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

Percentage Accurate: 79.7% → 94.3%

Time: 19.6s

Alternatives: 21

Speedup: 0.8×

• 37.7% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 79.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 94.3% accurate, 0.2× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1950000 \lor \neg \left(z \leq 2 \cdot 10^{-38}\right):\\ \;\;\;\;\frac{\mathsf{fma}\left(9, x \cdot \frac{y}{z}, \frac{b}{z}\right) + a \cdot \left(t \cdot -4\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(9 \cdot x\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= z -1950000.0) (not (<= z 2e-38)))
   (/ (+ (fma 9.0 (* x (/ y z)) (/ b z)) (* a (* t -4.0))) c)
   (/ (+ b (- (* y (* 9.0 x)) (* a (* t (* z 4.0))))) (* z c))))

C

assert(x < y);
assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((z <= -1950000.0) || !(z <= 2e-38)) {
		tmp = (fma(9.0, (x * (y / z)), (b / z)) + (a * (t * -4.0))) / c;
	} else {
		tmp = (b + ((y * (9.0 * x)) - (a * (t * (z * 4.0))))) / (z * c);
	}
	return tmp;
}

Julia

x, y = sort([x, y])
t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((z <= -1950000.0) || !(z <= 2e-38))
		tmp = Float64(Float64(fma(9.0, Float64(x * Float64(y / z)), Float64(b / z)) + Float64(a * Float64(t * -4.0))) / c);
	else
		tmp = Float64(Float64(b + Float64(Float64(y * Float64(9.0 * x)) - Float64(a * Float64(t * Float64(z * 4.0))))) / Float64(z * c));
	end
	return tmp
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[z, -1950000.0], N[Not[LessEqual[z, 2e-38]], $MachinePrecision]], N[(N[(N[(9.0 * N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision] + N[(b / z), $MachinePrecision]), $MachinePrecision] + N[(a * N[(t * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], N[(N[(b + N[(N[(y * N[(9.0 * x), $MachinePrecision]), $MachinePrecision] - N[(a * N[(t * N[(z * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.95e6 or 1.9999999999999999e-38 < z

   1. Initial program 63.0%

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

   2. Taylor expanded in x around 0 81.8%

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

   3. Taylor expanded in c around 0 90.0%

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

      1. cancel-sign-sub-inv 90.0%

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

      2. fma-def 90.0%

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

      3. associate-*r/ 92.3%

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

      4. metadata-eval 92.3%

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

      5. *-commutative 92.3%

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

      6. associate-*l* 92.3%

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

   5. Simplified 92.3%

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

   if -1.95e6 < z < 1.9999999999999999e-38

   1. Initial program 96.1%

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

4. Final simplification 94.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1950000 \lor \neg \left(z \leq 2 \cdot 10^{-38}\right):\\ \;\;\;\;\frac{\mathsf{fma}\left(9, x \cdot \frac{y}{z}, \frac{b}{z}\right) + a \cdot \left(t \cdot -4\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(9 \cdot x\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c}\\ \end{array} \]

Alternative 2: 87.1% accurate, 0.2× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} t_1 := \frac{b + \left(y \cdot \left(9 \cdot x\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c}\\ \mathbf{if}\;t_1 \leq -1 \cdot 10^{-175}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq 0:\\ \;\;\;\;\frac{1}{z} \cdot \frac{-4 \cdot \left(a \cdot \left(z \cdot t\right)\right) + 9 \cdot \left(x \cdot y\right)}{c}\\ \mathbf{elif}\;t_1 \leq \infty:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(-4 \cdot \frac{t}{c}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (+ b (- (* y (* 9.0 x)) (* a (* t (* z 4.0))))) (* z c))))
   (if (<= t_1 -1e-175)
     t_1
     (if (<= t_1 0.0)
       (* (/ 1.0 z) (/ (+ (* -4.0 (* a (* z t))) (* 9.0 (* x y))) c))
       (if (<= t_1 INFINITY) t_1 (* a (* -4.0 (/ t c))))))))

C

assert(x < y);
assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (b + ((y * (9.0 * x)) - (a * (t * (z * 4.0))))) / (z * c);
	double tmp;
	if (t_1 <= -1e-175) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = (1.0 / z) * (((-4.0 * (a * (z * t))) + (9.0 * (x * y))) / c);
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = a * (-4.0 * (t / c));
	}
	return tmp;
}

Java

assert x < y;
assert t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (b + ((y * (9.0 * x)) - (a * (t * (z * 4.0))))) / (z * c);
	double tmp;
	if (t_1 <= -1e-175) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = (1.0 / z) * (((-4.0 * (a * (z * t))) + (9.0 * (x * y))) / c);
	} else if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else {
		tmp = a * (-4.0 * (t / c));
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	t_1 = (b + ((y * (9.0 * x)) - (a * (t * (z * 4.0))))) / (z * c)
	tmp = 0
	if t_1 <= -1e-175:
		tmp = t_1
	elif t_1 <= 0.0:
		tmp = (1.0 / z) * (((-4.0 * (a * (z * t))) + (9.0 * (x * y))) / c)
	elif t_1 <= math.inf:
		tmp = t_1
	else:
		tmp = a * (-4.0 * (t / c))
	return tmp

Julia

x, y = sort([x, y])
t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(b + Float64(Float64(y * Float64(9.0 * x)) - Float64(a * Float64(t * Float64(z * 4.0))))) / Float64(z * c))
	tmp = 0.0
	if (t_1 <= -1e-175)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = Float64(Float64(1.0 / z) * Float64(Float64(Float64(-4.0 * Float64(a * Float64(z * t))) + Float64(9.0 * Float64(x * y))) / c));
	elseif (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = Float64(a * Float64(-4.0 * Float64(t / c)));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (b + ((y * (9.0 * x)) - (a * (t * (z * 4.0))))) / (z * c);
	tmp = 0.0;
	if (t_1 <= -1e-175)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = (1.0 / z) * (((-4.0 * (a * (z * t))) + (9.0 * (x * y))) / c);
	elseif (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = a * (-4.0 * (t / c));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(b + N[(N[(y * N[(9.0 * x), $MachinePrecision]), $MachinePrecision] - N[(a * N[(t * N[(z * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e-175], t$95$1, If[LessEqual[t$95$1, 0.0], N[(N[(1.0 / z), $MachinePrecision] * N[(N[(N[(-4.0 * N[(a * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(9.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, Infinity], t$95$1, N[(a * N[(-4.0 * N[(t / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)) b) (*.f64 z c)) < -1e-175 or 0.0 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)) b) (*.f64 z c)) < +inf.0

   1. Initial program 91.3%

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

   if -1e-175 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)) b) (*.f64 z c)) < 0.0

   1. Initial program 45.4%

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

      1. associate-+l- 45.4%

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

      2. associate-*r* 45.4%

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

      3. associate-*r* 45.4%

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

      4. *-un-lft-identity 45.4%

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

      5. times-frac 99.6%

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

      6. associate--r- 99.6%

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

      7. fma-neg 99.6%

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

      8. associate-*r* 99.6%

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

      9. distribute-rgt-neg-in 99.6%

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

      10. associate-*l* 99.6%

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

   3. Applied egg-rr 99.6%

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

   4. Taylor expanded in b around 0 88.2%

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

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

   1. Initial program 0.0%

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

   2. Taylor expanded in x around 0 67.9%

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

   3. Taylor expanded in z around inf 68.1%

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

      1. associate-*r/ 68.1%

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

      2. *-commutative 68.1%

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

      3. associate-/l* 68.1%

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

      4. associate-*r/ 88.7%

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

      5. associate-/r/ 88.7%

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

   5. Simplified 88.7%

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

4. Final simplification 90.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{b + \left(y \cdot \left(9 \cdot x\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c} \leq -1 \cdot 10^{-175}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(9 \cdot x\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c}\\ \mathbf{elif}\;\frac{b + \left(y \cdot \left(9 \cdot x\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c} \leq 0:\\ \;\;\;\;\frac{1}{z} \cdot \frac{-4 \cdot \left(a \cdot \left(z \cdot t\right)\right) + 9 \cdot \left(x \cdot y\right)}{c}\\ \mathbf{elif}\;\frac{b + \left(y \cdot \left(9 \cdot x\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c} \leq \infty:\\ \;\;\;\;\frac{b + \left(y \cdot \left(9 \cdot x\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(-4 \cdot \frac{t}{c}\right)\\ \end{array} \]

Alternative 3: 50.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} t_1 := a \cdot \left(-4 \cdot \frac{t}{c}\right)\\ t_2 := 9 \cdot \frac{x}{z \cdot \frac{c}{y}}\\ \mathbf{if}\;y \leq -10200:\\ \;\;\;\;9 \cdot \left(\frac{y}{c} \cdot \frac{x}{z}\right)\\ \mathbf{elif}\;y \leq 1.75 \cdot 10^{-71}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{-28}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+72}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{+121}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+130}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+144}:\\ \;\;\;\;b \cdot \frac{1}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* a (* -4.0 (/ t c)))) (t_2 (* 9.0 (/ x (* z (/ c y))))))
   (if (<= y -10200.0)
     (* 9.0 (* (/ y c) (/ x z)))
     (if (<= y 1.75e-71)
       t_1
       (if (<= y 4.2e-28)
         (/ (/ b c) z)
         (if (<= y 1.2e+72)
           t_1
           (if (<= y 2.2e+121)
             t_2
             (if (<= y 9e+130)
               (* -4.0 (* t (/ a c)))
               (if (<= y 9e+144) (* b (/ 1.0 (* z c))) t_2)))))))))

C

assert(x < y);
assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = a * (-4.0 * (t / c));
	double t_2 = 9.0 * (x / (z * (c / y)));
	double tmp;
	if (y <= -10200.0) {
		tmp = 9.0 * ((y / c) * (x / z));
	} else if (y <= 1.75e-71) {
		tmp = t_1;
	} else if (y <= 4.2e-28) {
		tmp = (b / c) / z;
	} else if (y <= 1.2e+72) {
		tmp = t_1;
	} else if (y <= 2.2e+121) {
		tmp = t_2;
	} else if (y <= 9e+130) {
		tmp = -4.0 * (t * (a / c));
	} else if (y <= 9e+144) {
		tmp = b * (1.0 / (z * c));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a * ((-4.0d0) * (t / c))
    t_2 = 9.0d0 * (x / (z * (c / y)))
    if (y <= (-10200.0d0)) then
        tmp = 9.0d0 * ((y / c) * (x / z))
    else if (y <= 1.75d-71) then
        tmp = t_1
    else if (y <= 4.2d-28) then
        tmp = (b / c) / z
    else if (y <= 1.2d+72) then
        tmp = t_1
    else if (y <= 2.2d+121) then
        tmp = t_2
    else if (y <= 9d+130) then
        tmp = (-4.0d0) * (t * (a / c))
    else if (y <= 9d+144) then
        tmp = b * (1.0d0 / (z * c))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

assert x < y;
assert t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = a * (-4.0 * (t / c));
	double t_2 = 9.0 * (x / (z * (c / y)));
	double tmp;
	if (y <= -10200.0) {
		tmp = 9.0 * ((y / c) * (x / z));
	} else if (y <= 1.75e-71) {
		tmp = t_1;
	} else if (y <= 4.2e-28) {
		tmp = (b / c) / z;
	} else if (y <= 1.2e+72) {
		tmp = t_1;
	} else if (y <= 2.2e+121) {
		tmp = t_2;
	} else if (y <= 9e+130) {
		tmp = -4.0 * (t * (a / c));
	} else if (y <= 9e+144) {
		tmp = b * (1.0 / (z * c));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	t_1 = a * (-4.0 * (t / c))
	t_2 = 9.0 * (x / (z * (c / y)))
	tmp = 0
	if y <= -10200.0:
		tmp = 9.0 * ((y / c) * (x / z))
	elif y <= 1.75e-71:
		tmp = t_1
	elif y <= 4.2e-28:
		tmp = (b / c) / z
	elif y <= 1.2e+72:
		tmp = t_1
	elif y <= 2.2e+121:
		tmp = t_2
	elif y <= 9e+130:
		tmp = -4.0 * (t * (a / c))
	elif y <= 9e+144:
		tmp = b * (1.0 / (z * c))
	else:
		tmp = t_2
	return tmp

