbf{if}\;t \leq -9 \cdot 10^{+130}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;t \leq -7.5 \cdot 10^{+77}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.3 \cdot 10^{+29}:\\ \;\;\;\;-4 \cdot \left(a \cdot \frac{t}{c}\right)\\ \mathbf{elif}\;t \leq -1.26 \cdot 10^{-129}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -4.8 \cdot 10^{-211}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.6 \cdot 10^{-260}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{-188}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{c} \cdot \frac{t}{-0.25}\\ \end{array} \end{array} \]

FPCore

NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* 9.0 (* (/ x c) (/ y z)))) (t_2 (/ (/ b c) z)))
   (if (<= t -9e+130)
     (* -4.0 (/ a (/ c t)))
     (if (<= t -7.5e+77)
       t_1
       (if (<= t -1.3e+29)
         (* -4.0 (* a (/ t c)))
         (if (<= t -1.26e-129)
           t_2
           (if (<= t -4.8e-211)
             t_1
             (if (<= t -1.6e-260)
               t_2
               (if (<= t 1.05e-188) t_1 (* (/ a c) (/ t -0.25)))))))))))

C

assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = 9.0 * ((x / c) * (y / z));
	double t_2 = (b / c) / z;
	double tmp;
	if (t <= -9e+130) {
		tmp = -4.0 * (a / (c / t));
	} else if (t <= -7.5e+77) {
		tmp = t_1;
	} else if (t <= -1.3e+29) {
		tmp = -4.0 * (a * (t / c));
	} else if (t <= -1.26e-129) {
		tmp = t_2;
	} else if (t <= -4.8e-211) {
		tmp = t_1;
	} else if (t <= -1.6e-260) {
		tmp = t_2;
	} else if (t <= 1.05e-188) {
		tmp = t_1;
	} else {
		tmp = (a / c) * (t / -0.25);
	}
	return tmp;
}

Fortran

NOTE: t and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = 9.0d0 * ((x / c) * (y / z))
    t_2 = (b / c) / z
    if (t <= (-9d+130)) then
        tmp = (-4.0d0) * (a / (c / t))
    else if (t <= (-7.5d+77)) then
        tmp = t_1
    else if (t <= (-1.3d+29)) then
        tmp = (-4.0d0) * (a * (t / c))
    else if (t <= (-1.26d-129)) then
        tmp = t_2
    else if (t <= (-4.8d-211)) then
        tmp = t_1
    else if (t <= (-1.6d-260)) then
        tmp = t_2
    else if (t <= 1.05d-188) then
        tmp = t_1
    else
        tmp = (a / c) * (t / (-0.25d0))
    end if
    code = tmp
end function

Java

assert t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = 9.0 * ((x / c) * (y / z));
	double t_2 = (b / c) / z;
	double tmp;
	if (t <= -9e+130) {
		tmp = -4.0 * (a / (c / t));
	} else if (t <= -7.5e+77) {
		tmp = t_1;
	} else if (t <= -1.3e+29) {
		tmp = -4.0 * (a * (t / c));
	} else if (t <= -1.26e-129) {
		tmp = t_2;
	} else if (t <= -4.8e-211) {
		tmp = t_1;
	} else if (t <= -1.6e-260) {
		tmp = t_2;
	} else if (t <= 1.05e-188) {
		tmp = t_1;
	} else {
		tmp = (a / c) * (t / -0.25);
	}
	return tmp;
}

Python

[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	t_1 = 9.0 * ((x / c) * (y / z))
	t_2 = (b / c) / z
	tmp = 0
	if t <= -9e+130:
		tmp = -4.0 * (a / (c / t))
	elif t <= -7.5e+77:
		tmp = t_1
	elif t <= -1.3e+29:
		tmp = -4.0 * (a * (t / c))
	elif t <= -1.26e-129:
		tmp = t_2
	elif t <= -4.8e-211:
		tmp = t_1
	elif t <= -1.6e-260:
		tmp = t_2
	elif t <= 1.05e-188:
		tmp = t_1
	else:
		tmp = (a / c) * (t / -0.25)
	return tmp

Julia

t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(9.0 * Float64(Float64(x / c) * Float64(y / z)))
	t_2 = Float64(Float64(b / c) / z)
	tmp = 0.0
	if (t <= -9e+130)
		tmp = Float64(-4.0 * Float64(a / Float64(c / t)));
	elseif (t <= -7.5e+77)
		tmp = t_1;
	elseif (t <= -1.3e+29)
		tmp = Float64(-4.0 * Float64(a * Float64(t / c)));
	elseif (t <= -1.26e-129)
		tmp = t_2;
	elseif (t <= -4.8e-211)
		tmp = t_1;
	elseif (t <= -1.6e-260)
		tmp = t_2;
	elseif (t <= 1.05e-188)
		tmp = t_1;
	else
		tmp = Float64(Float64(a / c) * Float64(t / -0.25));
	end
	return tmp
end

MATLAB

t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = 9.0 * ((x / c) * (y / z));
	t_2 = (b / c) / z;
	tmp = 0.0;
	if (t <= -9e+130)
		tmp = -4.0 * (a / (c / t));
	elseif (t <= -7.5e+77)
		tmp = t_1;
	elseif (t <= -1.3e+29)
		tmp = -4.0 * (a * (t / c));
	elseif (t <= -1.26e-129)
		tmp = t_2;
	elseif (t <= -4.8e-211)
		tmp = t_1;
	elseif (t <= -1.6e-260)
		tmp = t_2;
	elseif (t <= 1.05e-188)
		tmp = t_1;
	else
		tmp = (a / c) * (t / -0.25);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(9.0 * N[(N[(x / c), $MachinePrecision] * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision]}, If[LessEqual[t, -9e+130], N[(-4.0 * N[(a / N[(c / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -7.5e+77], t$95$1, If[LessEqual[t, -1.3e+29], N[(-4.0 * N[(a * N[(t / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.26e-129], t$95$2, If[LessEqual[t, -4.8e-211], t$95$1, If[LessEqual[t, -1.6e-260], t$95$2, If[LessEqual[t, 1.05e-188], t$95$1, N[(N[(a / c), $MachinePrecision] * N[(t / -0.25), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -9.00000000000000078e130

   1. Initial program 59.2%

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

   2. Taylor expanded in z around inf 59.9%

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

      1. *-commutative 59.9%

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

      2. associate-/l* 77.6%

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

   4. Simplified 77.6%

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

   if -9.00000000000000078e130 < t < -7.49999999999999955e77 or -1.2599999999999999e-129 < t < -4.8000000000000004e-211 or -1.59999999999999997e-260 < t < 1.05e-188

   1. Initial program 80.6%

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

   2. Taylor expanded in x around inf 45.0%

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

      1. *-commutative 45.0%

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

   4. Simplified 45.0%

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

   5. Taylor expanded in x around 0 45.0%

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

      1. times-frac 48.8%

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

   7. Simplified 48.8%

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

   if -7.49999999999999955e77 < t < -1.3e29

   1. Initial program 54.9%

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

      1. associate-+l- 54.9%

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

      2. associate-*l* 54.9%

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

      3. associate-*l* 63.7%

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

   3. Simplified 63.7%

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

   4. Taylor expanded in x around 0 54.9%

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

   5. Taylor expanded in b around 0 82.4%

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

   6. Taylor expanded in a around inf 38.1%

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

      1. associate-*r/ 72.8%

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

   8. Simplified 72.8%

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

   if -1.3e29 < t < -1.2599999999999999e-129 or -4.8000000000000004e-211 < t < -1.59999999999999997e-260

   1. Initial program 92.2%

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

      1. associate-+l- 92.2%

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

      2. associate-*r* 92.3%

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

      3. associate-*r* 92.3%

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

      4. *-un-lft-identity 92.3%

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

      5. times-frac 95.0%

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

      6. associate--r- 95.0%

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

      7. fma-neg 95.0%

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

      8. associate-*r* 95.0%

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

      9. distribute-rgt-neg-in 95.0%

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

      10. associate-*l* 95.0%

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

   3. Applied egg-rr 95.0%

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

   4. Taylor expanded in x around 0 87.2%

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

   5. Taylor expanded in b around inf 59.1%

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

      1. associate-/r* 61.8%

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

   7. Simplified 61.8%

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

   if 1.05e-188 < t

   1. Initial program 78.7%

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

      1. associate-+l- 78.7%

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

      2. associate-*r* 78.8%

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

      3. associate-*r* 82.2%

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

      4. clear-num 82.0%

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

      5. inv-pow 82.0%

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

      6. associate--r- 82.0%

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

      7. fma-neg 83.2%

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

      8. associate-*r* 79.8%

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

      9. distribute-rgt-neg-in 79.8%

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

      10. associate-*l* 79.8%

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

   3. Applied egg-rr 79.8%

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

   5. Simplified 82.0%

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

   6. Taylor expanded in z around inf 47.3%

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

      1. *-commutative 47.3%

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

      2. *-commutative 47.3%

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

      3. associate-*l/ 47.3%

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

      4. *-commutative 47.3%

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

   8. Simplified 47.3%

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

      1. times-frac 47.6%

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

   10. Applied egg-rr 47.6%

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

       1. inv-pow 47.6%

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

       2. unpow-prod-down 47.7%

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

       3. inv-pow 47.7%

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

       4. clear-num 47.7%

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

   12. Applied egg-rr 47.7%

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

       1. unpow-1 47.7%

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

       2. associate-*r/ 47.7%

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

       3. *-rgt-identity 47.7%

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

       4. associate-/r* 48.3%

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

       5. associate-*r/ 48.3%

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

       6. associate-/l* 47.3%

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

       7. times-frac 47.8%

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

   14. Simplified 47.8%

       \[\leadsto \color{blue}{\frac{a}{c} \cdot \frac{t}{-0.25}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 55.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9 \cdot 10^{+130}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;t \leq -7.5 \cdot 10^{+77}:\\ \;\;\;\;9 \cdot \left(\frac{x}{c} \cdot \frac{y}{z}\right)\\ \mathbf{elif}\;t \leq -1.3 \cdot 10^{+29}:\\ \;\;\;\;-4 \cdot \left(a \cdot \frac{t}{c}\right)\\ \mathbf{elif}\;t \leq -1.26 \cdot 10^{-129}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;t \leq -4.8 \cdot 10^{-211}:\\ \;\;\;\;9 \cdot \left(\frac{x}{c} \cdot \frac{y}{z}\right)\\ \mathbf{elif}\;t \leq -1.6 \cdot 10^{-260}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{-188}:\\ \;\;\;\;9 \cdot \left(\frac{x}{c} \cdot \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{c} \cdot \frac{t}{-0.25}\\ \end{array} \]

