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

Percentage Accurate: 79.2% → 92.1%

Time: 15.7s

Alternatives: 12

Speedup: 0.7×

• 37.8% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 79.2% 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: 92.1% accurate, 0.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{+48} \lor \neg \left(z \leq 1.12 \cdot 10^{-26}\right):\\ \;\;\;\;9 \cdot \left(x \cdot \frac{\frac{y}{z}}{c}\right) + \mathsf{fma}\left(-4, a \cdot \frac{t}{c}, \frac{\frac{b}{z}}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{b + \mathsf{fma}\left(x, 9 \cdot y, t \cdot \left(a \cdot \left(z \cdot -4\right)\right)\right)}{z \cdot c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= z -1.05e+48) (not (<= z 1.12e-26)))
   (+ (* 9.0 (* x (/ (/ y z) c))) (fma -4.0 (* a (/ t c)) (/ (/ b z) c)))
   (/ (+ b (fma x (* 9.0 y) (* t (* a (* z -4.0))))) (* z c))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((z <= -1.05e+48) || !(z <= 1.12e-26)) {
		tmp = (9.0 * (x * ((y / z) / c))) + fma(-4.0, (a * (t / c)), ((b / z) / c));
	} else {
		tmp = (b + fma(x, (9.0 * y), (t * (a * (z * -4.0))))) / (z * c);
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((z <= -1.05e+48) || !(z <= 1.12e-26))
		tmp = Float64(Float64(9.0 * Float64(x * Float64(Float64(y / z) / c))) + fma(-4.0, Float64(a * Float64(t / c)), Float64(Float64(b / z) / c)));
	else
		tmp = Float64(Float64(b + fma(x, Float64(9.0 * y), Float64(t * Float64(a * Float64(z * -4.0))))) / Float64(z * c));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[z, -1.05e+48], N[Not[LessEqual[z, 1.12e-26]], $MachinePrecision]], N[(N[(9.0 * N[(x * N[(N[(y / z), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(-4.0 * N[(a * N[(t / c), $MachinePrecision]), $MachinePrecision] + N[(N[(b / z), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b + N[(x * N[(9.0 * y), $MachinePrecision] + N[(t * N[(a * N[(z * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.0499999999999999e48 or 1.12e-26 < z

   1. Initial program 59.2%

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

   3. Simplified 62.2%

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

   5. Taylor expanded in x around 0 78.5%

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

      1. +-commutative 78.5%

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

      2. metadata-eval 78.5%

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

      3. cancel-sign-sub-inv 78.5%

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

      4. associate--l+ 78.5%

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

      5. fma-define 78.5%

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

      6. associate-/l* 82.4%

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

      7. *-commutative 82.4%

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

      8. cancel-sign-sub-inv 82.4%

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

      9. metadata-eval 82.4%

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

      10. +-commutative 82.4%

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

      11. fma-define 82.4%

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

      12. associate-/l* 84.6%

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

      13. *-commutative 84.6%

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

   7. Simplified 84.6%

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

      1. fma-undefine 84.6%

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

      2. associate-/r* 87.4%

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

      3. associate-/r* 91.0%

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

   9. Applied egg-rr 91.0%

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

   if -1.0499999999999999e48 < z < 1.12e-26

   1. Initial program 96.6%

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

   3. Simplified 96.0%

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

4. Final simplification 93.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{+48} \lor \neg \left(z \leq 1.12 \cdot 10^{-26}\right):\\ \;\;\;\;9 \cdot \left(x \cdot \frac{\frac{y}{z}}{c}\right) + \mathsf{fma}\left(-4, a \cdot \frac{t}{c}, \frac{\frac{b}{z}}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{b + \mathsf{fma}\left(x, 9 \cdot y, t \cdot \left(a \cdot \left(z \cdot -4\right)\right)\right)}{z \cdot c}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 88.6% accurate, 0.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := y \cdot \left(9 \cdot x\right)\\ t_2 := \frac{b - \left(a \cdot \left(t \cdot \left(z \cdot 4\right)\right) - t\_1\right)}{z \cdot c}\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{-324}:\\ \;\;\;\;\left(t\_1 + \left(b - t \cdot \left(z \cdot \left(a \cdot 4\right)\right)\right)\right) \cdot \frac{1}{z \cdot c}\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;\frac{-4 \cdot \frac{a \cdot \left(z \cdot t\right)}{c} + \left(9 \cdot \frac{x \cdot y}{c} + \frac{b}{c}\right)}{z}\\ \mathbf{elif}\;t\_2 \leq \infty:\\ \;\;\;\;\frac{b + \left(t\_1 - \left(z \cdot 4\right) \cdot \left(a \cdot t\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(a \cdot \frac{t}{c}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* y (* 9.0 x)))
        (t_2 (/ (- b (- (* a (* t (* z 4.0))) t_1)) (* z c))))
   (if (<= t_2 -5e-324)
     (* (+ t_1 (- b (* t (* z (* a 4.0))))) (/ 1.0 (* z c)))
     (if (<= t_2 0.0)
       (/ (+ (* -4.0 (/ (* a (* z t)) c)) (+ (* 9.0 (/ (* x y) c)) (/ b c))) z)
       (if (<= t_2 INFINITY)
         (/ (+ b (- t_1 (* (* z 4.0) (* a t)))) (* z c))
         (* -4.0 (* a (/ t c))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = y * (9.0 * x);
	double t_2 = (b - ((a * (t * (z * 4.0))) - t_1)) / (z * c);
	double tmp;
	if (t_2 <= -5e-324) {
		tmp = (t_1 + (b - (t * (z * (a * 4.0))))) * (1.0 / (z * c));
	} else if (t_2 <= 0.0) {
		tmp = ((-4.0 * ((a * (z * t)) / c)) + ((9.0 * ((x * y) / c)) + (b / c))) / z;
	} else if (t_2 <= ((double) INFINITY)) {
		tmp = (b + (t_1 - ((z * 4.0) * (a * t)))) / (z * c);
	} else {
		tmp = -4.0 * (a * (t / c));
	}
	return tmp;
}