Julia

x, y = sort([x, y])
t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(a * Float64(-4.0 * Float64(t / c)))
	t_2 = Float64(9.0 * Float64(x / Float64(z * Float64(c / y))))
	tmp = 0.0
	if (y <= -10200.0)
		tmp = Float64(9.0 * Float64(Float64(y / c) * Float64(x / z)));
	elseif (y <= 1.75e-71)
		tmp = t_1;
	elseif (y <= 4.2e-28)
		tmp = Float64(Float64(b / c) / z);
	elseif (y <= 1.2e+72)
		tmp = t_1;
	elseif (y <= 2.2e+121)
		tmp = t_2;
	elseif (y <= 9e+130)
		tmp = Float64(-4.0 * Float64(t * Float64(a / c)));
	elseif (y <= 9e+144)
		tmp = Float64(b * Float64(1.0 / Float64(z * c)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = a * (-4.0 * (t / c));
	t_2 = 9.0 * (x / (z * (c / y)));
	tmp = 0.0;
	if (y <= -10200.0)
		tmp = 9.0 * ((y / c) * (x / z));
	elseif (y <= 1.75e-71)
		tmp = t_1;
	elseif (y <= 4.2e-28)
		tmp = (b / c) / z;
	elseif (y <= 1.2e+72)
		tmp = t_1;
	elseif (y <= 2.2e+121)
		tmp = t_2;
	elseif (y <= 9e+130)
		tmp = -4.0 * (t * (a / c));
	elseif (y <= 9e+144)
		tmp = b * (1.0 / (z * c));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(a * N[(-4.0 * N[(t / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(9.0 * N[(x / N[(z * N[(c / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -10200.0], N[(9.0 * N[(N[(y / c), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.75e-71], t$95$1, If[LessEqual[y, 4.2e-28], N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[y, 1.2e+72], t$95$1, If[LessEqual[y, 2.2e+121], t$95$2, If[LessEqual[y, 9e+130], N[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9e+144], N[(b * N[(1.0 / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if y < -10200

   1. Initial program 76.2%

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

   2. Taylor expanded in x around inf 55.2%

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

      1. *-commutative 55.2%

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

   4. Simplified 55.2%

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

   5. Taylor expanded in x around 0 55.2%

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

      1. *-commutative 55.2%

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

      2. times-frac 60.9%

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

   7. Simplified 60.9%

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

   if -10200 < y < 1.75e-71 or 4.20000000000000013e-28 < y < 1.20000000000000005e72

   1. Initial program 81.5%

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

   2. Taylor expanded in x around 0 81.6%

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

   3. Taylor expanded in z around inf 47.3%

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

      1. associate-*r/ 47.3%

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

      2. *-commutative 47.3%

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

      3. associate-/l* 47.3%

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

      4. associate-*r/ 50.5%

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

      5. associate-/r/ 50.5%

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

   5. Simplified 50.5%

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

   if 1.75e-71 < y < 4.20000000000000013e-28

   1. Initial program 99.8%

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

   2. Taylor expanded in b around inf 49.9%

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

      1. *-commutative 49.9%

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

   4. Simplified 49.9%

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

      1. div-inv 49.7%

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

   6. Applied egg-rr 49.7%

      \[\leadsto \color{blue}{b \cdot \frac{1}{z \cdot c}} \]
   7. Step-by-step derivation

      1. un-div-inv 49.9%

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

      2. *-commutative 49.9%

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

      3. associate-/r* 38.8%

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

   8. Applied egg-rr 38.8%

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

   if 1.20000000000000005e72 < y < 2.20000000000000001e121 or 8.99999999999999935e144 < y

   1. Initial program 78.7%

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

      1. associate-+l- 78.7%

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

      2. associate-*r* 78.8%

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

      3. associate-*r* 81.2%

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

      4. *-un-lft-identity 81.2%

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

      5. times-frac 76.8%

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

      6. associate--r- 76.8%

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

      7. fma-neg 79.2%

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

      8. associate-*r* 79.1%

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

      9. distribute-rgt-neg-in 79.1%

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

      10. associate-*l* 79.1%

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

   3. Applied egg-rr 79.1%

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

   4. Taylor expanded in c around 0 76.7%

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

   5. Taylor expanded in x around inf 60.0%

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

      1. associate-/r* 57.6%

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

      2. associate-/l* 64.4%

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

      3. associate-/l/ 64.6%

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

   7. Simplified 64.6%

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

   if 2.20000000000000001e121 < y < 9.00000000000000078e130

   1. Initial program 0.0%

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

   2. Taylor expanded in x around 0 51.5%

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

   3. Taylor expanded in z around inf 51.5%

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

      1. associate-*l/ 99.2%

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

   5. Simplified 99.2%

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

   if 9.00000000000000078e130 < y < 8.99999999999999935e144

   1. Initial program 100.0%

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

   2. Taylor expanded in b around inf 52.8%

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

      1. *-commutative 52.8%

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

   4. Simplified 52.8%

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

      1. div-inv 52.8%

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

   6. Applied egg-rr 52.8%

      \[\leadsto \color{blue}{b \cdot \frac{1}{z \cdot c}} \]
3. Recombined 6 regimes into one program.

4. Final simplification 55.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -10200:\\ \;\;\;\;9 \cdot \left(\frac{y}{c} \cdot \frac{x}{z}\right)\\ \mathbf{elif}\;y \leq 1.75 \cdot 10^{-71}:\\ \;\;\;\;a \cdot \left(-4 \cdot \frac{t}{c}\right)\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{-28}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+72}:\\ \;\;\;\;a \cdot \left(-4 \cdot \frac{t}{c}\right)\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{+121}:\\ \;\;\;\;9 \cdot \frac{x}{z \cdot \frac{c}{y}}\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+130}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+144}:\\ \;\;\;\;b \cdot \frac{1}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;9 \cdot \frac{x}{z \cdot \frac{c}{y}}\\ \end{array} \]

Alternative 4: 50.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} t_1 := a \cdot \left(-4 \cdot \frac{t}{c}\right)\\ \mathbf{if}\;y \leq -10200:\\ \;\;\;\;9 \cdot \left(\frac{y}{c} \cdot \frac{x}{z}\right)\\ \mathbf{elif}\;y \leq 8 \cdot 10^{-74}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{-29}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;y \leq 5.9 \cdot 10^{+72}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{+121}:\\ \;\;\;\;9 \cdot \frac{x \cdot y}{z \cdot c}\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{+128}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+144}:\\ \;\;\;\;b \cdot \frac{1}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;9 \cdot \frac{x}{z \cdot \frac{c}{y}}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* a (* -4.0 (/ t c)))))
   (if (<= y -10200.0)
     (* 9.0 (* (/ y c) (/ x z)))
     (if (<= y 8e-74)
       t_1
       (if (<= y 3.1e-29)
         (/ (/ b c) z)
         (if (<= y 5.9e+72)
           t_1
           (if (<= y 7.8e+121)
             (* 9.0 (/ (* x y) (* z c)))
             (if (<= y 7.5e+128)
               (* -4.0 (* t (/ a c)))
               (if (<= y 9e+144)
                 (* b (/ 1.0 (* z c)))
                 (* 9.0 (/ x (* z (/ c y)))))))))))))

C

assert(x < y);
assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = a * (-4.0 * (t / c));
	double tmp;
	if (y <= -10200.0) {
		tmp = 9.0 * ((y / c) * (x / z));
	} else if (y <= 8e-74) {
		tmp = t_1;
	} else if (y <= 3.1e-29) {
		tmp = (b / c) / z;
	} else if (y <= 5.9e+72) {
		tmp = t_1;
	} else if (y <= 7.8e+121) {
		tmp = 9.0 * ((x * y) / (z * c));
	} else if (y <= 7.5e+128) {
		tmp = -4.0 * (t * (a / c));
	} else if (y <= 9e+144) {
		tmp = b * (1.0 / (z * c));
	} else {
		tmp = 9.0 * (x / (z * (c / y)));
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * ((-4.0d0) * (t / c))
    if (y <= (-10200.0d0)) then
        tmp = 9.0d0 * ((y / c) * (x / z))
    else if (y <= 8d-74) then
        tmp = t_1
    else if (y <= 3.1d-29) then
        tmp = (b / c) / z
    else if (y <= 5.9d+72) then
        tmp = t_1
    else if (y <= 7.8d+121) then
        tmp = 9.0d0 * ((x * y) / (z * c))
    else if (y <= 7.5d+128) then
        tmp = (-4.0d0) * (t * (a / c))
    else if (y <= 9d+144) then
        tmp = b * (1.0d0 / (z * c))
    else
        tmp = 9.0d0 * (x / (z * (c / y)))
    end if
    code = tmp
end function

Java

assert x < y;
assert t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = a * (-4.0 * (t / c));
	double tmp;
	if (y <= -10200.0) {
		tmp = 9.0 * ((y / c) * (x / z));
	} else if (y <= 8e-74) {
		tmp = t_1;
	} else if (y <= 3.1e-29) {
		tmp = (b / c) / z;
	} else if (y <= 5.9e+72) {
		tmp = t_1;
	} else if (y <= 7.8e+121) {
		tmp = 9.0 * ((x * y) / (z * c));
	} else if (y <= 7.5e+128) {
		tmp = -4.0 * (t * (a / c));
	} else if (y <= 9e+144) {
		tmp = b * (1.0 / (z * c));
	} else {
		tmp = 9.0 * (x / (z * (c / y)));
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	t_1 = a * (-4.0 * (t / c))
	tmp = 0
	if y <= -10200.0:
		tmp = 9.0 * ((y / c) * (x / z))
	elif y <= 8e-74:
		tmp = t_1
	elif y <= 3.1e-29:
		tmp = (b / c) / z
	elif y <= 5.9e+72:
		tmp = t_1
	elif y <= 7.8e+121:
		tmp = 9.0 * ((x * y) / (z * c))
	elif y <= 7.5e+128:
		tmp = -4.0 * (t * (a / c))
	elif y <= 9e+144:
		tmp = b * (1.0 / (z * c))
	else:
		tmp = 9.0 * (x / (z * (c / y)))
	return tmp