Alternative 6: 85.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{+118} \lor \neg \left(z \leq 8.6 \cdot 10^{+58}\right):\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right) + \frac{b}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c}\\ \end{array} \end{array} \]

FPCore

NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= z -2.3e+118) (not (<= z 8.6e+58)))
   (/ (+ (* -4.0 (* a t)) (/ b z)) c)
   (/ (+ b (- (* y (* x 9.0)) (* a (* t (* z 4.0))))) (* z c))))

C

assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((z <= -2.3e+118) || !(z <= 8.6e+58)) {
		tmp = ((-4.0 * (a * t)) + (b / z)) / c;
	} else {
		tmp = (b + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (z * c);
	}
	return tmp;
}

Fortran

NOTE: t and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if ((z <= (-2.3d+118)) .or. (.not. (z <= 8.6d+58))) then
        tmp = (((-4.0d0) * (a * t)) + (b / z)) / c
    else
        tmp = (b + ((y * (x * 9.0d0)) - (a * (t * (z * 4.0d0))))) / (z * c)
    end if
    code = tmp
end function

Java

assert t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((z <= -2.3e+118) || !(z <= 8.6e+58)) {
		tmp = ((-4.0 * (a * t)) + (b / z)) / c;
	} else {
		tmp = (b + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (z * c);
	}
	return tmp;
}

Python

[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if (z <= -2.3e+118) or not (z <= 8.6e+58):
		tmp = ((-4.0 * (a * t)) + (b / z)) / c
	else:
		tmp = (b + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (z * c)
	return tmp

Julia

t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((z <= -2.3e+118) || !(z <= 8.6e+58))
		tmp = Float64(Float64(Float64(-4.0 * Float64(a * t)) + Float64(b / z)) / 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

t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((z <= -2.3e+118) || ~((z <= 8.6e+58)))
		tmp = ((-4.0 * (a * t)) + (b / z)) / c;
	else
		tmp = (b + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (z * c);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[z, -2.3e+118], N[Not[LessEqual[z, 8.6e+58]], $MachinePrecision]], N[(N[(N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision] + N[(b / z), $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 < -2.30000000000000016e118 or 8.59999999999999982e58 < z

   1. Initial program 51.2%

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

      1. associate-+l- 51.2%

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

      2. associate-*l* 51.2%

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

      3. associate-*l* 59.0%

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

   3. Simplified 59.0%

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

   4. Taylor expanded in x around 0 45.8%

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

   5. Taylor expanded in b around 0 75.8%

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

   6. Taylor expanded in c around 0 81.5%

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

   if -2.30000000000000016e118 < z < 8.59999999999999982e58

   1. Initial program 93.4%

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

4. Final simplification 89.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{+118} \lor \neg \left(z \leq 8.6 \cdot 10^{+58}\right):\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right) + \frac{b}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c}\\ \end{array} \]

Alternative 7: 50.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} t_1 := 9 \cdot \left(\frac{x}{z} \cdot \frac{y}{c}\right)\\ \mathbf{if}\;z \leq -8.2 \cdot 10^{-29}:\\ \;\;\;\;\frac{a \cdot \left(-4 \cdot t\right)}{c}\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{-157}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{-249}:\\ \;\;\;\;\frac{1}{\frac{z \cdot c}{b}}\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-274}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{-16}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(a \cdot \frac{t}{c}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* 9.0 (* (/ x z) (/ y c)))))
   (if (<= z -8.2e-29)
     (/ (* a (* -4.0 t)) c)
     (if (<= z -3.8e-157)
       t_1
       (if (<= z -5.5e-249)
         (/ 1.0 (/ (* z c) b))
         (if (<= z 6e-274)
           t_1
           (if (<= z 1.95e-16) (/ b (* z c)) (* -4.0 (* a (/ t c))))))))))

C

assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = 9.0 * ((x / z) * (y / c));
	double tmp;
	if (z <= -8.2e-29) {
		tmp = (a * (-4.0 * t)) / c;
	} else if (z <= -3.8e-157) {
		tmp = t_1;
	} else if (z <= -5.5e-249) {
		tmp = 1.0 / ((z * c) / b);
	} else if (z <= 6e-274) {
		tmp = t_1;
	} else if (z <= 1.95e-16) {
		tmp = b / (z * c);
	} else {
		tmp = -4.0 * (a * (t / c));
	}
	return tmp;
}

Fortran

NOTE: t and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 9.0d0 * ((x / z) * (y / c))
    if (z <= (-8.2d-29)) then
        tmp = (a * ((-4.0d0) * t)) / c
    else if (z <= (-3.8d-157)) then
        tmp = t_1
    else if (z <= (-5.5d-249)) then
        tmp = 1.0d0 / ((z * c) / b)
    else if (z <= 6d-274) then
        tmp = t_1
    else if (z <= 1.95d-16) then
        tmp = b / (z * c)
    else
        tmp = (-4.0d0) * (a * (t / c))
    end if
    code = tmp
end function

Java

assert t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = 9.0 * ((x / z) * (y / c));
	double tmp;
	if (z <= -8.2e-29) {
		tmp = (a * (-4.0 * t)) / c;
	} else if (z <= -3.8e-157) {
		tmp = t_1;
	} else if (z <= -5.5e-249) {
		tmp = 1.0 / ((z * c) / b);
	} else if (z <= 6e-274) {
		tmp = t_1;
	} else if (z <= 1.95e-16) {
		tmp = b / (z * c);
	} else {
		tmp = -4.0 * (a * (t / c));
	}
	return tmp;
}

Python

[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	t_1 = 9.0 * ((x / z) * (y / c))
	tmp = 0
	if z <= -8.2e-29:
		tmp = (a * (-4.0 * t)) / c
	elif z <= -3.8e-157:
		tmp = t_1
	elif z <= -5.5e-249:
		tmp = 1.0 / ((z * c) / b)
	elif z <= 6e-274:
		tmp = t_1
	elif z <= 1.95e-16:
		tmp = b / (z * c)
	else:
		tmp = -4.0 * (a * (t / c))
	return tmp

Julia

t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(9.0 * Float64(Float64(x / z) * Float64(y / c)))
	tmp = 0.0
	if (z <= -8.2e-29)
		tmp = Float64(Float64(a * Float64(-4.0 * t)) / c);
	elseif (z <= -3.8e-157)
		tmp = t_1;
	elseif (z <= -5.5e-249)
		tmp = Float64(1.0 / Float64(Float64(z * c) / b));
	elseif (z <= 6e-274)
		tmp = t_1;
	elseif (z <= 1.95e-16)
		tmp = Float64(b / Float64(z * c));
	else
		tmp = Float64(-4.0 * Float64(a * Float64(t / c)));
	end
	return tmp
end

MATLAB

t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = 9.0 * ((x / z) * (y / c));
	tmp = 0.0;
	if (z <= -8.2e-29)
		tmp = (a * (-4.0 * t)) / c;
	elseif (z <= -3.8e-157)
		tmp = t_1;
	elseif (z <= -5.5e-249)
		tmp = 1.0 / ((z * c) / b);
	elseif (z <= 6e-274)
		tmp = t_1;
	elseif (z <= 1.95e-16)
		tmp = b / (z * c);
	else
		tmp = -4.0 * (a * (t / c));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(9.0 * N[(N[(x / z), $MachinePrecision] * N[(y / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -8.2e-29], N[(N[(a * N[(-4.0 * t), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[z, -3.8e-157], t$95$1, If[LessEqual[z, -5.5e-249], N[(1.0 / N[(N[(z * c), $MachinePrecision] / b), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6e-274], t$95$1, If[LessEqual[z, 1.95e-16], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(-4.0 * N[(a * N[(t / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -8.1999999999999996e-29

   1. Initial program 72.5%

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

   2. Taylor expanded in z around inf 60.5%

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

      1. associate-*r/ 60.5%

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

      2. *-commutative 60.5%

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

      3. associate-*r* 60.5%

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

   4. Simplified 60.5%

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

   if -8.1999999999999996e-29 < z < -3.8000000000000002e-157 or -5.49999999999999999e-249 < z < 5.99999999999999954e-274