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = y * (9.0 * x);
	double t_2 = (b - ((a * (t * (z * 4.0))) - t_1)) / (z * c);
	double tmp;
	if (t_2 <= -5e-324) {
		tmp = (t_1 + (b - (t * (z * (a * 4.0))))) * (1.0 / (z * c));
	} else if (t_2 <= 0.0) {
		tmp = ((-4.0 * ((a * (z * t)) / c)) + ((9.0 * ((x * y) / c)) + (b / c))) / z;
	} else if (t_2 <= Double.POSITIVE_INFINITY) {
		tmp = (b + (t_1 - ((z * 4.0) * (a * t)))) / (z * c);
	} else {
		tmp = -4.0 * (a * (t / c));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	t_1 = y * (9.0 * x)
	t_2 = (b - ((a * (t * (z * 4.0))) - t_1)) / (z * c)
	tmp = 0
	if t_2 <= -5e-324:
		tmp = (t_1 + (b - (t * (z * (a * 4.0))))) * (1.0 / (z * c))
	elif t_2 <= 0.0:
		tmp = ((-4.0 * ((a * (z * t)) / c)) + ((9.0 * ((x * y) / c)) + (b / c))) / z
	elif t_2 <= math.inf:
		tmp = (b + (t_1 - ((z * 4.0) * (a * t)))) / (z * c)
	else:
		tmp = -4.0 * (a * (t / c))
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(y * Float64(9.0 * x))
	t_2 = Float64(Float64(b - Float64(Float64(a * Float64(t * Float64(z * 4.0))) - t_1)) / Float64(z * c))
	tmp = 0.0
	if (t_2 <= -5e-324)
		tmp = Float64(Float64(t_1 + Float64(b - Float64(t * Float64(z * Float64(a * 4.0))))) * Float64(1.0 / Float64(z * c)));
	elseif (t_2 <= 0.0)
		tmp = Float64(Float64(Float64(-4.0 * Float64(Float64(a * Float64(z * t)) / c)) + Float64(Float64(9.0 * Float64(Float64(x * y) / c)) + Float64(b / c))) / z);
	elseif (t_2 <= Inf)
		tmp = Float64(Float64(b + Float64(t_1 - Float64(Float64(z * 4.0) * Float64(a * t)))) / Float64(z * c));
	else
		tmp = Float64(-4.0 * Float64(a * Float64(t / c)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = y * (9.0 * x);
	t_2 = (b - ((a * (t * (z * 4.0))) - t_1)) / (z * c);
	tmp = 0.0;
	if (t_2 <= -5e-324)
		tmp = (t_1 + (b - (t * (z * (a * 4.0))))) * (1.0 / (z * c));
	elseif (t_2 <= 0.0)
		tmp = ((-4.0 * ((a * (z * t)) / c)) + ((9.0 * ((x * y) / c)) + (b / c))) / z;
	elseif (t_2 <= Inf)
		tmp = (b + (t_1 - ((z * 4.0) * (a * t)))) / (z * c);
	else
		tmp = -4.0 * (a * (t / c));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(y * N[(9.0 * x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b - N[(N[(a * N[(t * N[(z * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -5e-324], N[(N[(t$95$1 + N[(b - N[(t * N[(z * N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(1.0 / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 0.0], N[(N[(N[(-4.0 * N[(N[(a * N[(z * t), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision] + N[(N[(9.0 * N[(N[(x * y), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision] + N[(b / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t$95$2, Infinity], N[(N[(b + N[(t$95$1 - N[(N[(z * 4.0), $MachinePrecision] * N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(-4.0 * N[(a * N[(t / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x #s(literal 9 binary64)) y) (*.f64 (*.f64 (*.f64 z #s(literal 4 binary64)) t) a)) b) (*.f64 z c)) < -4.94066e-324

   1. Initial program 92.0%

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

      1. associate-+l- 92.0%

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

      2. *-commutative 92.0%

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

      3. associate-*r* 91.2%

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

      4. *-commutative 91.2%

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

      5. associate-+l- 91.2%

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

      6. associate-*l* 91.2%

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

      7. associate-*l* 92.0%

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

      8. *-commutative 92.0%

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

   3. Simplified 92.0%

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

   5. Taylor expanded in z around 0 92.0%

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

      1. associate-*r* 92.0%

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

      2. *-commutative 92.0%

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

   7. Simplified 92.0%

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

      1. div-inv 92.0%

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

      2. associate-+l- 92.0%

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

      3. associate-*r* 91.9%

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

      4. associate-*l* 91.1%

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

      5. *-commutative 91.1%

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

   9. Applied egg-rr 91.1%

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

   if -4.94066e-324 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x #s(literal 9 binary64)) y) (*.f64 (*.f64 (*.f64 z #s(literal 4 binary64)) t) a)) b) (*.f64 z c)) < 0.0

   1. Initial program 34.6%

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

   3. Simplified 33.7%

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

   5. Taylor expanded in z around 0 99.6%

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

   if 0.0 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x #s(literal 9 binary64)) y) (*.f64 (*.f64 (*.f64 z #s(literal 4 binary64)) t) a)) b) (*.f64 z c)) < +inf.0

   1. Initial program 87.4%

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

      1. associate-+l- 87.4%

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

      2. *-commutative 87.4%

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

      3. associate-*r* 90.2%

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

      4. *-commutative 90.2%

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

      5. associate-+l- 90.2%

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

      6. associate-*l* 90.2%

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

      7. associate-*l* 90.1%

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

      8. *-commutative 90.1%

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

   3. Simplified 90.1%

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

   5. Taylor expanded in x around 0 90.1%

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

      1. associate-*r* 90.1%

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

   7. Simplified 90.1%

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

   if +inf.0 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x #s(literal 9 binary64)) y) (*.f64 (*.f64 (*.f64 z #s(literal 4 binary64)) t) a)) b) (*.f64 z c))