Julia

x, y = sort([x, y])
t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(a * Float64(-4.0 * Float64(t / c)))
	tmp = 0.0
	if (y <= -10200.0)
		tmp = Float64(9.0 * Float64(Float64(y / c) * Float64(x / z)));
	elseif (y <= 8e-74)
		tmp = t_1;
	elseif (y <= 3.1e-29)
		tmp = Float64(Float64(b / c) / z);
	elseif (y <= 5.9e+72)
		tmp = t_1;
	elseif (y <= 7.8e+121)
		tmp = Float64(9.0 * Float64(Float64(x * y) / Float64(z * c)));
	elseif (y <= 7.5e+128)
		tmp = Float64(-4.0 * Float64(t * Float64(a / c)));
	elseif (y <= 9e+144)
		tmp = Float64(b * Float64(1.0 / Float64(z * c)));
	else
		tmp = Float64(9.0 * Float64(x / Float64(z * Float64(c / y))));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = a * (-4.0 * (t / c));
	tmp = 0.0;
	if (y <= -10200.0)
		tmp = 9.0 * ((y / c) * (x / z));
	elseif (y <= 8e-74)
		tmp = t_1;
	elseif (y <= 3.1e-29)
		tmp = (b / c) / z;
	elseif (y <= 5.9e+72)
		tmp = t_1;
	elseif (y <= 7.8e+121)
		tmp = 9.0 * ((x * y) / (z * c));
	elseif (y <= 7.5e+128)
		tmp = -4.0 * (t * (a / c));
	elseif (y <= 9e+144)
		tmp = b * (1.0 / (z * c));
	else
		tmp = 9.0 * (x / (z * (c / y)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(a * N[(-4.0 * N[(t / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -10200.0], N[(9.0 * N[(N[(y / c), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 8e-74], t$95$1, If[LessEqual[y, 3.1e-29], N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[y, 5.9e+72], t$95$1, If[LessEqual[y, 7.8e+121], N[(9.0 * N[(N[(x * y), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7.5e+128], N[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9e+144], N[(b * N[(1.0 / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(9.0 * N[(x / N[(z * N[(c / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if y < -10200

   1. Initial program 76.2%

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

   2. Taylor expanded in x around inf 55.2%

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

      1. *-commutative 55.2%

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

   4. Simplified 55.2%

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

   5. Taylor expanded in x around 0 55.2%

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

      1. *-commutative 55.2%

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

      2. times-frac 60.9%

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

   7. Simplified 60.9%

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

   if -10200 < y < 7.99999999999999966e-74 or 3.10000000000000026e-29 < y < 5.9000000000000002e72

   1. Initial program 81.3%

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

   2. Taylor expanded in x around 0 81.3%

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

   3. Taylor expanded in z around inf 47.9%

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

      1. associate-*r/ 47.9%

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

      2. *-commutative 47.9%

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

      3. associate-/l* 47.9%

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

      4. associate-*r/ 51.2%

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

      5. associate-/r/ 51.2%

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

   5. Simplified 51.2%

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

   if 7.99999999999999966e-74 < y < 3.10000000000000026e-29

   1. Initial program 99.7%

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

   2. Taylor expanded in b around inf 50.0%

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

      1. *-commutative 50.0%

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

   4. Simplified 50.0%

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

      1. div-inv 49.9%

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

   6. Applied egg-rr 49.9%

      \[\leadsto \color{blue}{b \cdot \frac{1}{z \cdot c}} \]
   7. Step-by-step derivation

      1. un-div-inv 50.0%

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

      2. *-commutative 50.0%

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

      3. associate-/r* 31.9%

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

   8. Applied egg-rr 31.9%

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

   if 5.9000000000000002e72 < y < 7.79999999999999967e121

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 51.7%

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

      1. *-commutative 51.7%

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

   4. Simplified 51.7%

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

   if 7.79999999999999967e121 < y < 7.50000000000000076e128

   1. Initial program 0.0%

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

   2. Taylor expanded in x around 0 51.5%

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

   3. Taylor expanded in z around inf 51.5%

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

      1. associate-*l/ 99.2%

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

   5. Simplified 99.2%

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

   if 7.50000000000000076e128 < y < 8.99999999999999935e144

   1. Initial program 100.0%

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

   2. Taylor expanded in b around inf 52.8%

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

      1. *-commutative 52.8%

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

   4. Simplified 52.8%

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

      1. div-inv 52.8%

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

   6. Applied egg-rr 52.8%

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

   if 8.99999999999999935e144 < y

   1. Initial program 75.1%

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

      1. associate-+l- 75.1%

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

      2. associate-*r* 75.1%

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

      3. associate-*r* 77.9%

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

      4. *-un-lft-identity 77.9%

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

      5. times-frac 72.8%

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

      6. associate--r- 72.8%

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

      7. fma-neg 75.6%

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

      8. associate-*r* 75.5%

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

      9. distribute-rgt-neg-in 75.5%

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

      10. associate-*l* 75.5%

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

   3. Applied egg-rr 75.5%

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

   4. Taylor expanded in c around 0 72.7%

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

   5. Taylor expanded in x around inf 61.5%

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

      1. associate-/r* 61.3%

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

      2. associate-/l* 69.3%

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

      3. associate-/l/ 66.8%

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

   7. Simplified 66.8%

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

4. Final simplification 55.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -10200:\\ \;\;\;\;9 \cdot \left(\frac{y}{c} \cdot \frac{x}{z}\right)\\ \mathbf{elif}\;y \leq 8 \cdot 10^{-74}:\\ \;\;\;\;a \cdot \left(-4 \cdot \frac{t}{c}\right)\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{-29}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;y \leq 5.9 \cdot 10^{+72}:\\ \;\;\;\;a \cdot \left(-4 \cdot \frac{t}{c}\right)\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{+121}:\\ \;\;\;\;9 \cdot \frac{x \cdot y}{z \cdot c}\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{+128}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+144}:\\ \;\;\;\;b \cdot \frac{1}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;9 \cdot \frac{x}{z \cdot \frac{c}{y}}\\ \end{array} \]

Alternative 5: 50.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} t_1 := a \cdot \left(-4 \cdot \frac{t}{c}\right)\\ \mathbf{if}\;y \leq -7800:\\ \;\;\;\;\left(x \cdot \frac{y}{c}\right) \cdot \frac{9}{z}\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{-70}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 3 \cdot 10^{-29}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{+72}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+119}:\\ \;\;\;\;9 \cdot \frac{x \cdot y}{z \cdot c}\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{+131}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+144}:\\ \;\;\;\;b \cdot \frac{1}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;9 \cdot \frac{x}{z \cdot \frac{c}{y}}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* a (* -4.0 (/ t c)))))
   (if (<= y -7800.0)
     (* (* x (/ y c)) (/ 9.0 z))
     (if (<= y 1.3e-70)
       t_1
       (if (<= y 3e-29)
         (/ (/ b c) z)
         (if (<= y 6.2e+72)
           t_1
           (if (<= y 1.2e+119)
             (* 9.0 (/ (* x y) (* z c)))
             (if (<= y 1.55e+131)
               (* -4.0 (* t (/ a c)))
               (if (<= y 9e+144)
                 (* b (/ 1.0 (* z c)))
                 (* 9.0 (/ x (* z (/ c y)))))))))))))

C

assert(x < y);
assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = a * (-4.0 * (t / c));
	double tmp;
	if (y <= -7800.0) {
		tmp = (x * (y / c)) * (9.0 / z);
	} else if (y <= 1.3e-70) {
		tmp = t_1;
	} else if (y <= 3e-29) {
		tmp = (b / c) / z;
	} else if (y <= 6.2e+72) {
		tmp = t_1;
	} else if (y <= 1.2e+119) {
		tmp = 9.0 * ((x * y) / (z * c));
	} else if (y <= 1.55e+131) {
		tmp = -4.0 * (t * (a / c));
	} else if (y <= 9e+144) {
		tmp = b * (1.0 / (z * c));
	} else {
		tmp = 9.0 * (x / (z * (c / y)));
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * ((-4.0d0) * (t / c))
    if (y <= (-7800.0d0)) then
        tmp = (x * (y / c)) * (9.0d0 / z)
    else if (y <= 1.3d-70) then
        tmp = t_1
    else if (y <= 3d-29) then
        tmp = (b / c) / z
    else if (y <= 6.2d+72) then
        tmp = t_1
    else if (y <= 1.2d+119) then
        tmp = 9.0d0 * ((x * y) / (z * c))
    else if (y <= 1.55d+131) then
        tmp = (-4.0d0) * (t * (a / c))
    else if (y <= 9d+144) then
        tmp = b * (1.0d0 / (z * c))
    else
        tmp = 9.0d0 * (x / (z * (c / y)))
    end if
    code = tmp
end function

Java

assert x < y;
assert t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = a * (-4.0 * (t / c));
	double tmp;
	if (y <= -7800.0) {
		tmp = (x * (y / c)) * (9.0 / z);
	} else if (y <= 1.3e-70) {
		tmp = t_1;
	} else if (y <= 3e-29) {
		tmp = (b / c) / z;
	} else if (y <= 6.2e+72) {
		tmp = t_1;
	} else if (y <= 1.2e+119) {
		tmp = 9.0 * ((x * y) / (z * c));
	} else if (y <= 1.55e+131) {
		tmp = -4.0 * (t * (a / c));
	} else if (y <= 9e+144) {
		tmp = b * (1.0 / (z * c));
	} else {
		tmp = 9.0 * (x / (z * (c / y)));
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	t_1 = a * (-4.0 * (t / c))
	tmp = 0
	if y <= -7800.0:
		tmp = (x * (y / c)) * (9.0 / z)
	elif y <= 1.3e-70:
		tmp = t_1
	elif y <= 3e-29:
		tmp = (b / c) / z
	elif y <= 6.2e+72:
		tmp = t_1
	elif y <= 1.2e+119:
		tmp = 9.0 * ((x * y) / (z * c))
	elif y <= 1.55e+131:
		tmp = -4.0 * (t * (a / c))
	elif y <= 9e+144:
		tmp = b * (1.0 / (z * c))
	else:
		tmp = 9.0 * (x / (z * (c / y)))
	return tmp

Julia

x, y = sort([x, y])
t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(a * Float64(-4.0 * Float64(t / c)))
	tmp = 0.0
	if (y <= -7800.0)
		tmp = Float64(Float64(x * Float64(y / c)) * Float64(9.0 / z));
	elseif (y <= 1.3e-70)
		tmp = t_1;
	elseif (y <= 3e-29)
		tmp = Float64(Float64(b / c) / z);
	elseif (y <= 6.2e+72)
		tmp = t_1;
	elseif (y <= 1.2e+119)
		tmp = Float64(9.0 * Float64(Float64(x * y) / Float64(z * c)));
	elseif (y <= 1.55e+131)
		tmp = Float64(-4.0 * Float64(t * Float64(a / c)));
	elseif (y <= 9e+144)
		tmp = Float64(b * Float64(1.0 / Float64(z * c)));
	else
		tmp = Float64(9.0 * Float64(x / Float64(z * Float64(c / y))));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = a * (-4.0 * (t / c));
	tmp = 0.0;
	if (y <= -7800.0)
		tmp = (x * (y / c)) * (9.0 / z);
	elseif (y <= 1.3e-70)
		tmp = t_1;
	elseif (y <= 3e-29)
		tmp = (b / c) / z;
	elseif (y <= 6.2e+72)
		tmp = t_1;
	elseif (y <= 1.2e+119)
		tmp = 9.0 * ((x * y) / (z * c));
	elseif (y <= 1.55e+131)
		tmp = -4.0 * (t * (a / c));
	elseif (y <= 9e+144)
		tmp = b * (1.0 / (z * c));
	else
		tmp = 9.0 * (x / (z * (c / y)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(a * N[(-4.0 * N[(t / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -7800.0], N[(N[(x * N[(y / c), $MachinePrecision]), $MachinePrecision] * N[(9.0 / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.3e-70], t$95$1, If[LessEqual[y, 3e-29], N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[y, 6.2e+72], t$95$1, If[LessEqual[y, 1.2e+119], N[(9.0 * N[(N[(x * y), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.55e+131], N[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9e+144], N[(b * N[(1.0 / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(9.0 * N[(x / N[(z * N[(c / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if y < -7800