   1. Initial program 95.7%

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

   2. Taylor expanded in x around inf 63.8%

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

      1. *-commutative 63.8%

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

   4. Simplified 63.8%

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

   5. Taylor expanded in x around 0 63.8%

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

      1. *-commutative 63.8%

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

      2. times-frac 67.8%

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

   7. Simplified 67.8%

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

   if -3.8000000000000002e-157 < z < -5.49999999999999999e-249

   1. Initial program 93.9%

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

      1. associate-+l- 93.9%

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

      2. associate-*r* 94.0%

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

      3. associate-*r* 94.0%

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

      4. clear-num 94.1%

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

      5. inv-pow 94.1%

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

      6. associate--r- 94.1%

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

      7. fma-neg 94.1%

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

      8. associate-*r* 94.1%

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

      9. distribute-rgt-neg-in 94.1%

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

      10. associate-*l* 94.1%

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

   3. Applied egg-rr 94.1%

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

   5. Simplified 94.0%

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

   6. Taylor expanded in b around inf 75.4%

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

   if 5.99999999999999954e-274 < z < 1.94999999999999989e-16

   1. Initial program 91.7%

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

   2. Taylor expanded in b around inf 58.8%

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

      1. *-commutative 58.8%

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

   4. Simplified 58.8%

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

   if 1.94999999999999989e-16 < z

   1. Initial program 61.5%

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

      1. associate-+l- 61.5%

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

      2. associate-*l* 61.5%

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

      3. associate-*l* 64.5%

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

   3. Simplified 64.5%

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

   4. Taylor expanded in x around 0 45.7%

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

   5. Taylor expanded in b around 0 62.0%

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

   6. Taylor expanded in a around inf 51.7%

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

      1. associate-*r/ 62.3%

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

   8. Simplified 62.3%

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

4. Final simplification 62.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.2 \cdot 10^{-29}:\\ \;\;\;\;\frac{a \cdot \left(-4 \cdot t\right)}{c}\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{-157}:\\ \;\;\;\;9 \cdot \left(\frac{x}{z} \cdot \frac{y}{c}\right)\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{-249}:\\ \;\;\;\;\frac{1}{\frac{z \cdot c}{b}}\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-274}:\\ \;\;\;\;9 \cdot \left(\frac{x}{z} \cdot \frac{y}{c}\right)\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{-16}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(a \cdot \frac{t}{c}\right)\\ \end{array} \]

Alternative 8: 50.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.75 \cdot 10^{-28}:\\ \;\;\;\;\frac{a \cdot \left(-4 \cdot t\right)}{c}\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{-156}:\\ \;\;\;\;9 \cdot \left(\frac{x}{z} \cdot \frac{y}{c}\right)\\ \mathbf{elif}\;z \leq -3.9 \cdot 10^{-249}:\\ \;\;\;\;\frac{1}{\frac{z \cdot c}{b}}\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-181}:\\ \;\;\;\;9 \cdot \frac{x \cdot y}{z \cdot c}\\ \mathbf{elif}\;z \leq 3.35 \cdot 10^{-18}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(a \cdot \frac{t}{c}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= z -1.75e-28)
   (/ (* a (* -4.0 t)) c)
   (if (<= z -1.2e-156)
     (* 9.0 (* (/ x z) (/ y c)))
     (if (<= z -3.9e-249)
       (/ 1.0 (/ (* z c) b))
       (if (<= z 3.6e-181)
         (* 9.0 (/ (* x y) (* z c)))
         (if (<= z 3.35e-18) (/ b (* z c)) (* -4.0 (* a (/ t c)))))))))

C

assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (z <= -1.75e-28) {
		tmp = (a * (-4.0 * t)) / c;
	} else if (z <= -1.2e-156) {
		tmp = 9.0 * ((x / z) * (y / c));
	} else if (z <= -3.9e-249) {
		tmp = 1.0 / ((z * c) / b);
	} else if (z <= 3.6e-181) {
		tmp = 9.0 * ((x * y) / (z * c));
	} else if (z <= 3.35e-18) {
		tmp = b / (z * c);
	} else {
		tmp = -4.0 * (a * (t / c));
	}
	return tmp;
}

Fortran

NOTE: t and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (z <= (-1.75d-28)) then
        tmp = (a * ((-4.0d0) * t)) / c
    else if (z <= (-1.2d-156)) then
        tmp = 9.0d0 * ((x / z) * (y / c))
    else if (z <= (-3.9d-249)) then
        tmp = 1.0d0 / ((z * c) / b)
    else if (z <= 3.6d-181) then
        tmp = 9.0d0 * ((x * y) / (z * c))
    else if (z <= 3.35d-18) then
        tmp = b / (z * c)
    else
        tmp = (-4.0d0) * (a * (t / c))
    end if
    code = tmp
end function

Java

assert t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (z <= -1.75e-28) {
		tmp = (a * (-4.0 * t)) / c;
	} else if (z <= -1.2e-156) {
		tmp = 9.0 * ((x / z) * (y / c));
	} else if (z <= -3.9e-249) {
		tmp = 1.0 / ((z * c) / b);
	} else if (z <= 3.6e-181) {
		tmp = 9.0 * ((x * y) / (z * c));
	} else if (z <= 3.35e-18) {
		tmp = b / (z * c);
	} else {
		tmp = -4.0 * (a * (t / c));
	}
	return tmp;
}

Python

[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if z <= -1.75e-28:
		tmp = (a * (-4.0 * t)) / c
	elif z <= -1.2e-156:
		tmp = 9.0 * ((x / z) * (y / c))
	elif z <= -3.9e-249:
		tmp = 1.0 / ((z * c) / b)
	elif z <= 3.6e-181:
		tmp = 9.0 * ((x * y) / (z * c))
	elif z <= 3.35e-18:
		tmp = b / (z * c)
	else:
		tmp = -4.0 * (a * (t / c))
	return tmp

Julia

t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (z <= -1.75e-28)
		tmp = Float64(Float64(a * Float64(-4.0 * t)) / c);
	elseif (z <= -1.2e-156)
		tmp = Float64(9.0 * Float64(Float64(x / z) * Float64(y / c)));
	elseif (z <= -3.9e-249)
		tmp = Float64(1.0 / Float64(Float64(z * c) / b));
	elseif (z <= 3.6e-181)
		tmp = Float64(9.0 * Float64(Float64(x * y) / Float64(z * c)));
	elseif (z <= 3.35e-18)
		tmp = Float64(b / Float64(z * c));
	else
		tmp = Float64(-4.0 * Float64(a * Float64(t / c)));
	end
	return tmp
end

MATLAB

t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (z <= -1.75e-28)
		tmp = (a * (-4.0 * t)) / c;
	elseif (z <= -1.2e-156)
		tmp = 9.0 * ((x / z) * (y / c));
	elseif (z <= -3.9e-249)
		tmp = 1.0 / ((z * c) / b);
	elseif (z <= 3.6e-181)
		tmp = 9.0 * ((x * y) / (z * c));
	elseif (z <= 3.35e-18)
		tmp = b / (z * c);
	else
		tmp = -4.0 * (a * (t / c));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[z, -1.75e-28], N[(N[(a * N[(-4.0 * t), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[z, -1.2e-156], N[(9.0 * N[(N[(x / z), $MachinePrecision] * N[(y / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -3.9e-249], N[(1.0 / N[(N[(z * c), $MachinePrecision] / b), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.6e-181], N[(9.0 * N[(N[(x * y), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.35e-18], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(-4.0 * N[(a * N[(t / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -1.75e-28

   1. Initial program 72.5%

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

   2. Taylor expanded in z around inf 60.5%

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

      1. associate-*r/ 60.5%

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

      2. *-commutative 60.5%

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

      3. associate-*r* 60.5%

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

   4. Simplified 60.5%

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

   if -1.75e-28 < z < -1.2e-156

   1. Initial program 92.4%

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

   2. Taylor expanded in x around inf 58.5%

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

      1. *-commutative 58.5%

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

   4. Simplified 58.5%

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

   5. Taylor expanded in x around 0 58.5%

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

      1. *-commutative 58.5%

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

      2. times-frac 66.0%

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

   7. Simplified 66.0%

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

   if -1.2e-156 < z < -3.8999999999999999e-249

   1. Initial program 93.9%

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

      1. associate-+l- 93.9%

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

      2. associate-*r* 94.0%

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

      3. associate-*r* 94.0%

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

      4. clear-num 94.1%

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

      5. inv-pow 94.1%

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

      6. associate--r- 94.1%

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

      7. fma-neg 94.1%

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

      8. associate-*r* 94.1%

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

      9. distribute-rgt-neg-in 94.1%

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

      10. associate-*l* 94.1%

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

   3. Applied egg-rr 94.1%

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

   5. Simplified 94.0%

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

   6. Taylor expanded in b around inf 75.4%

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

   if -3.8999999999999999e-249 < z < 3.5999999999999999e-181

   1. Initial program 97.3%

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

   2. Taylor expanded in x around inf 67.1%

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

      1. *-commutative 67.1%

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

   4. Simplified 67.1%

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

   if 3.5999999999999999e-181 < z < 3.3499999999999999e-18

   1. Initial program 90.4%

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

   2. Taylor expanded in b around inf 59.6%

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

      1. *-commutative 59.6%

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

   4. Simplified 59.6%

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

   if 3.3499999999999999e-18 < z

   1. Initial program 61.5%

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

      1. associate-+l- 61.5%

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

      2. associate-*l* 61.5%

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

      3. associate-*l* 64.5%

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

   3. Simplified 64.5%

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

   4. Taylor expanded in x around 0 45.7%

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

   5. Taylor expanded in b around 0 62.0%

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

   6. Taylor expanded in a around inf 51.7%

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

      1. associate-*r/ 62.3%

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

   8. Simplified 62.3%

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

4. Final simplification 63.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.75 \cdot 10^{-28}:\\ \;\;\;\;\frac{a \cdot \left(-4 \cdot t\right)}{c}\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{-156}:\\ \;\;\;\;9 \cdot \left(\frac{x}{z} \cdot \frac{y}{c}\right)\\ \mathbf{elif}\;z \leq -3.9 \cdot 10^{-249}:\\ \;\;\;\;\frac{1}{\frac{z \cdot c}{b}}\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-181}:\\ \;\;\;\;9 \cdot \frac{x \cdot y}{z \cdot c}\\ \mathbf{elif}\;z \leq 3.35 \cdot 10^{-18}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(a \cdot \frac{t}{c}\right)\\ \end{array} \]

