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

Percentage Accurate: 78.8% → 93.8%

Time: 27.6s

Alternatives: 20

Speedup: 0.8×

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

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 78.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 93.8% accurate, 0.1× speedup

Math

\[\begin{array}{l} [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -8.4 \cdot 10^{-13} \lor \neg \left(z \leq 1.7 \cdot 10^{+32}\right):\\ \;\;\;\;\mathsf{fma}\left(-4, a \cdot t, \mathsf{fma}\left(9, x \cdot \frac{y}{z}, \frac{b}{z}\right)\right) \cdot \frac{1}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b - \left(a \cdot \left(t \cdot \left(z \cdot 4\right)\right) - y \cdot \left(9 \cdot x\right)\right)}{z \cdot c}\\ \end{array} \end{array} \]

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 -8.4e-13) (not (<= z 1.7e+32)))
   (* (fma -4.0 (* a t) (fma 9.0 (* x (/ y z)) (/ b z))) (/ 1.0 c))
   (/ (- b (- (* a (* t (* z 4.0))) (* y (* 9.0 x)))) (* 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 <= -8.4e-13) || !(z <= 1.7e+32)) {
		tmp = fma(-4.0, (a * t), fma(9.0, (x * (y / z)), (b / z))) * (1.0 / c);
	} else {
		tmp = (b - ((a * (t * (z * 4.0))) - (y * (9.0 * x)))) / (z * 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-13) || !(z <= 1.7e+32))
		tmp = Float64(fma(-4.0, Float64(a * t), fma(9.0, Float64(x * Float64(y / z)), Float64(b / z))) * Float64(1.0 / c));
	else
		tmp = Float64(Float64(b - Float64(Float64(a * Float64(t * Float64(z * 4.0))) - Float64(y * Float64(9.0 * x)))) / Float64(z * 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[Or[LessEqual[z, -8.4e-13], N[Not[LessEqual[z, 1.7e+32]], $MachinePrecision]], N[(N[(-4.0 * N[(a * t), $MachinePrecision] + N[(9.0 * N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision] + N[(b / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(1.0 / c), $MachinePrecision]), $MachinePrecision], N[(N[(b - N[(N[(a * N[(t * N[(z * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * N[(9.0 * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -8.39999999999999955e-13 or 1.69999999999999989e32 < z

   1. Initial program 63.1%

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

      1. associate-+l- 63.1%

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

      2. *-commutative 63.1%

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

      3. associate-*r* 60.0%

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

      4. *-commutative 60.0%

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

      5. associate-+l- 60.0%

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

   3. Simplified 63.3%

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

      1. associate-/r* 76.7%

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

      2. div-inv 76.6%

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

      3. associate-+l- 76.6%

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

      4. associate-*r* 72.0%

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

      5. associate-+l- 72.0%

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

      6. associate-*l* 72.0%

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

      7. associate-*r* 76.6%

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

   5. Applied egg-rr 76.6%

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

   6. Taylor expanded in x around 0 91.1%

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

      1. cancel-sign-sub-inv 91.1%

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

      2. metadata-eval 91.1%

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

      3. +-commutative 91.1%

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

      4. fma-def 91.1%

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

      5. fma-def 91.1%

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

      6. associate-*r/ 93.4%

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

   8. Simplified 93.4%

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

   if -8.39999999999999955e-13 < z < 1.69999999999999989e32

   1. Initial program 96.2%

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

4. Final simplification 94.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.4 \cdot 10^{-13} \lor \neg \left(z \leq 1.7 \cdot 10^{+32}\right):\\ \;\;\;\;\mathsf{fma}\left(-4, a \cdot t, \mathsf{fma}\left(9, x \cdot \frac{y}{z}, \frac{b}{z}\right)\right) \cdot \frac{1}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b - \left(a \cdot \left(t \cdot \left(z \cdot 4\right)\right) - y \cdot \left(9 \cdot x\right)\right)}{z \cdot c}\\ \end{array} \]

Alternative 2: 88.1% accurate, 0.2× speedup

Math

\[\begin{array}{l} [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} t_1 := \frac{b - \left(a \cdot \left(t \cdot \left(z \cdot 4\right)\right) - y \cdot \left(9 \cdot x\right)\right)}{z \cdot c}\\ \mathbf{if}\;t_1 \leq -2 \cdot 10^{-111}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq 0:\\ \;\;\;\;\frac{\left(\left(a \cdot t\right) \cdot \left(z \cdot 4\right) - x \cdot \left(9 \cdot y\right)\right) - b}{c} \cdot \frac{-1}{z}\\ \mathbf{elif}\;t_1 \leq \infty:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \end{array} \end{array} \]

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 (- (* a (* t (* z 4.0))) (* y (* 9.0 x)))) (* z c))))
   (if (<= t_1 -2e-111)
     t_1
     (if (<= t_1 0.0)
       (* (/ (- (- (* (* a t) (* z 4.0)) (* x (* 9.0 y))) b) c) (/ -1.0 z))
       (if (<= t_1 INFINITY) t_1 (* -4.0 (/ a (/ c t))))))))

C

assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (b - ((a * (t * (z * 4.0))) - (y * (9.0 * x)))) / (z * c);
	double tmp;
	if (t_1 <= -2e-111) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = (((((a * t) * (z * 4.0)) - (x * (9.0 * y))) - b) / c) * (-1.0 / z);
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = -4.0 * (a / (c / t));
	}
	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 - ((a * (t * (z * 4.0))) - (y * (9.0 * x)))) / (z * c);
	double tmp;
	if (t_1 <= -2e-111) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = (((((a * t) * (z * 4.0)) - (x * (9.0 * y))) - b) / c) * (-1.0 / z);
	} else if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else {
		tmp = -4.0 * (a / (c / t));
	}
	return tmp;
}

Python

[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	t_1 = (b - ((a * (t * (z * 4.0))) - (y * (9.0 * x)))) / (z * c)
	tmp = 0
	if t_1 <= -2e-111:
		tmp = t_1
	elif t_1 <= 0.0:
		tmp = (((((a * t) * (z * 4.0)) - (x * (9.0 * y))) - b) / c) * (-1.0 / z)
	elif t_1 <= math.inf:
		tmp = t_1
	else:
		tmp = -4.0 * (a / (c / t))
	return tmp

Julia

t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(b - Float64(Float64(a * Float64(t * Float64(z * 4.0))) - Float64(y * Float64(9.0 * x)))) / Float64(z * c))
	tmp = 0.0
	if (t_1 <= -2e-111)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = Float64(Float64(Float64(Float64(Float64(Float64(a * t) * Float64(z * 4.0)) - Float64(x * Float64(9.0 * y))) - b) / c) * Float64(-1.0 / z));
	elseif (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = Float64(-4.0 * Float64(a / Float64(c / t)));
	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 - ((a * (t * (z * 4.0))) - (y * (9.0 * x)))) / (z * c);
	tmp = 0.0;
	if (t_1 <= -2e-111)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = (((((a * t) * (z * 4.0)) - (x * (9.0 * y))) - b) / c) * (-1.0 / z);
	elseif (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = -4.0 * (a / (c / t));
	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[(a * N[(t * N[(z * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * N[(9.0 * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e-111], t$95$1, If[LessEqual[t$95$1, 0.0], N[(N[(N[(N[(N[(N[(a * t), $MachinePrecision] * N[(z * 4.0), $MachinePrecision]), $MachinePrecision] - N[(x * N[(9.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision] / c), $MachinePrecision] * N[(-1.0 / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, Infinity], t$95$1, N[(-4.0 * N[(a / N[(c / t), $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)) < -2.00000000000000018e-111 or 0.0 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)) b) (*.f64 z c)) < +inf.0

   1. Initial program 92.0%

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

   if -2.00000000000000018e-111 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)) b) (*.f64 z c)) < 0.0

   1. Initial program 36.5%

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

      1. associate-+l- 36.5%

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

      2. *-commutative 36.5%

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

      3. associate-*r* 30.1%

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

      4. *-commutative 30.1%

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

      5. associate-+l- 30.1%

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

   3. Simplified 36.5%

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

      1. *-un-lft-identity 36.5%

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

      2. times-frac 99.8%

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

      3. associate-+l- 99.8%

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

      4. associate-*r* 99.7%

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

      5. associate-+l- 99.7%

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

      6. associate-*l* 99.7%

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

      7. associate-*r* 99.8%

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

   5. Applied egg-rr 99.8%

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

   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. *-commutative 0.0%

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

      3. associate-*r* 1.1%

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

      4. *-commutative 1.1%

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

      5. associate-+l- 1.1%

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

   3. Simplified 1.1%

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

   4. Taylor expanded in z around inf 68.7%

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

      1. *-commutative 68.7%

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

      2. associate-/l* 85.7%

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

   6. Simplified 85.7%

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

4. Final simplification 92.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{b - \left(a \cdot \left(t \cdot \left(z \cdot 4\right)\right) - y \cdot \left(9 \cdot x\right)\right)}{z \cdot c} \leq -2 \cdot 10^{-111}:\\ \;\;\;\;\frac{b - \left(a \cdot \left(t \cdot \left(z \cdot 4\right)\right) - y \cdot \left(9 \cdot x\right)\right)}{z \cdot c}\\ \mathbf{elif}\;\frac{b - \left(a \cdot \left(t \cdot \left(z \cdot 4\right)\right) - y \cdot \left(9 \cdot x\right)\right)}{z \cdot c} \leq 0:\\ \;\;\;\;\frac{\left(\left(a \cdot t\right) \cdot \left(z \cdot 4\right) - x \cdot \left(9 \cdot y\right)\right) - b}{c} \cdot \frac{-1}{z}\\ \mathbf{elif}\;\frac{b - \left(a \cdot \left(t \cdot \left(z \cdot 4\right)\right) - y \cdot \left(9 \cdot x\right)\right)}{z \cdot c} \leq \infty:\\ \;\;\;\;\frac{b - \left(a \cdot \left(t \cdot \left(z \cdot 4\right)\right) - y \cdot \left(9 \cdot x\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \end{array} \]

Alternative 3: 89.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;c \leq -0.086 \lor \neg \left(c \leq 3 \cdot 10^{-148}\right):\\ \;\;\;\;-4 \cdot \frac{a \cdot t}{c} + \frac{\frac{b}{c} - -9 \cdot \left(x \cdot \frac{y}{c}\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(\left(a \cdot t\right) \cdot \left(z \cdot 4\right) - x \cdot \left(9 \cdot y\right)\right) - b}{z} \cdot \frac{-1}{c}\\ \end{array} \end{array} \]

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 (<= c -0.086) (not (<= c 3e-148)))
   (+ (* -4.0 (/ (* a t) c)) (/ (- (/ b c) (* -9.0 (* x (/ y c)))) z))
   (* (/ (- (- (* (* a t) (* z 4.0)) (* x (* 9.0 y))) b) z) (/ -1.0 c))))

C

assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((c <= -0.086) || !(c <= 3e-148)) {
		tmp = (-4.0 * ((a * t) / c)) + (((b / c) - (-9.0 * (x * (y / c)))) / z);
	} else {
		tmp = (((((a * t) * (z * 4.0)) - (x * (9.0 * y))) - b) / z) * (-1.0 / 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 ((c <= (-0.086d0)) .or. (.not. (c <= 3d-148))) then
        tmp = ((-4.0d0) * ((a * t) / c)) + (((b / c) - ((-9.0d0) * (x * (y / c)))) / z)
    else
        tmp = (((((a * t) * (z * 4.0d0)) - (x * (9.0d0 * y))) - b) / z) * ((-1.0d0) / 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 ((c <= -0.086) || !(c <= 3e-148)) {
		tmp = (-4.0 * ((a * t) / c)) + (((b / c) - (-9.0 * (x * (y / c)))) / z);
	} else {
		tmp = (((((a * t) * (z * 4.0)) - (x * (9.0 * y))) - b) / z) * (-1.0 / c);
	}
	return tmp;
}

Python

[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if (c <= -0.086) or not (c <= 3e-148):
		tmp = (-4.0 * ((a * t) / c)) + (((b / c) - (-9.0 * (x * (y / c)))) / z)
	else:
		tmp = (((((a * t) * (z * 4.0)) - (x * (9.0 * y))) - b) / z) * (-1.0 / c)
	return tmp

Julia

t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((c <= -0.086) || !(c <= 3e-148))
		tmp = Float64(Float64(-4.0 * Float64(Float64(a * t) / c)) + Float64(Float64(Float64(b / c) - Float64(-9.0 * Float64(x * Float64(y / c)))) / z));
	else
		tmp = Float64(Float64(Float64(Float64(Float64(Float64(a * t) * Float64(z * 4.0)) - Float64(x * Float64(9.0 * y))) - b) / z) * Float64(-1.0 / 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 ((c <= -0.086) || ~((c <= 3e-148)))
		tmp = (-4.0 * ((a * t) / c)) + (((b / c) - (-9.0 * (x * (y / c)))) / z);
	else
		tmp = (((((a * t) * (z * 4.0)) - (x * (9.0 * y))) - b) / z) * (-1.0 / 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[c, -0.086], N[Not[LessEqual[c, 3e-148]], $MachinePrecision]], N[(N[(-4.0 * N[(N[(a * t), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(b / c), $MachinePrecision] - N[(-9.0 * N[(x * N[(y / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(N[(N[(a * t), $MachinePrecision] * N[(z * 4.0), $MachinePrecision]), $MachinePrecision] - N[(x * N[(9.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision] / z), $MachinePrecision] * N[(-1.0 / c), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -0.085999999999999993 or 2.99999999999999998e-148 < c

   1. Initial program 68.5%

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

      1. associate-+l- 68.5%

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

      2. *-commutative 68.5%

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

      3. associate-*r* 67.9%

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

      4. *-commutative 67.9%

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

      5. associate-+l- 67.9%

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

   3. Simplified 65.4%

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

      1. associate-/r* 71.1%

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

      2. div-inv 71.0%

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

      3. associate-+l- 71.0%

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

      4. associate-*r* 68.3%

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

      5. associate-+l- 68.3%

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

      6. associate-*l* 68.3%

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

      7. associate-*r* 71.0%

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

   5. Applied egg-rr 71.0%

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

   6. Taylor expanded in x around 0 80.3%

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

      1. cancel-sign-sub-inv 80.3%

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

      2. metadata-eval 80.3%

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

      3. +-commutative 80.3%

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

      4. fma-def 80.3%

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

      5. fma-def 80.2%

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

      6. associate-*r/ 80.8%

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

   8. Simplified 80.8%

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

   9. Taylor expanded in z around -inf 85.9%

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

       1. associate-*l/ 90.4%

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

       2. mul-1-neg 90.4%

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

       3. unsub-neg 90.4%

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

       4. associate-*l/ 85.9%

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

       5. mul-1-neg 85.9%

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

       6. unsub-neg 85.9%

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

       7. *-rgt-identity 85.9%

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

       8. associate-*r/ 85.9%

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

       9. associate-*l* 88.3%

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

       10. associate-*r/ 88.3%

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

       11. *-rgt-identity 88.3%

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

   11. Simplified 88.3%

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

   if -0.085999999999999993 < c < 2.99999999999999998e-148

   1. Initial program 94.9%

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

      1. associate-+l- 94.9%

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

      2. *-commutative 94.9%

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

      3. associate-*r* 93.3%

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

      4. *-commutative 93.3%

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

      5. associate-+l- 93.3%

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

   3. Simplified 95.8%

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

      1. associate-/r* 96.6%

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

      2. div-inv 96.6%

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

      3. associate-+l- 96.6%

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

      4. associate-*r* 94.9%

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

      5. associate-+l- 94.9%

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

      6. associate-*l* 94.9%

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

      7. associate-*r* 96.5%

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

   5. Applied egg-rr 96.5%

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

4. Final simplification 91.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -0.086 \lor \neg \left(c \leq 3 \cdot 10^{-148}\right):\\ \;\;\;\;-4 \cdot \frac{a \cdot t}{c} + \frac{\frac{b}{c} - -9 \cdot \left(x \cdot \frac{y}{c}\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(\left(a \cdot t\right) \cdot \left(z \cdot 4\right) - x \cdot \left(9 \cdot y\right)\right) - b}{z} \cdot \frac{-1}{c}\\ \end{array} \]

Alternative 4: 46.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} t_1 := 9 \cdot \frac{x \cdot y}{z \cdot c}\\ \mathbf{if}\;b \leq -5.2 \cdot 10^{+139}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;b \leq -4.6 \cdot 10^{+17}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -7.8 \cdot 10^{-174}:\\ \;\;\;\;-4 \cdot \frac{t}{\frac{c}{a}}\\ \mathbf{elif}\;b \leq -4.8 \cdot 10^{-229}:\\ \;\;\;\;y \cdot \frac{9}{\frac{c}{\frac{x}{z}}}\\ \mathbf{elif}\;b \leq 8.4 \cdot 10^{-216}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;b \leq 0.006:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 3.5 \cdot 10^{+227}:\\ \;\;\;\;-4 \cdot \left(a \cdot \frac{1}{\frac{c}{t}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \end{array} \end{array} \]

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 y) (* z c)))))
   (if (<= b -5.2e+139)
     (/ b (* z c))
     (if (<= b -4.6e+17)
       t_1
       (if (<= b -7.8e-174)
         (* -4.0 (/ t (/ c a)))
         (if (<= b -4.8e-229)
           (* y (/ 9.0 (/ c (/ x z))))
           (if (<= b 8.4e-216)
             (* -4.0 (* t (/ a c)))
             (if (<= b 0.006)
               t_1
               (if (<= b 3.5e+227)
                 (* -4.0 (* a (/ 1.0 (/ c t))))
                 (/ (/ b c) z))))))))))

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 * y) / (z * c));
	double tmp;
	if (b <= -5.2e+139) {
		tmp = b / (z * c);
	} else if (b <= -4.6e+17) {
		tmp = t_1;
	} else if (b <= -7.8e-174) {
		tmp = -4.0 * (t / (c / a));
	} else if (b <= -4.8e-229) {
		tmp = y * (9.0 / (c / (x / z)));
	} else if (b <= 8.4e-216) {
		tmp = -4.0 * (t * (a / c));
	} else if (b <= 0.006) {
		tmp = t_1;
	} else if (b <= 3.5e+227) {
		tmp = -4.0 * (a * (1.0 / (c / t)));
	} else {
		tmp = (b / c) / z;
	}
	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 * y) / (z * c))
    if (b <= (-5.2d+139)) then
        tmp = b / (z * c)
    else if (b <= (-4.6d+17)) then
        tmp = t_1
    else if (b <= (-7.8d-174)) then
        tmp = (-4.0d0) * (t / (c / a))
    else if (b <= (-4.8d-229)) then
        tmp = y * (9.0d0 / (c / (x / z)))
    else if (b <= 8.4d-216) then
        tmp = (-4.0d0) * (t * (a / c))
    else if (b <= 0.006d0) then
        tmp = t_1
    else if (b <= 3.5d+227) then
        tmp = (-4.0d0) * (a * (1.0d0 / (c / t)))
    else
        tmp = (b / c) / z
    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 * y) / (z * c));
	double tmp;
	if (b <= -5.2e+139) {
		tmp = b / (z * c);
	} else if (b <= -4.6e+17) {
		tmp = t_1;
	} else if (b <= -7.8e-174) {
		tmp = -4.0 * (t / (c / a));
	} else if (b <= -4.8e-229) {
		tmp = y * (9.0 / (c / (x / z)));
	} else if (b <= 8.4e-216) {
		tmp = -4.0 * (t * (a / c));
	} else if (b <= 0.006) {
		tmp = t_1;
	} else if (b <= 3.5e+227) {
		tmp = -4.0 * (a * (1.0 / (c / t)));
	} else {
		tmp = (b / c) / z;
	}
	return tmp;
}

Python

[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	t_1 = 9.0 * ((x * y) / (z * c))
	tmp = 0
	if b <= -5.2e+139:
		tmp = b / (z * c)
	elif b <= -4.6e+17:
		tmp = t_1
	elif b <= -7.8e-174:
		tmp = -4.0 * (t / (c / a))
	elif b <= -4.8e-229:
		tmp = y * (9.0 / (c / (x / z)))
	elif b <= 8.4e-216:
		tmp = -4.0 * (t * (a / c))
	elif b <= 0.006:
		tmp = t_1
	elif b <= 3.5e+227:
		tmp = -4.0 * (a * (1.0 / (c / t)))
	else:
		tmp = (b / c) / z
	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 * y) / Float64(z * c)))
	tmp = 0.0
	if (b <= -5.2e+139)
		tmp = Float64(b / Float64(z * c));
	elseif (b <= -4.6e+17)
		tmp = t_1;
	elseif (b <= -7.8e-174)
		tmp = Float64(-4.0 * Float64(t / Float64(c / a)));
	elseif (b <= -4.8e-229)
		tmp = Float64(y * Float64(9.0 / Float64(c / Float64(x / z))));
	elseif (b <= 8.4e-216)
		tmp = Float64(-4.0 * Float64(t * Float64(a / c)));
	elseif (b <= 0.006)
		tmp = t_1;
	elseif (b <= 3.5e+227)
		tmp = Float64(-4.0 * Float64(a * Float64(1.0 / Float64(c / t))));
	else
		tmp = Float64(Float64(b / c) / z);
	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 * y) / (z * c));
	tmp = 0.0;
	if (b <= -5.2e+139)
		tmp = b / (z * c);
	elseif (b <= -4.6e+17)
		tmp = t_1;
	elseif (b <= -7.8e-174)
		tmp = -4.0 * (t / (c / a));
	elseif (b <= -4.8e-229)
		tmp = y * (9.0 / (c / (x / z)));
	elseif (b <= 8.4e-216)
		tmp = -4.0 * (t * (a / c));
	elseif (b <= 0.006)
		tmp = t_1;
	elseif (b <= 3.5e+227)
		tmp = -4.0 * (a * (1.0 / (c / t)));
	else
		tmp = (b / c) / z;
	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 * y), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -5.2e+139], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -4.6e+17], t$95$1, If[LessEqual[b, -7.8e-174], N[(-4.0 * N[(t / N[(c / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -4.8e-229], N[(y * N[(9.0 / N[(c / N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 8.4e-216], N[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 0.006], t$95$1, If[LessEqual[b, 3.5e+227], N[(-4.0 * N[(a * N[(1.0 / N[(c / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if b < -5.20000000000000044e139

   1. Initial program 77.1%

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

      1. associate-+l- 77.1%

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

      2. *-commutative 77.1%

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

      3. associate-*r* 79.7%

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

      4. *-commutative 79.7%

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

      5. associate-+l- 79.7%

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

   3. Simplified 80.0%

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

   4. Taylor expanded in b around inf 74.2%

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

      1. *-commutative 74.2%

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

   6. Simplified 74.2%

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

   if -5.20000000000000044e139 < b < -4.6e17 or 8.4000000000000006e-216 < b < 0.0060000000000000001