   1. Initial program 0.0%

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

   3. Simplified 4.3%

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

   5. Taylor expanded in x around 0 41.9%

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

      1. +-commutative 41.9%

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

      2. metadata-eval 41.9%

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

      3. cancel-sign-sub-inv 41.9%

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

      4. associate--l+ 41.9%

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

      5. fma-define 41.9%

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

      6. associate-/l* 43.3%

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

      7. *-commutative 43.3%

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

      8. cancel-sign-sub-inv 43.3%

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

      9. metadata-eval 43.3%

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

      10. +-commutative 43.3%

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

      11. fma-define 43.3%

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

      12. associate-/l* 78.2%

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

      13. *-commutative 78.2%

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

   7. Simplified 78.2%

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

   8. Taylor expanded in z around inf 47.0%

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

      1. associate-*r/ 81.9%

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

   10. Simplified 81.9%

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

4. Final simplification 90.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{b - \left(a \cdot \left(t \cdot \left(z \cdot 4\right)\right) - y \cdot \left(9 \cdot x\right)\right)}{z \cdot c} \leq -5 \cdot 10^{-324}:\\ \;\;\;\;\left(y \cdot \left(9 \cdot x\right) + \left(b - t \cdot \left(z \cdot \left(a \cdot 4\right)\right)\right)\right) \cdot \frac{1}{z \cdot c}\\ \mathbf{elif}\;\frac{b - \left(a \cdot \left(t \cdot \left(z \cdot 4\right)\right) - y \cdot \left(9 \cdot x\right)\right)}{z \cdot c} \leq 0:\\ \;\;\;\;\frac{-4 \cdot \frac{a \cdot \left(z \cdot t\right)}{c} + \left(9 \cdot \frac{x \cdot y}{c} + \frac{b}{c}\right)}{z}\\ \mathbf{elif}\;\frac{b - \left(a \cdot \left(t \cdot \left(z \cdot 4\right)\right) - y \cdot \left(9 \cdot x\right)\right)}{z \cdot c} \leq \infty:\\ \;\;\;\;\frac{b + \left(y \cdot \left(9 \cdot x\right) - \left(z \cdot 4\right) \cdot \left(a \cdot t\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(a \cdot \frac{t}{c}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 85.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := y \cdot \left(9 \cdot x\right)\\ \mathbf{if}\;\frac{b - \left(a \cdot \left(t \cdot \left(z \cdot 4\right)\right) - t\_1\right)}{z \cdot c} \leq \infty:\\ \;\;\;\;\frac{b + \left(t\_1 - \left(z \cdot 4\right) \cdot \left(a \cdot t\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(a \cdot \frac{t}{c}\right)\\ \end{array} \end{array} \]

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x #s(literal 9 binary64)) y) (*.f64 (*.f64 (*.f64 z #s(literal 4 binary64)) t) a)) b) (*.f64 z c)) < +inf.0

   1. Initial program 86.6%

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

      1. associate-+l- 86.6%

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

      2. *-commutative 86.6%

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

      3. associate-*r* 87.4%

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

      4. *-commutative 87.4%

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

      5. associate-+l- 87.4%

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

      6. associate-*l* 87.4%

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

      7. associate-*l* 87.9%

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

      8. *-commutative 87.9%

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

   3. Simplified 87.9%

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

   5. Taylor expanded in x around 0 87.9%

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

      1. associate-*r* 87.9%

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

   7. Simplified 87.9%

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

   if +inf.0 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x #s(literal 9 binary64)) y) (*.f64 (*.f64 (*.f64 z #s(literal 4 binary64)) t) a)) b) (*.f64 z c))

   1. Initial program 0.0%

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

   3. Simplified 4.3%

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

   5. Taylor expanded in x around 0 41.9%

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

      1. +-commutative 41.9%

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

      2. metadata-eval 41.9%

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

      3. cancel-sign-sub-inv 41.9%

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

      4. associate--l+ 41.9%

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

      5. fma-define 41.9%

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

      6. associate-/l* 43.3%

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

      7. *-commutative 43.3%

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

      8. cancel-sign-sub-inv 43.3%

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

      9. metadata-eval 43.3%

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

      10. +-commutative 43.3%

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

      11. fma-define 43.3%

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

      12. associate-/l* 78.2%

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

      13. *-commutative 78.2%

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

   7. Simplified 78.2%

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

   8. Taylor expanded in z around inf 47.0%

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

      1. associate-*r/ 81.9%

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

   10. Simplified 81.9%

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

4. Final simplification 87.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{b - \left(a \cdot \left(t \cdot \left(z \cdot 4\right)\right) - y \cdot \left(9 \cdot x\right)\right)}{z \cdot c} \leq \infty:\\ \;\;\;\;\frac{b + \left(y \cdot \left(9 \cdot x\right) - \left(z \cdot 4\right) \cdot \left(a \cdot t\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(a \cdot \frac{t}{c}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 84.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{+138} \lor \neg \left(z \leq 3.8 \cdot 10^{+100}\right):\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right) + 9 \cdot \frac{x \cdot y}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + \left(x \cdot \left(9 \cdot y\right) - \left(z \cdot t\right) \cdot \left(a \cdot 4\right)\right)}{z \cdot c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= z -5.2e+138) (not (<= z 3.8e+100)))
   (/ (+ (* -4.0 (* a t)) (* 9.0 (/ (* x y) z))) c)
   (/ (+ b (- (* x (* 9.0 y)) (* (* z t) (* a 4.0)))) (* z c))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((z <= -5.2e+138) || !(z <= 3.8e+100)) {
		tmp = ((-4.0 * (a * t)) + (9.0 * ((x * y) / z))) / c;
	} else {
		tmp = (b + ((x * (9.0 * y)) - ((z * t) * (a * 4.0)))) / (z * c);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c 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 <= (-5.2d+138)) .or. (.not. (z <= 3.8d+100))) then
        tmp = (((-4.0d0) * (a * t)) + (9.0d0 * ((x * y) / z))) / c
    else
        tmp = (b + ((x * (9.0d0 * y)) - ((z * t) * (a * 4.0d0)))) / (z * c)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((z <= -5.2e+138) || !(z <= 3.8e+100)) {
		tmp = ((-4.0 * (a * t)) + (9.0 * ((x * y) / z))) / c;
	} else {
		tmp = (b + ((x * (9.0 * y)) - ((z * t) * (a * 4.0)))) / (z * c);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if (z <= -5.2e+138) or not (z <= 3.8e+100):
		tmp = ((-4.0 * (a * t)) + (9.0 * ((x * y) / z))) / c
	else:
		tmp = (b + ((x * (9.0 * y)) - ((z * t) * (a * 4.0)))) / (z * c)
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((z <= -5.2e+138) || !(z <= 3.8e+100))
		tmp = Float64(Float64(Float64(-4.0 * Float64(a * t)) + Float64(9.0 * Float64(Float64(x * y) / z))) / c);
	else
		tmp = Float64(Float64(b + Float64(Float64(x * Float64(9.0 * y)) - Float64(Float64(z * t) * Float64(a * 4.0)))) / Float64(z * c));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((z <= -5.2e+138) || ~((z <= 3.8e+100)))
		tmp = ((-4.0 * (a * t)) + (9.0 * ((x * y) / z))) / c;
	else
		tmp = (b + ((x * (9.0 * y)) - ((z * t) * (a * 4.0)))) / (z * c);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[z, -5.2e+138], N[Not[LessEqual[z, 3.8e+100]], $MachinePrecision]], N[(N[(N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision] + N[(9.0 * N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], N[(N[(b + N[(N[(x * N[(9.0 * y), $MachinePrecision]), $MachinePrecision] - N[(N[(z * t), $MachinePrecision] * N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.2000000000000002e138 or 3.79999999999999963e100 < z