Alternative 9: 50.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{-29}:\\ \;\;\;\;\left(a \cdot t\right) \cdot \frac{1}{c \cdot -0.25}\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{-158}:\\ \;\;\;\;9 \cdot \left(\frac{x}{z} \cdot \frac{y}{c}\right)\\ \mathbf{elif}\;z \leq -7.4 \cdot 10^{-246}:\\ \;\;\;\;\frac{1}{\frac{z \cdot c}{b}}\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-181}:\\ \;\;\;\;9 \cdot \frac{x \cdot y}{z \cdot c}\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{-17}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(a \cdot \frac{t}{c}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= z -3.2e-29)
   (* (* a t) (/ 1.0 (* c -0.25)))
   (if (<= z -5.5e-158)
     (* 9.0 (* (/ x z) (/ y c)))
     (if (<= z -7.4e-246)
       (/ 1.0 (/ (* z c) b))
       (if (<= z 1.4e-181)
         (* 9.0 (/ (* x y) (* z c)))
         (if (<= z 1.85e-17) (/ b (* z c)) (* -4.0 (* a (/ t c)))))))))

C

assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (z <= -3.2e-29) {
		tmp = (a * t) * (1.0 / (c * -0.25));
	} else if (z <= -5.5e-158) {
		tmp = 9.0 * ((x / z) * (y / c));
	} else if (z <= -7.4e-246) {
		tmp = 1.0 / ((z * c) / b);
	} else if (z <= 1.4e-181) {
		tmp = 9.0 * ((x * y) / (z * c));
	} else if (z <= 1.85e-17) {
		tmp = b / (z * c);
	} else {
		tmp = -4.0 * (a * (t / c));
	}
	return tmp;
}

Fortran

NOTE: t and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (z <= (-3.2d-29)) then
        tmp = (a * t) * (1.0d0 / (c * (-0.25d0)))
    else if (z <= (-5.5d-158)) then
        tmp = 9.0d0 * ((x / z) * (y / c))
    else if (z <= (-7.4d-246)) then
        tmp = 1.0d0 / ((z * c) / b)
    else if (z <= 1.4d-181) then
        tmp = 9.0d0 * ((x * y) / (z * c))
    else if (z <= 1.85d-17) then
        tmp = b / (z * c)
    else
        tmp = (-4.0d0) * (a * (t / c))
    end if
    code = tmp
end function

Java

assert t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (z <= -3.2e-29) {
		tmp = (a * t) * (1.0 / (c * -0.25));
	} else if (z <= -5.5e-158) {
		tmp = 9.0 * ((x / z) * (y / c));
	} else if (z <= -7.4e-246) {
		tmp = 1.0 / ((z * c) / b);
	} else if (z <= 1.4e-181) {
		tmp = 9.0 * ((x * y) / (z * c));
	} else if (z <= 1.85e-17) {
		tmp = b / (z * c);
	} else {
		tmp = -4.0 * (a * (t / c));
	}
	return tmp;
}

Python

[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if z <= -3.2e-29:
		tmp = (a * t) * (1.0 / (c * -0.25))
	elif z <= -5.5e-158:
		tmp = 9.0 * ((x / z) * (y / c))
	elif z <= -7.4e-246:
		tmp = 1.0 / ((z * c) / b)
	elif z <= 1.4e-181:
		tmp = 9.0 * ((x * y) / (z * c))
	elif z <= 1.85e-17:
		tmp = b / (z * c)
	else:
		tmp = -4.0 * (a * (t / c))
	return tmp

Julia

t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (z <= -3.2e-29)
		tmp = Float64(Float64(a * t) * Float64(1.0 / Float64(c * -0.25)));
	elseif (z <= -5.5e-158)
		tmp = Float64(9.0 * Float64(Float64(x / z) * Float64(y / c)));
	elseif (z <= -7.4e-246)
		tmp = Float64(1.0 / Float64(Float64(z * c) / b));
	elseif (z <= 1.4e-181)
		tmp = Float64(9.0 * Float64(Float64(x * y) / Float64(z * c)));
	elseif (z <= 1.85e-17)
		tmp = Float64(b / Float64(z * c));
	else
		tmp = Float64(-4.0 * Float64(a * Float64(t / c)));
	end
	return tmp
end

MATLAB

t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (z <= -3.2e-29)
		tmp = (a * t) * (1.0 / (c * -0.25));
	elseif (z <= -5.5e-158)
		tmp = 9.0 * ((x / z) * (y / c));
	elseif (z <= -7.4e-246)
		tmp = 1.0 / ((z * c) / b);
	elseif (z <= 1.4e-181)
		tmp = 9.0 * ((x * y) / (z * c));
	elseif (z <= 1.85e-17)
		tmp = b / (z * c);
	else
		tmp = -4.0 * (a * (t / c));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[z, -3.2e-29], N[(N[(a * t), $MachinePrecision] * N[(1.0 / N[(c * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -5.5e-158], N[(9.0 * N[(N[(x / z), $MachinePrecision] * N[(y / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -7.4e-246], N[(1.0 / N[(N[(z * c), $MachinePrecision] / b), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.4e-181], N[(9.0 * N[(N[(x * y), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.85e-17], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(-4.0 * N[(a * N[(t / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -3.2e-29

   1. Initial program 72.5%

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

      1. associate-+l- 72.5%

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

      2. associate-*r* 72.5%

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

      3. associate-*r* 78.7%

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

      4. clear-num 78.6%

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

      5. inv-pow 78.6%

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

      6. associate--r- 78.6%

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

      7. fma-neg 78.6%

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

      8. associate-*r* 72.4%

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

      9. distribute-rgt-neg-in 72.4%

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

      10. associate-*l* 72.4%

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

   3. Applied egg-rr 72.4%

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

   5. Simplified 78.6%

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

   6. Taylor expanded in z around inf 60.3%

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

      1. *-commutative 60.3%

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

      2. *-commutative 60.3%

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

      3. associate-*l/ 60.3%

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

      4. *-commutative 60.3%

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

   8. Simplified 60.3%

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

      1. associate-/r/ 60.5%

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

   10. Applied egg-rr 60.5%

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

   if -3.2e-29 < z < -5.50000000000000025e-158

   1. Initial program 92.4%

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

   2. Taylor expanded in x around inf 58.5%

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

      1. *-commutative 58.5%

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

   4. Simplified 58.5%

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

   5. Taylor expanded in x around 0 58.5%

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

      1. *-commutative 58.5%

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

      2. times-frac 66.0%

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

   7. Simplified 66.0%

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

   if -5.50000000000000025e-158 < z < -7.4e-246

   1. Initial program 93.9%

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

      1. associate-+l- 93.9%

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

      2. associate-*r* 94.0%

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

      3. associate-*r* 94.0%

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

      4. clear-num 94.1%

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

      5. inv-pow 94.1%

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

      6. associate--r- 94.1%

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

      7. fma-neg 94.1%

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

      8. associate-*r* 94.1%

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

      9. distribute-rgt-neg-in 94.1%

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

      10. associate-*l* 94.1%

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

   3. Applied egg-rr 94.1%

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

   5. Simplified 94.0%

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

   6. Taylor expanded in b around inf 75.4%

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

   if -7.4e-246 < z < 1.39999999999999993e-181

   1. Initial program 97.3%

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

   2. Taylor expanded in x around inf 67.1%

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

      1. *-commutative 67.1%

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

   4. Simplified 67.1%

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

   if 1.39999999999999993e-181 < z < 1.8499999999999999e-17

   1. Initial program 90.4%

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

   2. Taylor expanded in b around inf 59.6%

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

      1. *-commutative 59.6%

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

   4. Simplified 59.6%

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

   if 1.8499999999999999e-17 < z

   1. Initial program 61.5%

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

      1. associate-+l- 61.5%

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

      2. associate-*l* 61.5%

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

      3. associate-*l* 64.5%

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

   3. Simplified 64.5%

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

   4. Taylor expanded in x around 0 45.7%

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

   5. Taylor expanded in b around 0 62.0%

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

   6. Taylor expanded in a around inf 51.7%

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

      1. associate-*r/ 62.3%

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

   8. Simplified 62.3%

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

4. Final simplification 63.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{-29}:\\ \;\;\;\;\left(a \cdot t\right) \cdot \frac{1}{c \cdot -0.25}\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{-158}:\\ \;\;\;\;9 \cdot \left(\frac{x}{z} \cdot \frac{y}{c}\right)\\ \mathbf{elif}\;z \leq -7.4 \cdot 10^{-246}:\\ \;\;\;\;\frac{1}{\frac{z \cdot c}{b}}\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-181}:\\ \;\;\;\;9 \cdot \frac{x \cdot y}{z \cdot c}\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{-17}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(a \cdot \frac{t}{c}\right)\\ \end{array} \]