   1. Initial program 87.7%

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

      1. associate-+l- 87.7%

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

      2. *-commutative 87.7%

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

      3. associate-*r* 86.0%

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

      4. *-commutative 86.0%

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

      5. associate-+l- 86.0%

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

   3. Simplified 87.9%

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

   4. Taylor expanded in x around inf 66.5%

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

   if -4.6e17 < b < -7.7999999999999997e-174

   1. Initial program 72.4%

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

      1. associate-+l- 72.4%

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

      2. *-commutative 72.4%

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

      3. associate-*r* 75.4%

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

      4. *-commutative 75.4%

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

      5. associate-+l- 75.4%

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

   3. Simplified 75.4%

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

      1. associate-/r* 75.7%

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

      2. div-inv 75.7%

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

      3. associate-+l- 75.7%

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

      4. associate-*r* 70.2%

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

      5. associate-+l- 70.2%

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

      6. associate-*l* 70.1%

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

      7. associate-*r* 75.6%

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

   5. Applied egg-rr 75.6%

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

   6. Taylor expanded in z around inf 62.0%

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

      1. *-commutative 62.0%

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

      2. associate-/l* 64.7%

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

   8. Simplified 64.7%

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

   if -7.7999999999999997e-174 < b < -4.8e-229

   1. Initial program 83.4%

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

      1. associate-+l- 83.4%

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

      2. *-commutative 83.4%

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

      3. associate-*r* 83.5%

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

      4. *-commutative 83.5%

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

      5. associate-+l- 83.5%

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

   3. Simplified 83.5%

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

      1. associate-/r* 88.6%

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

      2. div-inv 88.6%

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

      3. associate-+l- 88.6%

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

      4. associate-*r* 88.6%

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

      5. associate-+l- 88.6%

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

      6. associate-*l* 88.6%

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

      7. associate-*r* 88.7%

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

   5. Applied egg-rr 88.7%

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

   6. Taylor expanded in x around 0 88.6%

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

      1. cancel-sign-sub-inv 88.6%

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

      2. metadata-eval 88.6%

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

      3. +-commutative 88.6%

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

      4. fma-def 88.6%

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

      5. fma-def 88.6%

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

      6. associate-*r/ 83.2%

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

   8. Simplified 83.2%

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

   9. Taylor expanded in z around -inf 74.7%

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

       1. associate-*l/ 75.0%

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

       2. mul-1-neg 75.0%

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

       3. unsub-neg 75.0%

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

       4. associate-*l/ 74.7%

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

       5. mul-1-neg 74.7%

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

       6. unsub-neg 74.7%

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

       7. *-rgt-identity 74.7%

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

       8. associate-*r/ 74.7%

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

       9. associate-*l* 78.0%

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

       10. associate-*r/ 78.0%

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

       11. *-rgt-identity 78.0%

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

   11. Simplified 78.0%

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

   12. Taylor expanded in x around inf 48.6%

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

       1. *-commutative 48.6%

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

       2. times-frac 59.2%

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

       3. associate-*l* 59.2%

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

       4. *-commutative 59.2%

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

       5. associate-*r/ 53.9%

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

       6. associate-*l/ 59.1%

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

       7. *-commutative 59.1%

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

       8. *-commutative 59.1%

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

       9. associate-/l* 59.4%

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

   14. Simplified 59.4%

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

   if -4.8e-229 < b < 8.4000000000000006e-216

   1. Initial program 76.7%

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

      1. associate-+l- 76.7%

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

      2. *-commutative 76.7%

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

      3. associate-*r* 70.9%

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

      4. *-commutative 70.9%

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

      5. associate-+l- 70.9%

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

   3. Simplified 65.6%

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

   4. Taylor expanded in z around inf 56.1%

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

      1. *-commutative 56.1%

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

      2. associate-/l* 67.1%

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

   6. Simplified 67.1%

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

      1. associate-/r/ 62.0%

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

   8. Applied egg-rr 62.0%

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

   if 0.0060000000000000001 < b < 3.4999999999999999e227

   1. Initial program 82.2%

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

      1. associate-+l- 82.2%

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

      2. *-commutative 82.2%

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

      3. associate-*r* 77.1%

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

      4. *-commutative 77.1%

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

      5. associate-+l- 77.1%

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

   3. Simplified 77.0%

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

   4. Taylor expanded in z around inf 51.4%

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

      1. *-commutative 51.4%

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

      2. associate-/l* 58.2%

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

   6. Simplified 58.2%

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

      1. div-inv 58.2%

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

   8. Applied egg-rr 58.2%

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

   if 3.4999999999999999e227 < b

   1. Initial program 76.8%

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

      1. associate-+l- 76.8%

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

      2. *-commutative 76.8%

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

      3. associate-*r* 80.5%

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

      4. *-commutative 80.5%

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

      5. associate-+l- 80.5%

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

   3. Simplified 80.5%

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

   4. Taylor expanded in b around inf 72.4%

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

      1. associate-/r* 87.4%

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

   6. Simplified 87.4%

      \[\leadsto \color{blue}{\frac{\frac{b}{c}}{z}} \]
3. Recombined 7 regimes into one program.

4. Final simplification 66.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5.2 \cdot 10^{+139}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;b \leq -4.6 \cdot 10^{+17}:\\ \;\;\;\;9 \cdot \frac{x \cdot y}{z \cdot c}\\ \mathbf{elif}\;b \leq -7.8 \cdot 10^{-174}:\\ \;\;\;\;-4 \cdot \frac{t}{\frac{c}{a}}\\ \mathbf{elif}\;b \leq -4.8 \cdot 10^{-229}:\\ \;\;\;\;y \cdot \frac{9}{\frac{c}{\frac{x}{z}}}\\ \mathbf{elif}\;b \leq 8.4 \cdot 10^{-216}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;b \leq 0.006:\\ \;\;\;\;9 \cdot \frac{x \cdot y}{z \cdot c}\\ \mathbf{elif}\;b \leq 3.5 \cdot 10^{+227}:\\ \;\;\;\;-4 \cdot \left(a \cdot \frac{1}{\frac{c}{t}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \end{array} \]

Alternative 5: 46.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;b \leq -5.5 \cdot 10^{+139}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;b \leq -7.8 \cdot 10^{+20}:\\ \;\;\;\;\left(x \cdot \frac{y}{z}\right) \cdot \frac{9}{c}\\ \mathbf{elif}\;b \leq -4.2 \cdot 10^{-174}:\\ \;\;\;\;-4 \cdot \frac{t}{\frac{c}{a}}\\ \mathbf{elif}\;b \leq -4.4 \cdot 10^{-229}:\\ \;\;\;\;y \cdot \frac{9}{\frac{c}{\frac{x}{z}}}\\ \mathbf{elif}\;b \leq 5.6 \cdot 10^{-215}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;b \leq 0.0046:\\ \;\;\;\;9 \cdot \frac{x \cdot y}{z \cdot c}\\ \mathbf{elif}\;b \leq 3.5 \cdot 10^{+227}:\\ \;\;\;\;-4 \cdot \left(a \cdot \frac{1}{\frac{c}{t}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \end{array} \end{array} \]

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 (<= b -5.5e+139)
   (/ b (* z c))
   (if (<= b -7.8e+20)
     (* (* x (/ y z)) (/ 9.0 c))
     (if (<= b -4.2e-174)
       (* -4.0 (/ t (/ c a)))
       (if (<= b -4.4e-229)
         (* y (/ 9.0 (/ c (/ x z))))
         (if (<= b 5.6e-215)
           (* -4.0 (* t (/ a c)))
           (if (<= b 0.0046)
             (* 9.0 (/ (* x y) (* z c)))
             (if (<= b 3.5e+227)
               (* -4.0 (* a (/ 1.0 (/ c t))))
               (/ (/ b c) z)))))))))

C

assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (b <= -5.5e+139) {
		tmp = b / (z * c);
	} else if (b <= -7.8e+20) {
		tmp = (x * (y / z)) * (9.0 / c);
	} else if (b <= -4.2e-174) {
		tmp = -4.0 * (t / (c / a));
	} else if (b <= -4.4e-229) {
		tmp = y * (9.0 / (c / (x / z)));
	} else if (b <= 5.6e-215) {
		tmp = -4.0 * (t * (a / c));
	} else if (b <= 0.0046) {
		tmp = 9.0 * ((x * y) / (z * c));
	} else if (b <= 3.5e+227) {
		tmp = -4.0 * (a * (1.0 / (c / t)));
	} else {
		tmp = (b / c) / z;
	}
	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 (b <= (-5.5d+139)) then
        tmp = b / (z * c)
    else if (b <= (-7.8d+20)) then
        tmp = (x * (y / z)) * (9.0d0 / c)
    else if (b <= (-4.2d-174)) then
        tmp = (-4.0d0) * (t / (c / a))
    else if (b <= (-4.4d-229)) then
        tmp = y * (9.0d0 / (c / (x / z)))
    else if (b <= 5.6d-215) then
        tmp = (-4.0d0) * (t * (a / c))
    else if (b <= 0.0046d0) then
        tmp = 9.0d0 * ((x * y) / (z * c))
    else if (b <= 3.5d+227) then
        tmp = (-4.0d0) * (a * (1.0d0 / (c / t)))
    else
        tmp = (b / c) / z
    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 (b <= -5.5e+139) {
		tmp = b / (z * c);
	} else if (b <= -7.8e+20) {
		tmp = (x * (y / z)) * (9.0 / c);
	} else if (b <= -4.2e-174) {
		tmp = -4.0 * (t / (c / a));
	} else if (b <= -4.4e-229) {
		tmp = y * (9.0 / (c / (x / z)));
	} else if (b <= 5.6e-215) {
		tmp = -4.0 * (t * (a / c));
	} else if (b <= 0.0046) {
		tmp = 9.0 * ((x * y) / (z * c));
	} else if (b <= 3.5e+227) {
		tmp = -4.0 * (a * (1.0 / (c / t)));
	} else {
		tmp = (b / c) / z;
	}
	return tmp;
}

Python

[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if b <= -5.5e+139:
		tmp = b / (z * c)
	elif b <= -7.8e+20:
		tmp = (x * (y / z)) * (9.0 / c)
	elif b <= -4.2e-174:
		tmp = -4.0 * (t / (c / a))
	elif b <= -4.4e-229:
		tmp = y * (9.0 / (c / (x / z)))
	elif b <= 5.6e-215:
		tmp = -4.0 * (t * (a / c))
	elif b <= 0.0046:
		tmp = 9.0 * ((x * y) / (z * c))
	elif b <= 3.5e+227:
		tmp = -4.0 * (a * (1.0 / (c / t)))
	else:
		tmp = (b / c) / z
	return tmp

Julia

t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (b <= -5.5e+139)
		tmp = Float64(b / Float64(z * c));
	elseif (b <= -7.8e+20)
		tmp = Float64(Float64(x * Float64(y / z)) * Float64(9.0 / c));
	elseif (b <= -4.2e-174)
		tmp = Float64(-4.0 * Float64(t / Float64(c / a)));
	elseif (b <= -4.4e-229)
		tmp = Float64(y * Float64(9.0 / Float64(c / Float64(x / z))));
	elseif (b <= 5.6e-215)
		tmp = Float64(-4.0 * Float64(t * Float64(a / c)));
	elseif (b <= 0.0046)
		tmp = Float64(9.0 * Float64(Float64(x * y) / Float64(z * c)));
	elseif (b <= 3.5e+227)
		tmp = Float64(-4.0 * Float64(a * Float64(1.0 / Float64(c / t))));
	else
		tmp = Float64(Float64(b / c) / z);
	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 (b <= -5.5e+139)
		tmp = b / (z * c);
	elseif (b <= -7.8e+20)
		tmp = (x * (y / z)) * (9.0 / c);
	elseif (b <= -4.2e-174)
		tmp = -4.0 * (t / (c / a));
	elseif (b <= -4.4e-229)
		tmp = y * (9.0 / (c / (x / z)));
	elseif (b <= 5.6e-215)
		tmp = -4.0 * (t * (a / c));
	elseif (b <= 0.0046)
		tmp = 9.0 * ((x * y) / (z * c));
	elseif (b <= 3.5e+227)
		tmp = -4.0 * (a * (1.0 / (c / t)));
	else
		tmp = (b / c) / z;
	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[b, -5.5e+139], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -7.8e+20], N[(N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision] * N[(9.0 / c), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -4.2e-174], N[(-4.0 * N[(t / N[(c / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -4.4e-229], N[(y * N[(9.0 / N[(c / N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 5.6e-215], N[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 0.0046], N[(9.0 * N[(N[(x * y), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.5e+227], N[(-4.0 * N[(a * N[(1.0 / N[(c / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if b < -5.4999999999999996e139

   1. Initial program 77.1%

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

      1. associate-+l- 77.1%

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

      2. *-commutative 77.1%

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

      3. associate-*r* 79.7%

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

      4. *-commutative 79.7%

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

      5. associate-+l- 79.7%

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

   3. Simplified 80.0%

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

   4. Taylor expanded in b around inf 74.2%

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

      1. *-commutative 74.2%

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

   6. Simplified 74.2%

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

   if -5.4999999999999996e139 < b < -7.8e20

   1. Initial program 95.4%

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

      1. associate-+l- 95.4%

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

      2. *-commutative 95.4%

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

      3. associate-*r* 95.8%

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

      4. *-commutative 95.8%

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

      5. associate-+l- 95.8%

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

   3. Simplified 95.8%

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

      1. associate-/r* 99.7%

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

      2. div-inv 99.7%

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

      3. associate-+l- 99.7%

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

      4. associate-*r* 95.3%

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

      5. associate-+l- 95.3%

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

      6. associate-*l* 95.2%

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

      7. associate-*r* 99.6%

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

   5. Applied egg-rr 99.6%

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

   6. Taylor expanded in x around inf 63.6%

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

      1. associate-*r/ 63.6%

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

      2. *-commutative 63.6%

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

      3. *-commutative 63.6%

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

      4. times-frac 63.6%

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

      5. associate-*r/ 63.6%

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

   8. Simplified 63.6%

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

   if -7.8e20 < b < -4.20000000000000021e-174

   1. Initial program 72.4%

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

      1. associate-+l- 72.4%

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

      2. *-commutative 72.4%

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

      3. associate-*r* 75.4%

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

      4. *-commutative 75.4%

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

      5. associate-+l- 75.4%

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

   3. Simplified 75.4%

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

      1. associate-/r* 75.7%

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

      2. div-inv 75.7%

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

      3. associate-+l- 75.7%

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

      4. associate-*r* 70.2%

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

      5. associate-+l- 70.2%

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

      6. associate-*l* 70.1%

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

      7. associate-*r* 75.6%

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

   5. Applied egg-rr 75.6%

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

   6. Taylor expanded in z around inf 62.0%

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

      1. *-commutative 62.0%

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

      2. associate-/l* 64.7%

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

   8. Simplified 64.7%

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

   if -4.20000000000000021e-174 < b < -4.3999999999999998e-229

   1. Initial program 83.4%

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

      1. associate-+l- 83.4%

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

      2. *-commutative 83.4%

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

      3. associate-*r* 83.5%

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

      4. *-commutative 83.5%

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

      5. associate-+l- 83.5%

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

   3. Simplified 83.5%

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

      1. associate-/r* 88.6%

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

      2. div-inv 88.6%

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

      3. associate-+l- 88.6%

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

      4. associate-*r* 88.6%

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

      5. associate-+l- 88.6%

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

      6. associate-*l* 88.6%

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

      7. associate-*r* 88.7%

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

   5. Applied egg-rr 88.7%

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

   6. Taylor expanded in x around 0 88.6%

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

      1. cancel-sign-sub-inv 88.6%

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

      2. metadata-eval 88.6%

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

      3. +-commutative 88.6%

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

      4. fma-def 88.6%

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

      5. fma-def 88.6%

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

      6. associate-*r/ 83.2%

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

   8. Simplified 83.2%

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

   9. Taylor expanded in z around -inf 74.7%

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

       1. associate-*l/ 75.0%

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

       2. mul-1-neg 75.0%

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

       3. unsub-neg 75.0%

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

       4. associate-*l/ 74.7%

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

       5. mul-1-neg 74.7%

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

       6. unsub-neg 74.7%

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

       7. *-rgt-identity 74.7%

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

       8. associate-*r/ 74.7%

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

       9. associate-*l* 78.0%

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

       10. associate-*r/ 78.0%

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

       11. *-rgt-identity 78.0%

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

   11. Simplified 78.0%

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

   12. Taylor expanded in x around inf 48.6%

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

       1. *-commutative 48.6%

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

       2. times-frac 59.2%

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

       3. associate-*l* 59.2%

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

       4. *-commutative 59.2%

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

       5. associate-*r/ 53.9%

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

       6. associate-*l/ 59.1%

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

       7. *-commutative 59.1%

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

       8. *-commutative 59.1%

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

       9. associate-/l* 59.4%

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

   14. Simplified 59.4%

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

   if -4.3999999999999998e-229 < b < 5.59999999999999972e-215

   1. Initial program 76.7%

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

      1. associate-+l- 76.7%

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

      2. *-commutative 76.7%

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

      3. associate-*r* 70.9%

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

      4. *-commutative 70.9%

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

      5. associate-+l- 70.9%

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

   3. Simplified 65.6%

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

   4. Taylor expanded in z around inf 56.1%

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

      1. *-commutative 56.1%

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

      2. associate-/l* 67.1%

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

   6. Simplified 67.1%

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

      1. associate-/r/ 62.0%

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

   8. Applied egg-rr 62.0%

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

   if 5.59999999999999972e-215 < b < 0.0045999999999999999

   1. Initial program 82.5%

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

      1. associate-+l- 82.5%

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

      2. *-commutative 82.5%

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

      3. associate-*r* 79.3%

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

      4. *-commutative 79.3%

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

      5. associate-+l- 79.3%

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

   3. Simplified 82.5%

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

   4. Taylor expanded in x around inf 68.6%

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

   if 0.0045999999999999999 < b < 3.4999999999999999e227

   1. Initial program 82.2%

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

      1. associate-+l- 82.2%

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

      2. *-commutative 82.2%

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

      3. associate-*r* 77.1%

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

      4. *-commutative 77.1%

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

      5. associate-+l- 77.1%

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

   3. Simplified 77.0%

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

   4. Taylor expanded in z around inf 51.4%

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

      1. *-commutative 51.4%

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

      2. associate-/l* 58.2%

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

   6. Simplified 58.2%

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

      1. div-inv 58.2%

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

   8. Applied egg-rr 58.2%

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

   if 3.4999999999999999e227 < b

   1. Initial program 76.8%

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

      1. associate-+l- 76.8%

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

      2. *-commutative 76.8%

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

      3. associate-*r* 80.5%

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

      4. *-commutative 80.5%

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

      5. associate-+l- 80.5%

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

   3. Simplified 80.5%

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

   4. Taylor expanded in b around inf 72.4%

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

      1. associate-/r* 87.4%

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

   6. Simplified 87.4%

      \[\leadsto \color{blue}{\frac{\frac{b}{c}}{z}} \]
3. Recombined 8 regimes into one program.

4. Final simplification 66.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5.5 \cdot 10^{+139}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;b \leq -7.8 \cdot 10^{+20}:\\ \;\;\;\;\left(x \cdot \frac{y}{z}\right) \cdot \frac{9}{c}\\ \mathbf{elif}\;b \leq -4.2 \cdot 10^{-174}:\\ \;\;\;\;-4 \cdot \frac{t}{\frac{c}{a}}\\ \mathbf{elif}\;b \leq -4.4 \cdot 10^{-229}:\\ \;\;\;\;y \cdot \frac{9}{\frac{c}{\frac{x}{z}}}\\ \mathbf{elif}\;b \leq 5.6 \cdot 10^{-215}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;b \leq 0.0046:\\ \;\;\;\;9 \cdot \frac{x \cdot y}{z \cdot c}\\ \mathbf{elif}\;b \leq 3.5 \cdot 10^{+227}:\\ \;\;\;\;-4 \cdot \left(a \cdot \frac{1}{\frac{c}{t}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \end{array} \]

Alternative 6: 47.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} t_1 := \frac{9}{z} \cdot \frac{x}{\frac{c}{y}}\\ \mathbf{if}\;b \leq -4.7 \cdot 10^{+139}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;b \leq -9.6 \cdot 10^{+18}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -2.3 \cdot 10^{-177}:\\ \;\;\;\;-4 \cdot \frac{t}{\frac{c}{a}}\\ \mathbf{elif}\;b \leq -2.7 \cdot 10^{-191}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 4.35 \cdot 10^{-215}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;b \leq 0.029:\\ \;\;\;\;9 \cdot \frac{x \cdot y}{z \cdot c}\\ \mathbf{elif}\;b \leq 3.6 \cdot 10^{+227}:\\ \;\;\;\;-4 \cdot \left(a \cdot \frac{1}{\frac{c}{t}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \end{array} \end{array} \]

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 z) (/ x (/ c y)))))
   (if (<= b -4.7e+139)
     (/ b (* z c))
     (if (<= b -9.6e+18)
       t_1
       (if (<= b -2.3e-177)
         (* -4.0 (/ t (/ c a)))
         (if (<= b -2.7e-191)
           t_1
           (if (<= b 4.35e-215)
             (* -4.0 (* t (/ a c)))
             (if (<= b 0.029)
               (* 9.0 (/ (* x y) (* z c)))
               (if (<= b 3.6e+227)
                 (* -4.0 (* a (/ 1.0 (/ c t))))
                 (/ (/ b c) z))))))))))

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 / z) * (x / (c / y));
	double tmp;
	if (b <= -4.7e+139) {
		tmp = b / (z * c);
	} else if (b <= -9.6e+18) {
		tmp = t_1;
	} else if (b <= -2.3e-177) {
		tmp = -4.0 * (t / (c / a));
	} else if (b <= -2.7e-191) {
		tmp = t_1;
	} else if (b <= 4.35e-215) {
		tmp = -4.0 * (t * (a / c));
	} else if (b <= 0.029) {
		tmp = 9.0 * ((x * y) / (z * c));
	} else if (b <= 3.6e+227) {
		tmp = -4.0 * (a * (1.0 / (c / t)));
	} else {
		tmp = (b / c) / z;
	}
	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 / z) * (x / (c / y))
    if (b <= (-4.7d+139)) then
        tmp = b / (z * c)
    else if (b <= (-9.6d+18)) then
        tmp = t_1
    else if (b <= (-2.3d-177)) then
        tmp = (-4.0d0) * (t / (c / a))
    else if (b <= (-2.7d-191)) then
        tmp = t_1
    else if (b <= 4.35d-215) then
        tmp = (-4.0d0) * (t * (a / c))
    else if (b <= 0.029d0) then
        tmp = 9.0d0 * ((x * y) / (z * c))
    else if (b <= 3.6d+227) then
        tmp = (-4.0d0) * (a * (1.0d0 / (c / t)))
    else
        tmp = (b / c) / z
    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 / z) * (x / (c / y));
	double tmp;
	if (b <= -4.7e+139) {
		tmp = b / (z * c);
	} else if (b <= -9.6e+18) {
		tmp = t_1;
	} else if (b <= -2.3e-177) {
		tmp = -4.0 * (t / (c / a));
	} else if (b <= -2.7e-191) {
		tmp = t_1;
	} else if (b <= 4.35e-215) {
		tmp = -4.0 * (t * (a / c));
	} else if (b <= 0.029) {
		tmp = 9.0 * ((x * y) / (z * c));
	} else if (b <= 3.6e+227) {
		tmp = -4.0 * (a * (1.0 / (c / t)));
	} else {
		tmp = (b / c) / z;
	}
	return tmp;
}