   1. Initial program 46.4%

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

   3. Simplified 50.0%

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

   5. Taylor expanded in x around 0 76.3%

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

      1. +-commutative 76.3%

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

      2. metadata-eval 76.3%

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

      3. cancel-sign-sub-inv 76.3%

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

      4. associate--l+ 76.3%

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

      5. fma-define 76.3%

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

      6. associate-/l* 78.9%

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

      7. *-commutative 78.9%

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

      8. cancel-sign-sub-inv 78.9%

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

      9. metadata-eval 78.9%

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

      10. +-commutative 78.9%

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

      11. fma-define 78.9%

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

      12. associate-/l* 81.3%

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

      13. *-commutative 81.3%

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

   7. Simplified 81.3%

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

   8. Taylor expanded in b around 0 71.7%

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

   9. Taylor expanded in c around 0 74.3%

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

   if -5.2000000000000002e138 < z < 3.79999999999999963e100

   1. Initial program 92.1%

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

      1. associate-+l- 92.1%

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

      2. *-commutative 92.1%

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

      3. associate-*r* 91.6%

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

      4. *-commutative 91.6%

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

      5. associate-+l- 91.6%

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

      6. associate-*l* 91.6%

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

      7. associate-*l* 90.5%

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

      8. *-commutative 90.5%

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

   3. Simplified 90.5%

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

   5. Taylor expanded in z around 0 92.1%

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

      1. associate-*r* 92.1%

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

      2. *-commutative 92.1%

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

   7. Simplified 92.1%

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

4. Final simplification 86.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{+138} \lor \neg \left(z \leq 3.8 \cdot 10^{+100}\right):\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right) + 9 \cdot \frac{x \cdot y}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + \left(x \cdot \left(9 \cdot y\right) - \left(z \cdot t\right) \cdot \left(a \cdot 4\right)\right)}{z \cdot c}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 49.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -1.06 \cdot 10^{+70}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;t \leq -3.3 \cdot 10^{-88}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{-282}:\\ \;\;\;\;9 \cdot \left(x \cdot \frac{y}{z \cdot c}\right)\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{-121}:\\ \;\;\;\;\frac{b}{c} \cdot \frac{1}{z}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(a \cdot \frac{t}{c}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= t -1.06e+70)
   (* -4.0 (* t (/ a c)))
   (if (<= t -3.3e-88)
     (/ b (* z c))
     (if (<= t 1.7e-282)
       (* 9.0 (* x (/ y (* z c))))
       (if (<= t 2.6e-121) (* (/ b c) (/ 1.0 z)) (* -4.0 (* a (/ t c))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (t <= -1.06e+70) {
		tmp = -4.0 * (t * (a / c));
	} else if (t <= -3.3e-88) {
		tmp = b / (z * c);
	} else if (t <= 1.7e-282) {
		tmp = 9.0 * (x * (y / (z * c)));
	} else if (t <= 2.6e-121) {
		tmp = (b / c) * (1.0 / z);
	} else {
		tmp = -4.0 * (a * (t / c));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (t <= (-1.06d+70)) then
        tmp = (-4.0d0) * (t * (a / c))
    else if (t <= (-3.3d-88)) then
        tmp = b / (z * c)
    else if (t <= 1.7d-282) then
        tmp = 9.0d0 * (x * (y / (z * c)))
    else if (t <= 2.6d-121) then
        tmp = (b / c) * (1.0d0 / z)
    else
        tmp = (-4.0d0) * (a * (t / c))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (t <= -1.06e+70) {
		tmp = -4.0 * (t * (a / c));
	} else if (t <= -3.3e-88) {
		tmp = b / (z * c);
	} else if (t <= 1.7e-282) {
		tmp = 9.0 * (x * (y / (z * c)));
	} else if (t <= 2.6e-121) {
		tmp = (b / c) * (1.0 / z);
	} else {
		tmp = -4.0 * (a * (t / c));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if t <= -1.06e+70:
		tmp = -4.0 * (t * (a / c))
	elif t <= -3.3e-88:
		tmp = b / (z * c)
	elif t <= 1.7e-282:
		tmp = 9.0 * (x * (y / (z * c)))
	elif t <= 2.6e-121:
		tmp = (b / c) * (1.0 / z)
	else:
		tmp = -4.0 * (a * (t / c))
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (t <= -1.06e+70)
		tmp = Float64(-4.0 * Float64(t * Float64(a / c)));
	elseif (t <= -3.3e-88)
		tmp = Float64(b / Float64(z * c));
	elseif (t <= 1.7e-282)
		tmp = Float64(9.0 * Float64(x * Float64(y / Float64(z * c))));
	elseif (t <= 2.6e-121)
		tmp = Float64(Float64(b / c) * Float64(1.0 / z));
	else
		tmp = Float64(-4.0 * Float64(a * Float64(t / c)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (t <= -1.06e+70)
		tmp = -4.0 * (t * (a / c));
	elseif (t <= -3.3e-88)
		tmp = b / (z * c);
	elseif (t <= 1.7e-282)
		tmp = 9.0 * (x * (y / (z * c)));
	elseif (t <= 2.6e-121)
		tmp = (b / c) * (1.0 / z);
	else
		tmp = -4.0 * (a * (t / c));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[t, -1.06e+70], N[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -3.3e-88], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.7e-282], N[(9.0 * N[(x * N[(y / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.6e-121], N[(N[(b / c), $MachinePrecision] * N[(1.0 / z), $MachinePrecision]), $MachinePrecision], N[(-4.0 * N[(a * N[(t / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -1.06e70