Alternative 10: 50.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{-28}:\\ \;\;\;\;\left(a \cdot t\right) \cdot \frac{1}{c \cdot -0.25}\\ \mathbf{elif}\;z \leq -2.9 \cdot 10^{-158}:\\ \;\;\;\;9 \cdot \left(\frac{x}{z} \cdot \frac{y}{c}\right)\\ \mathbf{elif}\;z \leq -1.02 \cdot 10^{-244}:\\ \;\;\;\;\frac{1}{\frac{z \cdot c}{b}}\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{-183}:\\ \;\;\;\;\frac{9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \mathbf{elif}\;z \leq 2.55 \cdot 10^{-17}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(a \cdot \frac{t}{c}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= z -1.45e-28)
   (* (* a t) (/ 1.0 (* c -0.25)))
   (if (<= z -2.9e-158)
     (* 9.0 (* (/ x z) (/ y c)))
     (if (<= z -1.02e-244)
       (/ 1.0 (/ (* z c) b))
       (if (<= z 6.6e-183)
         (/ (* 9.0 (* x y)) (* z c))
         (if (<= z 2.55e-17) (/ b (* z c)) (* -4.0 (* a (/ t c)))))))))

C

assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (z <= -1.45e-28) {
		tmp = (a * t) * (1.0 / (c * -0.25));
	} else if (z <= -2.9e-158) {
		tmp = 9.0 * ((x / z) * (y / c));
	} else if (z <= -1.02e-244) {
		tmp = 1.0 / ((z * c) / b);
	} else if (z <= 6.6e-183) {
		tmp = (9.0 * (x * y)) / (z * c);
	} else if (z <= 2.55e-17) {
		tmp = b / (z * c);
	} else {
		tmp = -4.0 * (a * (t / c));
	}
	return tmp;
}

Fortran

NOTE: t and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (z <= (-1.45d-28)) then
        tmp = (a * t) * (1.0d0 / (c * (-0.25d0)))
    else if (z <= (-2.9d-158)) then
        tmp = 9.0d0 * ((x / z) * (y / c))
    else if (z <= (-1.02d-244)) then
        tmp = 1.0d0 / ((z * c) / b)
    else if (z <= 6.6d-183) then
        tmp = (9.0d0 * (x * y)) / (z * c)
    else if (z <= 2.55d-17) then
        tmp = b / (z * c)
    else
        tmp = (-4.0d0) * (a * (t / c))
    end if
    code = tmp
end function

Java

assert t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (z <= -1.45e-28) {
		tmp = (a * t) * (1.0 / (c * -0.25));
	} else if (z <= -2.9e-158) {
		tmp = 9.0 * ((x / z) * (y / c));
	} else if (z <= -1.02e-244) {
		tmp = 1.0 / ((z * c) / b);
	} else if (z <= 6.6e-183) {
		tmp = (9.0 * (x * y)) / (z * c);
	} else if (z <= 2.55e-17) {
		tmp = b / (z * c);
	} else {
		tmp = -4.0 * (a * (t / c));
	}
	return tmp;
}

Python

[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if z <= -1.45e-28:
		tmp = (a * t) * (1.0 / (c * -0.25))
	elif z <= -2.9e-158:
		tmp = 9.0 * ((x / z) * (y / c))
	elif z <= -1.02e-244:
		tmp = 1.0 / ((z * c) / b)
	elif z <= 6.6e-183:
		tmp = (9.0 * (x * y)) / (z * c)
	elif z <= 2.55e-17:
		tmp = b / (z * c)
	else:
		tmp = -4.0 * (a * (t / c))
	return tmp

Julia

t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (z <= -1.45e-28)
		tmp = Float64(Float64(a * t) * Float64(1.0 / Float64(c * -0.25)));
	elseif (z <= -2.9e-158)
		tmp = Float64(9.0 * Float64(Float64(x / z) * Float64(y / c)));
	elseif (z <= -1.02e-244)
		tmp = Float64(1.0 / Float64(Float64(z * c) / b));
	elseif (z <= 6.6e-183)
		tmp = Float64(Float64(9.0 * Float64(x * y)) / Float64(z * c));
	elseif (z <= 2.55e-17)
		tmp = Float64(b / Float64(z * c));
	else
		tmp = Float64(-4.0 * Float64(a * Float64(t / c)));
	end
	return tmp
end

MATLAB

t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (z <= -1.45e-28)
		tmp = (a * t) * (1.0 / (c * -0.25));
	elseif (z <= -2.9e-158)
		tmp = 9.0 * ((x / z) * (y / c));
	elseif (z <= -1.02e-244)
		tmp = 1.0 / ((z * c) / b);
	elseif (z <= 6.6e-183)
		tmp = (9.0 * (x * y)) / (z * c);
	elseif (z <= 2.55e-17)
		tmp = b / (z * c);
	else
		tmp = -4.0 * (a * (t / c));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[z, -1.45e-28], N[(N[(a * t), $MachinePrecision] * N[(1.0 / N[(c * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.9e-158], N[(9.0 * N[(N[(x / z), $MachinePrecision] * N[(y / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.02e-244], N[(1.0 / N[(N[(z * c), $MachinePrecision] / b), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.6e-183], N[(N[(9.0 * N[(x * y), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.55e-17], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(-4.0 * N[(a * N[(t / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -1.45000000000000006e-28

   1. Initial program 72.5%

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

      1. associate-+l- 72.5%

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

      2. associate-*r* 72.5%

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

      3. associate-*r* 78.7%

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

      4. clear-num 78.6%

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

      5. inv-pow 78.6%

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

      6. associate--r- 78.6%

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

      7. fma-neg 78.6%

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

      8. associate-*r* 72.4%

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

      9. distribute-rgt-neg-in 72.4%

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

      10. associate-*l* 72.4%

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

   3. Applied egg-rr 72.4%

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

   5. Simplified 78.6%

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

   6. Taylor expanded in z around inf 60.3%

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

      1. *-commutative 60.3%

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

      2. *-commutative 60.3%

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

      3. associate-*l/ 60.3%

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

      4. *-commutative 60.3%

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

   8. Simplified 60.3%

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

      1. associate-/r/ 60.5%

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

   10. Applied egg-rr 60.5%

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

   if -1.45000000000000006e-28 < z < -2.8999999999999998e-158

   1. Initial program 92.4%

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

   2. Taylor expanded in x around inf 58.5%

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

      1. *-commutative 58.5%

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

   4. Simplified 58.5%

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

   5. Taylor expanded in x around 0 58.5%

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

      1. *-commutative 58.5%

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

      2. times-frac 66.0%

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

   7. Simplified 66.0%

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

   if -2.8999999999999998e-158 < z < -1.02000000000000006e-244

   1. Initial program 93.9%

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

      1. associate-+l- 93.9%

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

      2. associate-*r* 94.0%

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

      3. associate-*r* 94.0%

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

      4. clear-num 94.1%

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

      5. inv-pow 94.1%

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

      6. associate--r- 94.1%

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

      7. fma-neg 94.1%

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

      8. associate-*r* 94.1%

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

      9. distribute-rgt-neg-in 94.1%

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

      10. associate-*l* 94.1%

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

   3. Applied egg-rr 94.1%

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

   5. Simplified 94.0%

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

   6. Taylor expanded in b around inf 75.4%

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

   if -1.02000000000000006e-244 < z < 6.5999999999999999e-183

   1. Initial program 97.3%

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

   2. Taylor expanded in x around inf 67.1%

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

      1. *-commutative 67.1%

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

   4. Simplified 67.1%

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

      1. associate-*r/ 67.3%

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

   6. Applied egg-rr 67.3%

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

   if 6.5999999999999999e-183 < z < 2.5500000000000001e-17

   1. Initial program 90.4%

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

   2. Taylor expanded in b around inf 59.6%

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

      1. *-commutative 59.6%

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

   4. Simplified 59.6%

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

   if 2.5500000000000001e-17 < z

   1. Initial program 61.5%

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

      1. associate-+l- 61.5%

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

      2. associate-*l* 61.5%

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

      3. associate-*l* 64.5%

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

   3. Simplified 64.5%

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

   4. Taylor expanded in x around 0 45.7%

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

   5. Taylor expanded in b around 0 62.0%

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

   6. Taylor expanded in a around inf 51.7%

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

      1. associate-*r/ 62.3%

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

   8. Simplified 62.3%

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

4. Final simplification 63.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{-28}:\\ \;\;\;\;\left(a \cdot t\right) \cdot \frac{1}{c \cdot -0.25}\\ \mathbf{elif}\;z \leq -2.9 \cdot 10^{-158}:\\ \;\;\;\;9 \cdot \left(\frac{x}{z} \cdot \frac{y}{c}\right)\\ \mathbf{elif}\;z \leq -1.02 \cdot 10^{-244}:\\ \;\;\;\;\frac{1}{\frac{z \cdot c}{b}}\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{-183}:\\ \;\;\;\;\frac{9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \mathbf{elif}\;z \leq 2.55 \cdot 10^{-17}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(a \cdot \frac{t}{c}\right)\\ \end{array} \]

Alternative 11: 50.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.75 \cdot 10^{-29}:\\ \;\;\;\;\left(a \cdot t\right) \cdot \frac{1}{c \cdot -0.25}\\ \mathbf{elif}\;z \leq -1.45 \cdot 10^{-183}:\\ \;\;\;\;\frac{1}{z} \cdot \left(9 \cdot \frac{x}{\frac{c}{y}}\right)\\ \mathbf{elif}\;z \leq -1.46 \cdot 10^{-248}:\\ \;\;\;\;\frac{1}{\frac{z \cdot c}{b}}\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-183}:\\ \;\;\;\;\frac{9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{-18}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(a \cdot \frac{t}{c}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= z -1.75e-29)
   (* (* a t) (/ 1.0 (* c -0.25)))
   (if (<= z -1.45e-183)
     (* (/ 1.0 z) (* 9.0 (/ x (/ c y))))
     (if (<= z -1.46e-248)
       (/ 1.0 (/ (* z c) b))
       (if (<= z 9.5e-183)
         (/ (* 9.0 (* x y)) (* z c))
         (if (<= z 5.6e-18) (/ b (* z c)) (* -4.0 (* a (/ t c)))))))))