Python

[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	t_1 = (9.0 / z) * (x / (c / y))
	tmp = 0
	if b <= -4.7e+139:
		tmp = b / (z * c)
	elif b <= -9.6e+18:
		tmp = t_1
	elif b <= -2.3e-177:
		tmp = -4.0 * (t / (c / a))
	elif b <= -2.7e-191:
		tmp = t_1
	elif b <= 4.35e-215:
		tmp = -4.0 * (t * (a / c))
	elif b <= 0.029:
		tmp = 9.0 * ((x * y) / (z * c))
	elif b <= 3.6e+227:
		tmp = -4.0 * (a * (1.0 / (c / t)))
	else:
		tmp = (b / c) / z
	return tmp

Julia

t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(9.0 / z) * Float64(x / Float64(c / y)))
	tmp = 0.0
	if (b <= -4.7e+139)
		tmp = Float64(b / Float64(z * c));
	elseif (b <= -9.6e+18)
		tmp = t_1;
	elseif (b <= -2.3e-177)
		tmp = Float64(-4.0 * Float64(t / Float64(c / a)));
	elseif (b <= -2.7e-191)
		tmp = t_1;
	elseif (b <= 4.35e-215)
		tmp = Float64(-4.0 * Float64(t * Float64(a / c)));
	elseif (b <= 0.029)
		tmp = Float64(9.0 * Float64(Float64(x * y) / Float64(z * c)));
	elseif (b <= 3.6e+227)
		tmp = Float64(-4.0 * Float64(a * Float64(1.0 / Float64(c / t))));
	else
		tmp = Float64(Float64(b / c) / z);
	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 / z) * (x / (c / y));
	tmp = 0.0;
	if (b <= -4.7e+139)
		tmp = b / (z * c);
	elseif (b <= -9.6e+18)
		tmp = t_1;
	elseif (b <= -2.3e-177)
		tmp = -4.0 * (t / (c / a));
	elseif (b <= -2.7e-191)
		tmp = t_1;
	elseif (b <= 4.35e-215)
		tmp = -4.0 * (t * (a / c));
	elseif (b <= 0.029)
		tmp = 9.0 * ((x * y) / (z * c));
	elseif (b <= 3.6e+227)
		tmp = -4.0 * (a * (1.0 / (c / t)));
	else
		tmp = (b / c) / z;
	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[(9.0 / z), $MachinePrecision] * N[(x / N[(c / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -4.7e+139], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -9.6e+18], t$95$1, If[LessEqual[b, -2.3e-177], N[(-4.0 * N[(t / N[(c / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -2.7e-191], t$95$1, If[LessEqual[b, 4.35e-215], N[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 0.029], N[(9.0 * N[(N[(x * y), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.6e+227], N[(-4.0 * N[(a * N[(1.0 / N[(c / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if b < -4.7000000000000001e139

   1. Initial program 77.1%

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

      1. associate-+l- 77.1%

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

      2. *-commutative 77.1%

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

      3. associate-*r* 79.7%

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

      4. *-commutative 79.7%

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

      5. associate-+l- 79.7%

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

   3. Simplified 80.0%

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

   4. Taylor expanded in b around inf 74.2%

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

      1. *-commutative 74.2%

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

   6. Simplified 74.2%

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

   if -4.7000000000000001e139 < b < -9.6e18 or -2.30000000000000022e-177 < b < -2.69999999999999999e-191

   1. Initial program 90.0%

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

      1. associate-+l- 90.0%

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

      2. *-commutative 90.0%

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

      3. associate-*r* 90.3%

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

      4. *-commutative 90.3%

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

      5. associate-+l- 90.3%

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

   3. Simplified 90.3%

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

      1. associate-/r* 96.4%

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

      2. div-inv 96.4%

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

      3. associate-+l- 96.4%

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

      4. associate-*r* 93.2%

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

      5. associate-+l- 93.2%

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

      6. associate-*l* 93.1%

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

      7. associate-*r* 96.3%

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

   5. Applied egg-rr 96.3%

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

   6. Taylor expanded in x around inf 63.5%

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

      1. associate-*r/ 63.5%

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

      2. *-commutative 63.5%

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

      3. times-frac 66.6%

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

      4. associate-/l* 69.8%

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

   8. Simplified 69.8%

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

   if -9.6e18 < b < -2.30000000000000022e-177

   1. Initial program 73.8%

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

      1. associate-+l- 73.8%

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

      2. *-commutative 73.8%

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

      3. associate-*r* 76.7%

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

      4. *-commutative 76.7%

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

      5. associate-+l- 76.7%

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

   3. Simplified 76.7%

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

      1. associate-/r* 77.0%

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

      2. div-inv 76.9%

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

      3. associate-+l- 76.9%

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

      4. associate-*r* 71.7%

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

      5. associate-+l- 71.7%

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

      6. associate-*l* 71.6%

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

      7. associate-*r* 76.8%

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

   5. Applied egg-rr 76.8%

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

   6. Taylor expanded in z around inf 61.4%

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

      1. *-commutative 61.4%

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

      2. associate-/l* 64.0%

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

   8. Simplified 64.0%

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

   if -2.69999999999999999e-191 < b < 4.35000000000000009e-215

   1. Initial program 78.8%

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

      1. associate-+l- 78.8%

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

      2. *-commutative 78.8%

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

      3. associate-*r* 74.2%

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

      4. *-commutative 74.2%

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

      5. associate-+l- 74.2%

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

   3. Simplified 69.9%

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

   4. Taylor expanded in z around inf 53.1%

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

      1. *-commutative 53.1%

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

      2. associate-/l* 62.0%

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

   6. Simplified 62.0%

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

      1. associate-/r/ 57.9%

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

   8. Applied egg-rr 57.9%

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

   if 4.35000000000000009e-215 < b < 0.0290000000000000015

   1. Initial program 82.5%

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

      1. associate-+l- 82.5%

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

      2. *-commutative 82.5%

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

      3. associate-*r* 79.3%

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

      4. *-commutative 79.3%

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

      5. associate-+l- 79.3%

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

   3. Simplified 82.5%

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

   4. Taylor expanded in x around inf 68.6%

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

   if 0.0290000000000000015 < b < 3.59999999999999991e227

   1. Initial program 82.2%

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

      1. associate-+l- 82.2%

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

      2. *-commutative 82.2%

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

      3. associate-*r* 77.1%

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

      4. *-commutative 77.1%

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

      5. associate-+l- 77.1%

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

   3. Simplified 77.0%

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

   4. Taylor expanded in z around inf 51.4%

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

      1. *-commutative 51.4%

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

      2. associate-/l* 58.2%

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

   6. Simplified 58.2%

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

      1. div-inv 58.2%

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

   8. Applied egg-rr 58.2%

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

   if 3.59999999999999991e227 < b

   1. Initial program 76.8%

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

      1. associate-+l- 76.8%

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

      2. *-commutative 76.8%

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

      3. associate-*r* 80.5%

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

      4. *-commutative 80.5%

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

      5. associate-+l- 80.5%

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

   3. Simplified 80.5%

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

   4. Taylor expanded in b around inf 72.4%

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

      1. associate-/r* 87.4%

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

   6. Simplified 87.4%

      \[\leadsto \color{blue}{\frac{\frac{b}{c}}{z}} \]
3. Recombined 7 regimes into one program.

4. Final simplification 66.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.7 \cdot 10^{+139}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;b \leq -9.6 \cdot 10^{+18}:\\ \;\;\;\;\frac{9}{z} \cdot \frac{x}{\frac{c}{y}}\\ \mathbf{elif}\;b \leq -2.3 \cdot 10^{-177}:\\ \;\;\;\;-4 \cdot \frac{t}{\frac{c}{a}}\\ \mathbf{elif}\;b \leq -2.7 \cdot 10^{-191}:\\ \;\;\;\;\frac{9}{z} \cdot \frac{x}{\frac{c}{y}}\\ \mathbf{elif}\;b \leq 4.35 \cdot 10^{-215}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;b \leq 0.029:\\ \;\;\;\;9 \cdot \frac{x \cdot y}{z \cdot c}\\ \mathbf{elif}\;b \leq 3.6 \cdot 10^{+227}:\\ \;\;\;\;-4 \cdot \left(a \cdot \frac{1}{\frac{c}{t}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \end{array} \]

Alternative 7: 47.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} t_1 := \frac{x}{z} \cdot \frac{9}{\frac{c}{y}}\\ \mathbf{if}\;b \leq -1.22 \cdot 10^{+140}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;b \leq -4.5 \cdot 10^{+17}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -8 \cdot 10^{-178}:\\ \;\;\;\;-4 \cdot \frac{t}{\frac{c}{a}}\\ \mathbf{elif}\;b \leq -3.5 \cdot 10^{-193}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 5.6 \cdot 10^{-215}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;b \leq 0.065:\\ \;\;\;\;9 \cdot \frac{x \cdot y}{z \cdot c}\\ \mathbf{elif}\;b \leq 3.5 \cdot 10^{+227}:\\ \;\;\;\;-4 \cdot \left(a \cdot \frac{1}{\frac{c}{t}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \end{array} \end{array} \]

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 (* (/ x z) (/ 9.0 (/ c y)))))
   (if (<= b -1.22e+140)
     (/ b (* z c))
     (if (<= b -4.5e+17)
       t_1
       (if (<= b -8e-178)
         (* -4.0 (/ t (/ c a)))
         (if (<= b -3.5e-193)
           t_1
           (if (<= b 5.6e-215)
             (* -4.0 (* t (/ a c)))
             (if (<= b 0.065)
               (* 9.0 (/ (* x y) (* z c)))
               (if (<= b 3.5e+227)
                 (* -4.0 (* a (/ 1.0 (/ c t))))
                 (/ (/ b c) z))))))))))

C

assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (x / z) * (9.0 / (c / y));
	double tmp;
	if (b <= -1.22e+140) {
		tmp = b / (z * c);
	} else if (b <= -4.5e+17) {
		tmp = t_1;
	} else if (b <= -8e-178) {
		tmp = -4.0 * (t / (c / a));
	} else if (b <= -3.5e-193) {
		tmp = t_1;
	} else if (b <= 5.6e-215) {
		tmp = -4.0 * (t * (a / c));
	} else if (b <= 0.065) {
		tmp = 9.0 * ((x * y) / (z * c));
	} else if (b <= 3.5e+227) {
		tmp = -4.0 * (a * (1.0 / (c / t)));
	} else {
		tmp = (b / c) / z;
	}
	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 = (x / z) * (9.0d0 / (c / y))
    if (b <= (-1.22d+140)) then
        tmp = b / (z * c)
    else if (b <= (-4.5d+17)) then
        tmp = t_1
    else if (b <= (-8d-178)) then
        tmp = (-4.0d0) * (t / (c / a))
    else if (b <= (-3.5d-193)) then
        tmp = t_1
    else if (b <= 5.6d-215) then
        tmp = (-4.0d0) * (t * (a / c))
    else if (b <= 0.065d0) then
        tmp = 9.0d0 * ((x * y) / (z * c))
    else if (b <= 3.5d+227) then
        tmp = (-4.0d0) * (a * (1.0d0 / (c / t)))
    else
        tmp = (b / c) / z
    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 = (x / z) * (9.0 / (c / y));
	double tmp;
	if (b <= -1.22e+140) {
		tmp = b / (z * c);
	} else if (b <= -4.5e+17) {
		tmp = t_1;
	} else if (b <= -8e-178) {
		tmp = -4.0 * (t / (c / a));
	} else if (b <= -3.5e-193) {
		tmp = t_1;
	} else if (b <= 5.6e-215) {
		tmp = -4.0 * (t * (a / c));
	} else if (b <= 0.065) {
		tmp = 9.0 * ((x * y) / (z * c));
	} else if (b <= 3.5e+227) {
		tmp = -4.0 * (a * (1.0 / (c / t)));
	} else {
		tmp = (b / c) / z;
	}
	return tmp;
}

Python

[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	t_1 = (x / z) * (9.0 / (c / y))
	tmp = 0
	if b <= -1.22e+140:
		tmp = b / (z * c)
	elif b <= -4.5e+17:
		tmp = t_1
	elif b <= -8e-178:
		tmp = -4.0 * (t / (c / a))
	elif b <= -3.5e-193:
		tmp = t_1
	elif b <= 5.6e-215:
		tmp = -4.0 * (t * (a / c))
	elif b <= 0.065:
		tmp = 9.0 * ((x * y) / (z * c))
	elif b <= 3.5e+227:
		tmp = -4.0 * (a * (1.0 / (c / t)))
	else:
		tmp = (b / c) / z
	return tmp

Julia

t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(x / z) * Float64(9.0 / Float64(c / y)))
	tmp = 0.0
	if (b <= -1.22e+140)
		tmp = Float64(b / Float64(z * c));
	elseif (b <= -4.5e+17)
		tmp = t_1;
	elseif (b <= -8e-178)
		tmp = Float64(-4.0 * Float64(t / Float64(c / a)));
	elseif (b <= -3.5e-193)
		tmp = t_1;
	elseif (b <= 5.6e-215)
		tmp = Float64(-4.0 * Float64(t * Float64(a / c)));
	elseif (b <= 0.065)
		tmp = Float64(9.0 * Float64(Float64(x * y) / Float64(z * c)));
	elseif (b <= 3.5e+227)
		tmp = Float64(-4.0 * Float64(a * Float64(1.0 / Float64(c / t))));
	else
		tmp = Float64(Float64(b / c) / z);
	end
	return tmp
end

MATLAB

t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (x / z) * (9.0 / (c / y));
	tmp = 0.0;
	if (b <= -1.22e+140)
		tmp = b / (z * c);
	elseif (b <= -4.5e+17)
		tmp = t_1;
	elseif (b <= -8e-178)
		tmp = -4.0 * (t / (c / a));
	elseif (b <= -3.5e-193)
		tmp = t_1;
	elseif (b <= 5.6e-215)
		tmp = -4.0 * (t * (a / c));
	elseif (b <= 0.065)
		tmp = 9.0 * ((x * y) / (z * c));
	elseif (b <= 3.5e+227)
		tmp = -4.0 * (a * (1.0 / (c / t)));
	else
		tmp = (b / c) / z;
	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[(x / z), $MachinePrecision] * N[(9.0 / N[(c / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.22e+140], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -4.5e+17], t$95$1, If[LessEqual[b, -8e-178], N[(-4.0 * N[(t / N[(c / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -3.5e-193], t$95$1, If[LessEqual[b, 5.6e-215], N[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 0.065], N[(9.0 * N[(N[(x * y), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.5e+227], N[(-4.0 * N[(a * N[(1.0 / N[(c / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if b < -1.22e140

   1. Initial program 77.1%

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

      1. associate-+l- 77.1%

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

      2. *-commutative 77.1%

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

      3. associate-*r* 79.7%

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

      4. *-commutative 79.7%

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

      5. associate-+l- 79.7%

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

   3. Simplified 80.0%

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

   4. Taylor expanded in b around inf 74.2%

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

      1. *-commutative 74.2%

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

   6. Simplified 74.2%

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

   if -1.22e140 < b < -4.5e17 or -7.9999999999999996e-178 < b < -3.50000000000000005e-193

   1. Initial program 90.0%

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

      1. associate-+l- 90.0%

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

      2. *-commutative 90.0%

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

      3. associate-*r* 90.3%

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

      4. *-commutative 90.3%

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

      5. associate-+l- 90.3%

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

   3. Simplified 90.3%

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

   4. Taylor expanded in x around inf 63.5%

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

      1. associate-*r/ 63.5%

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

      2. associate-*r* 63.5%

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

      3. *-commutative 63.5%

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

      4. associate-*r* 63.5%

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

      5. *-commutative 63.5%

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

      6. times-frac 69.9%

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

      7. associate-/l* 69.9%

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

   6. Simplified 69.9%

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

   if -4.5e17 < b < -7.9999999999999996e-178

   1. Initial program 73.8%

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

      1. associate-+l- 73.8%

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

      2. *-commutative 73.8%

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

      3. associate-*r* 76.7%

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

      4. *-commutative 76.7%

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

      5. associate-+l- 76.7%

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

   3. Simplified 76.7%

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

      1. associate-/r* 77.0%

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

      2. div-inv 76.9%

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

      3. associate-+l- 76.9%

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

      4. associate-*r* 71.7%

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

      5. associate-+l- 71.7%

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

      6. associate-*l* 71.6%

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

      7. associate-*r* 76.8%

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

   5. Applied egg-rr 76.8%

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

   6. Taylor expanded in z around inf 61.4%

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

      1. *-commutative 61.4%

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

      2. associate-/l* 64.0%

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

   8. Simplified 64.0%

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

   if -3.50000000000000005e-193 < b < 5.59999999999999972e-215

   1. Initial program 78.8%

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

      1. associate-+l- 78.8%

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

      2. *-commutative 78.8%

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

      3. associate-*r* 74.2%

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

      4. *-commutative 74.2%

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

      5. associate-+l- 74.2%

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

   3. Simplified 69.9%

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

   4. Taylor expanded in z around inf 53.1%

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

      1. *-commutative 53.1%

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

      2. associate-/l* 62.0%

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

   6. Simplified 62.0%

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

      1. associate-/r/ 57.9%

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

   8. Applied egg-rr 57.9%

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

   if 5.59999999999999972e-215 < b < 0.065000000000000002

   1. Initial program 82.5%

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

      1. associate-+l- 82.5%

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

      2. *-commutative 82.5%

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

      3. associate-*r* 79.3%

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

      4. *-commutative 79.3%

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

      5. associate-+l- 79.3%

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

   3. Simplified 82.5%

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

   4. Taylor expanded in x around inf 68.6%

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

   if 0.065000000000000002 < b < 3.4999999999999999e227

   1. Initial program 82.2%

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

      1. associate-+l- 82.2%

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

      2. *-commutative 82.2%

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

      3. associate-*r* 77.1%

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

      4. *-commutative 77.1%

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

      5. associate-+l- 77.1%

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

   3. Simplified 77.0%

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

   4. Taylor expanded in z around inf 51.4%

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

      1. *-commutative 51.4%

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

      2. associate-/l* 58.2%

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

   6. Simplified 58.2%

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

      1. div-inv 58.2%

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

   8. Applied egg-rr 58.2%

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

   if 3.4999999999999999e227 < b

   1. Initial program 76.8%

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

      1. associate-+l- 76.8%

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

      2. *-commutative 76.8%

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

      3. associate-*r* 80.5%

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

      4. *-commutative 80.5%

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

      5. associate-+l- 80.5%

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

   3. Simplified 80.5%

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

   4. Taylor expanded in b around inf 72.4%

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

      1. associate-/r* 87.4%

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

   6. Simplified 87.4%

      \[\leadsto \color{blue}{\frac{\frac{b}{c}}{z}} \]
3. Recombined 7 regimes into one program.