   1. Initial program 63.4%

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

   3. Simplified 66.5%

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

   5. Taylor expanded in x around 0 74.6%

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

      1. +-commutative 74.6%

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

      2. metadata-eval 74.6%

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

      3. cancel-sign-sub-inv 74.6%

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

      4. associate--l+ 74.6%

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

      5. fma-define 74.6%

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

      6. associate-/l* 74.7%

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

      7. *-commutative 74.7%

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

      8. cancel-sign-sub-inv 74.7%

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

      9. metadata-eval 74.7%

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

      10. +-commutative 74.7%

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

      11. fma-define 74.7%

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

      12. associate-/l* 84.0%

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

      13. *-commutative 84.0%

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

   7. Simplified 84.0%

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

      1. fma-undefine 84.0%

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

      2. associate-/r* 87.2%

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

      3. associate-/r* 87.3%

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

   9. Applied egg-rr 87.3%

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

   10. Taylor expanded in z around inf 60.6%

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

       1. associate-*r/ 60.6%

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

       2. associate-*r* 60.6%

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

       3. associate-*l/ 68.9%

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

       4. associate-*r/ 68.9%

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

       5. associate-*l* 68.9%

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

   12. Simplified 68.9%

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

   if -1.06e70 < t < -3.29999999999999994e-88

   1. Initial program 83.4%

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

   3. Simplified 83.4%

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

   5. Taylor expanded in b around inf 55.0%

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

      1. *-commutative 55.0%

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

   7. Simplified 55.0%

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

   if -3.29999999999999994e-88 < t < 1.69999999999999999e-282

   1. Initial program 85.9%

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

   3. Simplified 81.7%

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

   5. Taylor expanded in x around 0 79.4%

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

      1. +-commutative 79.4%

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

      2. metadata-eval 79.4%

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

      3. cancel-sign-sub-inv 79.4%

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

      4. associate--l+ 79.4%

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

      5. fma-define 79.4%

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

      6. associate-/l* 81.5%

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

      7. *-commutative 81.5%

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

      8. cancel-sign-sub-inv 81.5%

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

      9. metadata-eval 81.5%

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

      10. +-commutative 81.5%

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

      11. fma-define 81.5%

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

      12. associate-/l* 76.4%

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

      13. *-commutative 76.4%

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

   7. Simplified 76.4%

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

   8. Taylor expanded in x around inf 57.5%

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

      1. associate-/l* 59.5%

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

   10. Simplified 59.5%

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

   if 1.69999999999999999e-282 < t < 2.59999999999999986e-121

   1. Initial program 92.4%

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

   3. Simplified 92.4%

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

   6. Applied egg-rr 88.5%

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

   7. Taylor expanded in b around inf 63.0%

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

   if 2.59999999999999986e-121 < t

   1. Initial program 76.2%

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

   3. Simplified 79.8%

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

   5. Taylor expanded in x around 0 78.3%

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

      1. +-commutative 78.3%

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

      2. metadata-eval 78.3%

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

      3. cancel-sign-sub-inv 78.3%

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

      4. associate--l+ 78.3%

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

      5. fma-define 78.3%

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

      6. associate-/l* 77.3%

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

      7. *-commutative 77.3%

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

      8. cancel-sign-sub-inv 77.3%

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

      9. metadata-eval 77.3%

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

      10. +-commutative 77.3%

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

      11. fma-define 77.3%

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

      12. associate-/l* 80.3%

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

      13. *-commutative 80.3%

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

   7. Simplified 80.3%

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

   8. Taylor expanded in z around inf 52.0%

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

      1. associate-*r/ 58.2%

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

   10. Simplified 58.2%

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

4. Final simplification 61.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.06 \cdot 10^{+70}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;t \leq -3.3 \cdot 10^{-88}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{-282}:\\ \;\;\;\;9 \cdot \left(x \cdot \frac{y}{z \cdot c}\right)\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{-121}:\\ \;\;\;\;\frac{b}{c} \cdot \frac{1}{z}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(a \cdot \frac{t}{c}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 72.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;b \leq -2.3 \cdot 10^{+90}:\\ \;\;\;\;\frac{b + x \cdot \left(9 \cdot y\right)}{z \cdot c}\\ \mathbf{elif}\;b \leq 1.5 \cdot 10^{+21}:\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right) + 9 \cdot \frac{x \cdot y}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b - \left(z \cdot t\right) \cdot \left(a \cdot 4\right)}{z \cdot c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= b -2.3e+90)
   (/ (+ b (* x (* 9.0 y))) (* z c))
   (if (<= b 1.5e+21)
     (/ (+ (* -4.0 (* a t)) (* 9.0 (/ (* x y) z))) c)
     (/ (- b (* (* z t) (* a 4.0))) (* z c)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (b <= -2.3e+90) {
		tmp = (b + (x * (9.0 * y))) / (z * c);
	} else if (b <= 1.5e+21) {
		tmp = ((-4.0 * (a * t)) + (9.0 * ((x * y) / z))) / c;
	} else {
		tmp = (b - ((z * t) * (a * 4.0))) / (z * c);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c 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 <= (-2.3d+90)) then
        tmp = (b + (x * (9.0d0 * y))) / (z * c)
    else if (b <= 1.5d+21) then
        tmp = (((-4.0d0) * (a * t)) + (9.0d0 * ((x * y) / z))) / c
    else
        tmp = (b - ((z * t) * (a * 4.0d0))) / (z * c)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (b <= -2.3e+90) {
		tmp = (b + (x * (9.0 * y))) / (z * c);
	} else if (b <= 1.5e+21) {
		tmp = ((-4.0 * (a * t)) + (9.0 * ((x * y) / z))) / c;
	} else {
		tmp = (b - ((z * t) * (a * 4.0))) / (z * c);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if b <= -2.3e+90:
		tmp = (b + (x * (9.0 * y))) / (z * c)
	elif b <= 1.5e+21:
		tmp = ((-4.0 * (a * t)) + (9.0 * ((x * y) / z))) / c
	else:
		tmp = (b - ((z * t) * (a * 4.0))) / (z * c)
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (b <= -2.3e+90)
		tmp = Float64(Float64(b + Float64(x * Float64(9.0 * y))) / Float64(z * c));
	elseif (b <= 1.5e+21)
		tmp = Float64(Float64(Float64(-4.0 * Float64(a * t)) + Float64(9.0 * Float64(Float64(x * y) / z))) / c);
	else
		tmp = Float64(Float64(b - Float64(Float64(z * t) * Float64(a * 4.0))) / Float64(z * c));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (b <= -2.3e+90)
		tmp = (b + (x * (9.0 * y))) / (z * c);
	elseif (b <= 1.5e+21)
		tmp = ((-4.0 * (a * t)) + (9.0 * ((x * y) / z))) / c;
	else
		tmp = (b - ((z * t) * (a * 4.0))) / (z * c);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[b, -2.3e+90], N[(N[(b + N[(x * N[(9.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.5e+21], N[(N[(N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision] + N[(9.0 * N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], N[(N[(b - N[(N[(z * t), $MachinePrecision] * N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -2.3e90