C

assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (z <= -1.75e-29) {
		tmp = (a * t) * (1.0 / (c * -0.25));
	} else if (z <= -1.45e-183) {
		tmp = (1.0 / z) * (9.0 * (x / (c / y)));
	} else if (z <= -1.46e-248) {
		tmp = 1.0 / ((z * c) / b);
	} else if (z <= 9.5e-183) {
		tmp = (9.0 * (x * y)) / (z * c);
	} else if (z <= 5.6e-18) {
		tmp = b / (z * c);
	} else {
		tmp = -4.0 * (a * (t / c));
	}
	return tmp;
}

Fortran

NOTE: t and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (z <= (-1.75d-29)) then
        tmp = (a * t) * (1.0d0 / (c * (-0.25d0)))
    else if (z <= (-1.45d-183)) then
        tmp = (1.0d0 / z) * (9.0d0 * (x / (c / y)))
    else if (z <= (-1.46d-248)) then
        tmp = 1.0d0 / ((z * c) / b)
    else if (z <= 9.5d-183) then
        tmp = (9.0d0 * (x * y)) / (z * c)
    else if (z <= 5.6d-18) then
        tmp = b / (z * c)
    else
        tmp = (-4.0d0) * (a * (t / c))
    end if
    code = tmp
end function

Java

assert t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (z <= -1.75e-29) {
		tmp = (a * t) * (1.0 / (c * -0.25));
	} else if (z <= -1.45e-183) {
		tmp = (1.0 / z) * (9.0 * (x / (c / y)));
	} else if (z <= -1.46e-248) {
		tmp = 1.0 / ((z * c) / b);
	} else if (z <= 9.5e-183) {
		tmp = (9.0 * (x * y)) / (z * c);
	} else if (z <= 5.6e-18) {
		tmp = b / (z * c);
	} else {
		tmp = -4.0 * (a * (t / c));
	}
	return tmp;
}

Python

[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if z <= -1.75e-29:
		tmp = (a * t) * (1.0 / (c * -0.25))
	elif z <= -1.45e-183:
		tmp = (1.0 / z) * (9.0 * (x / (c / y)))
	elif z <= -1.46e-248:
		tmp = 1.0 / ((z * c) / b)
	elif z <= 9.5e-183:
		tmp = (9.0 * (x * y)) / (z * c)
	elif z <= 5.6e-18:
		tmp = b / (z * c)
	else:
		tmp = -4.0 * (a * (t / c))
	return tmp

Julia

t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (z <= -1.75e-29)
		tmp = Float64(Float64(a * t) * Float64(1.0 / Float64(c * -0.25)));
	elseif (z <= -1.45e-183)
		tmp = Float64(Float64(1.0 / z) * Float64(9.0 * Float64(x / Float64(c / y))));
	elseif (z <= -1.46e-248)
		tmp = Float64(1.0 / Float64(Float64(z * c) / b));
	elseif (z <= 9.5e-183)
		tmp = Float64(Float64(9.0 * Float64(x * y)) / Float64(z * c));
	elseif (z <= 5.6e-18)
		tmp = Float64(b / Float64(z * c));
	else
		tmp = Float64(-4.0 * Float64(a * Float64(t / c)));
	end
	return tmp
end

MATLAB

t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (z <= -1.75e-29)
		tmp = (a * t) * (1.0 / (c * -0.25));
	elseif (z <= -1.45e-183)
		tmp = (1.0 / z) * (9.0 * (x / (c / y)));
	elseif (z <= -1.46e-248)
		tmp = 1.0 / ((z * c) / b);
	elseif (z <= 9.5e-183)
		tmp = (9.0 * (x * y)) / (z * c);
	elseif (z <= 5.6e-18)
		tmp = b / (z * c);
	else
		tmp = -4.0 * (a * (t / c));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[z, -1.75e-29], N[(N[(a * t), $MachinePrecision] * N[(1.0 / N[(c * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.45e-183], N[(N[(1.0 / z), $MachinePrecision] * N[(9.0 * N[(x / N[(c / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.46e-248], N[(1.0 / N[(N[(z * c), $MachinePrecision] / b), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9.5e-183], N[(N[(9.0 * N[(x * y), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.6e-18], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(-4.0 * N[(a * N[(t / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -1.7499999999999999e-29

   1. Initial program 72.5%

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

      1. associate-+l- 72.5%

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

      2. associate-*r* 72.5%

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

      3. associate-*r* 78.7%

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

      4. clear-num 78.6%

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

      5. inv-pow 78.6%

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

      6. associate--r- 78.6%

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

      7. fma-neg 78.6%

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

      8. associate-*r* 72.4%

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

      9. distribute-rgt-neg-in 72.4%

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

      10. associate-*l* 72.4%

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

   3. Applied egg-rr 72.4%

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

   5. Simplified 78.6%

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

   6. Taylor expanded in z around inf 60.3%

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

      1. *-commutative 60.3%

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

      2. *-commutative 60.3%

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

      3. associate-*l/ 60.3%

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

      4. *-commutative 60.3%

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

   8. Simplified 60.3%

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

      1. associate-/r/ 60.5%

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

   10. Applied egg-rr 60.5%

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

   if -1.7499999999999999e-29 < z < -1.45e-183

   1. Initial program 90.2%

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

      1. associate-+l- 90.2%

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

      2. associate-*r* 90.2%

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

      3. associate-*r* 90.2%

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

      4. *-un-lft-identity 90.2%

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

      5. times-frac 90.1%

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

      6. associate--r- 90.1%

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

      7. fma-neg 90.1%

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

      8. associate-*r* 90.1%

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

      9. distribute-rgt-neg-in 90.1%

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

      10. associate-*l* 90.1%

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

   3. Applied egg-rr 90.1%

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

   4. Taylor expanded in x around inf 57.5%

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

      1. associate-/l* 67.0%

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

   6. Simplified 67.0%

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

   if -1.45e-183 < z < -1.4599999999999999e-248

   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- 99.7%

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

      2. associate-*r* 99.7%

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

      3. associate-*r* 99.7%

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

      4. clear-num 99.9%

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

      5. inv-pow 99.9%

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

      6. associate--r- 99.9%

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

      7. fma-neg 99.9%

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

      8. associate-*r* 99.9%

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

      9. distribute-rgt-neg-in 99.9%

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

      10. associate-*l* 99.9%

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

   3. Applied egg-rr 99.9%

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

   5. Simplified 99.9%

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

   6. Taylor expanded in b around inf 83.7%

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

   if -1.4599999999999999e-248 < z < 9.5000000000000008e-183

   1. Initial program 97.3%

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

   2. Taylor expanded in x around inf 67.1%

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

      1. *-commutative 67.1%

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

   4. Simplified 67.1%

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

      1. associate-*r/ 67.3%

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

   6. Applied egg-rr 67.3%

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

   if 9.5000000000000008e-183 < z < 5.60000000000000025e-18

   1. Initial program 90.4%

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

   2. Taylor expanded in b around inf 59.6%

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

      1. *-commutative 59.6%

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

   4. Simplified 59.6%

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

   if 5.60000000000000025e-18 < z

   1. Initial program 61.5%

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

      1. associate-+l- 61.5%

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

      2. associate-*l* 61.5%

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

      3. associate-*l* 64.5%

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

   3. Simplified 64.5%

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

   4. Taylor expanded in x around 0 45.7%

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

   5. Taylor expanded in b around 0 62.0%

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

   6. Taylor expanded in a around inf 51.7%

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

      1. associate-*r/ 62.3%

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

   8. Simplified 62.3%

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

4. Final simplification 63.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.75 \cdot 10^{-29}:\\ \;\;\;\;\left(a \cdot t\right) \cdot \frac{1}{c \cdot -0.25}\\ \mathbf{elif}\;z \leq -1.45 \cdot 10^{-183}:\\ \;\;\;\;\frac{1}{z} \cdot \left(9 \cdot \frac{x}{\frac{c}{y}}\right)\\ \mathbf{elif}\;z \leq -1.46 \cdot 10^{-248}:\\ \;\;\;\;\frac{1}{\frac{z \cdot c}{b}}\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-183}:\\ \;\;\;\;\frac{9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{-18}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(a \cdot \frac{t}{c}\right)\\ \end{array} \]

Alternative 12: 67.2% accurate, 1.3× speedup

Math

\[\begin{array}{l} [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{+16} \lor \neg \left(y \leq 3.1 \cdot 10^{+166}\right):\\ \;\;\;\;\frac{1}{z} \cdot \left(9 \cdot \frac{x}{\frac{c}{y}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right) + \frac{b}{z}}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= y -3.2e+16) (not (<= y 3.1e+166)))
   (* (/ 1.0 z) (* 9.0 (/ x (/ c y))))
   (/ (+ (* -4.0 (* a t)) (/ b z)) c)))

C

assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((y <= -3.2e+16) || !(y <= 3.1e+166)) {
		tmp = (1.0 / z) * (9.0 * (x / (c / y)));
	} else {
		tmp = ((-4.0 * (a * t)) + (b / z)) / c;
	}
	return tmp;
}