   1. Initial program 76.2%

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

      1. associate-+l- 76.2%

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

      2. associate-*r* 76.2%

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

      3. associate-*r* 76.2%

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

      4. *-un-lft-identity 76.2%

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

      5. times-frac 85.0%

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

      6. associate--r- 85.0%

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

      7. fma-neg 85.0%

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

      8. associate-*r* 83.6%

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

      9. distribute-rgt-neg-in 83.6%

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

      10. associate-*l* 83.6%

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

   3. Applied egg-rr 83.6%

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

   4. Taylor expanded in x around inf 55.2%

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

      1. associate-*r/ 55.2%

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

      2. *-commutative 55.2%

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

      3. times-frac 63.5%

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

      4. associate-*r/ 63.4%

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

   6. Simplified 63.4%

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

   if -7800 < y < 1.30000000000000001e-70 or 3.0000000000000003e-29 < y < 6.19999999999999977e72

   1. Initial program 81.5%

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

   2. Taylor expanded in x around 0 81.6%

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

   3. Taylor expanded in z around inf 47.3%

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

      1. associate-*r/ 47.3%

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

      2. *-commutative 47.3%

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

      3. associate-/l* 47.3%

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

      4. associate-*r/ 50.5%

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

      5. associate-/r/ 50.5%

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

   5. Simplified 50.5%

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

   if 1.30000000000000001e-70 < y < 3.0000000000000003e-29

   1. Initial program 99.8%

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

   2. Taylor expanded in b around inf 49.9%

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

      1. *-commutative 49.9%

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

   4. Simplified 49.9%

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

      1. div-inv 49.7%

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

   6. Applied egg-rr 49.7%

      \[\leadsto \color{blue}{b \cdot \frac{1}{z \cdot c}} \]
   7. Step-by-step derivation

      1. un-div-inv 49.9%

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

      2. *-commutative 49.9%

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

      3. associate-/r* 38.8%

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

   8. Applied egg-rr 38.8%

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

   if 6.19999999999999977e72 < y < 1.2e119

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 51.7%

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

      1. *-commutative 51.7%

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

   4. Simplified 51.7%

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

   if 1.2e119 < y < 1.55000000000000008e131

   1. Initial program 0.0%

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

   2. Taylor expanded in x around 0 51.5%

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

   3. Taylor expanded in z around inf 51.5%

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

      1. associate-*l/ 99.2%

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

   5. Simplified 99.2%

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

   if 1.55000000000000008e131 < y < 8.99999999999999935e144

   1. Initial program 100.0%

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

   2. Taylor expanded in b around inf 52.8%

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

      1. *-commutative 52.8%

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

   4. Simplified 52.8%

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

      1. div-inv 52.8%

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

   6. Applied egg-rr 52.8%

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

   if 8.99999999999999935e144 < y

   1. Initial program 75.1%

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

      1. associate-+l- 75.1%

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

      2. associate-*r* 75.1%

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

      3. associate-*r* 77.9%

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

      4. *-un-lft-identity 77.9%

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

      5. times-frac 72.8%

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

      6. associate--r- 72.8%

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

      7. fma-neg 75.6%

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

      8. associate-*r* 75.5%

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

      9. distribute-rgt-neg-in 75.5%

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

      10. associate-*l* 75.5%

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

   3. Applied egg-rr 75.5%

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

   4. Taylor expanded in c around 0 72.7%

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

   5. Taylor expanded in x around inf 61.5%

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

      1. associate-/r* 61.3%

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

      2. associate-/l* 69.3%

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

      3. associate-/l/ 66.8%

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

   7. Simplified 66.8%

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

4. Final simplification 56.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7800:\\ \;\;\;\;\left(x \cdot \frac{y}{c}\right) \cdot \frac{9}{z}\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{-70}:\\ \;\;\;\;a \cdot \left(-4 \cdot \frac{t}{c}\right)\\ \mathbf{elif}\;y \leq 3 \cdot 10^{-29}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{+72}:\\ \;\;\;\;a \cdot \left(-4 \cdot \frac{t}{c}\right)\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+119}:\\ \;\;\;\;9 \cdot \frac{x \cdot y}{z \cdot c}\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{+131}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+144}:\\ \;\;\;\;b \cdot \frac{1}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;9 \cdot \frac{x}{z \cdot \frac{c}{y}}\\ \end{array} \]

Alternative 6: 49.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} t_1 := a \cdot \left(-4 \cdot \frac{t}{c}\right)\\ \mathbf{if}\;y \leq -6800:\\ \;\;\;\;\left(x \cdot \frac{y}{c}\right) \cdot \frac{9}{z}\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{-73}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{-29}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{+39}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{+121}:\\ \;\;\;\;\frac{1}{0.1111111111111111 \cdot \frac{z \cdot c}{x \cdot y}}\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{+131}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+144}:\\ \;\;\;\;b \cdot \frac{1}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;9 \cdot \frac{x}{z \cdot \frac{c}{y}}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* a (* -4.0 (/ t c)))))
   (if (<= y -6800.0)
     (* (* x (/ y c)) (/ 9.0 z))
     (if (<= y 9.5e-73)
       t_1
       (if (<= y 2.5e-29)
         (/ (/ b c) z)
         (if (<= y 2.4e+39)
           t_1
           (if (<= y 2.1e+121)
             (/ 1.0 (* 0.1111111111111111 (/ (* z c) (* x y))))
             (if (<= y 1.55e+131)
               (* -4.0 (* t (/ a c)))
               (if (<= y 9e+144)
                 (* b (/ 1.0 (* z c)))
                 (* 9.0 (/ x (* z (/ c y)))))))))))))

C

assert(x < y);
assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = a * (-4.0 * (t / c));
	double tmp;
	if (y <= -6800.0) {
		tmp = (x * (y / c)) * (9.0 / z);
	} else if (y <= 9.5e-73) {
		tmp = t_1;
	} else if (y <= 2.5e-29) {
		tmp = (b / c) / z;
	} else if (y <= 2.4e+39) {
		tmp = t_1;
	} else if (y <= 2.1e+121) {
		tmp = 1.0 / (0.1111111111111111 * ((z * c) / (x * y)));
	} else if (y <= 1.55e+131) {
		tmp = -4.0 * (t * (a / c));
	} else if (y <= 9e+144) {
		tmp = b * (1.0 / (z * c));
	} else {
		tmp = 9.0 * (x / (z * (c / y)));
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * ((-4.0d0) * (t / c))
    if (y <= (-6800.0d0)) then
        tmp = (x * (y / c)) * (9.0d0 / z)
    else if (y <= 9.5d-73) then
        tmp = t_1
    else if (y <= 2.5d-29) then
        tmp = (b / c) / z
    else if (y <= 2.4d+39) then
        tmp = t_1
    else if (y <= 2.1d+121) then
        tmp = 1.0d0 / (0.1111111111111111d0 * ((z * c) / (x * y)))
    else if (y <= 1.55d+131) then
        tmp = (-4.0d0) * (t * (a / c))
    else if (y <= 9d+144) then
        tmp = b * (1.0d0 / (z * c))
    else
        tmp = 9.0d0 * (x / (z * (c / y)))
    end if
    code = tmp
end function

Java

assert x < y;
assert t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = a * (-4.0 * (t / c));
	double tmp;
	if (y <= -6800.0) {
		tmp = (x * (y / c)) * (9.0 / z);
	} else if (y <= 9.5e-73) {
		tmp = t_1;
	} else if (y <= 2.5e-29) {
		tmp = (b / c) / z;
	} else if (y <= 2.4e+39) {
		tmp = t_1;
	} else if (y <= 2.1e+121) {
		tmp = 1.0 / (0.1111111111111111 * ((z * c) / (x * y)));
	} else if (y <= 1.55e+131) {
		tmp = -4.0 * (t * (a / c));
	} else if (y <= 9e+144) {
		tmp = b * (1.0 / (z * c));
	} else {
		tmp = 9.0 * (x / (z * (c / y)));
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	t_1 = a * (-4.0 * (t / c))
	tmp = 0
	if y <= -6800.0:
		tmp = (x * (y / c)) * (9.0 / z)
	elif y <= 9.5e-73:
		tmp = t_1
	elif y <= 2.5e-29:
		tmp = (b / c) / z
	elif y <= 2.4e+39:
		tmp = t_1
	elif y <= 2.1e+121:
		tmp = 1.0 / (0.1111111111111111 * ((z * c) / (x * y)))
	elif y <= 1.55e+131:
		tmp = -4.0 * (t * (a / c))
	elif y <= 9e+144:
		tmp = b * (1.0 / (z * c))
	else:
		tmp = 9.0 * (x / (z * (c / y)))
	return tmp

Julia

x, y = sort([x, y])
t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(a * Float64(-4.0 * Float64(t / c)))
	tmp = 0.0
	if (y <= -6800.0)
		tmp = Float64(Float64(x * Float64(y / c)) * Float64(9.0 / z));
	elseif (y <= 9.5e-73)
		tmp = t_1;
	elseif (y <= 2.5e-29)
		tmp = Float64(Float64(b / c) / z);
	elseif (y <= 2.4e+39)
		tmp = t_1;
	elseif (y <= 2.1e+121)
		tmp = Float64(1.0 / Float64(0.1111111111111111 * Float64(Float64(z * c) / Float64(x * y))));
	elseif (y <= 1.55e+131)
		tmp = Float64(-4.0 * Float64(t * Float64(a / c)));
	elseif (y <= 9e+144)
		tmp = Float64(b * Float64(1.0 / Float64(z * c)));
	else
		tmp = Float64(9.0 * Float64(x / Float64(z * Float64(c / y))));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = a * (-4.0 * (t / c));
	tmp = 0.0;
	if (y <= -6800.0)
		tmp = (x * (y / c)) * (9.0 / z);
	elseif (y <= 9.5e-73)
		tmp = t_1;
	elseif (y <= 2.5e-29)
		tmp = (b / c) / z;
	elseif (y <= 2.4e+39)
		tmp = t_1;
	elseif (y <= 2.1e+121)
		tmp = 1.0 / (0.1111111111111111 * ((z * c) / (x * y)));
	elseif (y <= 1.55e+131)
		tmp = -4.0 * (t * (a / c));
	elseif (y <= 9e+144)
		tmp = b * (1.0 / (z * c));
	else
		tmp = 9.0 * (x / (z * (c / y)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(a * N[(-4.0 * N[(t / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -6800.0], N[(N[(x * N[(y / c), $MachinePrecision]), $MachinePrecision] * N[(9.0 / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9.5e-73], t$95$1, If[LessEqual[y, 2.5e-29], N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[y, 2.4e+39], t$95$1, If[LessEqual[y, 2.1e+121], N[(1.0 / N[(0.1111111111111111 * N[(N[(z * c), $MachinePrecision] / N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.55e+131], N[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9e+144], N[(b * N[(1.0 / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(9.0 * N[(x / N[(z * N[(c / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if y < -6800

   1. Initial program 76.2%

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

      1. associate-+l- 76.2%

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

      2. associate-*r* 76.2%

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

      3. associate-*r* 76.2%

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

      4. *-un-lft-identity 76.2%

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

      5. times-frac 85.0%

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

      6. associate--r- 85.0%

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

      7. fma-neg 85.0%

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

      8. associate-*r* 83.6%

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

      9. distribute-rgt-neg-in 83.6%

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

      10. associate-*l* 83.6%

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

   3. Applied egg-rr 83.6%

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

   4. Taylor expanded in x around inf 55.2%

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

      1. associate-*r/ 55.2%

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

      2. *-commutative 55.2%

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

      3. times-frac 63.5%

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

      4. associate-*r/ 63.4%

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

   6. Simplified 63.4%

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

   if -6800 < y < 9.50000000000000005e-73 or 2.49999999999999993e-29 < y < 2.4000000000000001e39