4. Final simplification 66.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.22 \cdot 10^{+140}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;b \leq -4.5 \cdot 10^{+17}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{9}{\frac{c}{y}}\\ \mathbf{elif}\;b \leq -8 \cdot 10^{-178}:\\ \;\;\;\;-4 \cdot \frac{t}{\frac{c}{a}}\\ \mathbf{elif}\;b \leq -3.5 \cdot 10^{-193}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{9}{\frac{c}{y}}\\ \mathbf{elif}\;b \leq 5.6 \cdot 10^{-215}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;b \leq 0.065:\\ \;\;\;\;9 \cdot \frac{x \cdot y}{z \cdot c}\\ \mathbf{elif}\;b \leq 3.5 \cdot 10^{+227}:\\ \;\;\;\;-4 \cdot \left(a \cdot \frac{1}{\frac{c}{t}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \end{array} \]

Alternative 8: 47.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} t_1 := \frac{x}{z} \cdot \frac{9}{\frac{c}{y}}\\ \mathbf{if}\;b \leq -4.8 \cdot 10^{+139}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;b \leq -6 \cdot 10^{+19}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -1.5 \cdot 10^{-178}:\\ \;\;\;\;-4 \cdot \frac{t}{\frac{c}{a}}\\ \mathbf{elif}\;b \leq -2.8 \cdot 10^{-191}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 8.5 \cdot 10^{-216}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;b \leq 0.0028:\\ \;\;\;\;\frac{9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \mathbf{elif}\;b \leq 3.5 \cdot 10^{+227}:\\ \;\;\;\;-4 \cdot \left(a \cdot \frac{1}{\frac{c}{t}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \end{array} \end{array} \]

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 (* (/ x z) (/ 9.0 (/ c y)))))
   (if (<= b -4.8e+139)
     (/ b (* z c))
     (if (<= b -6e+19)
       t_1
       (if (<= b -1.5e-178)
         (* -4.0 (/ t (/ c a)))
         (if (<= b -2.8e-191)
           t_1
           (if (<= b 8.5e-216)
             (* -4.0 (* t (/ a c)))
             (if (<= b 0.0028)
               (/ (* 9.0 (* x y)) (* z c))
               (if (<= b 3.5e+227)
                 (* -4.0 (* a (/ 1.0 (/ c t))))
                 (/ (/ b c) z))))))))))

C

assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (x / z) * (9.0 / (c / y));
	double tmp;
	if (b <= -4.8e+139) {
		tmp = b / (z * c);
	} else if (b <= -6e+19) {
		tmp = t_1;
	} else if (b <= -1.5e-178) {
		tmp = -4.0 * (t / (c / a));
	} else if (b <= -2.8e-191) {
		tmp = t_1;
	} else if (b <= 8.5e-216) {
		tmp = -4.0 * (t * (a / c));
	} else if (b <= 0.0028) {
		tmp = (9.0 * (x * y)) / (z * c);
	} else if (b <= 3.5e+227) {
		tmp = -4.0 * (a * (1.0 / (c / t)));
	} else {
		tmp = (b / c) / z;
	}
	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 = (x / z) * (9.0d0 / (c / y))
    if (b <= (-4.8d+139)) then
        tmp = b / (z * c)
    else if (b <= (-6d+19)) then
        tmp = t_1
    else if (b <= (-1.5d-178)) then
        tmp = (-4.0d0) * (t / (c / a))
    else if (b <= (-2.8d-191)) then
        tmp = t_1
    else if (b <= 8.5d-216) then
        tmp = (-4.0d0) * (t * (a / c))
    else if (b <= 0.0028d0) then
        tmp = (9.0d0 * (x * y)) / (z * c)
    else if (b <= 3.5d+227) then
        tmp = (-4.0d0) * (a * (1.0d0 / (c / t)))
    else
        tmp = (b / c) / z
    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 = (x / z) * (9.0 / (c / y));
	double tmp;
	if (b <= -4.8e+139) {
		tmp = b / (z * c);
	} else if (b <= -6e+19) {
		tmp = t_1;
	} else if (b <= -1.5e-178) {
		tmp = -4.0 * (t / (c / a));
	} else if (b <= -2.8e-191) {
		tmp = t_1;
	} else if (b <= 8.5e-216) {
		tmp = -4.0 * (t * (a / c));
	} else if (b <= 0.0028) {
		tmp = (9.0 * (x * y)) / (z * c);
	} else if (b <= 3.5e+227) {
		tmp = -4.0 * (a * (1.0 / (c / t)));
	} else {
		tmp = (b / c) / z;
	}
	return tmp;
}

Python

[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	t_1 = (x / z) * (9.0 / (c / y))
	tmp = 0
	if b <= -4.8e+139:
		tmp = b / (z * c)
	elif b <= -6e+19:
		tmp = t_1
	elif b <= -1.5e-178:
		tmp = -4.0 * (t / (c / a))
	elif b <= -2.8e-191:
		tmp = t_1
	elif b <= 8.5e-216:
		tmp = -4.0 * (t * (a / c))
	elif b <= 0.0028:
		tmp = (9.0 * (x * y)) / (z * c)
	elif b <= 3.5e+227:
		tmp = -4.0 * (a * (1.0 / (c / t)))
	else:
		tmp = (b / c) / z
	return tmp

Julia

t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(x / z) * Float64(9.0 / Float64(c / y)))
	tmp = 0.0
	if (b <= -4.8e+139)
		tmp = Float64(b / Float64(z * c));
	elseif (b <= -6e+19)
		tmp = t_1;
	elseif (b <= -1.5e-178)
		tmp = Float64(-4.0 * Float64(t / Float64(c / a)));
	elseif (b <= -2.8e-191)
		tmp = t_1;
	elseif (b <= 8.5e-216)
		tmp = Float64(-4.0 * Float64(t * Float64(a / c)));
	elseif (b <= 0.0028)
		tmp = Float64(Float64(9.0 * Float64(x * y)) / Float64(z * c));
	elseif (b <= 3.5e+227)
		tmp = Float64(-4.0 * Float64(a * Float64(1.0 / Float64(c / t))));
	else
		tmp = Float64(Float64(b / c) / z);
	end
	return tmp
end

MATLAB

t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (x / z) * (9.0 / (c / y));
	tmp = 0.0;
	if (b <= -4.8e+139)
		tmp = b / (z * c);
	elseif (b <= -6e+19)
		tmp = t_1;
	elseif (b <= -1.5e-178)
		tmp = -4.0 * (t / (c / a));
	elseif (b <= -2.8e-191)
		tmp = t_1;
	elseif (b <= 8.5e-216)
		tmp = -4.0 * (t * (a / c));
	elseif (b <= 0.0028)
		tmp = (9.0 * (x * y)) / (z * c);
	elseif (b <= 3.5e+227)
		tmp = -4.0 * (a * (1.0 / (c / t)));
	else
		tmp = (b / c) / z;
	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[(x / z), $MachinePrecision] * N[(9.0 / N[(c / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -4.8e+139], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -6e+19], t$95$1, If[LessEqual[b, -1.5e-178], N[(-4.0 * N[(t / N[(c / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -2.8e-191], t$95$1, If[LessEqual[b, 8.5e-216], N[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 0.0028], N[(N[(9.0 * N[(x * y), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.5e+227], N[(-4.0 * N[(a * N[(1.0 / N[(c / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if b < -4.80000000000000016e139

   1. Initial program 77.1%

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

      1. associate-+l- 77.1%

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

      2. *-commutative 77.1%

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

      3. associate-*r* 79.7%

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

      4. *-commutative 79.7%

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

      5. associate-+l- 79.7%

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

   3. Simplified 80.0%

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

   4. Taylor expanded in b around inf 74.2%

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

      1. *-commutative 74.2%

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

   6. Simplified 74.2%

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

   if -4.80000000000000016e139 < b < -6e19 or -1.4999999999999999e-178 < b < -2.80000000000000012e-191

   1. Initial program 90.0%

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

      1. associate-+l- 90.0%

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

      2. *-commutative 90.0%

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

      3. associate-*r* 90.3%

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

      4. *-commutative 90.3%

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

      5. associate-+l- 90.3%

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

   3. Simplified 90.3%

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

   4. Taylor expanded in x around inf 63.5%

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

      1. associate-*r/ 63.5%

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

      2. associate-*r* 63.5%

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

      3. *-commutative 63.5%

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

      4. associate-*r* 63.5%

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

      5. *-commutative 63.5%

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

      6. times-frac 69.9%

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

      7. associate-/l* 69.9%

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

   6. Simplified 69.9%

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

   if -6e19 < b < -1.4999999999999999e-178

   1. Initial program 73.8%

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

      1. associate-+l- 73.8%

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

      2. *-commutative 73.8%

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

      3. associate-*r* 76.7%

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

      4. *-commutative 76.7%

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

      5. associate-+l- 76.7%

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

   3. Simplified 76.7%

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

      1. associate-/r* 77.0%

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

      2. div-inv 76.9%

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

      3. associate-+l- 76.9%

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

      4. associate-*r* 71.7%

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

      5. associate-+l- 71.7%

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

      6. associate-*l* 71.6%

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

      7. associate-*r* 76.8%

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

   5. Applied egg-rr 76.8%

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

   6. Taylor expanded in z around inf 61.4%

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

      1. *-commutative 61.4%

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

      2. associate-/l* 64.0%

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

   8. Simplified 64.0%

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

   if -2.80000000000000012e-191 < b < 8.50000000000000003e-216

   1. Initial program 78.8%

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

      1. associate-+l- 78.8%

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

      2. *-commutative 78.8%

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

      3. associate-*r* 74.2%

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

      4. *-commutative 74.2%

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

      5. associate-+l- 74.2%

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

   3. Simplified 69.9%

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

   4. Taylor expanded in z around inf 53.1%

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

      1. *-commutative 53.1%

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

      2. associate-/l* 62.0%

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

   6. Simplified 62.0%

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

      1. associate-/r/ 57.9%

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

   8. Applied egg-rr 57.9%

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

   if 8.50000000000000003e-216 < b < 0.00279999999999999997

   1. Initial program 82.5%

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

      1. associate-+l- 82.5%

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

      2. *-commutative 82.5%

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

      3. associate-*r* 79.3%

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

      4. *-commutative 79.3%

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

      5. associate-+l- 79.3%

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

   3. Simplified 82.5%

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

   4. Taylor expanded in x around inf 68.6%

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

      1. associate-*r/ 68.6%

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

      2. *-commutative 68.6%

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

   6. Simplified 68.6%

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

   if 0.00279999999999999997 < b < 3.4999999999999999e227

   1. Initial program 82.2%

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

      1. associate-+l- 82.2%

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

      2. *-commutative 82.2%

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

      3. associate-*r* 77.1%

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

      4. *-commutative 77.1%

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

      5. associate-+l- 77.1%

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

   3. Simplified 77.0%

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

   4. Taylor expanded in z around inf 51.4%

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

      1. *-commutative 51.4%

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

      2. associate-/l* 58.2%

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

   6. Simplified 58.2%

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

      1. div-inv 58.2%

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

   8. Applied egg-rr 58.2%

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

   if 3.4999999999999999e227 < b

   1. Initial program 76.8%

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

      1. associate-+l- 76.8%

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

      2. *-commutative 76.8%

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

      3. associate-*r* 80.5%

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

      4. *-commutative 80.5%

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

      5. associate-+l- 80.5%

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

   3. Simplified 80.5%

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

   4. Taylor expanded in b around inf 72.4%

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

      1. associate-/r* 87.4%

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

   6. Simplified 87.4%

      \[\leadsto \color{blue}{\frac{\frac{b}{c}}{z}} \]
3. Recombined 7 regimes into one program.

4. Final simplification 66.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.8 \cdot 10^{+139}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;b \leq -6 \cdot 10^{+19}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{9}{\frac{c}{y}}\\ \mathbf{elif}\;b \leq -1.5 \cdot 10^{-178}:\\ \;\;\;\;-4 \cdot \frac{t}{\frac{c}{a}}\\ \mathbf{elif}\;b \leq -2.8 \cdot 10^{-191}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{9}{\frac{c}{y}}\\ \mathbf{elif}\;b \leq 8.5 \cdot 10^{-216}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;b \leq 0.0028:\\ \;\;\;\;\frac{9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \mathbf{elif}\;b \leq 3.5 \cdot 10^{+227}:\\ \;\;\;\;-4 \cdot \left(a \cdot \frac{1}{\frac{c}{t}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \end{array} \]

Alternative 9: 46.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} t_1 := \frac{x}{z} \cdot \frac{9}{\frac{c}{y}}\\ \mathbf{if}\;b \leq -4.7 \cdot 10^{+139}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;b \leq -2.8 \cdot 10^{+20}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -3.5 \cdot 10^{-178}:\\ \;\;\;\;-4 \cdot \frac{t}{\frac{c}{a}}\\ \mathbf{elif}\;b \leq -5.5 \cdot 10^{-203}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 1.7 \cdot 10^{-238}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;b \leq 0.0028:\\ \;\;\;\;\frac{9 \cdot x}{z \cdot \frac{c}{y}}\\ \mathbf{elif}\;b \leq 3.5 \cdot 10^{+227}:\\ \;\;\;\;-4 \cdot \left(a \cdot \frac{1}{\frac{c}{t}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \end{array} \end{array} \]

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 (* (/ x z) (/ 9.0 (/ c y)))))
   (if (<= b -4.7e+139)
     (/ b (* z c))
     (if (<= b -2.8e+20)
       t_1
       (if (<= b -3.5e-178)
         (* -4.0 (/ t (/ c a)))
         (if (<= b -5.5e-203)
           t_1
           (if (<= b 1.7e-238)
             (* -4.0 (/ a (/ c t)))
             (if (<= b 0.0028)
               (/ (* 9.0 x) (* z (/ c y)))
               (if (<= b 3.5e+227)
                 (* -4.0 (* a (/ 1.0 (/ c t))))
                 (/ (/ b c) z))))))))))

C

assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (x / z) * (9.0 / (c / y));
	double tmp;
	if (b <= -4.7e+139) {
		tmp = b / (z * c);
	} else if (b <= -2.8e+20) {
		tmp = t_1;
	} else if (b <= -3.5e-178) {
		tmp = -4.0 * (t / (c / a));
	} else if (b <= -5.5e-203) {
		tmp = t_1;
	} else if (b <= 1.7e-238) {
		tmp = -4.0 * (a / (c / t));
	} else if (b <= 0.0028) {
		tmp = (9.0 * x) / (z * (c / y));
	} else if (b <= 3.5e+227) {
		tmp = -4.0 * (a * (1.0 / (c / t)));
	} else {
		tmp = (b / c) / z;
	}
	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 = (x / z) * (9.0d0 / (c / y))
    if (b <= (-4.7d+139)) then
        tmp = b / (z * c)
    else if (b <= (-2.8d+20)) then
        tmp = t_1
    else if (b <= (-3.5d-178)) then
        tmp = (-4.0d0) * (t / (c / a))
    else if (b <= (-5.5d-203)) then
        tmp = t_1
    else if (b <= 1.7d-238) then
        tmp = (-4.0d0) * (a / (c / t))
    else if (b <= 0.0028d0) then
        tmp = (9.0d0 * x) / (z * (c / y))
    else if (b <= 3.5d+227) then
        tmp = (-4.0d0) * (a * (1.0d0 / (c / t)))
    else
        tmp = (b / c) / z
    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 = (x / z) * (9.0 / (c / y));
	double tmp;
	if (b <= -4.7e+139) {
		tmp = b / (z * c);
	} else if (b <= -2.8e+20) {
		tmp = t_1;
	} else if (b <= -3.5e-178) {
		tmp = -4.0 * (t / (c / a));
	} else if (b <= -5.5e-203) {
		tmp = t_1;
	} else if (b <= 1.7e-238) {
		tmp = -4.0 * (a / (c / t));
	} else if (b <= 0.0028) {
		tmp = (9.0 * x) / (z * (c / y));
	} else if (b <= 3.5e+227) {
		tmp = -4.0 * (a * (1.0 / (c / t)));
	} else {
		tmp = (b / c) / z;
	}
	return tmp;
}

Python

[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	t_1 = (x / z) * (9.0 / (c / y))
	tmp = 0
	if b <= -4.7e+139:
		tmp = b / (z * c)
	elif b <= -2.8e+20:
		tmp = t_1
	elif b <= -3.5e-178:
		tmp = -4.0 * (t / (c / a))
	elif b <= -5.5e-203:
		tmp = t_1
	elif b <= 1.7e-238:
		tmp = -4.0 * (a / (c / t))
	elif b <= 0.0028:
		tmp = (9.0 * x) / (z * (c / y))
	elif b <= 3.5e+227:
		tmp = -4.0 * (a * (1.0 / (c / t)))
	else:
		tmp = (b / c) / z
	return tmp

Julia

t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(x / z) * Float64(9.0 / Float64(c / y)))
	tmp = 0.0
	if (b <= -4.7e+139)
		tmp = Float64(b / Float64(z * c));
	elseif (b <= -2.8e+20)
		tmp = t_1;
	elseif (b <= -3.5e-178)
		tmp = Float64(-4.0 * Float64(t / Float64(c / a)));
	elseif (b <= -5.5e-203)
		tmp = t_1;
	elseif (b <= 1.7e-238)
		tmp = Float64(-4.0 * Float64(a / Float64(c / t)));
	elseif (b <= 0.0028)
		tmp = Float64(Float64(9.0 * x) / Float64(z * Float64(c / y)));
	elseif (b <= 3.5e+227)
		tmp = Float64(-4.0 * Float64(a * Float64(1.0 / Float64(c / t))));
	else
		tmp = Float64(Float64(b / c) / z);
	end
	return tmp
end

MATLAB

t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (x / z) * (9.0 / (c / y));
	tmp = 0.0;
	if (b <= -4.7e+139)
		tmp = b / (z * c);
	elseif (b <= -2.8e+20)
		tmp = t_1;
	elseif (b <= -3.5e-178)
		tmp = -4.0 * (t / (c / a));
	elseif (b <= -5.5e-203)
		tmp = t_1;
	elseif (b <= 1.7e-238)
		tmp = -4.0 * (a / (c / t));
	elseif (b <= 0.0028)
		tmp = (9.0 * x) / (z * (c / y));
	elseif (b <= 3.5e+227)
		tmp = -4.0 * (a * (1.0 / (c / t)));
	else
		tmp = (b / c) / z;
	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[(x / z), $MachinePrecision] * N[(9.0 / N[(c / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -4.7e+139], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -2.8e+20], t$95$1, If[LessEqual[b, -3.5e-178], N[(-4.0 * N[(t / N[(c / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -5.5e-203], t$95$1, If[LessEqual[b, 1.7e-238], N[(-4.0 * N[(a / N[(c / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 0.0028], N[(N[(9.0 * x), $MachinePrecision] / N[(z * N[(c / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.5e+227], N[(-4.0 * N[(a * N[(1.0 / N[(c / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if b < -4.7000000000000001e139

   1. Initial program 77.1%

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

      1. associate-+l- 77.1%

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

      2. *-commutative 77.1%

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

      3. associate-*r* 79.7%

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

      4. *-commutative 79.7%

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

      5. associate-+l- 79.7%

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

   3. Simplified 80.0%

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

   4. Taylor expanded in b around inf 74.2%

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

      1. *-commutative 74.2%

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

   6. Simplified 74.2%

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

   if -4.7000000000000001e139 < b < -2.8e20 or -3.49999999999999983e-178 < b < -5.5000000000000002e-203

   1. Initial program 90.0%

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

      1. associate-+l- 90.0%

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

      2. *-commutative 90.0%

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

      3. associate-*r* 90.3%

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

      4. *-commutative 90.3%

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

      5. associate-+l- 90.3%

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

   3. Simplified 90.3%

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

   4. Taylor expanded in x around inf 63.5%

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

      1. associate-*r/ 63.5%

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

      2. associate-*r* 63.5%

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

      3. *-commutative 63.5%

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

      4. associate-*r* 63.5%

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

      5. *-commutative 63.5%

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

      6. times-frac 69.9%

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

      7. associate-/l* 69.9%

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

   6. Simplified 69.9%

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

   if -2.8e20 < b < -3.49999999999999983e-178

   1. Initial program 73.8%

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

      1. associate-+l- 73.8%

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

      2. *-commutative 73.8%

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

      3. associate-*r* 76.7%

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

      4. *-commutative 76.7%

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

      5. associate-+l- 76.7%

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

   3. Simplified 76.7%

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

      1. associate-/r* 77.0%

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

      2. div-inv 76.9%

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

      3. associate-+l- 76.9%

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

      4. associate-*r* 71.7%

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

      5. associate-+l- 71.7%

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

      6. associate-*l* 71.6%

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

      7. associate-*r* 76.8%

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

   5. Applied egg-rr 76.8%

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

   6. Taylor expanded in z around inf 61.4%

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

      1. *-commutative 61.4%

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

      2. associate-/l* 64.0%

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

   8. Simplified 64.0%

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

   if -5.5000000000000002e-203 < b < 1.69999999999999992e-238

   1. Initial program 80.7%

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

      1. associate-+l- 80.7%

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

      2. *-commutative 80.7%

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

      3. associate-*r* 77.9%

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

      4. *-commutative 77.9%

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

      5. associate-+l- 77.9%

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

   3. Simplified 70.2%

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

   4. Taylor expanded in z around inf 53.5%

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

      1. *-commutative 53.5%

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

      2. associate-/l* 64.0%

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

   6. Simplified 64.0%

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

   if 1.69999999999999992e-238 < b < 0.00279999999999999997

   1. Initial program 80.2%

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

      1. associate-+l- 80.2%

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

      2. *-commutative 80.2%

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

      3. associate-*r* 75.1%

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

      4. *-commutative 75.1%

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

      5. associate-+l- 75.1%

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

   3. Simplified 80.2%

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

   4. Taylor expanded in x around inf 63.4%

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

      1. associate-*r/ 63.4%

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

      2. associate-*r* 63.5%

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

      3. *-commutative 63.5%

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

      4. associate-*r* 63.3%

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

      5. *-commutative 63.3%

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

      6. times-frac 63.4%

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

      7. associate-/l* 63.3%

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

   6. Simplified 63.3%

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

      1. frac-times 65.8%

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

   8. Applied egg-rr 65.8%

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

   if 0.00279999999999999997 < b < 3.4999999999999999e227

   1. Initial program 82.2%

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

      1. associate-+l- 82.2%

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

      2. *-commutative 82.2%

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

      3. associate-*r* 77.1%

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

      4. *-commutative 77.1%

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

      5. associate-+l- 77.1%

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

   3. Simplified 77.0%

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

   4. Taylor expanded in z around inf 51.4%

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

      1. *-commutative 51.4%

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

      2. associate-/l* 58.2%

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

   6. Simplified 58.2%

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

      1. div-inv 58.2%

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

   8. Applied egg-rr 58.2%

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

   if 3.4999999999999999e227 < b

   1. Initial program 76.8%

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

      1. associate-+l- 76.8%

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

      2. *-commutative 76.8%

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

      3. associate-*r* 80.5%

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

      4. *-commutative 80.5%

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

      5. associate-+l- 80.5%

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

   3. Simplified 80.5%

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

   4. Taylor expanded in b around inf 72.4%

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

      1. associate-/r* 87.4%

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

   6. Simplified 87.4%

      \[\leadsto \color{blue}{\frac{\frac{b}{c}}{z}} \]
3. Recombined 7 regimes into one program.