Fortran

NOTE: t and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if ((y <= (-3.2d+16)) .or. (.not. (y <= 3.1d+166))) then
        tmp = (1.0d0 / z) * (9.0d0 * (x / (c / y)))
    else
        tmp = (((-4.0d0) * (a * t)) + (b / z)) / c
    end if
    code = tmp
end function

Java

assert t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((y <= -3.2e+16) || !(y <= 3.1e+166)) {
		tmp = (1.0 / z) * (9.0 * (x / (c / y)));
	} else {
		tmp = ((-4.0 * (a * t)) + (b / z)) / c;
	}
	return tmp;
}

Python

[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if (y <= -3.2e+16) or not (y <= 3.1e+166):
		tmp = (1.0 / z) * (9.0 * (x / (c / y)))
	else:
		tmp = ((-4.0 * (a * t)) + (b / z)) / c
	return tmp

Julia

t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((y <= -3.2e+16) || !(y <= 3.1e+166))
		tmp = Float64(Float64(1.0 / z) * Float64(9.0 * Float64(x / Float64(c / y))));
	else
		tmp = Float64(Float64(Float64(-4.0 * Float64(a * t)) + Float64(b / z)) / c);
	end
	return tmp
end

MATLAB

t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((y <= -3.2e+16) || ~((y <= 3.1e+166)))
		tmp = (1.0 / z) * (9.0 * (x / (c / y)));
	else
		tmp = ((-4.0 * (a * t)) + (b / z)) / c;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[y, -3.2e+16], N[Not[LessEqual[y, 3.1e+166]], $MachinePrecision]], N[(N[(1.0 / z), $MachinePrecision] * N[(9.0 * N[(x / N[(c / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision] + N[(b / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.2e16 or 3.09999999999999983e166 < y

   1. Initial program 76.6%

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

      1. associate-+l- 76.6%

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

      2. associate-*r* 76.7%

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

      3. associate-*r* 77.9%

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

      4. *-un-lft-identity 77.9%

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

      5. times-frac 80.4%

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

      6. associate--r- 80.4%

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

      7. fma-neg 81.8%

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

      8. associate-*r* 81.8%

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

      9. distribute-rgt-neg-in 81.8%

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

      10. associate-*l* 81.8%

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

   3. Applied egg-rr 81.8%

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

   4. Taylor expanded in x around inf 57.2%

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

      1. associate-/l* 65.6%

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

   6. Simplified 65.6%

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

   if -3.2e16 < y < 3.09999999999999983e166

   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-+l- 79.5%

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

      2. associate-*l* 79.5%

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

      3. associate-*l* 81.9%

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

   3. Simplified 81.9%

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

   4. Taylor expanded in x around 0 67.2%

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

   5. Taylor expanded in b around 0 78.6%

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

   6. Taylor expanded in c around 0 76.6%

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

4. Final simplification 73.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{+16} \lor \neg \left(y \leq 3.1 \cdot 10^{+166}\right):\\ \;\;\;\;\frac{1}{z} \cdot \left(9 \cdot \frac{x}{\frac{c}{y}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right) + \frac{b}{z}}{c}\\ \end{array} \]

Alternative 13: 75.2% accurate, 1.3× speedup

Math

\[\begin{array}{l} [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -6.4 \cdot 10^{-24} \lor \neg \left(z \leq 3 \cdot 10^{+57}\right):\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right) + \frac{b}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + x \cdot \left(9 \cdot y\right)}{z \cdot c}\\ \end{array} \end{array} \]

FPCore

NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= z -6.4e-24) (not (<= z 3e+57)))
   (/ (+ (* -4.0 (* a t)) (/ b z)) c)
   (/ (+ b (* x (* 9.0 y))) (* z c))))

C

assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((z <= -6.4e-24) || !(z <= 3e+57)) {
		tmp = ((-4.0 * (a * t)) + (b / z)) / c;
	} else {
		tmp = (b + (x * (9.0 * y))) / (z * c);
	}
	return tmp;
}

Fortran

NOTE: t and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if ((z <= (-6.4d-24)) .or. (.not. (z <= 3d+57))) then
        tmp = (((-4.0d0) * (a * t)) + (b / z)) / c
    else
        tmp = (b + (x * (9.0d0 * y))) / (z * c)
    end if
    code = tmp
end function

Java

assert t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((z <= -6.4e-24) || !(z <= 3e+57)) {
		tmp = ((-4.0 * (a * t)) + (b / z)) / c;
	} else {
		tmp = (b + (x * (9.0 * y))) / (z * c);
	}
	return tmp;
}

Python

[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if (z <= -6.4e-24) or not (z <= 3e+57):
		tmp = ((-4.0 * (a * t)) + (b / z)) / c
	else:
		tmp = (b + (x * (9.0 * y))) / (z * c)
	return tmp

Julia

t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((z <= -6.4e-24) || !(z <= 3e+57))
		tmp = Float64(Float64(Float64(-4.0 * Float64(a * t)) + Float64(b / z)) / c);
	else
		tmp = Float64(Float64(b + Float64(x * Float64(9.0 * y))) / Float64(z * c));
	end
	return tmp
end

MATLAB

t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((z <= -6.4e-24) || ~((z <= 3e+57)))
		tmp = ((-4.0 * (a * t)) + (b / z)) / c;
	else
		tmp = (b + (x * (9.0 * y))) / (z * c);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[z, -6.4e-24], N[Not[LessEqual[z, 3e+57]], $MachinePrecision]], N[(N[(N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision] + N[(b / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], N[(N[(b + N[(x * N[(9.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -6.40000000000000025e-24 or 3e57 < z

   1. Initial program 64.7%

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

      1. associate-+l- 64.7%

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

      2. associate-*l* 64.7%

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

      3. associate-*l* 70.1%

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

   3. Simplified 70.1%

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

   4. Taylor expanded in x around 0 54.2%

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

   5. Taylor expanded in b around 0 75.7%

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

   6. Taylor expanded in c around 0 79.7%

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

   if -6.40000000000000025e-24 < z < 3e57

   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. Taylor expanded in x around inf 83.2%

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

      1. associate-*r* 83.1%

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

      2. *-commutative 83.1%

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

      3. associate-*r* 83.2%

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

   4. Simplified 83.2%

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

4. Final simplification 81.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.4 \cdot 10^{-24} \lor \neg \left(z \leq 3 \cdot 10^{+57}\right):\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right) + \frac{b}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + x \cdot \left(9 \cdot y\right)}{z \cdot c}\\ \end{array} \]

Alternative 14: 51.1% accurate, 1.7× speedup

Math

\[\begin{array}{l} [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -1.24 \cdot 10^{+29} \lor \neg \left(t \leq 5.8 \cdot 10^{-118}\right):\\ \;\;\;\;-4 \cdot \left(a \cdot \frac{t}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \end{array} \end{array} \]

FPCore

NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= t -1.24e+29) (not (<= t 5.8e-118)))
   (* -4.0 (* a (/ t c)))
   (/ b (* z c))))

C

assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((t <= -1.24e+29) || !(t <= 5.8e-118)) {
		tmp = -4.0 * (a * (t / c));
	} else {
		tmp = b / (z * c);
	}
	return tmp;
}

Fortran

NOTE: t and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if ((t <= (-1.24d+29)) .or. (.not. (t <= 5.8d-118))) then
        tmp = (-4.0d0) * (a * (t / c))
    else
        tmp = b / (z * c)
    end if
    code = tmp
end function

Java

assert t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((t <= -1.24e+29) || !(t <= 5.8e-118)) {
		tmp = -4.0 * (a * (t / c));
	} else {
		tmp = b / (z * c);
	}
	return tmp;
}

Python

[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if (t <= -1.24e+29) or not (t <= 5.8e-118):
		tmp = -4.0 * (a * (t / c))
	else:
		tmp = b / (z * c)
	return tmp

Julia

t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((t <= -1.24e+29) || !(t <= 5.8e-118))
		tmp = Float64(-4.0 * Float64(a * Float64(t / c)));
	else
		tmp = Float64(b / Float64(z * c));
	end
	return tmp
end

MATLAB

t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((t <= -1.24e+29) || ~((t <= 5.8e-118)))
		tmp = -4.0 * (a * (t / c));
	else
		tmp = b / (z * c);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[t, -1.24e+29], N[Not[LessEqual[t, 5.8e-118]], $MachinePrecision]], N[(-4.0 * N[(a * N[(t / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.24e29 or 5.79999999999999961e-118 < t

   1. Initial program 68.9%

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

      1. associate-+l- 68.9%

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

      2. associate-*l* 68.9%

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

      3. associate-*l* 72.7%

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

   3. Simplified 72.7%

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

   4. Taylor expanded in x around 0 53.3%

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

   5. Taylor expanded in b around 0 68.9%

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

   6. Taylor expanded in a around inf 51.3%

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

      1. associate-*r/ 59.8%

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

   8. Simplified 59.8%

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

   if -1.24e29 < t < 5.79999999999999961e-118

   1. Initial program 89.4%

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

   2. Taylor expanded in b around inf 50.3%

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

      1. *-commutative 50.3%

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

   4. Simplified 50.3%

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

4. Final simplification 55.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.24 \cdot 10^{+29} \lor \neg \left(t \leq 5.8 \cdot 10^{-118}\right):\\ \;\;\;\;-4 \cdot \left(a \cdot \frac{t}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \end{array} \]