   1. Initial program 80.6%

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

   2. Taylor expanded in x around 0 80.6%

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

   3. Taylor expanded in z around inf 49.0%

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

      1. associate-*r/ 49.0%

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

      2. *-commutative 49.0%

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

      3. associate-/l* 49.0%

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

      4. associate-*r/ 52.6%

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

      5. associate-/r/ 52.6%

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

   5. Simplified 52.6%

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

   if 9.50000000000000005e-73 < y < 2.49999999999999993e-29

   1. Initial program 99.7%

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

   2. Taylor expanded in b around inf 50.0%

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

      1. *-commutative 50.0%

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

   4. Simplified 50.0%

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

      1. div-inv 49.9%

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

   6. Applied egg-rr 49.9%

      \[\leadsto \color{blue}{b \cdot \frac{1}{z \cdot c}} \]
   7. Step-by-step derivation

      1. un-div-inv 50.0%

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

      2. *-commutative 50.0%

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

      3. associate-/r* 31.9%

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

   8. Applied egg-rr 31.9%

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

   if 2.4000000000000001e39 < y < 2.1000000000000002e121

   1. Initial program 93.8%

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

      1. associate-+l- 93.8%

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

      2. associate-*r* 93.7%

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

      3. associate-*r* 93.7%

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

      4. clear-num 93.7%

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

      5. inv-pow 93.7%

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

      6. associate--r- 93.7%

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

      7. fma-neg 93.7%

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

      8. associate-*r* 93.7%

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

      9. distribute-rgt-neg-in 93.7%

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

      10. associate-*l* 93.7%

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

   3. Applied egg-rr 93.7%

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

   5. Simplified 93.7%

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

   6. Taylor expanded in x around inf 51.9%

      \[\leadsto \frac{1}{\color{blue}{0.1111111111111111 \cdot \frac{c \cdot z}{x \cdot y}}} \]

   if 2.1000000000000002e121 < y < 1.55000000000000008e131

   1. Initial program 0.0%

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

   2. Taylor expanded in x around 0 51.5%

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

   3. Taylor expanded in z around inf 51.5%

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

      1. associate-*l/ 99.2%

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

   5. Simplified 99.2%

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

   if 1.55000000000000008e131 < y < 8.99999999999999935e144

   1. Initial program 100.0%

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

   2. Taylor expanded in b around inf 52.8%

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

      1. *-commutative 52.8%

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

   4. Simplified 52.8%

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

      1. div-inv 52.8%

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

   6. Applied egg-rr 52.8%

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

   if 8.99999999999999935e144 < y

   1. Initial program 75.1%

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

      1. associate-+l- 75.1%

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

      2. associate-*r* 75.1%

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

      3. associate-*r* 77.9%

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

      4. *-un-lft-identity 77.9%

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

      5. times-frac 72.8%

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

      6. associate--r- 72.8%

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

      7. fma-neg 75.6%

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

      8. associate-*r* 75.5%

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

      9. distribute-rgt-neg-in 75.5%

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

      10. associate-*l* 75.5%

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

   3. Applied egg-rr 75.5%

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

   4. Taylor expanded in c around 0 72.7%

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

   5. Taylor expanded in x around inf 61.5%

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

      1. associate-/r* 61.3%

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

      2. associate-/l* 69.3%

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

      3. associate-/l/ 66.8%

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

   7. Simplified 66.8%

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

4. Final simplification 56.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6800:\\ \;\;\;\;\left(x \cdot \frac{y}{c}\right) \cdot \frac{9}{z}\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{-73}:\\ \;\;\;\;a \cdot \left(-4 \cdot \frac{t}{c}\right)\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{-29}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{+39}:\\ \;\;\;\;a \cdot \left(-4 \cdot \frac{t}{c}\right)\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{+121}:\\ \;\;\;\;\frac{1}{0.1111111111111111 \cdot \frac{z \cdot c}{x \cdot y}}\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{+131}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+144}:\\ \;\;\;\;b \cdot \frac{1}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;9 \cdot \frac{x}{z \cdot \frac{c}{y}}\\ \end{array} \]

Alternative 7: 92.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -9000000 \lor \neg \left(z \leq 6.8 \cdot 10^{-50}\right):\\ \;\;\;\;\frac{\left(\frac{b}{z} + 9 \cdot \frac{x \cdot y}{z}\right) - 4 \cdot \left(a \cdot t\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(9 \cdot x\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= z -9000000.0) (not (<= z 6.8e-50)))
   (/ (- (+ (/ b z) (* 9.0 (/ (* x y) z))) (* 4.0 (* a t))) c)
   (/ (+ b (- (* y (* 9.0 x)) (* a (* t (* z 4.0))))) (* z c))))

C

assert(x < y);
assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((z <= -9000000.0) || !(z <= 6.8e-50)) {
		tmp = (((b / z) + (9.0 * ((x * y) / z))) - (4.0 * (a * t))) / c;
	} else {
		tmp = (b + ((y * (9.0 * x)) - (a * (t * (z * 4.0))))) / (z * c);
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if ((z <= (-9000000.0d0)) .or. (.not. (z <= 6.8d-50))) then
        tmp = (((b / z) + (9.0d0 * ((x * y) / z))) - (4.0d0 * (a * t))) / c
    else
        tmp = (b + ((y * (9.0d0 * x)) - (a * (t * (z * 4.0d0))))) / (z * c)
    end if
    code = tmp
end function

Java

assert x < y;
assert t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((z <= -9000000.0) || !(z <= 6.8e-50)) {
		tmp = (((b / z) + (9.0 * ((x * y) / z))) - (4.0 * (a * t))) / c;
	} else {
		tmp = (b + ((y * (9.0 * x)) - (a * (t * (z * 4.0))))) / (z * c);
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if (z <= -9000000.0) or not (z <= 6.8e-50):
		tmp = (((b / z) + (9.0 * ((x * y) / z))) - (4.0 * (a * t))) / c
	else:
		tmp = (b + ((y * (9.0 * x)) - (a * (t * (z * 4.0))))) / (z * c)
	return tmp

Julia

x, y = sort([x, y])
t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((z <= -9000000.0) || !(z <= 6.8e-50))
		tmp = Float64(Float64(Float64(Float64(b / z) + Float64(9.0 * Float64(Float64(x * y) / z))) - Float64(4.0 * Float64(a * t))) / c);
	else
		tmp = Float64(Float64(b + Float64(Float64(y * Float64(9.0 * x)) - Float64(a * Float64(t * Float64(z * 4.0))))) / Float64(z * c));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((z <= -9000000.0) || ~((z <= 6.8e-50)))
		tmp = (((b / z) + (9.0 * ((x * y) / z))) - (4.0 * (a * t))) / c;
	else
		tmp = (b + ((y * (9.0 * x)) - (a * (t * (z * 4.0))))) / (z * c);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[z, -9000000.0], N[Not[LessEqual[z, 6.8e-50]], $MachinePrecision]], N[(N[(N[(N[(b / z), $MachinePrecision] + N[(9.0 * N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], N[(N[(b + N[(N[(y * N[(9.0 * x), $MachinePrecision]), $MachinePrecision] - N[(a * N[(t * N[(z * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -9e6 or 6.80000000000000029e-50 < z

   1. Initial program 63.0%

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

   2. Taylor expanded in x around 0 81.8%

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

   3. Taylor expanded in c around 0 90.0%

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

   if -9e6 < z < 6.80000000000000029e-50

   1. Initial program 96.1%

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

4. Final simplification 93.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9000000 \lor \neg \left(z \leq 6.8 \cdot 10^{-50}\right):\\ \;\;\;\;\frac{\left(\frac{b}{z} + 9 \cdot \frac{x \cdot y}{z}\right) - 4 \cdot \left(a \cdot t\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(9 \cdot x\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c}\\ \end{array} \]

Alternative 8: 50.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} t_1 := a \cdot \left(-4 \cdot \frac{t}{c}\right)\\ t_2 := 9 \cdot \left(\frac{y}{c} \cdot \frac{x}{z}\right)\\ \mathbf{if}\;y \leq -15000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{-71}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 5 \cdot 10^{-29}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+72}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{+119}:\\ \;\;\;\;9 \cdot \left(\frac{y}{z} \cdot \frac{x}{c}\right)\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{+142}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* a (* -4.0 (/ t c)))) (t_2 (* 9.0 (* (/ y c) (/ x z)))))
   (if (<= y -15000.0)
     t_2
     (if (<= y 3.6e-71)
       t_1
       (if (<= y 5e-29)
         (/ (/ b c) z)
         (if (<= y 1.2e+72)
           t_1
           (if (<= y 3.6e+119)
             (* 9.0 (* (/ y z) (/ x c)))
             (if (<= y 1.85e+142) t_1 t_2))))))))

C

assert(x < y);
assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = a * (-4.0 * (t / c));
	double t_2 = 9.0 * ((y / c) * (x / z));
	double tmp;
	if (y <= -15000.0) {
		tmp = t_2;
	} else if (y <= 3.6e-71) {
		tmp = t_1;
	} else if (y <= 5e-29) {
		tmp = (b / c) / z;
	} else if (y <= 1.2e+72) {
		tmp = t_1;
	} else if (y <= 3.6e+119) {
		tmp = 9.0 * ((y / z) * (x / c));
	} else if (y <= 1.85e+142) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a * ((-4.0d0) * (t / c))
    t_2 = 9.0d0 * ((y / c) * (x / z))
    if (y <= (-15000.0d0)) then
        tmp = t_2
    else if (y <= 3.6d-71) then
        tmp = t_1
    else if (y <= 5d-29) then
        tmp = (b / c) / z
    else if (y <= 1.2d+72) then
        tmp = t_1
    else if (y <= 3.6d+119) then
        tmp = 9.0d0 * ((y / z) * (x / c))
    else if (y <= 1.85d+142) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

assert x < y;
assert t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = a * (-4.0 * (t / c));
	double t_2 = 9.0 * ((y / c) * (x / z));
	double tmp;
	if (y <= -15000.0) {
		tmp = t_2;
	} else if (y <= 3.6e-71) {
		tmp = t_1;
	} else if (y <= 5e-29) {
		tmp = (b / c) / z;
	} else if (y <= 1.2e+72) {
		tmp = t_1;
	} else if (y <= 3.6e+119) {
		tmp = 9.0 * ((y / z) * (x / c));
	} else if (y <= 1.85e+142) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	t_1 = a * (-4.0 * (t / c))
	t_2 = 9.0 * ((y / c) * (x / z))
	tmp = 0
	if y <= -15000.0:
		tmp = t_2
	elif y <= 3.6e-71:
		tmp = t_1
	elif y <= 5e-29:
		tmp = (b / c) / z
	elif y <= 1.2e+72:
		tmp = t_1
	elif y <= 3.6e+119:
		tmp = 9.0 * ((y / z) * (x / c))
	elif y <= 1.85e+142:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

x, y = sort([x, y])
t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(a * Float64(-4.0 * Float64(t / c)))
	t_2 = Float64(9.0 * Float64(Float64(y / c) * Float64(x / z)))
	tmp = 0.0
	if (y <= -15000.0)
		tmp = t_2;
	elseif (y <= 3.6e-71)
		tmp = t_1;
	elseif (y <= 5e-29)
		tmp = Float64(Float64(b / c) / z);
	elseif (y <= 1.2e+72)
		tmp = t_1;
	elseif (y <= 3.6e+119)
		tmp = Float64(9.0 * Float64(Float64(y / z) * Float64(x / c)));
	elseif (y <= 1.85e+142)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = a * (-4.0 * (t / c));
	t_2 = 9.0 * ((y / c) * (x / z));
	tmp = 0.0;
	if (y <= -15000.0)
		tmp = t_2;
	elseif (y <= 3.6e-71)
		tmp = t_1;
	elseif (y <= 5e-29)
		tmp = (b / c) / z;
	elseif (y <= 1.2e+72)
		tmp = t_1;
	elseif (y <= 3.6e+119)
		tmp = 9.0 * ((y / z) * (x / c));
	elseif (y <= 1.85e+142)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(a * N[(-4.0 * N[(t / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(9.0 * N[(N[(y / c), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -15000.0], t$95$2, If[LessEqual[y, 3.6e-71], t$95$1, If[LessEqual[y, 5e-29], N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[y, 1.2e+72], t$95$1, If[LessEqual[y, 3.6e+119], N[(9.0 * N[(N[(y / z), $MachinePrecision] * N[(x / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.85e+142], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -15000 or 1.8499999999999999e142 < y