   1. Initial program 79.8%

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

      1. associate-+l- 79.8%

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

      2. *-commutative 79.8%

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

      3. associate-*r* 77.5%

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

      4. *-commutative 77.5%

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

      5. associate-+l- 77.5%

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

      6. associate-*l* 77.5%

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

      7. associate-*l* 79.8%

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

      8. *-commutative 79.8%

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

   3. Simplified 79.8%

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

   5. Taylor expanded in z around 0 79.8%

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

      1. associate-*r* 79.8%

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

      2. *-commutative 79.8%

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

   7. Simplified 79.8%

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

   8. Taylor expanded in x around inf 75.2%

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

      1. associate-*r* 75.2%

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

      2. *-commutative 75.2%

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

      3. associate-*l* 75.2%

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

   10. Simplified 75.2%

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

   if -2.3e90 < b < 1.5e21

   1. Initial program 79.2%

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

   3. Simplified 81.2%

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

   5. Taylor expanded in x around 0 83.5%

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

      1. +-commutative 83.5%

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

      2. metadata-eval 83.5%

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

      3. cancel-sign-sub-inv 83.5%

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

      4. associate--l+ 83.5%

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

      5. fma-define 83.5%

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

      6. associate-/l* 82.3%

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

      7. *-commutative 82.3%

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

      8. cancel-sign-sub-inv 82.3%

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

      9. metadata-eval 82.3%

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

      10. +-commutative 82.3%

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

      11. fma-define 82.3%

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

      12. associate-/l* 82.0%

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

      13. *-commutative 82.0%

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

   7. Simplified 82.0%

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

   8. Taylor expanded in b around 0 78.5%

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

   9. Taylor expanded in c around 0 80.6%

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

   if 1.5e21 < b

   1. Initial program 71.6%

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

   3. Simplified 73.4%

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

   5. Taylor expanded in x around 0 66.8%

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

      1. metadata-eval 66.8%

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

      2. cancel-sign-sub-inv 66.8%

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

      3. associate-*r* 66.8%

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

      4. *-commutative 66.8%

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

   7. Simplified 66.8%

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

4. Final simplification 76.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.3 \cdot 10^{+90}:\\ \;\;\;\;\frac{b + x \cdot \left(9 \cdot y\right)}{z \cdot c}\\ \mathbf{elif}\;b \leq 1.5 \cdot 10^{+21}:\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right) + 9 \cdot \frac{x \cdot y}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b - \left(z \cdot t\right) \cdot \left(a \cdot 4\right)}{z \cdot c}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 68.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -2.7 \cdot 10^{+167} \lor \neg \left(t \leq 6.2 \cdot 10^{-54}\right):\\ \;\;\;\;-4 \cdot \left(a \cdot \frac{t}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{b + y \cdot \left(9 \cdot x\right)}{z \cdot c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= t -2.7e+167) (not (<= t 6.2e-54)))
   (* -4.0 (* a (/ t c)))
   (/ (+ b (* y (* 9.0 x))) (* z c))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((t <= -2.7e+167) || !(t <= 6.2e-54)) {
		tmp = -4.0 * (a * (t / c));
	} else {
		tmp = (b + (y * (9.0 * x))) / (z * c);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if ((t <= (-2.7d+167)) .or. (.not. (t <= 6.2d-54))) then
        tmp = (-4.0d0) * (a * (t / c))
    else
        tmp = (b + (y * (9.0d0 * x))) / (z * c)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((t <= -2.7e+167) || !(t <= 6.2e-54)) {
		tmp = -4.0 * (a * (t / c));
	} else {
		tmp = (b + (y * (9.0 * x))) / (z * c);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if (t <= -2.7e+167) or not (t <= 6.2e-54):
		tmp = -4.0 * (a * (t / c))
	else:
		tmp = (b + (y * (9.0 * x))) / (z * c)
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((t <= -2.7e+167) || !(t <= 6.2e-54))
		tmp = Float64(-4.0 * Float64(a * Float64(t / c)));
	else
		tmp = Float64(Float64(b + Float64(y * Float64(9.0 * x))) / Float64(z * c));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((t <= -2.7e+167) || ~((t <= 6.2e-54)))
		tmp = -4.0 * (a * (t / c));
	else
		tmp = (b + (y * (9.0 * x))) / (z * c);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[t, -2.7e+167], N[Not[LessEqual[t, 6.2e-54]], $MachinePrecision]], N[(-4.0 * N[(a * N[(t / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b + N[(y * N[(9.0 * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.70000000000000005e167 or 6.20000000000000008e-54 < t

   1. Initial program 71.7%

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

   3. Simplified 74.5%

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

   5. Taylor expanded in x around 0 75.1%

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

      1. +-commutative 75.1%

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

      2. metadata-eval 75.1%

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

      3. cancel-sign-sub-inv 75.1%

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

      4. associate--l+ 75.1%

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

      5. fma-define 75.1%

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

      6. associate-/l* 76.0%

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

      7. *-commutative 76.0%

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

      8. cancel-sign-sub-inv 76.0%

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

      9. metadata-eval 76.0%

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

      10. +-commutative 76.0%

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

      11. fma-define 76.0%

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

      12. associate-/l* 83.9%

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

      13. *-commutative 83.9%

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

   7. Simplified 83.9%

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

   8. Taylor expanded in z around inf 59.0%

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

      1. associate-*r/ 68.6%

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

   10. Simplified 68.6%

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

   if -2.70000000000000005e167 < t < 6.20000000000000008e-54

   1. Initial program 82.4%

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

   3. Simplified 82.3%

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

   5. Taylor expanded in t around 0 72.4%

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

      1. +-commutative 72.4%

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

      2. associate-*r* 72.4%

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

      3. *-commutative 72.4%

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

   7. Simplified 72.4%

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

4. Final simplification 70.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.7 \cdot 10^{+167} \lor \neg \left(t \leq 6.2 \cdot 10^{-54}\right):\\ \;\;\;\;-4 \cdot \left(a \cdot \frac{t}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{b + y \cdot \left(9 \cdot x\right)}{z \cdot c}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 68.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -2.4 \cdot 10^{+167} \lor \neg \left(t \leq 7.4 \cdot 10^{-54}\right):\\ \;\;\;\;-4 \cdot \left(a \cdot \frac{t}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{b + x \cdot \left(9 \cdot y\right)}{z \cdot c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= t -2.4e+167) (not (<= t 7.4e-54)))
   (* -4.0 (* a (/ t c)))
   (/ (+ b (* x (* 9.0 y))) (* z c))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((t <= -2.4e+167) || !(t <= 7.4e-54)) {
		tmp = -4.0 * (a * (t / c));
	} else {
		tmp = (b + (x * (9.0 * y))) / (z * c);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if ((t <= (-2.4d+167)) .or. (.not. (t <= 7.4d-54))) then
        tmp = (-4.0d0) * (a * (t / c))
    else
        tmp = (b + (x * (9.0d0 * y))) / (z * c)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((t <= -2.4e+167) || !(t <= 7.4e-54)) {
		tmp = -4.0 * (a * (t / c));
	} else {
		tmp = (b + (x * (9.0 * y))) / (z * c);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if (t <= -2.4e+167) or not (t <= 7.4e-54):
		tmp = -4.0 * (a * (t / c))
	else:
		tmp = (b + (x * (9.0 * y))) / (z * c)
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((t <= -2.4e+167) || !(t <= 7.4e-54))
		tmp = Float64(-4.0 * Float64(a * Float64(t / c)));
	else
		tmp = Float64(Float64(b + Float64(x * Float64(9.0 * y))) / Float64(z * c));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((t <= -2.4e+167) || ~((t <= 7.4e-54)))
		tmp = -4.0 * (a * (t / c));
	else
		tmp = (b + (x * (9.0 * y))) / (z * c);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[t, -2.4e+167], N[Not[LessEqual[t, 7.4e-54]], $MachinePrecision]], N[(-4.0 * N[(a * N[(t / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b + N[(x * N[(9.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.39999999999999999e167 or 7.4000000000000006e-54 < t