Alternative 15: 51.4% accurate, 1.7× speedup

Math

\[\begin{array}{l} [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -8.4 \cdot 10^{-10}:\\ \;\;\;\;\frac{a}{c} \cdot \frac{t}{-0.25}\\ \mathbf{elif}\;z \leq 2.05 \cdot 10^{-15}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(a \cdot \frac{t}{c}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= z -8.4e-10)
   (* (/ a c) (/ t -0.25))
   (if (<= z 2.05e-15) (/ b (* z c)) (* -4.0 (* a (/ t c))))))

C

assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (z <= -8.4e-10) {
		tmp = (a / c) * (t / -0.25);
	} else if (z <= 2.05e-15) {
		tmp = b / (z * c);
	} else {
		tmp = -4.0 * (a * (t / c));
	}
	return tmp;
}

Fortran

NOTE: t and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (z <= (-8.4d-10)) then
        tmp = (a / c) * (t / (-0.25d0))
    else if (z <= 2.05d-15) then
        tmp = b / (z * c)
    else
        tmp = (-4.0d0) * (a * (t / c))
    end if
    code = tmp
end function

Java

assert t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (z <= -8.4e-10) {
		tmp = (a / c) * (t / -0.25);
	} else if (z <= 2.05e-15) {
		tmp = b / (z * c);
	} else {
		tmp = -4.0 * (a * (t / c));
	}
	return tmp;
}

Python

[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if z <= -8.4e-10:
		tmp = (a / c) * (t / -0.25)
	elif z <= 2.05e-15:
		tmp = b / (z * c)
	else:
		tmp = -4.0 * (a * (t / c))
	return tmp

Julia

t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (z <= -8.4e-10)
		tmp = Float64(Float64(a / c) * Float64(t / -0.25));
	elseif (z <= 2.05e-15)
		tmp = Float64(b / Float64(z * c));
	else
		tmp = Float64(-4.0 * Float64(a * Float64(t / c)));
	end
	return tmp
end

MATLAB

t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (z <= -8.4e-10)
		tmp = (a / c) * (t / -0.25);
	elseif (z <= 2.05e-15)
		tmp = b / (z * c);
	else
		tmp = -4.0 * (a * (t / c));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[z, -8.4e-10], N[(N[(a / c), $MachinePrecision] * N[(t / -0.25), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.05e-15], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(-4.0 * N[(a * N[(t / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.3999999999999999e-10

   1. Initial program 68.8%

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

      1. associate-+l- 68.8%

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

      2. associate-*r* 68.8%

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

      3. associate-*r* 75.8%

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

      4. clear-num 75.7%

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

      5. inv-pow 75.7%

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

      6. associate--r- 75.7%

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

      7. fma-neg 75.7%

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

      8. associate-*r* 68.7%

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

      9. distribute-rgt-neg-in 68.7%

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

      10. associate-*l* 68.7%

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

   3. Applied egg-rr 68.7%

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

   5. Simplified 75.7%

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

   6. Taylor expanded in z around inf 62.9%

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

      1. *-commutative 62.9%

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

      2. *-commutative 62.9%

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

      3. associate-*l/ 62.9%

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

      4. *-commutative 62.9%

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

   8. Simplified 62.9%

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

      1. times-frac 59.4%

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

   10. Applied egg-rr 59.4%

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

       1. inv-pow 59.4%

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

       2. unpow-prod-down 59.6%

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

       3. inv-pow 59.6%

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

       4. clear-num 59.6%

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

   12. Applied egg-rr 59.6%

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

       1. unpow-1 59.6%

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

       2. associate-*r/ 59.7%

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

       3. *-rgt-identity 59.7%

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

       4. associate-/r* 57.4%

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

       5. associate-*r/ 57.4%

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

       6. associate-/l* 63.1%

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

       7. times-frac 59.7%

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

   14. Simplified 59.7%

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

   if -8.3999999999999999e-10 < z < 2.05000000000000018e-15

   1. Initial program 94.2%

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

   2. Taylor expanded in b around inf 52.8%

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

      1. *-commutative 52.8%

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

   4. Simplified 52.8%

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

   if 2.05000000000000018e-15 < z

   1. Initial program 61.5%

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

      1. associate-+l- 61.5%

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

      2. associate-*l* 61.5%

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

      3. associate-*l* 64.5%

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

   3. Simplified 64.5%

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

   4. Taylor expanded in x around 0 45.7%

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

   5. Taylor expanded in b around 0 62.0%

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

   6. Taylor expanded in a around inf 51.7%

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

      1. associate-*r/ 62.3%

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

   8. Simplified 62.3%

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

4. Final simplification 57.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.4 \cdot 10^{-10}:\\ \;\;\;\;\frac{a}{c} \cdot \frac{t}{-0.25}\\ \mathbf{elif}\;z \leq 2.05 \cdot 10^{-15}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(a \cdot \frac{t}{c}\right)\\ \end{array} \]

Alternative 16: 51.3% accurate, 1.7× speedup

Math

\[\begin{array}{l} [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{-10}:\\ \;\;\;\;\frac{a \cdot \left(-4 \cdot t\right)}{c}\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-11}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(a \cdot \frac{t}{c}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= z -6.2e-10)
   (/ (* a (* -4.0 t)) c)
   (if (<= z 3.2e-11) (/ b (* z c)) (* -4.0 (* a (/ t c))))))

C

assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (z <= -6.2e-10) {
		tmp = (a * (-4.0 * t)) / c;
	} else if (z <= 3.2e-11) {
		tmp = b / (z * c);
	} else {
		tmp = -4.0 * (a * (t / c));
	}
	return tmp;
}

Fortran

NOTE: t and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (z <= (-6.2d-10)) then
        tmp = (a * ((-4.0d0) * t)) / c
    else if (z <= 3.2d-11) then
        tmp = b / (z * c)
    else
        tmp = (-4.0d0) * (a * (t / c))
    end if
    code = tmp
end function

Java

assert t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (z <= -6.2e-10) {
		tmp = (a * (-4.0 * t)) / c;
	} else if (z <= 3.2e-11) {
		tmp = b / (z * c);
	} else {
		tmp = -4.0 * (a * (t / c));
	}
	return tmp;
}

Python

[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if z <= -6.2e-10:
		tmp = (a * (-4.0 * t)) / c
	elif z <= 3.2e-11:
		tmp = b / (z * c)
	else:
		tmp = -4.0 * (a * (t / c))
	return tmp

Julia

t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (z <= -6.2e-10)
		tmp = Float64(Float64(a * Float64(-4.0 * t)) / c);
	elseif (z <= 3.2e-11)
		tmp = Float64(b / Float64(z * c));
	else
		tmp = Float64(-4.0 * Float64(a * Float64(t / c)));
	end
	return tmp
end

MATLAB

t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (z <= -6.2e-10)
		tmp = (a * (-4.0 * t)) / c;
	elseif (z <= 3.2e-11)
		tmp = b / (z * c);
	else
		tmp = -4.0 * (a * (t / c));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[z, -6.2e-10], N[(N[(a * N[(-4.0 * t), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[z, 3.2e-11], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(-4.0 * N[(a * N[(t / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.2000000000000003e-10

   1. Initial program 68.8%

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

   2. Taylor expanded in z around inf 63.1%

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

      1. associate-*r/ 63.1%

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

      2. *-commutative 63.1%

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

      3. associate-*r* 63.1%

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

   4. Simplified 63.1%

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

   if -6.2000000000000003e-10 < z < 3.19999999999999994e-11

   1. Initial program 94.2%

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

   2. Taylor expanded in b around inf 52.8%

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

      1. *-commutative 52.8%

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

   4. Simplified 52.8%

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

   if 3.19999999999999994e-11 < z

   1. Initial program 61.5%

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

      1. associate-+l- 61.5%

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

      2. associate-*l* 61.5%

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

      3. associate-*l* 64.5%

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

   3. Simplified 64.5%

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

   4. Taylor expanded in x around 0 45.7%

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

   5. Taylor expanded in b around 0 62.0%

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

   6. Taylor expanded in a around inf 51.7%

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

      1. associate-*r/ 62.3%

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

   8. Simplified 62.3%

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

4. Final simplification 58.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{-10}:\\ \;\;\;\;\frac{a \cdot \left(-4 \cdot t\right)}{c}\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-11}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(a \cdot \frac{t}{c}\right)\\ \end{array} \]

Alternative 17: 36.0% accurate, 3.8× speedup

Math

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

FPCore

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

C

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

Fortran

NOTE: t and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    code = b / (z * c)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 78.6%

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

2. Taylor expanded in b around inf 38.4%

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

   1. *-commutative 38.4%

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

4. Simplified 38.4%

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

5. Final simplification 38.4%

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

Alternative 18: 35.7% accurate, 3.8× speedup

Math

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

FPCore

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

C

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

Fortran

NOTE: t and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    code = (b / c) / z
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 78.6%

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

   1. associate-+l- 78.6%

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

   2. associate-*r* 78.6%

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

   3. associate-*r* 80.6%

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

   4. *-un-lft-identity 80.6%

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

   5. times-frac 83.5%

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

   6. associate--r- 83.5%

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

   7. fma-neg 83.9%

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

   8. associate-*r* 81.6%

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

   9. distribute-rgt-neg-in 81.6%

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

   10. associate-*l* 81.6%

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

3. Applied egg-rr 81.6%

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

4. Taylor expanded in x around 0 76.1%

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

5. Taylor expanded in b around inf 38.4%

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

   1. associate-/r* 39.0%

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

7. Simplified 39.0%

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

8. Final simplification 39.0%

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

Developer target: 80.5% 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 2023310 
(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)))