4. Final simplification 67.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.7 \cdot 10^{+139}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;b \leq -2.8 \cdot 10^{+20}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{9}{\frac{c}{y}}\\ \mathbf{elif}\;b \leq -3.5 \cdot 10^{-178}:\\ \;\;\;\;-4 \cdot \frac{t}{\frac{c}{a}}\\ \mathbf{elif}\;b \leq -5.5 \cdot 10^{-203}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{9}{\frac{c}{y}}\\ \mathbf{elif}\;b \leq 1.7 \cdot 10^{-238}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;b \leq 0.0028:\\ \;\;\;\;\frac{9 \cdot x}{z \cdot \frac{c}{y}}\\ \mathbf{elif}\;b \leq 3.5 \cdot 10^{+227}:\\ \;\;\;\;-4 \cdot \left(a \cdot \frac{1}{\frac{c}{t}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \end{array} \]

Alternative 10: 47.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} t_1 := \frac{x}{z} \cdot \frac{9}{\frac{c}{y}}\\ \mathbf{if}\;b \leq -6.2 \cdot 10^{+139}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;b \leq -7 \cdot 10^{+20}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -8.2 \cdot 10^{-178}:\\ \;\;\;\;-4 \cdot \frac{t}{\frac{c}{a}}\\ \mathbf{elif}\;b \leq -1.2 \cdot 10^{-194}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 4.5 \cdot 10^{-240}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;b \leq 0.0062:\\ \;\;\;\;\frac{9 \cdot x}{\frac{z}{\frac{y}{c}}}\\ \mathbf{elif}\;b \leq 3.5 \cdot 10^{+227}:\\ \;\;\;\;-4 \cdot \left(a \cdot \frac{1}{\frac{c}{t}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \end{array} \end{array} \]

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 (* (/ x z) (/ 9.0 (/ c y)))))
   (if (<= b -6.2e+139)
     (/ b (* z c))
     (if (<= b -7e+20)
       t_1
       (if (<= b -8.2e-178)
         (* -4.0 (/ t (/ c a)))
         (if (<= b -1.2e-194)
           t_1
           (if (<= b 4.5e-240)
             (* -4.0 (/ a (/ c t)))
             (if (<= b 0.0062)
               (/ (* 9.0 x) (/ z (/ y c)))
               (if (<= b 3.5e+227)
                 (* -4.0 (* a (/ 1.0 (/ c t))))
                 (/ (/ b c) z))))))))))

C

assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (x / z) * (9.0 / (c / y));
	double tmp;
	if (b <= -6.2e+139) {
		tmp = b / (z * c);
	} else if (b <= -7e+20) {
		tmp = t_1;
	} else if (b <= -8.2e-178) {
		tmp = -4.0 * (t / (c / a));
	} else if (b <= -1.2e-194) {
		tmp = t_1;
	} else if (b <= 4.5e-240) {
		tmp = -4.0 * (a / (c / t));
	} else if (b <= 0.0062) {
		tmp = (9.0 * x) / (z / (y / c));
	} else if (b <= 3.5e+227) {
		tmp = -4.0 * (a * (1.0 / (c / t)));
	} else {
		tmp = (b / c) / z;
	}
	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 = (x / z) * (9.0d0 / (c / y))
    if (b <= (-6.2d+139)) then
        tmp = b / (z * c)
    else if (b <= (-7d+20)) then
        tmp = t_1
    else if (b <= (-8.2d-178)) then
        tmp = (-4.0d0) * (t / (c / a))
    else if (b <= (-1.2d-194)) then
        tmp = t_1
    else if (b <= 4.5d-240) then
        tmp = (-4.0d0) * (a / (c / t))
    else if (b <= 0.0062d0) then
        tmp = (9.0d0 * x) / (z / (y / c))
    else if (b <= 3.5d+227) then
        tmp = (-4.0d0) * (a * (1.0d0 / (c / t)))
    else
        tmp = (b / c) / z
    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 = (x / z) * (9.0 / (c / y));
	double tmp;
	if (b <= -6.2e+139) {
		tmp = b / (z * c);
	} else if (b <= -7e+20) {
		tmp = t_1;
	} else if (b <= -8.2e-178) {
		tmp = -4.0 * (t / (c / a));
	} else if (b <= -1.2e-194) {
		tmp = t_1;
	} else if (b <= 4.5e-240) {
		tmp = -4.0 * (a / (c / t));
	} else if (b <= 0.0062) {
		tmp = (9.0 * x) / (z / (y / c));
	} else if (b <= 3.5e+227) {
		tmp = -4.0 * (a * (1.0 / (c / t)));
	} else {
		tmp = (b / c) / z;
	}
	return tmp;
}

Python

[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	t_1 = (x / z) * (9.0 / (c / y))
	tmp = 0
	if b <= -6.2e+139:
		tmp = b / (z * c)
	elif b <= -7e+20:
		tmp = t_1
	elif b <= -8.2e-178:
		tmp = -4.0 * (t / (c / a))
	elif b <= -1.2e-194:
		tmp = t_1
	elif b <= 4.5e-240:
		tmp = -4.0 * (a / (c / t))
	elif b <= 0.0062:
		tmp = (9.0 * x) / (z / (y / c))
	elif b <= 3.5e+227:
		tmp = -4.0 * (a * (1.0 / (c / t)))
	else:
		tmp = (b / c) / z
	return tmp

Julia

t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(x / z) * Float64(9.0 / Float64(c / y)))
	tmp = 0.0
	if (b <= -6.2e+139)
		tmp = Float64(b / Float64(z * c));
	elseif (b <= -7e+20)
		tmp = t_1;
	elseif (b <= -8.2e-178)
		tmp = Float64(-4.0 * Float64(t / Float64(c / a)));
	elseif (b <= -1.2e-194)
		tmp = t_1;
	elseif (b <= 4.5e-240)
		tmp = Float64(-4.0 * Float64(a / Float64(c / t)));
	elseif (b <= 0.0062)
		tmp = Float64(Float64(9.0 * x) / Float64(z / Float64(y / c)));
	elseif (b <= 3.5e+227)
		tmp = Float64(-4.0 * Float64(a * Float64(1.0 / Float64(c / t))));
	else
		tmp = Float64(Float64(b / c) / z);
	end
	return tmp
end

MATLAB

t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (x / z) * (9.0 / (c / y));
	tmp = 0.0;
	if (b <= -6.2e+139)
		tmp = b / (z * c);
	elseif (b <= -7e+20)
		tmp = t_1;
	elseif (b <= -8.2e-178)
		tmp = -4.0 * (t / (c / a));
	elseif (b <= -1.2e-194)
		tmp = t_1;
	elseif (b <= 4.5e-240)
		tmp = -4.0 * (a / (c / t));
	elseif (b <= 0.0062)
		tmp = (9.0 * x) / (z / (y / c));
	elseif (b <= 3.5e+227)
		tmp = -4.0 * (a * (1.0 / (c / t)));
	else
		tmp = (b / c) / z;
	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[(x / z), $MachinePrecision] * N[(9.0 / N[(c / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -6.2e+139], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -7e+20], t$95$1, If[LessEqual[b, -8.2e-178], N[(-4.0 * N[(t / N[(c / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -1.2e-194], t$95$1, If[LessEqual[b, 4.5e-240], N[(-4.0 * N[(a / N[(c / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 0.0062], N[(N[(9.0 * x), $MachinePrecision] / N[(z / N[(y / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.5e+227], N[(-4.0 * N[(a * N[(1.0 / N[(c / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if b < -6.2e139

   1. Initial program 77.1%

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

      1. associate-+l- 77.1%

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

      2. *-commutative 77.1%

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

      3. associate-*r* 79.7%

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

      4. *-commutative 79.7%

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

      5. associate-+l- 79.7%

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

   3. Simplified 80.0%

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

   4. Taylor expanded in b around inf 74.2%

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

      1. *-commutative 74.2%

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

   6. Simplified 74.2%

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

   if -6.2e139 < b < -7e20 or -8.1999999999999998e-178 < b < -1.2e-194

   1. Initial program 90.0%

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

      1. associate-+l- 90.0%

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

      2. *-commutative 90.0%

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

      3. associate-*r* 90.3%

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

      4. *-commutative 90.3%

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

      5. associate-+l- 90.3%

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

   3. Simplified 90.3%

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

   4. Taylor expanded in x around inf 63.5%

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

      1. associate-*r/ 63.5%

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

      2. associate-*r* 63.5%

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

      3. *-commutative 63.5%

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

      4. associate-*r* 63.5%

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

      5. *-commutative 63.5%

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

      6. times-frac 69.9%

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

      7. associate-/l* 69.9%

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

   6. Simplified 69.9%

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

   if -7e20 < b < -8.1999999999999998e-178

   1. Initial program 73.8%

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

      1. associate-+l- 73.8%

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

      2. *-commutative 73.8%

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

      3. associate-*r* 76.7%

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

      4. *-commutative 76.7%

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

      5. associate-+l- 76.7%

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

   3. Simplified 76.7%

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

      1. associate-/r* 77.0%

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

      2. div-inv 76.9%

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

      3. associate-+l- 76.9%

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

      4. associate-*r* 71.7%

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

      5. associate-+l- 71.7%

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

      6. associate-*l* 71.6%

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

      7. associate-*r* 76.8%

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

   5. Applied egg-rr 76.8%

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

   6. Taylor expanded in z around inf 61.4%

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

      1. *-commutative 61.4%

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

      2. associate-/l* 64.0%

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

   8. Simplified 64.0%

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

   if -1.2e-194 < b < 4.5000000000000001e-240

   1. Initial program 80.7%

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

      1. associate-+l- 80.7%

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

      2. *-commutative 80.7%

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

      3. associate-*r* 77.9%

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

      4. *-commutative 77.9%

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

      5. associate-+l- 77.9%

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

   3. Simplified 70.2%

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

   4. Taylor expanded in z around inf 53.5%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   5. Step-by-step derivation

      1. *-commutative 53.5%

         \[\leadsto \color{blue}{\frac{a \cdot t}{c} \cdot -4} \]

      2. associate-/l* 64.0%

         \[\leadsto \color{blue}{\frac{a}{\frac{c}{t}}} \cdot -4 \]

   6. Simplified 64.0%

      \[\leadsto \color{blue}{\frac{a}{\frac{c}{t}} \cdot -4} \]

   if 4.5000000000000001e-240 < b < 0.00619999999999999978

   1. Initial program 80.2%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 80.2%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 80.2%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 75.1%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 75.1%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 75.1%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

   3. Simplified 80.2%

      \[\leadsto \color{blue}{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Step-by-step derivation

      1. associate-/r* 80.3%

         \[\leadsto \color{blue}{\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z}}{c}} \]

      2. div-inv 80.3%

         \[\leadsto \color{blue}{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z} \cdot \frac{1}{c}} \]

      3. associate-+l- 80.3%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b\right)}}{z} \cdot \frac{1}{c} \]

      4. associate-*r* 80.3%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a} - b\right)}{z} \cdot \frac{1}{c} \]

      5. associate-+l- 80.3%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}}{z} \cdot \frac{1}{c} \]

      6. associate-*l* 80.1%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z} \cdot \frac{1}{c} \]

      7. associate-*r* 80.1%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z} \cdot \frac{1}{c} \]

   5. Applied egg-rr 80.1%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z} \cdot \frac{1}{c}} \]

   6. Taylor expanded in x around 0 92.3%

      \[\leadsto \color{blue}{\left(\left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right) - 4 \cdot \left(a \cdot t\right)\right)} \cdot \frac{1}{c} \]
   7. Step-by-step derivation

      1. cancel-sign-sub-inv 92.3%

         \[\leadsto \color{blue}{\left(\left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right) + \left(-4\right) \cdot \left(a \cdot t\right)\right)} \cdot \frac{1}{c} \]

      2. metadata-eval 92.3%

         \[\leadsto \left(\left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right) + \color{blue}{-4} \cdot \left(a \cdot t\right)\right) \cdot \frac{1}{c} \]

      3. +-commutative 92.3%

         \[\leadsto \color{blue}{\left(-4 \cdot \left(a \cdot t\right) + \left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right)\right)} \cdot \frac{1}{c} \]

      4. fma-def 92.3%

         \[\leadsto \color{blue}{\mathsf{fma}\left(-4, a \cdot t, 9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right)} \cdot \frac{1}{c} \]

      5. fma-def 92.3%

         \[\leadsto \mathsf{fma}\left(-4, a \cdot t, \color{blue}{\mathsf{fma}\left(9, \frac{x \cdot y}{z}, \frac{b}{z}\right)}\right) \cdot \frac{1}{c} \]

      6. associate-*r/ 94.7%

         \[\leadsto \mathsf{fma}\left(-4, a \cdot t, \mathsf{fma}\left(9, \color{blue}{x \cdot \frac{y}{z}}, \frac{b}{z}\right)\right) \cdot \frac{1}{c} \]

   8. Simplified 94.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-4, a \cdot t, \mathsf{fma}\left(9, x \cdot \frac{y}{z}, \frac{b}{z}\right)\right)} \cdot \frac{1}{c} \]

   9. Taylor expanded in x around inf 63.4%

      \[\leadsto \color{blue}{9 \cdot \frac{x \cdot y}{c \cdot z}} \]
   10. Step-by-step derivation

       1. associate-/l* 68.3%

          \[\leadsto 9 \cdot \color{blue}{\frac{x}{\frac{c \cdot z}{y}}} \]

       2. associate-*r/ 68.4%

          \[\leadsto \color{blue}{\frac{9 \cdot x}{\frac{c \cdot z}{y}}} \]

       3. *-commutative 68.4%

          \[\leadsto \frac{\color{blue}{x \cdot 9}}{\frac{c \cdot z}{y}} \]

       4. *-commutative 68.4%

          \[\leadsto \frac{x \cdot 9}{\frac{\color{blue}{z \cdot c}}{y}} \]

       5. associate-/l* 65.9%

          \[\leadsto \frac{x \cdot 9}{\color{blue}{\frac{z}{\frac{y}{c}}}} \]

   11. Simplified 65.9%

       \[\leadsto \color{blue}{\frac{x \cdot 9}{\frac{z}{\frac{y}{c}}}} \]

   if 0.00619999999999999978 < b < 3.4999999999999999e227

   1. Initial program 82.2%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 82.2%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 82.2%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 77.1%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 77.1%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 77.1%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

   3. Simplified 77.0%

      \[\leadsto \color{blue}{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]

   4. Taylor expanded in z around inf 51.4%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   5. Step-by-step derivation

      1. *-commutative 51.4%

         \[\leadsto \color{blue}{\frac{a \cdot t}{c} \cdot -4} \]

      2. associate-/l* 58.2%

         \[\leadsto \color{blue}{\frac{a}{\frac{c}{t}}} \cdot -4 \]

   6. Simplified 58.2%

      \[\leadsto \color{blue}{\frac{a}{\frac{c}{t}} \cdot -4} \]
   7. Step-by-step derivation

      1. div-inv 58.2%

         \[\leadsto \color{blue}{\left(a \cdot \frac{1}{\frac{c}{t}}\right)} \cdot -4 \]

   8. Applied egg-rr 58.2%

      \[\leadsto \color{blue}{\left(a \cdot \frac{1}{\frac{c}{t}}\right)} \cdot -4 \]

   if 3.4999999999999999e227 < b

   1. Initial program 76.8%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 76.8%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 76.8%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 80.5%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 80.5%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 80.5%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

   3. Simplified 80.5%

      \[\leadsto \color{blue}{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]

   4. Taylor expanded in b around inf 72.4%

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
   5. Step-by-step derivation

      1. associate-/r* 87.4%

         \[\leadsto \color{blue}{\frac{\frac{b}{c}}{z}} \]

   6. Simplified 87.4%

      \[\leadsto \color{blue}{\frac{\frac{b}{c}}{z}} \]
3. Recombined 7 regimes into one program.

4. Final simplification 67.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -6.2 \cdot 10^{+139}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;b \leq -7 \cdot 10^{+20}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{9}{\frac{c}{y}}\\ \mathbf{elif}\;b \leq -8.2 \cdot 10^{-178}:\\ \;\;\;\;-4 \cdot \frac{t}{\frac{c}{a}}\\ \mathbf{elif}\;b \leq -1.2 \cdot 10^{-194}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{9}{\frac{c}{y}}\\ \mathbf{elif}\;b \leq 4.5 \cdot 10^{-240}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;b \leq 0.0062:\\ \;\;\;\;\frac{9 \cdot x}{\frac{z}{\frac{y}{c}}}\\ \mathbf{elif}\;b \leq 3.5 \cdot 10^{+227}:\\ \;\;\;\;-4 \cdot \left(a \cdot \frac{1}{\frac{c}{t}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \end{array} \]

Alternative 11: 85.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{+107} \lor \neg \left(z \leq 1.5 \cdot 10^{+177}\right):\\ \;\;\;\;\frac{\frac{b}{z} + -4 \cdot \left(a \cdot t\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b - \left(a \cdot \left(t \cdot \left(z \cdot 4\right)\right) - y \cdot \left(9 \cdot x\right)\right)}{z \cdot c}\\ \end{array} \end{array} \]

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 -6e+107) (not (<= z 1.5e+177)))
   (/ (+ (/ b z) (* -4.0 (* a t))) c)
   (/ (- b (- (* a (* t (* z 4.0))) (* y (* 9.0 x)))) (* 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 <= -6e+107) || !(z <= 1.5e+177)) {
		tmp = ((b / z) + (-4.0 * (a * t))) / c;
	} else {
		tmp = (b - ((a * (t * (z * 4.0))) - (y * (9.0 * x)))) / (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 <= (-6d+107)) .or. (.not. (z <= 1.5d+177))) then
        tmp = ((b / z) + ((-4.0d0) * (a * t))) / c
    else
        tmp = (b - ((a * (t * (z * 4.0d0))) - (y * (9.0d0 * x)))) / (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 <= -6e+107) || !(z <= 1.5e+177)) {
		tmp = ((b / z) + (-4.0 * (a * t))) / c;
	} else {
		tmp = (b - ((a * (t * (z * 4.0))) - (y * (9.0 * x)))) / (z * c);
	}
	return tmp;
}

Python

[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if (z <= -6e+107) or not (z <= 1.5e+177):
		tmp = ((b / z) + (-4.0 * (a * t))) / c
	else:
		tmp = (b - ((a * (t * (z * 4.0))) - (y * (9.0 * x)))) / (z * c)
	return tmp

Julia

t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((z <= -6e+107) || !(z <= 1.5e+177))
		tmp = Float64(Float64(Float64(b / z) + Float64(-4.0 * Float64(a * t))) / c);
	else
		tmp = Float64(Float64(b - Float64(Float64(a * Float64(t * Float64(z * 4.0))) - Float64(y * Float64(9.0 * x)))) / 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 <= -6e+107) || ~((z <= 1.5e+177)))
		tmp = ((b / z) + (-4.0 * (a * t))) / c;
	else
		tmp = (b - ((a * (t * (z * 4.0))) - (y * (9.0 * x)))) / (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, -6e+107], N[Not[LessEqual[z, 1.5e+177]], $MachinePrecision]], N[(N[(N[(b / z), $MachinePrecision] + N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], N[(N[(b - N[(N[(a * N[(t * N[(z * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * N[(9.0 * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -6.00000000000000046e107 or 1.5e177 < z

   1. Initial program 44.7%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 44.7%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 44.7%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 41.7%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 41.7%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 41.7%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

   3. Simplified 45.0%

      \[\leadsto \color{blue}{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Step-by-step derivation

      1. associate-/r* 67.6%

         \[\leadsto \color{blue}{\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z}}{c}} \]

      2. div-inv 67.6%

         \[\leadsto \color{blue}{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z} \cdot \frac{1}{c}} \]

      3. associate-+l- 67.6%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b\right)}}{z} \cdot \frac{1}{c} \]

      4. associate-*r* 60.2%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a} - b\right)}{z} \cdot \frac{1}{c} \]

      5. associate-+l- 60.2%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}}{z} \cdot \frac{1}{c} \]

      6. associate-*l* 60.2%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z} \cdot \frac{1}{c} \]

      7. associate-*r* 67.5%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z} \cdot \frac{1}{c} \]

   5. Applied egg-rr 67.5%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z} \cdot \frac{1}{c}} \]

   6. Taylor expanded in x around 0 87.8%

      \[\leadsto \color{blue}{\left(\left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right) - 4 \cdot \left(a \cdot t\right)\right)} \cdot \frac{1}{c} \]
   7. Step-by-step derivation

      1. cancel-sign-sub-inv 87.8%

         \[\leadsto \color{blue}{\left(\left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right) + \left(-4\right) \cdot \left(a \cdot t\right)\right)} \cdot \frac{1}{c} \]

      2. metadata-eval 87.8%

         \[\leadsto \left(\left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right) + \color{blue}{-4} \cdot \left(a \cdot t\right)\right) \cdot \frac{1}{c} \]

      3. +-commutative 87.8%

         \[\leadsto \color{blue}{\left(-4 \cdot \left(a \cdot t\right) + \left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right)\right)} \cdot \frac{1}{c} \]

      4. fma-def 87.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(-4, a \cdot t, 9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right)} \cdot \frac{1}{c} \]

      5. fma-def 87.8%

         \[\leadsto \mathsf{fma}\left(-4, a \cdot t, \color{blue}{\mathsf{fma}\left(9, \frac{x \cdot y}{z}, \frac{b}{z}\right)}\right) \cdot \frac{1}{c} \]

      6. associate-*r/ 92.3%

         \[\leadsto \mathsf{fma}\left(-4, a \cdot t, \mathsf{fma}\left(9, \color{blue}{x \cdot \frac{y}{z}}, \frac{b}{z}\right)\right) \cdot \frac{1}{c} \]

   8. Simplified 92.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-4, a \cdot t, \mathsf{fma}\left(9, x \cdot \frac{y}{z}, \frac{b}{z}\right)\right)} \cdot \frac{1}{c} \]

   9. Taylor expanded in x around 0 83.5%

      \[\leadsto \color{blue}{\frac{-4 \cdot \left(a \cdot t\right) + \frac{b}{z}}{c}} \]

   if -6.00000000000000046e107 < z < 1.5e177

   1. Initial program 92.3%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
3. Recombined 2 regimes into one program.

4. Final simplification 90.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{+107} \lor \neg \left(z \leq 1.5 \cdot 10^{+177}\right):\\ \;\;\;\;\frac{\frac{b}{z} + -4 \cdot \left(a \cdot t\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b - \left(a \cdot \left(t \cdot \left(z \cdot 4\right)\right) - y \cdot \left(9 \cdot x\right)\right)}{z \cdot c}\\ \end{array} \]

Alternative 12: 83.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} t_1 := -4 \cdot \left(a \cdot t\right)\\ \mathbf{if}\;z \leq -1.05 \cdot 10^{+71}:\\ \;\;\;\;\frac{t_1 + 9 \cdot \frac{x \cdot y}{z}}{c}\\ \mathbf{elif}\;z \leq 2.55 \cdot 10^{+174}:\\ \;\;\;\;\frac{b - \left(\left(a \cdot t\right) \cdot \left(z \cdot 4\right) - y \cdot \left(9 \cdot x\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{z} + t_1}{c}\\ \end{array} \end{array} \]

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
 (let* ((t_1 (* -4.0 (* a t))))
   (if (<= z -1.05e+71)
     (/ (+ t_1 (* 9.0 (/ (* x y) z))) c)
     (if (<= z 2.55e+174)
       (/ (- b (- (* (* a t) (* z 4.0)) (* y (* 9.0 x)))) (* z c))
       (/ (+ (/ b z) t_1) c)))))

C

assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = -4.0 * (a * t);
	double tmp;
	if (z <= -1.05e+71) {
		tmp = (t_1 + (9.0 * ((x * y) / z))) / c;
	} else if (z <= 2.55e+174) {
		tmp = (b - (((a * t) * (z * 4.0)) - (y * (9.0 * x)))) / (z * c);
	} else {
		tmp = ((b / z) + t_1) / 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 = (-4.0d0) * (a * t)
    if (z <= (-1.05d+71)) then
        tmp = (t_1 + (9.0d0 * ((x * y) / z))) / c
    else if (z <= 2.55d+174) then
        tmp = (b - (((a * t) * (z * 4.0d0)) - (y * (9.0d0 * x)))) / (z * c)
    else
        tmp = ((b / z) + t_1) / 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 = -4.0 * (a * t);
	double tmp;
	if (z <= -1.05e+71) {
		tmp = (t_1 + (9.0 * ((x * y) / z))) / c;
	} else if (z <= 2.55e+174) {
		tmp = (b - (((a * t) * (z * 4.0)) - (y * (9.0 * x)))) / (z * c);
	} else {
		tmp = ((b / z) + t_1) / c;
	}
	return tmp;
}

Python

[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	t_1 = -4.0 * (a * t)
	tmp = 0
	if z <= -1.05e+71:
		tmp = (t_1 + (9.0 * ((x * y) / z))) / c
	elif z <= 2.55e+174:
		tmp = (b - (((a * t) * (z * 4.0)) - (y * (9.0 * x)))) / (z * c)
	else:
		tmp = ((b / z) + t_1) / c
	return tmp