   1. Initial program 71.7%

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

   3. Simplified 74.5%

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

   5. Taylor expanded in x around 0 75.1%

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

      1. +-commutative 75.1%

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

      2. metadata-eval 75.1%

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

      3. cancel-sign-sub-inv 75.1%

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

      4. associate--l+ 75.1%

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

      5. fma-define 75.1%

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

      6. associate-/l* 76.0%

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

      7. *-commutative 76.0%

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

      8. cancel-sign-sub-inv 76.0%

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

      9. metadata-eval 76.0%

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

      10. +-commutative 76.0%

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

      11. fma-define 76.0%

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

      12. associate-/l* 83.9%

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

      13. *-commutative 83.9%

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

   7. Simplified 83.9%

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

   8. Taylor expanded in z around inf 59.0%

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

      1. associate-*r/ 68.6%

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

   10. Simplified 68.6%

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

   if -2.39999999999999999e167 < t < 7.4000000000000006e-54

   1. Initial program 82.4%

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

      1. associate-+l- 82.4%

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

      2. *-commutative 82.4%

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

      3. associate-*r* 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%

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

      6. associate-*l* 82.3%

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

      7. associate-*l* 83.8%

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

      8. *-commutative 83.8%

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

   3. Simplified 83.8%

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

   5. Taylor expanded in z around 0 82.4%

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

      1. associate-*r* 82.4%

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

      2. *-commutative 82.4%

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

   7. Simplified 82.4%

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

   8. Taylor expanded in x around inf 72.4%

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

      1. associate-*r* 72.4%

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

      2. *-commutative 72.4%

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

      3. associate-*l* 72.4%

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

   10. Simplified 72.4%

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

4. Final simplification 70.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.4 \cdot 10^{+167} \lor \neg \left(t \leq 7.4 \cdot 10^{-54}\right):\\ \;\;\;\;-4 \cdot \left(a \cdot \frac{t}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{b + x \cdot \left(9 \cdot y\right)}{z \cdot c}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 50.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -1.06 \cdot 10^{+70} \lor \neg \left(t \leq 6.6 \cdot 10^{-122}\right):\\ \;\;\;\;-4 \cdot \left(a \cdot \frac{t}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= t -1.06e+70) (not (<= t 6.6e-122)))
   (* -4.0 (* a (/ t c)))
   (/ b (* z c))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((t <= -1.06e+70) || !(t <= 6.6e-122)) {
		tmp = -4.0 * (a * (t / c));
	} else {
		tmp = b / (z * c);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if ((t <= (-1.06d+70)) .or. (.not. (t <= 6.6d-122))) then
        tmp = (-4.0d0) * (a * (t / c))
    else
        tmp = b / (z * c)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((t <= -1.06e+70) || !(t <= 6.6e-122)) {
		tmp = -4.0 * (a * (t / c));
	} else {
		tmp = b / (z * c);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if (t <= -1.06e+70) or not (t <= 6.6e-122):
		tmp = -4.0 * (a * (t / c))
	else:
		tmp = b / (z * c)
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((t <= -1.06e+70) || !(t <= 6.6e-122))
		tmp = Float64(-4.0 * Float64(a * Float64(t / c)));
	else
		tmp = Float64(b / Float64(z * c));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((t <= -1.06e+70) || ~((t <= 6.6e-122)))
		tmp = -4.0 * (a * (t / c));
	else
		tmp = b / (z * c);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[t, -1.06e+70], N[Not[LessEqual[t, 6.6e-122]], $MachinePrecision]], N[(-4.0 * N[(a * N[(t / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.06e70 or 6.59999999999999999e-122 < t

   1. Initial program 71.0%

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

   3. Simplified 74.5%

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

   5. Taylor expanded in x around 0 76.8%

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

      1. +-commutative 76.8%

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

      2. metadata-eval 76.8%

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

      3. cancel-sign-sub-inv 76.8%

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

      4. associate--l+ 76.8%

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

      5. fma-define 76.8%

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

      6. associate-/l* 76.2%

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

      7. *-commutative 76.2%

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

      8. cancel-sign-sub-inv 76.2%

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

      9. metadata-eval 76.2%

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

      10. +-commutative 76.2%

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

      11. fma-define 76.2%

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

      12. associate-/l* 81.8%

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

      13. *-commutative 81.8%

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

   7. Simplified 81.8%

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

   8. Taylor expanded in z around inf 55.5%

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

      1. associate-*r/ 62.3%

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

   10. Simplified 62.3%

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

   if -1.06e70 < t < 6.59999999999999999e-122

   1. Initial program 86.8%

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

   3. Simplified 84.9%

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

   5. Taylor expanded in b around inf 47.1%

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

      1. *-commutative 47.1%

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

   7. Simplified 47.1%

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

4. Final simplification 56.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.06 \cdot 10^{+70} \lor \neg \left(t \leq 6.6 \cdot 10^{-122}\right):\\ \;\;\;\;-4 \cdot \left(a \cdot \frac{t}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 49.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -8.5 \cdot 10^{+70}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{-122}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(a \cdot \frac{t}{c}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= t -8.5e+70)
   (* -4.0 (* t (/ a c)))
   (if (<= t 1.6e-122) (/ b (* z c)) (* -4.0 (* a (/ t c))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (t <= -8.5e+70) {
		tmp = -4.0 * (t * (a / c));
	} else if (t <= 1.6e-122) {
		tmp = b / (z * c);
	} else {
		tmp = -4.0 * (a * (t / c));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (t <= (-8.5d+70)) then
        tmp = (-4.0d0) * (t * (a / c))
    else if (t <= 1.6d-122) then
        tmp = b / (z * c)
    else
        tmp = (-4.0d0) * (a * (t / c))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (t <= -8.5e+70) {
		tmp = -4.0 * (t * (a / c));
	} else if (t <= 1.6e-122) {
		tmp = b / (z * c);
	} else {
		tmp = -4.0 * (a * (t / c));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if t <= -8.5e+70:
		tmp = -4.0 * (t * (a / c))
	elif t <= 1.6e-122:
		tmp = b / (z * c)
	else:
		tmp = -4.0 * (a * (t / c))
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (t <= -8.5e+70)
		tmp = Float64(-4.0 * Float64(t * Float64(a / c)));
	elseif (t <= 1.6e-122)
		tmp = Float64(b / Float64(z * c));
	else
		tmp = Float64(-4.0 * Float64(a * Float64(t / c)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (t <= -8.5e+70)
		tmp = -4.0 * (t * (a / c));
	elseif (t <= 1.6e-122)
		tmp = b / (z * c);
	else
		tmp = -4.0 * (a * (t / c));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[t, -8.5e+70], N[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.6e-122], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(-4.0 * N[(a * N[(t / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -8.4999999999999996e70