   1. Initial program 75.8%

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

   2. Taylor expanded in x around inf 57.4%

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

      1. *-commutative 57.4%

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

   4. Simplified 57.4%

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

   5. Taylor expanded in x around 0 57.4%

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

      1. *-commutative 57.4%

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

      2. times-frac 62.9%

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

   7. Simplified 62.9%

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

   if -15000 < y < 3.6e-71 or 4.99999999999999986e-29 < y < 1.20000000000000005e72 or 3.60000000000000001e119 < y < 1.8499999999999999e142

   1. Initial program 80.6%

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

   2. Taylor expanded in x around 0 80.7%

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

   3. Taylor expanded in z around inf 46.7%

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

      1. associate-*r/ 46.7%

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

      2. *-commutative 46.7%

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

      3. associate-/l* 46.7%

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

      4. associate-*r/ 51.2%

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

      5. associate-/r/ 51.2%

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

   5. Simplified 51.2%

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

   if 3.6e-71 < y < 4.99999999999999986e-29

   1. Initial program 99.8%

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

   2. Taylor expanded in b around inf 49.9%

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

      1. *-commutative 49.9%

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

   4. Simplified 49.9%

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

      1. div-inv 49.7%

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

   6. Applied egg-rr 49.7%

      \[\leadsto \color{blue}{b \cdot \frac{1}{z \cdot c}} \]
   7. Step-by-step derivation

      1. un-div-inv 49.9%

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

      2. *-commutative 49.9%

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

      3. associate-/r* 38.8%

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

   8. Applied egg-rr 38.8%

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

   if 1.20000000000000005e72 < y < 3.60000000000000001e119

   1. Initial program 100.0%

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

      1. associate-+l- 100.0%

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

      2. associate-*r* 100.0%

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

      3. associate-*r* 100.0%

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

      4. *-un-lft-identity 100.0%

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

      5. times-frac 100.0%

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

      6. associate--r- 100.0%

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

      7. fma-neg 100.0%

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

      8. associate-*r* 100.0%

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

      9. distribute-rgt-neg-in 100.0%

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

      10. associate-*l* 100.0%

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

   3. Applied egg-rr 100.0%

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

   4. Taylor expanded in x around inf 51.7%

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

      1. times-frac 51.4%

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

   6. Simplified 51.4%

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

4. Final simplification 55.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -15000:\\ \;\;\;\;9 \cdot \left(\frac{y}{c} \cdot \frac{x}{z}\right)\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{-71}:\\ \;\;\;\;a \cdot \left(-4 \cdot \frac{t}{c}\right)\\ \mathbf{elif}\;y \leq 5 \cdot 10^{-29}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+72}:\\ \;\;\;\;a \cdot \left(-4 \cdot \frac{t}{c}\right)\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{+119}:\\ \;\;\;\;9 \cdot \left(\frac{y}{z} \cdot \frac{x}{c}\right)\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{+142}:\\ \;\;\;\;a \cdot \left(-4 \cdot \frac{t}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;9 \cdot \left(\frac{y}{c} \cdot \frac{x}{z}\right)\\ \end{array} \]

Alternative 9: 71.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;b \leq -5.5 \cdot 10^{+110}:\\ \;\;\;\;\frac{1}{\frac{c}{\frac{b + -4 \cdot \left(z \cdot \left(a \cdot t\right)\right)}{z}}}\\ \mathbf{elif}\;b \leq 6 \cdot 10^{-61}:\\ \;\;\;\;9 \cdot \frac{x \cdot y}{z \cdot c} - 4 \cdot \frac{a \cdot t}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{z} \cdot \frac{b + 9 \cdot \left(x \cdot y\right)}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= b -5.5e+110)
   (/ 1.0 (/ c (/ (+ b (* -4.0 (* z (* a t)))) z)))
   (if (<= b 6e-61)
     (- (* 9.0 (/ (* x y) (* z c))) (* 4.0 (/ (* a t) c)))
     (* (/ 1.0 z) (/ (+ b (* 9.0 (* x y))) c)))))

C

assert(x < y);
assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (b <= -5.5e+110) {
		tmp = 1.0 / (c / ((b + (-4.0 * (z * (a * t)))) / z));
	} else if (b <= 6e-61) {
		tmp = (9.0 * ((x * y) / (z * c))) - (4.0 * ((a * t) / c));
	} else {
		tmp = (1.0 / z) * ((b + (9.0 * (x * y))) / c);
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (b <= (-5.5d+110)) then
        tmp = 1.0d0 / (c / ((b + ((-4.0d0) * (z * (a * t)))) / z))
    else if (b <= 6d-61) then
        tmp = (9.0d0 * ((x * y) / (z * c))) - (4.0d0 * ((a * t) / c))
    else
        tmp = (1.0d0 / z) * ((b + (9.0d0 * (x * y))) / c)
    end if
    code = tmp
end function

Java

assert x < y;
assert t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (b <= -5.5e+110) {
		tmp = 1.0 / (c / ((b + (-4.0 * (z * (a * t)))) / z));
	} else if (b <= 6e-61) {
		tmp = (9.0 * ((x * y) / (z * c))) - (4.0 * ((a * t) / c));
	} else {
		tmp = (1.0 / z) * ((b + (9.0 * (x * y))) / c);
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if b <= -5.5e+110:
		tmp = 1.0 / (c / ((b + (-4.0 * (z * (a * t)))) / z))
	elif b <= 6e-61:
		tmp = (9.0 * ((x * y) / (z * c))) - (4.0 * ((a * t) / c))
	else:
		tmp = (1.0 / z) * ((b + (9.0 * (x * y))) / c)
	return tmp

Julia

x, y = sort([x, y])
t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (b <= -5.5e+110)
		tmp = Float64(1.0 / Float64(c / Float64(Float64(b + Float64(-4.0 * Float64(z * Float64(a * t)))) / z)));
	elseif (b <= 6e-61)
		tmp = Float64(Float64(9.0 * Float64(Float64(x * y) / Float64(z * c))) - Float64(4.0 * Float64(Float64(a * t) / c)));
	else
		tmp = Float64(Float64(1.0 / z) * Float64(Float64(b + Float64(9.0 * Float64(x * y))) / c));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (b <= -5.5e+110)
		tmp = 1.0 / (c / ((b + (-4.0 * (z * (a * t)))) / z));
	elseif (b <= 6e-61)
		tmp = (9.0 * ((x * y) / (z * c))) - (4.0 * ((a * t) / c));
	else
		tmp = (1.0 / z) * ((b + (9.0 * (x * y))) / c);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[b, -5.5e+110], N[(1.0 / N[(c / N[(N[(b + N[(-4.0 * N[(z * N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 6e-61], N[(N[(9.0 * N[(N[(x * y), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * N[(N[(a * t), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(1.0 / z), $MachinePrecision] * N[(N[(b + N[(9.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -5.49999999999999996e110

   1. Initial program 73.7%

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

      1. associate-+l- 73.7%

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

      2. associate-*r* 73.7%

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

      3. associate-*r* 73.7%

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

      4. clear-num 73.7%

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

      5. inv-pow 73.7%

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

      6. associate--r- 73.7%

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

      7. fma-neg 73.7%

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

      8. associate-*r* 73.7%

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

      9. distribute-rgt-neg-in 73.7%

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

      10. associate-*l* 73.7%

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

   3. Applied egg-rr 73.7%

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

   5. Simplified 73.7%

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

   6. Taylor expanded in x around 0 68.8%

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

      1. associate-/l* 66.8%

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

      2. associate-*r* 71.3%

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

   8. Simplified 71.3%

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

   if -5.49999999999999996e110 < b < 6.00000000000000024e-61

   1. Initial program 81.5%

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

   2. Taylor expanded in x around 0 82.2%

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

   3. Taylor expanded in b around 0 80.7%

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

   if 6.00000000000000024e-61 < b

   1. Initial program 79.7%

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

      1. associate-+l- 79.7%

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

      2. associate-*r* 79.8%

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

      3. associate-*r* 76.9%

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

      4. *-un-lft-identity 76.9%

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

      5. times-frac 82.6%

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

      6. associate--r- 82.6%

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

      7. fma-neg 84.1%

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

      8. associate-*r* 87.0%

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

      9. distribute-rgt-neg-in 87.0%

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

      10. associate-*l* 87.0%

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

   3. Applied egg-rr 87.0%

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

   4. Taylor expanded in z around 0 68.2%

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

4. Final simplification 75.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5.5 \cdot 10^{+110}:\\ \;\;\;\;\frac{1}{\frac{c}{\frac{b + -4 \cdot \left(z \cdot \left(a \cdot t\right)\right)}{z}}}\\ \mathbf{elif}\;b \leq 6 \cdot 10^{-61}:\\ \;\;\;\;9 \cdot \frac{x \cdot y}{z \cdot c} - 4 \cdot \frac{a \cdot t}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{z} \cdot \frac{b + 9 \cdot \left(x \cdot y\right)}{c}\\ \end{array} \]

Alternative 10: 63.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} t_1 := \frac{1}{z} \cdot \frac{b + 9 \cdot \left(x \cdot y\right)}{c}\\ \mathbf{if}\;a \leq 10^{+19}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{+62}:\\ \;\;\;\;a \cdot \left(-4 \cdot \frac{t}{c}\right)\\ \mathbf{elif}\;a \leq 7 \cdot 10^{+125}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (/ 1.0 z) (/ (+ b (* 9.0 (* x y))) c))))
   (if (<= a 1e+19)
     t_1
     (if (<= a 9.5e+62)
       (* a (* -4.0 (/ t c)))
       (if (<= a 7e+125) t_1 (* -4.0 (/ a (/ c t))))))))

C

assert(x < y);
assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (1.0 / z) * ((b + (9.0 * (x * y))) / c);
	double tmp;
	if (a <= 1e+19) {
		tmp = t_1;
	} else if (a <= 9.5e+62) {
		tmp = a * (-4.0 * (t / c));
	} else if (a <= 7e+125) {
		tmp = t_1;
	} else {
		tmp = -4.0 * (a / (c / t));
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (1.0d0 / z) * ((b + (9.0d0 * (x * y))) / c)
    if (a <= 1d+19) then
        tmp = t_1
    else if (a <= 9.5d+62) then
        tmp = a * ((-4.0d0) * (t / c))
    else if (a <= 7d+125) then
        tmp = t_1
    else
        tmp = (-4.0d0) * (a / (c / t))
    end if
    code = tmp
end function