Julia

t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(-4.0 * Float64(a * t))
	tmp = 0.0
	if (z <= -1.05e+71)
		tmp = Float64(Float64(t_1 + Float64(9.0 * Float64(Float64(x * y) / z))) / c);
	elseif (z <= 2.55e+174)
		tmp = Float64(Float64(b - Float64(Float64(Float64(a * t) * Float64(z * 4.0)) - Float64(y * Float64(9.0 * x)))) / Float64(z * c));
	else
		tmp = Float64(Float64(Float64(b / z) + t_1) / 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 = -4.0 * (a * t);
	tmp = 0.0;
	if (z <= -1.05e+71)
		tmp = (t_1 + (9.0 * ((x * y) / z))) / c;
	elseif (z <= 2.55e+174)
		tmp = (b - (((a * t) * (z * 4.0)) - (y * (9.0 * x)))) / (z * c);
	else
		tmp = ((b / z) + t_1) / 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[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.05e+71], N[(N[(t$95$1 + N[(9.0 * N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[z, 2.55e+174], N[(N[(b - N[(N[(N[(a * t), $MachinePrecision] * N[(z * 4.0), $MachinePrecision]), $MachinePrecision] - N[(y * N[(9.0 * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(N[(N[(b / z), $MachinePrecision] + t$95$1), $MachinePrecision] / c), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.04999999999999995e71

   1. Initial program 52.1%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 52.1%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 52.1%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 46.1%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 46.1%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 46.1%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

   3. Simplified 50.6%

      \[\leadsto \color{blue}{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Step-by-step derivation

      1. associate-/r* 71.1%

         \[\leadsto \color{blue}{\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z}}{c}} \]

      2. div-inv 71.1%

         \[\leadsto \color{blue}{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z} \cdot \frac{1}{c}} \]

      3. associate-+l- 71.1%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b\right)}}{z} \cdot \frac{1}{c} \]

      4. associate-*r* 64.9%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a} - b\right)}{z} \cdot \frac{1}{c} \]

      5. associate-+l- 64.9%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}}{z} \cdot \frac{1}{c} \]

      6. associate-*l* 64.9%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z} \cdot \frac{1}{c} \]

      7. associate-*r* 71.1%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z} \cdot \frac{1}{c} \]

   5. Applied egg-rr 71.1%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z} \cdot \frac{1}{c}} \]

   6. Taylor expanded in x around 0 87.3%

      \[\leadsto \color{blue}{\left(\left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right) - 4 \cdot \left(a \cdot t\right)\right)} \cdot \frac{1}{c} \]
   7. Step-by-step derivation

      1. cancel-sign-sub-inv 87.3%

         \[\leadsto \color{blue}{\left(\left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right) + \left(-4\right) \cdot \left(a \cdot t\right)\right)} \cdot \frac{1}{c} \]

      2. metadata-eval 87.3%

         \[\leadsto \left(\left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right) + \color{blue}{-4} \cdot \left(a \cdot t\right)\right) \cdot \frac{1}{c} \]

      3. +-commutative 87.3%

         \[\leadsto \color{blue}{\left(-4 \cdot \left(a \cdot t\right) + \left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right)\right)} \cdot \frac{1}{c} \]

      4. fma-def 87.3%

         \[\leadsto \color{blue}{\mathsf{fma}\left(-4, a \cdot t, 9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right)} \cdot \frac{1}{c} \]

      5. fma-def 87.4%

         \[\leadsto \mathsf{fma}\left(-4, a \cdot t, \color{blue}{\mathsf{fma}\left(9, \frac{x \cdot y}{z}, \frac{b}{z}\right)}\right) \cdot \frac{1}{c} \]

      6. associate-*r/ 91.5%

         \[\leadsto \mathsf{fma}\left(-4, a \cdot t, \mathsf{fma}\left(9, \color{blue}{x \cdot \frac{y}{z}}, \frac{b}{z}\right)\right) \cdot \frac{1}{c} \]

   8. Simplified 91.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-4, a \cdot t, \mathsf{fma}\left(9, x \cdot \frac{y}{z}, \frac{b}{z}\right)\right)} \cdot \frac{1}{c} \]

   9. Taylor expanded in b around 0 77.3%

      \[\leadsto \color{blue}{\frac{-4 \cdot \left(a \cdot t\right) + 9 \cdot \frac{x \cdot y}{z}}{c}} \]

   if -1.04999999999999995e71 < z < 2.5499999999999999e174

   1. Initial program 92.9%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 92.9%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 92.9%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 92.9%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 92.9%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 92.9%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

   3. Simplified 90.8%

      \[\leadsto \color{blue}{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]

   if 2.5499999999999999e174 < z

   1. Initial program 46.9%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 46.9%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 46.9%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 46.8%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 46.8%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 46.8%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

   3. Simplified 50.2%

      \[\leadsto \color{blue}{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Step-by-step derivation

      1. associate-/r* 67.6%

         \[\leadsto \color{blue}{\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z}}{c}} \]

      2. div-inv 67.5%

         \[\leadsto \color{blue}{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z} \cdot \frac{1}{c}} \]

      3. associate-+l- 67.5%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b\right)}}{z} \cdot \frac{1}{c} \]

      4. associate-*r* 61.1%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a} - b\right)}{z} \cdot \frac{1}{c} \]

      5. associate-+l- 61.1%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}}{z} \cdot \frac{1}{c} \]

      6. associate-*l* 61.1%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z} \cdot \frac{1}{c} \]

      7. associate-*r* 67.5%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z} \cdot \frac{1}{c} \]

   5. Applied egg-rr 67.5%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z} \cdot \frac{1}{c}} \]

   6. Taylor expanded in x around 0 93.0%

      \[\leadsto \color{blue}{\left(\left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right) - 4 \cdot \left(a \cdot t\right)\right)} \cdot \frac{1}{c} \]
   7. Step-by-step derivation

      1. cancel-sign-sub-inv 93.0%

         \[\leadsto \color{blue}{\left(\left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right) + \left(-4\right) \cdot \left(a \cdot t\right)\right)} \cdot \frac{1}{c} \]

      2. metadata-eval 93.0%

         \[\leadsto \left(\left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right) + \color{blue}{-4} \cdot \left(a \cdot t\right)\right) \cdot \frac{1}{c} \]

      3. +-commutative 93.0%

         \[\leadsto \color{blue}{\left(-4 \cdot \left(a \cdot t\right) + \left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right)\right)} \cdot \frac{1}{c} \]

      4. fma-def 93.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(-4, a \cdot t, 9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right)} \cdot \frac{1}{c} \]

      5. fma-def 93.0%

         \[\leadsto \mathsf{fma}\left(-4, a \cdot t, \color{blue}{\mathsf{fma}\left(9, \frac{x \cdot y}{z}, \frac{b}{z}\right)}\right) \cdot \frac{1}{c} \]

      6. associate-*r/ 96.4%

         \[\leadsto \mathsf{fma}\left(-4, a \cdot t, \mathsf{fma}\left(9, \color{blue}{x \cdot \frac{y}{z}}, \frac{b}{z}\right)\right) \cdot \frac{1}{c} \]

   8. Simplified 96.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-4, a \cdot t, \mathsf{fma}\left(9, x \cdot \frac{y}{z}, \frac{b}{z}\right)\right)} \cdot \frac{1}{c} \]

   9. Taylor expanded in x around 0 93.2%

      \[\leadsto \color{blue}{\frac{-4 \cdot \left(a \cdot t\right) + \frac{b}{z}}{c}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 88.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{+71}:\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right) + 9 \cdot \frac{x \cdot y}{z}}{c}\\ \mathbf{elif}\;z \leq 2.55 \cdot 10^{+174}:\\ \;\;\;\;\frac{b - \left(\left(a \cdot t\right) \cdot \left(z \cdot 4\right) - y \cdot \left(9 \cdot x\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{z} + -4 \cdot \left(a \cdot t\right)}{c}\\ \end{array} \]

Alternative 13: 46.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} t_1 := 9 \cdot \frac{x \cdot y}{z \cdot c}\\ \mathbf{if}\;b \leq -7.4 \cdot 10^{+142}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;b \leq -2.85 \cdot 10^{+17}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -3.25 \cdot 10^{-170}:\\ \;\;\;\;-4 \cdot \frac{t}{\frac{c}{a}}\\ \mathbf{elif}\;b \leq -4.8 \cdot 10^{-229}:\\ \;\;\;\;y \cdot \frac{9}{\frac{c}{\frac{x}{z}}}\\ \mathbf{elif}\;b \leq 8.5 \cdot 10^{-216}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;b \leq 0.0048:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 2.1 \cdot 10^{+228}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \end{array} \end{array} \]

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 y) (* z c)))))
   (if (<= b -7.4e+142)
     (/ b (* z c))
     (if (<= b -2.85e+17)
       t_1
       (if (<= b -3.25e-170)
         (* -4.0 (/ t (/ c a)))
         (if (<= b -4.8e-229)
           (* y (/ 9.0 (/ c (/ x z))))
           (if (<= b 8.5e-216)
             (* -4.0 (* t (/ a c)))
             (if (<= b 0.0048)
               t_1
               (if (<= b 2.1e+228)
                 (* -4.0 (/ a (/ c t)))
                 (/ (/ b c) z))))))))))

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 * y) / (z * c));
	double tmp;
	if (b <= -7.4e+142) {
		tmp = b / (z * c);
	} else if (b <= -2.85e+17) {
		tmp = t_1;
	} else if (b <= -3.25e-170) {
		tmp = -4.0 * (t / (c / a));
	} else if (b <= -4.8e-229) {
		tmp = y * (9.0 / (c / (x / z)));
	} else if (b <= 8.5e-216) {
		tmp = -4.0 * (t * (a / c));
	} else if (b <= 0.0048) {
		tmp = t_1;
	} else if (b <= 2.1e+228) {
		tmp = -4.0 * (a / (c / t));
	} else {
		tmp = (b / c) / z;
	}
	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 * y) / (z * c))
    if (b <= (-7.4d+142)) then
        tmp = b / (z * c)
    else if (b <= (-2.85d+17)) then
        tmp = t_1
    else if (b <= (-3.25d-170)) then
        tmp = (-4.0d0) * (t / (c / a))
    else if (b <= (-4.8d-229)) then
        tmp = y * (9.0d0 / (c / (x / z)))
    else if (b <= 8.5d-216) then
        tmp = (-4.0d0) * (t * (a / c))
    else if (b <= 0.0048d0) then
        tmp = t_1
    else if (b <= 2.1d+228) then
        tmp = (-4.0d0) * (a / (c / t))
    else
        tmp = (b / c) / z
    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 * y) / (z * c));
	double tmp;
	if (b <= -7.4e+142) {
		tmp = b / (z * c);
	} else if (b <= -2.85e+17) {
		tmp = t_1;
	} else if (b <= -3.25e-170) {
		tmp = -4.0 * (t / (c / a));
	} else if (b <= -4.8e-229) {
		tmp = y * (9.0 / (c / (x / z)));
	} else if (b <= 8.5e-216) {
		tmp = -4.0 * (t * (a / c));
	} else if (b <= 0.0048) {
		tmp = t_1;
	} else if (b <= 2.1e+228) {
		tmp = -4.0 * (a / (c / t));
	} else {
		tmp = (b / c) / z;
	}
	return tmp;
}

Python

[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	t_1 = 9.0 * ((x * y) / (z * c))
	tmp = 0
	if b <= -7.4e+142:
		tmp = b / (z * c)
	elif b <= -2.85e+17:
		tmp = t_1
	elif b <= -3.25e-170:
		tmp = -4.0 * (t / (c / a))
	elif b <= -4.8e-229:
		tmp = y * (9.0 / (c / (x / z)))
	elif b <= 8.5e-216:
		tmp = -4.0 * (t * (a / c))
	elif b <= 0.0048:
		tmp = t_1
	elif b <= 2.1e+228:
		tmp = -4.0 * (a / (c / t))
	else:
		tmp = (b / c) / z
	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 * y) / Float64(z * c)))
	tmp = 0.0
	if (b <= -7.4e+142)
		tmp = Float64(b / Float64(z * c));
	elseif (b <= -2.85e+17)
		tmp = t_1;
	elseif (b <= -3.25e-170)
		tmp = Float64(-4.0 * Float64(t / Float64(c / a)));
	elseif (b <= -4.8e-229)
		tmp = Float64(y * Float64(9.0 / Float64(c / Float64(x / z))));
	elseif (b <= 8.5e-216)
		tmp = Float64(-4.0 * Float64(t * Float64(a / c)));
	elseif (b <= 0.0048)
		tmp = t_1;
	elseif (b <= 2.1e+228)
		tmp = Float64(-4.0 * Float64(a / Float64(c / t)));
	else
		tmp = Float64(Float64(b / c) / z);
	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 * y) / (z * c));
	tmp = 0.0;
	if (b <= -7.4e+142)
		tmp = b / (z * c);
	elseif (b <= -2.85e+17)
		tmp = t_1;
	elseif (b <= -3.25e-170)
		tmp = -4.0 * (t / (c / a));
	elseif (b <= -4.8e-229)
		tmp = y * (9.0 / (c / (x / z)));
	elseif (b <= 8.5e-216)
		tmp = -4.0 * (t * (a / c));
	elseif (b <= 0.0048)
		tmp = t_1;
	elseif (b <= 2.1e+228)
		tmp = -4.0 * (a / (c / t));
	else
		tmp = (b / c) / z;
	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 * y), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -7.4e+142], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -2.85e+17], t$95$1, If[LessEqual[b, -3.25e-170], N[(-4.0 * N[(t / N[(c / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -4.8e-229], N[(y * N[(9.0 / N[(c / N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 8.5e-216], N[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 0.0048], t$95$1, If[LessEqual[b, 2.1e+228], N[(-4.0 * N[(a / N[(c / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if b < -7.3999999999999995e142

   1. Initial program 77.1%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 77.1%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 77.1%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 79.7%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 79.7%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 79.7%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

   3. Simplified 80.0%

      \[\leadsto \color{blue}{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]

   4. Taylor expanded in b around inf 74.2%

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
   5. Step-by-step derivation

      1. *-commutative 74.2%

         \[\leadsto \frac{b}{\color{blue}{z \cdot c}} \]

   6. Simplified 74.2%

      \[\leadsto \color{blue}{\frac{b}{z \cdot c}} \]

   if -7.3999999999999995e142 < b < -2.85e17 or 8.50000000000000003e-216 < b < 0.00479999999999999958

   1. Initial program 87.7%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 87.7%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 87.7%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 86.0%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 86.0%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 86.0%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

   3. Simplified 87.9%

      \[\leadsto \color{blue}{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]

   4. Taylor expanded in x around inf 66.5%

      \[\leadsto \color{blue}{9 \cdot \frac{x \cdot y}{c \cdot z}} \]

   if -2.85e17 < b < -3.25000000000000018e-170

   1. Initial program 72.4%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 72.4%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 72.4%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 75.4%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 75.4%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 75.4%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

   3. Simplified 75.4%

      \[\leadsto \color{blue}{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Step-by-step derivation

      1. associate-/r* 75.7%

         \[\leadsto \color{blue}{\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z}}{c}} \]

      2. div-inv 75.7%

         \[\leadsto \color{blue}{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z} \cdot \frac{1}{c}} \]

      3. associate-+l- 75.7%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b\right)}}{z} \cdot \frac{1}{c} \]

      4. associate-*r* 70.2%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a} - b\right)}{z} \cdot \frac{1}{c} \]

      5. associate-+l- 70.2%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}}{z} \cdot \frac{1}{c} \]

      6. associate-*l* 70.1%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z} \cdot \frac{1}{c} \]

      7. associate-*r* 75.6%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z} \cdot \frac{1}{c} \]

   5. Applied egg-rr 75.6%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z} \cdot \frac{1}{c}} \]

   6. Taylor expanded in z around inf 62.0%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   7. Step-by-step derivation

      1. *-commutative 62.0%

         \[\leadsto -4 \cdot \frac{\color{blue}{t \cdot a}}{c} \]

      2. associate-/l* 64.7%

         \[\leadsto -4 \cdot \color{blue}{\frac{t}{\frac{c}{a}}} \]

   8. Simplified 64.7%

      \[\leadsto \color{blue}{-4 \cdot \frac{t}{\frac{c}{a}}} \]

   if -3.25000000000000018e-170 < b < -4.8e-229

   1. Initial program 83.4%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 83.4%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 83.4%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 83.5%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 83.5%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 83.5%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

   3. Simplified 83.5%

      \[\leadsto \color{blue}{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Step-by-step derivation

      1. associate-/r* 88.6%

         \[\leadsto \color{blue}{\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z}}{c}} \]

      2. div-inv 88.6%

         \[\leadsto \color{blue}{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z} \cdot \frac{1}{c}} \]

      3. associate-+l- 88.6%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b\right)}}{z} \cdot \frac{1}{c} \]

      4. associate-*r* 88.6%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a} - b\right)}{z} \cdot \frac{1}{c} \]

      5. associate-+l- 88.6%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}}{z} \cdot \frac{1}{c} \]

      6. associate-*l* 88.6%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z} \cdot \frac{1}{c} \]

      7. associate-*r* 88.7%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z} \cdot \frac{1}{c} \]

   5. Applied egg-rr 88.7%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z} \cdot \frac{1}{c}} \]

   6. Taylor expanded in x around 0 88.6%

      \[\leadsto \color{blue}{\left(\left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right) - 4 \cdot \left(a \cdot t\right)\right)} \cdot \frac{1}{c} \]
   7. Step-by-step derivation

      1. cancel-sign-sub-inv 88.6%

         \[\leadsto \color{blue}{\left(\left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right) + \left(-4\right) \cdot \left(a \cdot t\right)\right)} \cdot \frac{1}{c} \]

      2. metadata-eval 88.6%

         \[\leadsto \left(\left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right) + \color{blue}{-4} \cdot \left(a \cdot t\right)\right) \cdot \frac{1}{c} \]

      3. +-commutative 88.6%

         \[\leadsto \color{blue}{\left(-4 \cdot \left(a \cdot t\right) + \left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right)\right)} \cdot \frac{1}{c} \]

      4. fma-def 88.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(-4, a \cdot t, 9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right)} \cdot \frac{1}{c} \]

      5. fma-def 88.6%

         \[\leadsto \mathsf{fma}\left(-4, a \cdot t, \color{blue}{\mathsf{fma}\left(9, \frac{x \cdot y}{z}, \frac{b}{z}\right)}\right) \cdot \frac{1}{c} \]

      6. associate-*r/ 83.2%

         \[\leadsto \mathsf{fma}\left(-4, a \cdot t, \mathsf{fma}\left(9, \color{blue}{x \cdot \frac{y}{z}}, \frac{b}{z}\right)\right) \cdot \frac{1}{c} \]

   8. Simplified 83.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-4, a \cdot t, \mathsf{fma}\left(9, x \cdot \frac{y}{z}, \frac{b}{z}\right)\right)} \cdot \frac{1}{c} \]

   9. Taylor expanded in z around -inf 74.7%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c} + -1 \cdot \frac{-9 \cdot \frac{x \cdot y}{c} + -1 \cdot \frac{b}{c}}{z}} \]
   10. Step-by-step derivation

       1. associate-*l/ 75.0%

          \[\leadsto -4 \cdot \color{blue}{\left(\frac{a}{c} \cdot t\right)} + -1 \cdot \frac{-9 \cdot \frac{x \cdot y}{c} + -1 \cdot \frac{b}{c}}{z} \]

       2. mul-1-neg 75.0%

          \[\leadsto -4 \cdot \left(\frac{a}{c} \cdot t\right) + \color{blue}{\left(-\frac{-9 \cdot \frac{x \cdot y}{c} + -1 \cdot \frac{b}{c}}{z}\right)} \]

       3. unsub-neg 75.0%

          \[\leadsto \color{blue}{-4 \cdot \left(\frac{a}{c} \cdot t\right) - \frac{-9 \cdot \frac{x \cdot y}{c} + -1 \cdot \frac{b}{c}}{z}} \]

       4. associate-*l/ 74.7%

          \[\leadsto -4 \cdot \color{blue}{\frac{a \cdot t}{c}} - \frac{-9 \cdot \frac{x \cdot y}{c} + -1 \cdot \frac{b}{c}}{z} \]

       5. mul-1-neg 74.7%

          \[\leadsto -4 \cdot \frac{a \cdot t}{c} - \frac{-9 \cdot \frac{x \cdot y}{c} + \color{blue}{\left(-\frac{b}{c}\right)}}{z} \]

       6. unsub-neg 74.7%

          \[\leadsto -4 \cdot \frac{a \cdot t}{c} - \frac{\color{blue}{-9 \cdot \frac{x \cdot y}{c} - \frac{b}{c}}}{z} \]

       7. *-rgt-identity 74.7%

          \[\leadsto -4 \cdot \frac{a \cdot t}{c} - \frac{-9 \cdot \frac{\color{blue}{\left(x \cdot y\right) \cdot 1}}{c} - \frac{b}{c}}{z} \]

       8. associate-*r/ 74.7%

          \[\leadsto -4 \cdot \frac{a \cdot t}{c} - \frac{-9 \cdot \color{blue}{\left(\left(x \cdot y\right) \cdot \frac{1}{c}\right)} - \frac{b}{c}}{z} \]

       9. associate-*l* 78.0%

          \[\leadsto -4 \cdot \frac{a \cdot t}{c} - \frac{-9 \cdot \color{blue}{\left(x \cdot \left(y \cdot \frac{1}{c}\right)\right)} - \frac{b}{c}}{z} \]

       10. associate-*r/ 78.0%

           \[\leadsto -4 \cdot \frac{a \cdot t}{c} - \frac{-9 \cdot \left(x \cdot \color{blue}{\frac{y \cdot 1}{c}}\right) - \frac{b}{c}}{z} \]

       11. *-rgt-identity 78.0%

           \[\leadsto -4 \cdot \frac{a \cdot t}{c} - \frac{-9 \cdot \left(x \cdot \frac{\color{blue}{y}}{c}\right) - \frac{b}{c}}{z} \]

   11. Simplified 78.0%

       \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c} - \frac{-9 \cdot \left(x \cdot \frac{y}{c}\right) - \frac{b}{c}}{z}} \]

   12. Taylor expanded in x around inf 48.6%

       \[\leadsto \color{blue}{9 \cdot \frac{x \cdot y}{c \cdot z}} \]
   13. Step-by-step derivation

       1. *-commutative 48.6%

          \[\leadsto 9 \cdot \frac{x \cdot y}{\color{blue}{z \cdot c}} \]

       2. times-frac 59.2%

          \[\leadsto 9 \cdot \color{blue}{\left(\frac{x}{z} \cdot \frac{y}{c}\right)} \]

       3. associate-*l* 59.2%

          \[\leadsto \color{blue}{\left(9 \cdot \frac{x}{z}\right) \cdot \frac{y}{c}} \]

       4. *-commutative 59.2%

          \[\leadsto \color{blue}{\left(\frac{x}{z} \cdot 9\right)} \cdot \frac{y}{c} \]

       5. associate-*r/ 53.9%

          \[\leadsto \color{blue}{\frac{\left(\frac{x}{z} \cdot 9\right) \cdot y}{c}} \]

       6. associate-*l/ 59.1%

          \[\leadsto \color{blue}{\frac{\frac{x}{z} \cdot 9}{c} \cdot y} \]

       7. *-commutative 59.1%

          \[\leadsto \color{blue}{y \cdot \frac{\frac{x}{z} \cdot 9}{c}} \]

       8. *-commutative 59.1%

          \[\leadsto y \cdot \frac{\color{blue}{9 \cdot \frac{x}{z}}}{c} \]

       9. associate-/l* 59.4%

          \[\leadsto y \cdot \color{blue}{\frac{9}{\frac{c}{\frac{x}{z}}}} \]

   14. Simplified 59.4%

       \[\leadsto \color{blue}{y \cdot \frac{9}{\frac{c}{\frac{x}{z}}}} \]

   if -4.8e-229 < b < 8.50000000000000003e-216

   1. Initial program 76.7%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 76.7%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 76.7%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 70.9%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 70.9%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 70.9%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

   3. Simplified 65.6%

      \[\leadsto \color{blue}{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]

   4. Taylor expanded in z around inf 56.1%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   5. Step-by-step derivation

      1. *-commutative 56.1%

         \[\leadsto \color{blue}{\frac{a \cdot t}{c} \cdot -4} \]

      2. associate-/l* 67.1%

         \[\leadsto \color{blue}{\frac{a}{\frac{c}{t}}} \cdot -4 \]

   6. Simplified 67.1%

      \[\leadsto \color{blue}{\frac{a}{\frac{c}{t}} \cdot -4} \]
   7. Step-by-step derivation

      1. associate-/r/ 62.0%

         \[\leadsto \color{blue}{\left(\frac{a}{c} \cdot t\right)} \cdot -4 \]

   8. Applied egg-rr 62.0%

      \[\leadsto \color{blue}{\left(\frac{a}{c} \cdot t\right)} \cdot -4 \]

   if 0.00479999999999999958 < b < 2.09999999999999994e228

   1. Initial program 82.2%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 82.2%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 82.2%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 77.1%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 77.1%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 77.1%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

   3. Simplified 77.0%

      \[\leadsto \color{blue}{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]

   4. Taylor expanded in z around inf 51.4%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   5. Step-by-step derivation

      1. *-commutative 51.4%

         \[\leadsto \color{blue}{\frac{a \cdot t}{c} \cdot -4} \]

      2. associate-/l* 58.2%

         \[\leadsto \color{blue}{\frac{a}{\frac{c}{t}}} \cdot -4 \]

   6. Simplified 58.2%

      \[\leadsto \color{blue}{\frac{a}{\frac{c}{t}} \cdot -4} \]

   if 2.09999999999999994e228 < b

   1. Initial program 76.8%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 76.8%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 76.8%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 80.5%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 80.5%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 80.5%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

   3. Simplified 80.5%

      \[\leadsto \color{blue}{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]

   4. Taylor expanded in b around inf 72.4%

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
   5. Step-by-step derivation

      1. associate-/r* 87.4%

         \[\leadsto \color{blue}{\frac{\frac{b}{c}}{z}} \]

   6. Simplified 87.4%

      \[\leadsto \color{blue}{\frac{\frac{b}{c}}{z}} \]
3. Recombined 7 regimes into one program.