   1. Initial program 63.4%

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

   3. Simplified 66.5%

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

   5. Taylor expanded in x around 0 74.6%

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

      1. +-commutative 74.6%

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

      2. metadata-eval 74.6%

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

      3. cancel-sign-sub-inv 74.6%

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

      4. associate--l+ 74.6%

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

      5. fma-define 74.6%

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

      6. associate-/l* 74.7%

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

      7. *-commutative 74.7%

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

      8. cancel-sign-sub-inv 74.7%

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

      9. metadata-eval 74.7%

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

      10. +-commutative 74.7%

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

      11. fma-define 74.7%

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

      12. associate-/l* 84.0%

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

      13. *-commutative 84.0%

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

   7. Simplified 84.0%

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

      1. fma-undefine 84.0%

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

      2. associate-/r* 87.2%

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

      3. associate-/r* 87.3%

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

   9. Applied egg-rr 87.3%

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

   10. Taylor expanded in z around inf 60.6%

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

       1. associate-*r/ 60.6%

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

       2. associate-*r* 60.6%

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

       3. associate-*l/ 68.9%

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

       4. associate-*r/ 68.9%

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

       5. associate-*l* 68.9%

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

   12. Simplified 68.9%

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

   if -8.4999999999999996e70 < t < 1.6000000000000001e-122

   1. Initial program 86.8%

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

   3. Simplified 84.9%

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

   5. Taylor expanded in b around inf 47.1%

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

      1. *-commutative 47.1%

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

   7. Simplified 47.1%

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

   if 1.6000000000000001e-122 < t

   1. Initial program 76.2%

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

   3. Simplified 79.8%

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

   5. Taylor expanded in x around 0 78.3%

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

      1. +-commutative 78.3%

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

      2. metadata-eval 78.3%

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

      3. cancel-sign-sub-inv 78.3%

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

      4. associate--l+ 78.3%

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

      5. fma-define 78.3%

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

      6. associate-/l* 77.3%

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

      7. *-commutative 77.3%

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

      8. cancel-sign-sub-inv 77.3%

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

      9. metadata-eval 77.3%

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

      10. +-commutative 77.3%

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

      11. fma-define 77.3%

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

      12. associate-/l* 80.3%

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

      13. *-commutative 80.3%

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

   7. Simplified 80.3%

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

   8. Taylor expanded in z around inf 52.0%

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

      1. associate-*r/ 58.2%

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

   10. Simplified 58.2%

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

4. Final simplification 56.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.5 \cdot 10^{+70}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{-122}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(a \cdot \frac{t}{c}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 34.7% accurate, 3.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 77.4%

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

3. Simplified 78.7%

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

5. Taylor expanded in x around 0 78.4%

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

   1. +-commutative 78.4%

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

   2. metadata-eval 78.4%

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

   3. cancel-sign-sub-inv 78.4%

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

   4. associate--l+ 78.4%

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

   5. fma-define 78.5%

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

   6. associate-/l* 77.8%

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

   7. *-commutative 77.8%

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

   8. cancel-sign-sub-inv 77.8%

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

   9. metadata-eval 77.8%

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

   10. +-commutative 77.8%

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

   11. fma-define 77.8%

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

   12. associate-/l* 80.1%

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

   13. *-commutative 80.1%

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

7. Simplified 80.1%

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

8. Taylor expanded in b around inf 33.3%

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

   1. associate-/r* 34.8%

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

10. Simplified 34.8%

    \[\leadsto \color{blue}{\frac{\frac{b}{c}}{z}} \]
11. Add Preprocessing

Alternative 12: 35.0% accurate, 3.8× speedup

Math

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

FPCore

NOTE: x, y, z, t, a, b, and c 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(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	return b / (z * c);
}

Fortran

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

Python

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

Julia

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

MATLAB

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

Wolfram

NOTE: x, y, z, t, a, b, and c 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 77.4%

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

3. Simplified 78.7%

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

5. Taylor expanded in b around inf 33.3%

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

   1. *-commutative 33.3%

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

7. Simplified 33.3%

   \[\leadsto \color{blue}{\frac{b}{z \cdot c}} \]
8. Add Preprocessing

Developer Target 1: 80.5% accurate, 0.1× 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 2024170 
(FPCore (x y z t a b c)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, J"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< (/ (+ (- (* (* x 9) y) (* (* (* z 4) t) a)) b) (* z c)) -220031348160821/200000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (/ (+ (- (* (* x 9) y) (* (* z 4) (* t a))) b) (* z c)) (if (< (/ (+ (- (* (* x 9) y) (* (* (* z 4) t) a)) b) (* z c)) 0) (/ (/ (+ (- (* (* x 9) y) (* (* (* z 4) t) a)) b) z) c) (if (< (/ (+ (- (* (* x 9) y) (* (* (* z 4) t) a)) b) (* z c)) 365902434742109/31250000000000000000000000000000000000000000000000000000000000000000) (/ (+ (- (* (* x 9) y) (* (* z 4) (* t a))) b) (* z c)) (if (< (/ (+ (- (* (* x 9) y) (* (* (* z 4) t) a)) b) (* z c)) 28768236795461370000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (- (+ (* (* 9 (/ y c)) (/ x z)) (/ b (* c z))) (* 4 (/ (* a t) c))) (if (< (/ (+ (- (* (* x 9) y) (* (* (* z 4) t) a)) b) (* z c)) 138385150424563190000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (/ (+ (- (* (* x 9) y) (* (* z 4) (* t a))) b) (* z c)) (- (+ (* 9 (* (/ y (* c z)) x)) (/ b (* c z))) (* 4 (/ (* a t) c)))))))))

  (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)))