Java

assert x < y;
assert t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (1.0 / z) * ((b + (9.0 * (x * y))) / c);
	double tmp;
	if (a <= 1e+19) {
		tmp = t_1;
	} else if (a <= 9.5e+62) {
		tmp = a * (-4.0 * (t / c));
	} else if (a <= 7e+125) {
		tmp = t_1;
	} else {
		tmp = -4.0 * (a / (c / t));
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	t_1 = (1.0 / z) * ((b + (9.0 * (x * y))) / c)
	tmp = 0
	if a <= 1e+19:
		tmp = t_1
	elif a <= 9.5e+62:
		tmp = a * (-4.0 * (t / c))
	elif a <= 7e+125:
		tmp = t_1
	else:
		tmp = -4.0 * (a / (c / t))
	return tmp

Julia

x, y = sort([x, y])
t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(1.0 / z) * Float64(Float64(b + Float64(9.0 * Float64(x * y))) / c))
	tmp = 0.0
	if (a <= 1e+19)
		tmp = t_1;
	elseif (a <= 9.5e+62)
		tmp = Float64(a * Float64(-4.0 * Float64(t / c)));
	elseif (a <= 7e+125)
		tmp = t_1;
	else
		tmp = Float64(-4.0 * Float64(a / Float64(c / t)));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (1.0 / z) * ((b + (9.0 * (x * y))) / c);
	tmp = 0.0;
	if (a <= 1e+19)
		tmp = t_1;
	elseif (a <= 9.5e+62)
		tmp = a * (-4.0 * (t / c));
	elseif (a <= 7e+125)
		tmp = t_1;
	else
		tmp = -4.0 * (a / (c / t));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(1.0 / z), $MachinePrecision] * N[(N[(b + N[(9.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, 1e+19], t$95$1, If[LessEqual[a, 9.5e+62], N[(a * N[(-4.0 * N[(t / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 7e+125], t$95$1, N[(-4.0 * N[(a / N[(c / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if a < 1e19 or 9.5000000000000003e62 < a < 7.00000000000000023e125

   1. Initial program 79.3%

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

      1. associate-+l- 79.3%

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

      2. associate-*r* 79.3%

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

      3. associate-*r* 78.9%

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

      4. *-un-lft-identity 78.9%

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

      5. times-frac 82.3%

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

      6. associate--r- 82.3%

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

      7. fma-neg 82.3%

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

      8. associate-*r* 82.8%

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

      9. distribute-rgt-neg-in 82.8%

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

      10. associate-*l* 82.8%

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

   3. Applied egg-rr 82.8%

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

   4. Taylor expanded in z around 0 66.9%

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

   if 1e19 < a < 9.5000000000000003e62

   1. Initial program 64.2%

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

   2. Taylor expanded in x around 0 76.4%

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

   3. Taylor expanded in z around inf 51.7%

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

      1. associate-*r/ 51.7%

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

      2. *-commutative 51.7%

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

      3. associate-/l* 51.7%

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

      4. associate-*r/ 75.0%

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

      5. associate-/r/ 75.0%

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

   5. Simplified 75.0%

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

   if 7.00000000000000023e125 < a

   1. Initial program 85.7%

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

   2. Taylor expanded in z around inf 65.3%

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

      1. *-commutative 65.3%

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

      2. associate-/l* 71.9%

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

   4. Simplified 71.9%

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

4. Final simplification 67.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 10^{+19}:\\ \;\;\;\;\frac{1}{z} \cdot \frac{b + 9 \cdot \left(x \cdot y\right)}{c}\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{+62}:\\ \;\;\;\;a \cdot \left(-4 \cdot \frac{t}{c}\right)\\ \mathbf{elif}\;a \leq 7 \cdot 10^{+125}:\\ \;\;\;\;\frac{1}{z} \cdot \frac{b + 9 \cdot \left(x \cdot y\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \end{array} \]

Alternative 11: 63.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} t_1 := b + 9 \cdot \left(x \cdot y\right)\\ \mathbf{if}\;a \leq 1.45 \cdot 10^{+19}:\\ \;\;\;\;\frac{1}{z} \cdot \frac{t_1}{c}\\ \mathbf{elif}\;a \leq 9.2 \cdot 10^{+62}:\\ \;\;\;\;a \cdot \left(-4 \cdot \frac{t}{c}\right)\\ \mathbf{elif}\;a \leq 5.6 \cdot 10^{+126}:\\ \;\;\;\;\frac{1}{\frac{z \cdot c}{t_1}}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ b (* 9.0 (* x y)))))
   (if (<= a 1.45e+19)
     (* (/ 1.0 z) (/ t_1 c))
     (if (<= a 9.2e+62)
       (* a (* -4.0 (/ t c)))
       (if (<= a 5.6e+126) (/ 1.0 (/ (* z c) t_1)) (* -4.0 (/ a (/ c t))))))))

C

assert(x < y);
assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = b + (9.0 * (x * y));
	double tmp;
	if (a <= 1.45e+19) {
		tmp = (1.0 / z) * (t_1 / c);
	} else if (a <= 9.2e+62) {
		tmp = a * (-4.0 * (t / c));
	} else if (a <= 5.6e+126) {
		tmp = 1.0 / ((z * c) / t_1);
	} else {
		tmp = -4.0 * (a / (c / t));
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b + (9.0d0 * (x * y))
    if (a <= 1.45d+19) then
        tmp = (1.0d0 / z) * (t_1 / c)
    else if (a <= 9.2d+62) then
        tmp = a * ((-4.0d0) * (t / c))
    else if (a <= 5.6d+126) then
        tmp = 1.0d0 / ((z * c) / t_1)
    else
        tmp = (-4.0d0) * (a / (c / t))
    end if
    code = tmp
end function

Java

assert x < y;
assert t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = b + (9.0 * (x * y));
	double tmp;
	if (a <= 1.45e+19) {
		tmp = (1.0 / z) * (t_1 / c);
	} else if (a <= 9.2e+62) {
		tmp = a * (-4.0 * (t / c));
	} else if (a <= 5.6e+126) {
		tmp = 1.0 / ((z * c) / t_1);
	} else {
		tmp = -4.0 * (a / (c / t));
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	t_1 = b + (9.0 * (x * y))
	tmp = 0
	if a <= 1.45e+19:
		tmp = (1.0 / z) * (t_1 / c)
	elif a <= 9.2e+62:
		tmp = a * (-4.0 * (t / c))
	elif a <= 5.6e+126:
		tmp = 1.0 / ((z * c) / t_1)
	else:
		tmp = -4.0 * (a / (c / t))
	return tmp

Julia

x, y = sort([x, y])
t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(b + Float64(9.0 * Float64(x * y)))
	tmp = 0.0
	if (a <= 1.45e+19)
		tmp = Float64(Float64(1.0 / z) * Float64(t_1 / c));
	elseif (a <= 9.2e+62)
		tmp = Float64(a * Float64(-4.0 * Float64(t / c)));
	elseif (a <= 5.6e+126)
		tmp = Float64(1.0 / Float64(Float64(z * c) / t_1));
	else
		tmp = Float64(-4.0 * Float64(a / Float64(c / t)));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = b + (9.0 * (x * y));
	tmp = 0.0;
	if (a <= 1.45e+19)
		tmp = (1.0 / z) * (t_1 / c);
	elseif (a <= 9.2e+62)
		tmp = a * (-4.0 * (t / c));
	elseif (a <= 5.6e+126)
		tmp = 1.0 / ((z * c) / t_1);
	else
		tmp = -4.0 * (a / (c / t));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(b + N[(9.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, 1.45e+19], N[(N[(1.0 / z), $MachinePrecision] * N[(t$95$1 / c), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 9.2e+62], N[(a * N[(-4.0 * N[(t / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 5.6e+126], N[(1.0 / N[(N[(z * c), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision], N[(-4.0 * N[(a / N[(c / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if a < 1.45e19

   1. Initial program 78.4%

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

      1. associate-+l- 78.4%

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

      2. associate-*r* 78.4%

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

      3. associate-*r* 78.0%

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

      4. *-un-lft-identity 78.0%

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

      5. times-frac 82.2%

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

      6. associate--r- 82.2%

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

      7. fma-neg 82.2%

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

      8. associate-*r* 82.6%

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

      9. distribute-rgt-neg-in 82.6%

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

      10. associate-*l* 82.6%

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

   3. Applied egg-rr 82.6%

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

   4. Taylor expanded in z around 0 66.7%

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

   if 1.45e19 < a < 9.19999999999999936e62

   1. Initial program 64.2%

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

   2. Taylor expanded in x around 0 76.4%

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

   3. Taylor expanded in z around inf 51.7%

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

      1. associate-*r/ 51.7%

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

      2. *-commutative 51.7%

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

      3. associate-/l* 51.7%

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

      4. associate-*r/ 75.0%

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

      5. associate-/r/ 75.0%

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

   5. Simplified 75.0%

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

   if 9.19999999999999936e62 < a < 5.60000000000000018e126

   1. Initial program 91.8%

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

      1. associate-+l- 91.8%

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

      2. associate-*r* 91.9%

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

      3. associate-*r* 91.8%

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

      4. clear-num 92.0%

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

      5. inv-pow 92.0%

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

      6. associate--r- 92.0%

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

      7. fma-neg 92.0%

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

      8. associate-*r* 92.0%

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

      9. distribute-rgt-neg-in 92.0%

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

      10. associate-*l* 92.0%

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

   3. Applied egg-rr 92.0%

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

   5. Simplified 92.0%

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

   6. Taylor expanded in z around 0 77.2%

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

   if 5.60000000000000018e126 < a

   1. Initial program 85.7%

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

   2. Taylor expanded in z around inf 65.3%

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

      1. *-commutative 65.3%

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

      2. associate-/l* 71.9%

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

   4. Simplified 71.9%

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

4. Final simplification 68.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 1.45 \cdot 10^{+19}:\\ \;\;\;\;\frac{1}{z} \cdot \frac{b + 9 \cdot \left(x \cdot y\right)}{c}\\ \mathbf{elif}\;a \leq 9.2 \cdot 10^{+62}:\\ \;\;\;\;a \cdot \left(-4 \cdot \frac{t}{c}\right)\\ \mathbf{elif}\;a \leq 5.6 \cdot 10^{+126}:\\ \;\;\;\;\frac{1}{\frac{z \cdot c}{b + 9 \cdot \left(x \cdot y\right)}}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \end{array} \]

Alternative 12: 64.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} t_1 := b + 9 \cdot \left(x \cdot y\right)\\ \mathbf{if}\;a \leq 1.95 \cdot 10^{+18}:\\ \;\;\;\;\frac{1}{z} \cdot \frac{t_1}{c}\\ \mathbf{elif}\;a \leq 2.15 \cdot 10^{+62}:\\ \;\;\;\;\frac{b - 4 \cdot \left(a \cdot \left(z \cdot t\right)\right)}{z \cdot c}\\ \mathbf{elif}\;a \leq 1.06 \cdot 10^{+126}:\\ \;\;\;\;\frac{1}{\frac{z \cdot c}{t_1}}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ b (* 9.0 (* x y)))))
   (if (<= a 1.95e+18)
     (* (/ 1.0 z) (/ t_1 c))
     (if (<= a 2.15e+62)
       (/ (- b (* 4.0 (* a (* z t)))) (* z c))
       (if (<= a 1.06e+126) (/ 1.0 (/ (* z c) t_1)) (* -4.0 (/ a (/ c t))))))))

C

assert(x < y);
assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = b + (9.0 * (x * y));
	double tmp;
	if (a <= 1.95e+18) {
		tmp = (1.0 / z) * (t_1 / c);
	} else if (a <= 2.15e+62) {
		tmp = (b - (4.0 * (a * (z * t)))) / (z * c);
	} else if (a <= 1.06e+126) {
		tmp = 1.0 / ((z * c) / t_1);
	} else {
		tmp = -4.0 * (a / (c / t));
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b + (9.0d0 * (x * y))
    if (a <= 1.95d+18) then
        tmp = (1.0d0 / z) * (t_1 / c)
    else if (a <= 2.15d+62) then
        tmp = (b - (4.0d0 * (a * (z * t)))) / (z * c)
    else if (a <= 1.06d+126) then
        tmp = 1.0d0 / ((z * c) / t_1)
    else
        tmp = (-4.0d0) * (a / (c / t))
    end if
    code = tmp
end function