4. Final simplification 66.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -7.4 \cdot 10^{+142}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;b \leq -2.85 \cdot 10^{+17}:\\ \;\;\;\;9 \cdot \frac{x \cdot y}{z \cdot c}\\ \mathbf{elif}\;b \leq -3.25 \cdot 10^{-170}:\\ \;\;\;\;-4 \cdot \frac{t}{\frac{c}{a}}\\ \mathbf{elif}\;b \leq -4.8 \cdot 10^{-229}:\\ \;\;\;\;y \cdot \frac{9}{\frac{c}{\frac{x}{z}}}\\ \mathbf{elif}\;b \leq 8.5 \cdot 10^{-216}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;b \leq 0.0048:\\ \;\;\;\;9 \cdot \frac{x \cdot y}{z \cdot c}\\ \mathbf{elif}\;b \leq 2.1 \cdot 10^{+228}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \end{array} \]

Alternative 14: 75.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} t_1 := -4 \cdot \left(a \cdot t\right)\\ \mathbf{if}\;b \leq -3.15 \cdot 10^{+90} \lor \neg \left(b \leq 1.1 \cdot 10^{+17}\right):\\ \;\;\;\;\frac{\frac{b}{z} + t_1}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{t_1 + 9 \cdot \frac{x \cdot y}{z}}{c}\\ \end{array} \end{array} \]

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
 (let* ((t_1 (* -4.0 (* a t))))
   (if (or (<= b -3.15e+90) (not (<= b 1.1e+17)))
     (/ (+ (/ b z) t_1) c)
     (/ (+ t_1 (* 9.0 (/ (* x y) z))) c))))

C

assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = -4.0 * (a * t);
	double tmp;
	if ((b <= -3.15e+90) || !(b <= 1.1e+17)) {
		tmp = ((b / z) + t_1) / c;
	} else {
		tmp = (t_1 + (9.0 * ((x * 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) :: t_1
    real(8) :: tmp
    t_1 = (-4.0d0) * (a * t)
    if ((b <= (-3.15d+90)) .or. (.not. (b <= 1.1d+17))) then
        tmp = ((b / z) + t_1) / c
    else
        tmp = (t_1 + (9.0d0 * ((x * 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 t_1 = -4.0 * (a * t);
	double tmp;
	if ((b <= -3.15e+90) || !(b <= 1.1e+17)) {
		tmp = ((b / z) + t_1) / c;
	} else {
		tmp = (t_1 + (9.0 * ((x * y) / z))) / c;
	}
	return tmp;
}

Python

[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	t_1 = -4.0 * (a * t)
	tmp = 0
	if (b <= -3.15e+90) or not (b <= 1.1e+17):
		tmp = ((b / z) + t_1) / c
	else:
		tmp = (t_1 + (9.0 * ((x * y) / z))) / c
	return tmp

Julia

t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(-4.0 * Float64(a * t))
	tmp = 0.0
	if ((b <= -3.15e+90) || !(b <= 1.1e+17))
		tmp = Float64(Float64(Float64(b / z) + t_1) / c);
	else
		tmp = Float64(Float64(t_1 + Float64(9.0 * Float64(Float64(x * y) / z))) / 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 = -4.0 * (a * t);
	tmp = 0.0;
	if ((b <= -3.15e+90) || ~((b <= 1.1e+17)))
		tmp = ((b / z) + t_1) / c;
	else
		tmp = (t_1 + (9.0 * ((x * 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_] := Block[{t$95$1 = N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[b, -3.15e+90], N[Not[LessEqual[b, 1.1e+17]], $MachinePrecision]], N[(N[(N[(b / z), $MachinePrecision] + t$95$1), $MachinePrecision] / c), $MachinePrecision], N[(N[(t$95$1 + N[(9.0 * N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if b < -3.15e90 or 1.1e17 < b

   1. Initial program 79.9%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 79.9%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 79.9%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 79.1%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 79.1%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 79.1%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

   3. Simplified 79.9%

      \[\leadsto \color{blue}{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Step-by-step derivation

      1. associate-/r* 84.4%

         \[\leadsto \color{blue}{\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z}}{c}} \]

      2. div-inv 84.3%

         \[\leadsto \color{blue}{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z} \cdot \frac{1}{c}} \]

      3. associate-+l- 84.3%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b\right)}}{z} \cdot \frac{1}{c} \]

      4. associate-*r* 81.9%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a} - b\right)}{z} \cdot \frac{1}{c} \]

      5. associate-+l- 81.9%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}}{z} \cdot \frac{1}{c} \]

      6. associate-*l* 81.9%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z} \cdot \frac{1}{c} \]

      7. associate-*r* 84.3%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z} \cdot \frac{1}{c} \]

   5. Applied egg-rr 84.3%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z} \cdot \frac{1}{c}} \]

   6. Taylor expanded in x around 0 86.7%

      \[\leadsto \color{blue}{\left(\left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right) - 4 \cdot \left(a \cdot t\right)\right)} \cdot \frac{1}{c} \]
   7. Step-by-step derivation

      1. cancel-sign-sub-inv 86.7%

         \[\leadsto \color{blue}{\left(\left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right) + \left(-4\right) \cdot \left(a \cdot t\right)\right)} \cdot \frac{1}{c} \]

      2. metadata-eval 86.7%

         \[\leadsto \left(\left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right) + \color{blue}{-4} \cdot \left(a \cdot t\right)\right) \cdot \frac{1}{c} \]

      3. +-commutative 86.7%

         \[\leadsto \color{blue}{\left(-4 \cdot \left(a \cdot t\right) + \left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right)\right)} \cdot \frac{1}{c} \]

      4. fma-def 86.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(-4, a \cdot t, 9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right)} \cdot \frac{1}{c} \]

      5. fma-def 86.7%

         \[\leadsto \mathsf{fma}\left(-4, a \cdot t, \color{blue}{\mathsf{fma}\left(9, \frac{x \cdot y}{z}, \frac{b}{z}\right)}\right) \cdot \frac{1}{c} \]

      6. associate-*r/ 87.5%

         \[\leadsto \mathsf{fma}\left(-4, a \cdot t, \mathsf{fma}\left(9, \color{blue}{x \cdot \frac{y}{z}}, \frac{b}{z}\right)\right) \cdot \frac{1}{c} \]

   8. Simplified 87.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-4, a \cdot t, \mathsf{fma}\left(9, x \cdot \frac{y}{z}, \frac{b}{z}\right)\right)} \cdot \frac{1}{c} \]

   9. Taylor expanded in x around 0 84.2%

      \[\leadsto \color{blue}{\frac{-4 \cdot \left(a \cdot t\right) + \frac{b}{z}}{c}} \]

   if -3.15e90 < b < 1.1e17

   1. Initial program 80.4%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 80.4%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 80.4%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 79.1%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 79.1%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 79.1%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

   3. Simplified 77.9%

      \[\leadsto \color{blue}{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Step-by-step derivation

      1. associate-/r* 80.7%

         \[\leadsto \color{blue}{\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z}}{c}} \]

      2. div-inv 80.6%

         \[\leadsto \color{blue}{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z} \cdot \frac{1}{c}} \]

      3. associate-+l- 80.6%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b\right)}}{z} \cdot \frac{1}{c} \]

      4. associate-*r* 78.5%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a} - b\right)}{z} \cdot \frac{1}{c} \]

      5. associate-+l- 78.5%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}}{z} \cdot \frac{1}{c} \]

      6. associate-*l* 78.4%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z} \cdot \frac{1}{c} \]

      7. associate-*r* 80.6%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z} \cdot \frac{1}{c} \]

   5. Applied egg-rr 80.6%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z} \cdot \frac{1}{c}} \]

   6. Taylor expanded in x around 0 87.9%

      \[\leadsto \color{blue}{\left(\left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right) - 4 \cdot \left(a \cdot t\right)\right)} \cdot \frac{1}{c} \]
   7. Step-by-step derivation

      1. cancel-sign-sub-inv 87.9%

         \[\leadsto \color{blue}{\left(\left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right) + \left(-4\right) \cdot \left(a \cdot t\right)\right)} \cdot \frac{1}{c} \]

      2. metadata-eval 87.9%

         \[\leadsto \left(\left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right) + \color{blue}{-4} \cdot \left(a \cdot t\right)\right) \cdot \frac{1}{c} \]

      3. +-commutative 87.9%

         \[\leadsto \color{blue}{\left(-4 \cdot \left(a \cdot t\right) + \left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right)\right)} \cdot \frac{1}{c} \]

      4. fma-def 87.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(-4, a \cdot t, 9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right)} \cdot \frac{1}{c} \]

      5. fma-def 87.9%

         \[\leadsto \mathsf{fma}\left(-4, a \cdot t, \color{blue}{\mathsf{fma}\left(9, \frac{x \cdot y}{z}, \frac{b}{z}\right)}\right) \cdot \frac{1}{c} \]

      6. associate-*r/ 86.5%

         \[\leadsto \mathsf{fma}\left(-4, a \cdot t, \mathsf{fma}\left(9, \color{blue}{x \cdot \frac{y}{z}}, \frac{b}{z}\right)\right) \cdot \frac{1}{c} \]

   8. Simplified 86.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-4, a \cdot t, \mathsf{fma}\left(9, x \cdot \frac{y}{z}, \frac{b}{z}\right)\right)} \cdot \frac{1}{c} \]

   9. Taylor expanded in b around 0 86.0%

      \[\leadsto \color{blue}{\frac{-4 \cdot \left(a \cdot t\right) + 9 \cdot \frac{x \cdot y}{z}}{c}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 85.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.15 \cdot 10^{+90} \lor \neg \left(b \leq 1.1 \cdot 10^{+17}\right):\\ \;\;\;\;\frac{\frac{b}{z} + -4 \cdot \left(a \cdot t\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right) + 9 \cdot \frac{x \cdot y}{z}}{c}\\ \end{array} \]

Alternative 15: 47.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} t_1 := 9 \cdot \frac{x \cdot y}{z \cdot c}\\ \mathbf{if}\;b \leq -4.8 \cdot 10^{+139}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;b \leq -2.4 \cdot 10^{+18}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 5.6 \cdot 10^{-215}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;b \leq 0.049:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 2.1 \cdot 10^{+228}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \end{array} \end{array} \]

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 y) (* z c)))))
   (if (<= b -4.8e+139)
     (/ b (* z c))
     (if (<= b -2.4e+18)
       t_1
       (if (<= b 5.6e-215)
         (* -4.0 (* t (/ a c)))
         (if (<= b 0.049)
           t_1
           (if (<= b 2.1e+228) (* -4.0 (/ a (/ c t))) (/ (/ b c) z))))))))

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 * y) / (z * c));
	double tmp;
	if (b <= -4.8e+139) {
		tmp = b / (z * c);
	} else if (b <= -2.4e+18) {
		tmp = t_1;
	} else if (b <= 5.6e-215) {
		tmp = -4.0 * (t * (a / c));
	} else if (b <= 0.049) {
		tmp = t_1;
	} else if (b <= 2.1e+228) {
		tmp = -4.0 * (a / (c / t));
	} else {
		tmp = (b / c) / z;
	}
	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 * y) / (z * c))
    if (b <= (-4.8d+139)) then
        tmp = b / (z * c)
    else if (b <= (-2.4d+18)) then
        tmp = t_1
    else if (b <= 5.6d-215) then
        tmp = (-4.0d0) * (t * (a / c))
    else if (b <= 0.049d0) then
        tmp = t_1
    else if (b <= 2.1d+228) then
        tmp = (-4.0d0) * (a / (c / t))
    else
        tmp = (b / c) / z
    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 * y) / (z * c));
	double tmp;
	if (b <= -4.8e+139) {
		tmp = b / (z * c);
	} else if (b <= -2.4e+18) {
		tmp = t_1;
	} else if (b <= 5.6e-215) {
		tmp = -4.0 * (t * (a / c));
	} else if (b <= 0.049) {
		tmp = t_1;
	} else if (b <= 2.1e+228) {
		tmp = -4.0 * (a / (c / t));
	} else {
		tmp = (b / c) / z;
	}
	return tmp;
}

Python

[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	t_1 = 9.0 * ((x * y) / (z * c))
	tmp = 0
	if b <= -4.8e+139:
		tmp = b / (z * c)
	elif b <= -2.4e+18:
		tmp = t_1
	elif b <= 5.6e-215:
		tmp = -4.0 * (t * (a / c))
	elif b <= 0.049:
		tmp = t_1
	elif b <= 2.1e+228:
		tmp = -4.0 * (a / (c / t))
	else:
		tmp = (b / c) / z
	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 * y) / Float64(z * c)))
	tmp = 0.0
	if (b <= -4.8e+139)
		tmp = Float64(b / Float64(z * c));
	elseif (b <= -2.4e+18)
		tmp = t_1;
	elseif (b <= 5.6e-215)
		tmp = Float64(-4.0 * Float64(t * Float64(a / c)));
	elseif (b <= 0.049)
		tmp = t_1;
	elseif (b <= 2.1e+228)
		tmp = Float64(-4.0 * Float64(a / Float64(c / t)));
	else
		tmp = Float64(Float64(b / c) / z);
	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 * y) / (z * c));
	tmp = 0.0;
	if (b <= -4.8e+139)
		tmp = b / (z * c);
	elseif (b <= -2.4e+18)
		tmp = t_1;
	elseif (b <= 5.6e-215)
		tmp = -4.0 * (t * (a / c));
	elseif (b <= 0.049)
		tmp = t_1;
	elseif (b <= 2.1e+228)
		tmp = -4.0 * (a / (c / t));
	else
		tmp = (b / c) / z;
	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 * y), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -4.8e+139], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -2.4e+18], t$95$1, If[LessEqual[b, 5.6e-215], N[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 0.049], t$95$1, If[LessEqual[b, 2.1e+228], N[(-4.0 * N[(a / N[(c / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -4.80000000000000016e139

   1. Initial program 77.1%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 77.1%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 77.1%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 79.7%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 79.7%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 79.7%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

   3. Simplified 80.0%

      \[\leadsto \color{blue}{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]

   4. Taylor expanded in b around inf 74.2%

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
   5. Step-by-step derivation

      1. *-commutative 74.2%

         \[\leadsto \frac{b}{\color{blue}{z \cdot c}} \]

   6. Simplified 74.2%

      \[\leadsto \color{blue}{\frac{b}{z \cdot c}} \]

   if -4.80000000000000016e139 < b < -2.4e18 or 5.59999999999999972e-215 < b < 0.049000000000000002

   1. Initial program 87.7%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 87.7%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 87.7%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 86.0%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 86.0%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 86.0%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

   3. Simplified 87.9%

      \[\leadsto \color{blue}{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]

   4. Taylor expanded in x around inf 66.5%

      \[\leadsto \color{blue}{9 \cdot \frac{x \cdot y}{c \cdot z}} \]

   if -2.4e18 < b < 5.59999999999999972e-215

   1. Initial program 76.3%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 76.3%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 76.3%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 75.4%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 75.4%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 75.4%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

   3. Simplified 73.4%

      \[\leadsto \color{blue}{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]

   4. Taylor expanded in z around inf 54.3%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   5. Step-by-step derivation

      1. *-commutative 54.3%

         \[\leadsto \color{blue}{\frac{a \cdot t}{c} \cdot -4} \]

      2. associate-/l* 60.7%

         \[\leadsto \color{blue}{\frac{a}{\frac{c}{t}}} \cdot -4 \]

   6. Simplified 60.7%

      \[\leadsto \color{blue}{\frac{a}{\frac{c}{t}} \cdot -4} \]
   7. Step-by-step derivation

      1. associate-/r/ 58.6%

         \[\leadsto \color{blue}{\left(\frac{a}{c} \cdot t\right)} \cdot -4 \]

   8. Applied egg-rr 58.6%

      \[\leadsto \color{blue}{\left(\frac{a}{c} \cdot t\right)} \cdot -4 \]

   if 0.049000000000000002 < b < 2.09999999999999994e228

   1. Initial program 82.2%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 82.2%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 82.2%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 77.1%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 77.1%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 77.1%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

   3. Simplified 77.0%

      \[\leadsto \color{blue}{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]

   4. Taylor expanded in z around inf 51.4%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   5. Step-by-step derivation

      1. *-commutative 51.4%

         \[\leadsto \color{blue}{\frac{a \cdot t}{c} \cdot -4} \]

      2. associate-/l* 58.2%

         \[\leadsto \color{blue}{\frac{a}{\frac{c}{t}}} \cdot -4 \]

   6. Simplified 58.2%

      \[\leadsto \color{blue}{\frac{a}{\frac{c}{t}} \cdot -4} \]

   if 2.09999999999999994e228 < b

   1. Initial program 76.8%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 76.8%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 76.8%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 80.5%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 80.5%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 80.5%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

   3. Simplified 80.5%

      \[\leadsto \color{blue}{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]

   4. Taylor expanded in b around inf 72.4%

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
   5. Step-by-step derivation

      1. associate-/r* 87.4%

         \[\leadsto \color{blue}{\frac{\frac{b}{c}}{z}} \]

   6. Simplified 87.4%

      \[\leadsto \color{blue}{\frac{\frac{b}{c}}{z}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 65.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.8 \cdot 10^{+139}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;b \leq -2.4 \cdot 10^{+18}:\\ \;\;\;\;9 \cdot \frac{x \cdot y}{z \cdot c}\\ \mathbf{elif}\;b \leq 5.6 \cdot 10^{-215}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;b \leq 0.049:\\ \;\;\;\;9 \cdot \frac{x \cdot y}{z \cdot c}\\ \mathbf{elif}\;b \leq 2.1 \cdot 10^{+228}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \end{array} \]

Alternative 16: 74.4% accurate, 1.3× speedup

Math

\[\begin{array}{l} [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{-131} \lor \neg \left(z \leq 1.05 \cdot 10^{+21}\right):\\ \;\;\;\;\frac{\frac{b}{z} + -4 \cdot \left(a \cdot t\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \end{array} \end{array} \]

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 -4e-131) (not (<= z 1.05e+21)))
   (/ (+ (/ b z) (* -4.0 (* a t))) c)
   (/ (+ b (* 9.0 (* x 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 <= -4e-131) || !(z <= 1.05e+21)) {
		tmp = ((b / z) + (-4.0 * (a * t))) / c;
	} else {
		tmp = (b + (9.0 * (x * 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 <= (-4d-131)) .or. (.not. (z <= 1.05d+21))) then
        tmp = ((b / z) + ((-4.0d0) * (a * t))) / c
    else
        tmp = (b + (9.0d0 * (x * 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 <= -4e-131) || !(z <= 1.05e+21)) {
		tmp = ((b / z) + (-4.0 * (a * t))) / c;
	} else {
		tmp = (b + (9.0 * (x * y))) / (z * c);
	}
	return tmp;
}

Python

[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if (z <= -4e-131) or not (z <= 1.05e+21):
		tmp = ((b / z) + (-4.0 * (a * t))) / c
	else:
		tmp = (b + (9.0 * (x * 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 <= -4e-131) || !(z <= 1.05e+21))
		tmp = Float64(Float64(Float64(b / z) + Float64(-4.0 * Float64(a * t))) / c);
	else
		tmp = Float64(Float64(b + Float64(9.0 * Float64(x * 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 <= -4e-131) || ~((z <= 1.05e+21)))
		tmp = ((b / z) + (-4.0 * (a * t))) / c;
	else
		tmp = (b + (9.0 * (x * 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, -4e-131], N[Not[LessEqual[z, 1.05e+21]], $MachinePrecision]], N[(N[(N[(b / z), $MachinePrecision] + N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], N[(N[(b + N[(9.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.9999999999999999e-131 or 1.05e21 < z

   1. Initial program 70.2%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 70.2%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 70.2%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 67.8%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 67.8%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 67.8%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

   3. Simplified 69.2%

      \[\leadsto \color{blue}{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Step-by-step derivation

      1. associate-/r* 79.4%

         \[\leadsto \color{blue}{\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z}}{c}} \]

      2. div-inv 79.3%

         \[\leadsto \color{blue}{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z} \cdot \frac{1}{c}} \]

      3. associate-+l- 79.3%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b\right)}}{z} \cdot \frac{1}{c} \]

      4. associate-*r* 75.6%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a} - b\right)}{z} \cdot \frac{1}{c} \]

      5. associate-+l- 75.6%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}}{z} \cdot \frac{1}{c} \]

      6. associate-*l* 75.5%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z} \cdot \frac{1}{c} \]

      7. associate-*r* 79.3%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z} \cdot \frac{1}{c} \]

   5. Applied egg-rr 79.3%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z} \cdot \frac{1}{c}} \]

   6. Taylor expanded in x around 0 90.9%

      \[\leadsto \color{blue}{\left(\left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right) - 4 \cdot \left(a \cdot t\right)\right)} \cdot \frac{1}{c} \]
   7. Step-by-step derivation

      1. cancel-sign-sub-inv 90.9%

         \[\leadsto \color{blue}{\left(\left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right) + \left(-4\right) \cdot \left(a \cdot t\right)\right)} \cdot \frac{1}{c} \]

      2. metadata-eval 90.9%

         \[\leadsto \left(\left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right) + \color{blue}{-4} \cdot \left(a \cdot t\right)\right) \cdot \frac{1}{c} \]

      3. +-commutative 90.9%

         \[\leadsto \color{blue}{\left(-4 \cdot \left(a \cdot t\right) + \left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right)\right)} \cdot \frac{1}{c} \]

      4. fma-def 90.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(-4, a \cdot t, 9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right)} \cdot \frac{1}{c} \]

      5. fma-def 90.9%

         \[\leadsto \mathsf{fma}\left(-4, a \cdot t, \color{blue}{\mathsf{fma}\left(9, \frac{x \cdot y}{z}, \frac{b}{z}\right)}\right) \cdot \frac{1}{c} \]

      6. associate-*r/ 92.8%

         \[\leadsto \mathsf{fma}\left(-4, a \cdot t, \mathsf{fma}\left(9, \color{blue}{x \cdot \frac{y}{z}}, \frac{b}{z}\right)\right) \cdot \frac{1}{c} \]

   8. Simplified 92.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-4, a \cdot t, \mathsf{fma}\left(9, x \cdot \frac{y}{z}, \frac{b}{z}\right)\right)} \cdot \frac{1}{c} \]

   9. Taylor expanded in x around 0 79.1%

      \[\leadsto \color{blue}{\frac{-4 \cdot \left(a \cdot t\right) + \frac{b}{z}}{c}} \]

   if -3.9999999999999999e-131 < z < 1.05e21

   1. Initial program 95.1%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 95.1%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 95.1%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 96.1%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 96.1%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 96.1%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

   3. Simplified 93.3%

      \[\leadsto \color{blue}{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]

   4. Taylor expanded in x around inf 86.6%

      \[\leadsto \frac{\color{blue}{9 \cdot \left(x \cdot y\right)} + b}{z \cdot c} \]
3. Recombined 2 regimes into one program.

4. Final simplification 82.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{-131} \lor \neg \left(z \leq 1.05 \cdot 10^{+21}\right):\\ \;\;\;\;\frac{\frac{b}{z} + -4 \cdot \left(a \cdot t\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \end{array} \]

Alternative 17: 66.4% accurate, 1.3× speedup

Math

\[\begin{array}{l} [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{-45}:\\ \;\;\;\;\frac{9 \cdot x}{z \cdot \frac{c}{y}}\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{+213}:\\ \;\;\;\;\frac{\frac{b}{z} + -4 \cdot \left(a \cdot t\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{9}{z} \cdot \frac{x}{\frac{c}{y}}\\ \end{array} \end{array} \]

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 (<= y -1.6e-45)
   (/ (* 9.0 x) (* z (/ c y)))
   (if (<= y 1.15e+213)
     (/ (+ (/ b z) (* -4.0 (* a t))) c)
     (* (/ 9.0 z) (/ x (/ c y))))))

C

assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (y <= -1.6e-45) {
		tmp = (9.0 * x) / (z * (c / y));
	} else if (y <= 1.15e+213) {
		tmp = ((b / z) + (-4.0 * (a * t))) / c;
	} else {
		tmp = (9.0 / z) * (x / (c / y));
	}
	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 <= (-1.6d-45)) then
        tmp = (9.0d0 * x) / (z * (c / y))
    else if (y <= 1.15d+213) then
        tmp = ((b / z) + ((-4.0d0) * (a * t))) / c
    else
        tmp = (9.0d0 / z) * (x / (c / y))
    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 <= -1.6e-45) {
		tmp = (9.0 * x) / (z * (c / y));
	} else if (y <= 1.15e+213) {
		tmp = ((b / z) + (-4.0 * (a * t))) / c;
	} else {
		tmp = (9.0 / z) * (x / (c / y));
	}
	return tmp;
}

Python

[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if y <= -1.6e-45:
		tmp = (9.0 * x) / (z * (c / y))
	elif y <= 1.15e+213:
		tmp = ((b / z) + (-4.0 * (a * t))) / c
	else:
		tmp = (9.0 / z) * (x / (c / y))
	return tmp

Julia

t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (y <= -1.6e-45)
		tmp = Float64(Float64(9.0 * x) / Float64(z * Float64(c / y)));
	elseif (y <= 1.15e+213)
		tmp = Float64(Float64(Float64(b / z) + Float64(-4.0 * Float64(a * t))) / c);
	else
		tmp = Float64(Float64(9.0 / z) * Float64(x / Float64(c / y)));
	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 <= -1.6e-45)
		tmp = (9.0 * x) / (z * (c / y));
	elseif (y <= 1.15e+213)
		tmp = ((b / z) + (-4.0 * (a * t))) / c;
	else
		tmp = (9.0 / z) * (x / (c / y));
	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[y, -1.6e-45], N[(N[(9.0 * x), $MachinePrecision] / N[(z * N[(c / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.15e+213], N[(N[(N[(b / z), $MachinePrecision] + N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], N[(N[(9.0 / z), $MachinePrecision] * N[(x / N[(c / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.60000000000000004e-45

   1. Initial program 83.9%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 83.9%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 83.9%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 82.3%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 82.3%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 82.3%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

   3. Simplified 82.5%

      \[\leadsto \color{blue}{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]

   4. Taylor expanded in x around inf 53.5%

      \[\leadsto \color{blue}{9 \cdot \frac{x \cdot y}{c \cdot z}} \]
   5. Step-by-step derivation

      1. associate-*r/ 53.5%

         \[\leadsto \color{blue}{\frac{9 \cdot \left(x \cdot y\right)}{c \cdot z}} \]

      2. associate-*r* 53.5%

         \[\leadsto \frac{\color{blue}{\left(9 \cdot x\right) \cdot y}}{c \cdot z} \]

      3. *-commutative 53.5%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right)} \cdot y}{c \cdot z} \]

      4. associate-*r* 53.4%

         \[\leadsto \frac{\color{blue}{x \cdot \left(9 \cdot y\right)}}{c \cdot z} \]

      5. *-commutative 53.4%

         \[\leadsto \frac{x \cdot \left(9 \cdot y\right)}{\color{blue}{z \cdot c}} \]

      6. times-frac 57.4%

         \[\leadsto \color{blue}{\frac{x}{z} \cdot \frac{9 \cdot y}{c}} \]

      7. associate-/l* 57.4%

         \[\leadsto \frac{x}{z} \cdot \color{blue}{\frac{9}{\frac{c}{y}}} \]

   6. Simplified 57.4%

      \[\leadsto \color{blue}{\frac{x}{z} \cdot \frac{9}{\frac{c}{y}}} \]
   7. Step-by-step derivation

      1. frac-times 59.9%

         \[\leadsto \color{blue}{\frac{x \cdot 9}{z \cdot \frac{c}{y}}} \]

   8. Applied egg-rr 59.9%

      \[\leadsto \color{blue}{\frac{x \cdot 9}{z \cdot \frac{c}{y}}} \]

   if -1.60000000000000004e-45 < y < 1.14999999999999999e213

   1. Initial program 78.4%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 78.4%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 78.4%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 77.4%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 77.4%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 77.4%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

   3. Simplified 78.0%

      \[\leadsto \color{blue}{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Step-by-step derivation

      1. associate-/r* 83.8%

         \[\leadsto \color{blue}{\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z}}{c}} \]

      2. div-inv 83.7%

         \[\leadsto \color{blue}{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z} \cdot \frac{1}{c}} \]

      3. associate-+l- 83.7%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b\right)}}{z} \cdot \frac{1}{c} \]

      4. associate-*r* 81.0%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a} - b\right)}{z} \cdot \frac{1}{c} \]

      5. associate-+l- 81.0%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}}{z} \cdot \frac{1}{c} \]

      6. associate-*l* 80.9%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z} \cdot \frac{1}{c} \]

      7. associate-*r* 83.7%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z} \cdot \frac{1}{c} \]

   5. Applied egg-rr 83.7%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z} \cdot \frac{1}{c}} \]

   6. Taylor expanded in x around 0 92.0%

      \[\leadsto \color{blue}{\left(\left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right) - 4 \cdot \left(a \cdot t\right)\right)} \cdot \frac{1}{c} \]
   7. Step-by-step derivation

      1. cancel-sign-sub-inv 92.0%

         \[\leadsto \color{blue}{\left(\left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right) + \left(-4\right) \cdot \left(a \cdot t\right)\right)} \cdot \frac{1}{c} \]

      2. metadata-eval 92.0%

         \[\leadsto \left(\left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right) + \color{blue}{-4} \cdot \left(a \cdot t\right)\right) \cdot \frac{1}{c} \]

      3. +-commutative 92.0%

         \[\leadsto \color{blue}{\left(-4 \cdot \left(a \cdot t\right) + \left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right)\right)} \cdot \frac{1}{c} \]

      4. fma-def 92.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(-4, a \cdot t, 9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right)} \cdot \frac{1}{c} \]

      5. fma-def 92.0%

         \[\leadsto \mathsf{fma}\left(-4, a \cdot t, \color{blue}{\mathsf{fma}\left(9, \frac{x \cdot y}{z}, \frac{b}{z}\right)}\right) \cdot \frac{1}{c} \]

      6. associate-*r/ 91.4%

         \[\leadsto \mathsf{fma}\left(-4, a \cdot t, \mathsf{fma}\left(9, \color{blue}{x \cdot \frac{y}{z}}, \frac{b}{z}\right)\right) \cdot \frac{1}{c} \]

   8. Simplified 91.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-4, a \cdot t, \mathsf{fma}\left(9, x \cdot \frac{y}{z}, \frac{b}{z}\right)\right)} \cdot \frac{1}{c} \]

   9. Taylor expanded in x around 0 74.7%

      \[\leadsto \color{blue}{\frac{-4 \cdot \left(a \cdot t\right) + \frac{b}{z}}{c}} \]

   if 1.14999999999999999e213 < y

   1. Initial program 83.4%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 83.4%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 83.4%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 83.2%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 83.2%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 83.2%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

   3. Simplified 75.4%

      \[\leadsto \color{blue}{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Step-by-step derivation

      1. associate-/r* 79.7%

         \[\leadsto \color{blue}{\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z}}{c}} \]

      2. div-inv 79.8%

         \[\leadsto \color{blue}{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z} \cdot \frac{1}{c}} \]

      3. associate-+l- 79.8%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b\right)}}{z} \cdot \frac{1}{c} \]

      4. associate-*r* 84.0%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a} - b\right)}{z} \cdot \frac{1}{c} \]

      5. associate-+l- 84.0%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}}{z} \cdot \frac{1}{c} \]

      6. associate-*l* 84.0%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z} \cdot \frac{1}{c} \]

      7. associate-*r* 79.8%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z} \cdot \frac{1}{c} \]

   5. Applied egg-rr 79.8%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z} \cdot \frac{1}{c}} \]

   6. Taylor expanded in x around inf 75.4%

      \[\leadsto \color{blue}{9 \cdot \frac{x \cdot y}{c \cdot z}} \]
   7. Step-by-step derivation

      1. associate-*r/ 75.5%

         \[\leadsto \color{blue}{\frac{9 \cdot \left(x \cdot y\right)}{c \cdot z}} \]

      2. *-commutative 75.5%

         \[\leadsto \frac{9 \cdot \left(x \cdot y\right)}{\color{blue}{z \cdot c}} \]

      3. times-frac 79.5%

         \[\leadsto \color{blue}{\frac{9}{z} \cdot \frac{x \cdot y}{c}} \]

      4. associate-/l* 79.9%

         \[\leadsto \frac{9}{z} \cdot \color{blue}{\frac{x}{\frac{c}{y}}} \]

   8. Simplified 79.9%

      \[\leadsto \color{blue}{\frac{9}{z} \cdot \frac{x}{\frac{c}{y}}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 71.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{-45}:\\ \;\;\;\;\frac{9 \cdot x}{z \cdot \frac{c}{y}}\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{+213}:\\ \;\;\;\;\frac{\frac{b}{z} + -4 \cdot \left(a \cdot t\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{9}{z} \cdot \frac{x}{\frac{c}{y}}\\ \end{array} \]

Alternative 18: 49.1% accurate, 1.7× speedup

Math

\[\begin{array}{l} [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;b \leq -1.6 \cdot 10^{+90}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;b \leq 2.3 \cdot 10^{+168}:\\ \;\;\;\;-4 \cdot \frac{t}{\frac{c}{a}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \end{array} \end{array} \]

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 (<= b -1.6e+90)
   (/ b (* z c))
   (if (<= b 2.3e+168) (* -4.0 (/ t (/ c a))) (/ (/ b c) z))))

C

assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (b <= -1.6e+90) {
		tmp = b / (z * c);
	} else if (b <= 2.3e+168) {
		tmp = -4.0 * (t / (c / a));
	} else {
		tmp = (b / c) / z;
	}
	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 (b <= (-1.6d+90)) then
        tmp = b / (z * c)
    else if (b <= 2.3d+168) then
        tmp = (-4.0d0) * (t / (c / a))
    else
        tmp = (b / c) / z
    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 (b <= -1.6e+90) {
		tmp = b / (z * c);
	} else if (b <= 2.3e+168) {
		tmp = -4.0 * (t / (c / a));
	} else {
		tmp = (b / c) / z;
	}
	return tmp;
}

Python

[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if b <= -1.6e+90:
		tmp = b / (z * c)
	elif b <= 2.3e+168:
		tmp = -4.0 * (t / (c / a))
	else:
		tmp = (b / c) / z
	return tmp

Julia

t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (b <= -1.6e+90)
		tmp = Float64(b / Float64(z * c));
	elseif (b <= 2.3e+168)
		tmp = Float64(-4.0 * Float64(t / Float64(c / a)));
	else
		tmp = Float64(Float64(b / c) / z);
	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 (b <= -1.6e+90)
		tmp = b / (z * c);
	elseif (b <= 2.3e+168)
		tmp = -4.0 * (t / (c / a));
	else
		tmp = (b / c) / z;
	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[b, -1.6e+90], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.3e+168], N[(-4.0 * N[(t / N[(c / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.59999999999999999e90

   1. Initial program 79.1%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 79.1%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 79.1%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 81.4%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 81.4%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 81.4%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

   3. Simplified 81.7%

      \[\leadsto \color{blue}{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]

   4. Taylor expanded in b around inf 72.3%

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
   5. Step-by-step derivation

      1. *-commutative 72.3%

         \[\leadsto \frac{b}{\color{blue}{z \cdot c}} \]

   6. Simplified 72.3%

      \[\leadsto \color{blue}{\frac{b}{z \cdot c}} \]

   if -1.59999999999999999e90 < b < 2.2999999999999999e168

   1. Initial program 82.0%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 82.0%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 82.0%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 79.9%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 79.9%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 79.9%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

   3. Simplified 78.9%

      \[\leadsto \color{blue}{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
   4. Step-by-step derivation

      1. associate-/r* 80.7%

         \[\leadsto \color{blue}{\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z}}{c}} \]

      2. div-inv 80.6%

         \[\leadsto \color{blue}{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z} \cdot \frac{1}{c}} \]

      3. associate-+l- 80.6%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - b\right)}}{z} \cdot \frac{1}{c} \]

      4. associate-*r* 79.5%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a} - b\right)}{z} \cdot \frac{1}{c} \]

      5. associate-+l- 79.5%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}}{z} \cdot \frac{1}{c} \]

      6. associate-*l* 79.4%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z} \cdot \frac{1}{c} \]

      7. associate-*r* 80.6%

         \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z} \cdot \frac{1}{c} \]

   5. Applied egg-rr 80.6%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z} \cdot \frac{1}{c}} \]

   6. Taylor expanded in z around inf 49.0%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   7. Step-by-step derivation

      1. *-commutative 49.0%

         \[\leadsto -4 \cdot \frac{\color{blue}{t \cdot a}}{c} \]

      2. associate-/l* 51.9%

         \[\leadsto -4 \cdot \color{blue}{\frac{t}{\frac{c}{a}}} \]

   8. Simplified 51.9%

      \[\leadsto \color{blue}{-4 \cdot \frac{t}{\frac{c}{a}}} \]

   if 2.2999999999999999e168 < b

   1. Initial program 73.2%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 73.2%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 73.2%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 73.2%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 73.2%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 73.2%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

   3. Simplified 75.5%

      \[\leadsto \color{blue}{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]

   4. Taylor expanded in b around inf 66.0%

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
   5. Step-by-step derivation

      1. associate-/r* 75.1%

         \[\leadsto \color{blue}{\frac{\frac{b}{c}}{z}} \]

   6. Simplified 75.1%

      \[\leadsto \color{blue}{\frac{\frac{b}{c}}{z}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 58.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.6 \cdot 10^{+90}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;b \leq 2.3 \cdot 10^{+168}:\\ \;\;\;\;-4 \cdot \frac{t}{\frac{c}{a}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \end{array} \]

Alternative 19: 49.0% accurate, 1.7× speedup

Math

\[\begin{array}{l} [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;b \leq -1.52 \cdot 10^{+90}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;b \leq 3.4 \cdot 10^{+184}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \end{array} \end{array} \]

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 (<= b -1.52e+90)
   (/ b (* z c))
   (if (<= b 3.4e+184) (* -4.0 (* t (/ a c))) (/ (/ b c) z))))

C

assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (b <= -1.52e+90) {
		tmp = b / (z * c);
	} else if (b <= 3.4e+184) {
		tmp = -4.0 * (t * (a / c));
	} else {
		tmp = (b / c) / z;
	}
	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 (b <= (-1.52d+90)) then
        tmp = b / (z * c)
    else if (b <= 3.4d+184) then
        tmp = (-4.0d0) * (t * (a / c))
    else
        tmp = (b / c) / z
    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 (b <= -1.52e+90) {
		tmp = b / (z * c);
	} else if (b <= 3.4e+184) {
		tmp = -4.0 * (t * (a / c));
	} else {
		tmp = (b / c) / z;
	}
	return tmp;
}

Python

[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if b <= -1.52e+90:
		tmp = b / (z * c)
	elif b <= 3.4e+184:
		tmp = -4.0 * (t * (a / c))
	else:
		tmp = (b / c) / z
	return tmp

Julia

t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (b <= -1.52e+90)
		tmp = Float64(b / Float64(z * c));
	elseif (b <= 3.4e+184)
		tmp = Float64(-4.0 * Float64(t * Float64(a / c)));
	else
		tmp = Float64(Float64(b / c) / z);
	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 (b <= -1.52e+90)
		tmp = b / (z * c);
	elseif (b <= 3.4e+184)
		tmp = -4.0 * (t * (a / c));
	else
		tmp = (b / c) / z;
	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[b, -1.52e+90], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.4e+184], N[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.52000000000000009e90

   1. Initial program 79.1%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 79.1%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 79.1%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 81.4%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 81.4%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 81.4%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

   3. Simplified 81.7%

      \[\leadsto \color{blue}{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]

   4. Taylor expanded in b around inf 72.3%

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
   5. Step-by-step derivation

      1. *-commutative 72.3%

         \[\leadsto \frac{b}{\color{blue}{z \cdot c}} \]

   6. Simplified 72.3%

      \[\leadsto \color{blue}{\frac{b}{z \cdot c}} \]

   if -1.52000000000000009e90 < b < 3.4000000000000002e184

   1. Initial program 81.3%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 81.3%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 81.3%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 79.2%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 79.2%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 79.2%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

   3. Simplified 78.3%

      \[\leadsto \color{blue}{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]

   4. Taylor expanded in z around inf 49.1%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   5. Step-by-step derivation

      1. *-commutative 49.1%

         \[\leadsto \color{blue}{\frac{a \cdot t}{c} \cdot -4} \]

      2. associate-/l* 53.3%

         \[\leadsto \color{blue}{\frac{a}{\frac{c}{t}}} \cdot -4 \]

   6. Simplified 53.3%

      \[\leadsto \color{blue}{\frac{a}{\frac{c}{t}} \cdot -4} \]
   7. Step-by-step derivation

      1. associate-/r/ 52.3%

         \[\leadsto \color{blue}{\left(\frac{a}{c} \cdot t\right)} \cdot -4 \]

   8. Applied egg-rr 52.3%

      \[\leadsto \color{blue}{\left(\frac{a}{c} \cdot t\right)} \cdot -4 \]

   if 3.4000000000000002e184 < b

   1. Initial program 75.7%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 75.7%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 75.7%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 75.7%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 75.7%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 75.7%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

   3. Simplified 78.2%

      \[\leadsto \color{blue}{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]

   4. Taylor expanded in b around inf 67.6%

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
   5. Step-by-step derivation

      1. associate-/r* 77.8%

         \[\leadsto \color{blue}{\frac{\frac{b}{c}}{z}} \]

   6. Simplified 77.8%

      \[\leadsto \color{blue}{\frac{\frac{b}{c}}{z}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 59.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.52 \cdot 10^{+90}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;b \leq 3.4 \cdot 10^{+184}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \end{array} \]

Alternative 20: 34.8% 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 80.2%

   \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
2. Step-by-step derivation

   1. associate-+l- 80.2%

      \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

   2. *-commutative 80.2%

      \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

   3. associate-*r* 79.1%

      \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

   4. *-commutative 79.1%

      \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

   5. associate-+l- 79.1%

      \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

3. Simplified 78.8%

   \[\leadsto \color{blue}{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]

4. Taylor expanded in b around inf 35.2%

   \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
5. Step-by-step derivation

   1. *-commutative 35.2%

      \[\leadsto \frac{b}{\color{blue}{z \cdot c}} \]

6. Simplified 35.2%

   \[\leadsto \color{blue}{\frac{b}{z \cdot c}} \]

7. Final simplification 35.2%

   \[\leadsto \frac{b}{z \cdot c} \]

Developer target: 80.3% 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 2023283 
(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)))