Java

assert x < y;
assert t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = b + (9.0 * (x * y));
	double tmp;
	if (a <= 1.95e+18) {
		tmp = (1.0 / z) * (t_1 / c);
	} else if (a <= 2.15e+62) {
		tmp = (b - (4.0 * (a * (z * t)))) / (z * c);
	} else if (a <= 1.06e+126) {
		tmp = 1.0 / ((z * c) / t_1);
	} else {
		tmp = -4.0 * (a / (c / t));
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	t_1 = b + (9.0 * (x * y))
	tmp = 0
	if a <= 1.95e+18:
		tmp = (1.0 / z) * (t_1 / c)
	elif a <= 2.15e+62:
		tmp = (b - (4.0 * (a * (z * t)))) / (z * c)
	elif a <= 1.06e+126:
		tmp = 1.0 / ((z * c) / t_1)
	else:
		tmp = -4.0 * (a / (c / t))
	return tmp

Julia

x, y = sort([x, y])
t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(b + Float64(9.0 * Float64(x * y)))
	tmp = 0.0
	if (a <= 1.95e+18)
		tmp = Float64(Float64(1.0 / z) * Float64(t_1 / c));
	elseif (a <= 2.15e+62)
		tmp = Float64(Float64(b - Float64(4.0 * Float64(a * Float64(z * t)))) / Float64(z * c));
	elseif (a <= 1.06e+126)
		tmp = Float64(1.0 / Float64(Float64(z * c) / t_1));
	else
		tmp = Float64(-4.0 * Float64(a / Float64(c / t)));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = b + (9.0 * (x * y));
	tmp = 0.0;
	if (a <= 1.95e+18)
		tmp = (1.0 / z) * (t_1 / c);
	elseif (a <= 2.15e+62)
		tmp = (b - (4.0 * (a * (z * t)))) / (z * c);
	elseif (a <= 1.06e+126)
		tmp = 1.0 / ((z * c) / t_1);
	else
		tmp = -4.0 * (a / (c / t));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(b + N[(9.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, 1.95e+18], N[(N[(1.0 / z), $MachinePrecision] * N[(t$95$1 / c), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.15e+62], N[(N[(b - N[(4.0 * N[(a * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.06e+126], N[(1.0 / N[(N[(z * c), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision], N[(-4.0 * N[(a / N[(c / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if a < 1.95e18

   1. Initial program 78.3%

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

      1. associate-+l- 78.3%

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

      2. associate-*r* 78.3%

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

      3. associate-*r* 77.9%

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

      4. *-un-lft-identity 77.9%

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

      5. times-frac 82.1%

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

      6. associate--r- 82.1%

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

      7. fma-neg 82.1%

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

      8. associate-*r* 82.5%

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

      9. distribute-rgt-neg-in 82.5%

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

      10. associate-*l* 82.5%

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

   3. Applied egg-rr 82.5%

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

   4. Taylor expanded in z around 0 66.5%

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

   if 1.95e18 < a < 2.1499999999999998e62

   1. Initial program 76.7%

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

      1. associate-+l- 76.7%

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

      2. associate-*l* 76.7%

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

      3. associate-*l* 64.9%

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

   3. Simplified 64.9%

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

   4. Taylor expanded in x around 0 51.9%

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

   if 2.1499999999999998e62 < a < 1.0600000000000001e126

   1. Initial program 85.3%

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

      1. associate-+l- 85.3%

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

      2. associate-*r* 85.4%

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

      3. associate-*r* 85.3%

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

      4. clear-num 85.4%

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

      5. inv-pow 85.4%

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

      6. associate--r- 85.4%

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

      7. fma-neg 85.4%

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

      8. associate-*r* 85.4%

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

      9. distribute-rgt-neg-in 85.4%

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

      10. associate-*l* 85.4%

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

   3. Applied egg-rr 85.4%

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

   5. Simplified 85.4%

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

   6. Taylor expanded in z around 0 72.0%

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

   if 1.0600000000000001e126 < a

   1. Initial program 85.7%

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

   2. Taylor expanded in z around inf 65.3%

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

      1. *-commutative 65.3%

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

      2. associate-/l* 71.9%

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

   4. Simplified 71.9%

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

4. Final simplification 67.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 1.95 \cdot 10^{+18}:\\ \;\;\;\;\frac{1}{z} \cdot \frac{b + 9 \cdot \left(x \cdot y\right)}{c}\\ \mathbf{elif}\;a \leq 2.15 \cdot 10^{+62}:\\ \;\;\;\;\frac{b - 4 \cdot \left(a \cdot \left(z \cdot t\right)\right)}{z \cdot c}\\ \mathbf{elif}\;a \leq 1.06 \cdot 10^{+126}:\\ \;\;\;\;\frac{1}{\frac{z \cdot c}{b + 9 \cdot \left(x \cdot y\right)}}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \end{array} \]

Alternative 13: 50.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} t_1 := 9 \cdot \left(\frac{y}{z} \cdot \frac{x}{c}\right)\\ t_2 := -4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{if}\;t \leq -2.2 \cdot 10^{+84}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -1.65 \cdot 10^{-211}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.05 \cdot 10^{-302}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{-34}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* 9.0 (* (/ y z) (/ x c)))) (t_2 (* -4.0 (/ a (/ c t)))))
   (if (<= t -2.2e+84)
     t_2
     (if (<= t -1.65e-211)
       t_1
       (if (<= t -1.05e-302) (/ (/ b c) z) (if (<= t 2.8e-34) t_1 t_2))))))

C

assert(x < y);
assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = 9.0 * ((y / z) * (x / c));
	double t_2 = -4.0 * (a / (c / t));
	double tmp;
	if (t <= -2.2e+84) {
		tmp = t_2;
	} else if (t <= -1.65e-211) {
		tmp = t_1;
	} else if (t <= -1.05e-302) {
		tmp = (b / c) / z;
	} else if (t <= 2.8e-34) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = 9.0d0 * ((y / z) * (x / c))
    t_2 = (-4.0d0) * (a / (c / t))
    if (t <= (-2.2d+84)) then
        tmp = t_2
    else if (t <= (-1.65d-211)) then
        tmp = t_1
    else if (t <= (-1.05d-302)) then
        tmp = (b / c) / z
    else if (t <= 2.8d-34) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

assert x < y;
assert t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = 9.0 * ((y / z) * (x / c));
	double t_2 = -4.0 * (a / (c / t));
	double tmp;
	if (t <= -2.2e+84) {
		tmp = t_2;
	} else if (t <= -1.65e-211) {
		tmp = t_1;
	} else if (t <= -1.05e-302) {
		tmp = (b / c) / z;
	} else if (t <= 2.8e-34) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	t_1 = 9.0 * ((y / z) * (x / c))
	t_2 = -4.0 * (a / (c / t))
	tmp = 0
	if t <= -2.2e+84:
		tmp = t_2
	elif t <= -1.65e-211:
		tmp = t_1
	elif t <= -1.05e-302:
		tmp = (b / c) / z
	elif t <= 2.8e-34:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

x, y = sort([x, y])
t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(9.0 * Float64(Float64(y / z) * Float64(x / c)))
	t_2 = Float64(-4.0 * Float64(a / Float64(c / t)))
	tmp = 0.0
	if (t <= -2.2e+84)
		tmp = t_2;
	elseif (t <= -1.65e-211)
		tmp = t_1;
	elseif (t <= -1.05e-302)
		tmp = Float64(Float64(b / c) / z);
	elseif (t <= 2.8e-34)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = 9.0 * ((y / z) * (x / c));
	t_2 = -4.0 * (a / (c / t));
	tmp = 0.0;
	if (t <= -2.2e+84)
		tmp = t_2;
	elseif (t <= -1.65e-211)
		tmp = t_1;
	elseif (t <= -1.05e-302)
		tmp = (b / c) / z;
	elseif (t <= 2.8e-34)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(9.0 * N[(N[(y / z), $MachinePrecision] * N[(x / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(-4.0 * N[(a / N[(c / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.2e+84], t$95$2, If[LessEqual[t, -1.65e-211], t$95$1, If[LessEqual[t, -1.05e-302], N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t, 2.8e-34], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.1999999999999998e84 or 2.79999999999999997e-34 < t

   1. Initial program 73.4%

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

   2. Taylor expanded in z around inf 47.7%

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

      1. *-commutative 47.7%

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

      2. associate-/l* 57.1%

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

   4. Simplified 57.1%

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

   if -2.1999999999999998e84 < t < -1.6500000000000001e-211 or -1.05000000000000006e-302 < t < 2.79999999999999997e-34

   1. Initial program 85.7%

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

      1. associate-+l- 85.7%

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

      2. associate-*r* 85.7%

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

      3. associate-*r* 85.7%

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

      4. *-un-lft-identity 85.7%

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

      5. times-frac 87.4%

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

      6. associate--r- 87.4%

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

      7. fma-neg 87.4%

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

      8. associate-*r* 87.4%

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

      9. distribute-rgt-neg-in 87.4%

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

      10. associate-*l* 87.4%

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

   3. Applied egg-rr 87.4%

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

   4. Taylor expanded in x around inf 44.4%

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

      1. times-frac 42.5%

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

   6. Simplified 42.5%

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

   if -1.6500000000000001e-211 < t < -1.05000000000000006e-302

   1. Initial program 85.1%

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

   2. Taylor expanded in b around inf 53.6%

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

      1. *-commutative 53.6%

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

   4. Simplified 53.6%

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

      1. div-inv 53.6%

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

   6. Applied egg-rr 53.6%

      \[\leadsto \color{blue}{b \cdot \frac{1}{z \cdot c}} \]
   7. Step-by-step derivation

      1. un-div-inv 53.6%

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

      2. *-commutative 53.6%

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

      3. associate-/r* 61.2%

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

   8. Applied egg-rr 61.2%

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

4. Final simplification 50.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.2 \cdot 10^{+84}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;t \leq -1.65 \cdot 10^{-211}:\\ \;\;\;\;9 \cdot \left(\frac{y}{z} \cdot \frac{x}{c}\right)\\ \mathbf{elif}\;t \leq -1.05 \cdot 10^{-302}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{-34}:\\ \;\;\;\;9 \cdot \left(\frac{y}{z} \cdot \frac{x}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \end{array} \]

Alternative 14: 68.4% accurate, 1.3× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -1.2 \cdot 10^{+141}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;t \leq 2 \cdot 10^{-6}:\\ \;\;\;\;\frac{b + y \cdot \left(9 \cdot x\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= t -1.2e+141)
   (* -4.0 (/ a (/ c t)))
   (if (<= t 2e-6) (/ (+ b (* y (* 9.0 x))) (* z c)) (* -4.0 (* t (/ a c))))))

C

assert(x < y);
assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (t <= -1.2e+141) {
		tmp = -4.0 * (a / (c / t));
	} else if (t <= 2e-6) {
		tmp = (b + (y * (9.0 * x))) / (z * c);
	} else {
		tmp = -4.0 * (t * (a / c));
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (t <= (-1.2d+141)) then
        tmp = (-4.0d0) * (a / (c / t))
    else if (t <= 2d-6) then
        tmp = (b + (y * (9.0d0 * x))) / (z * c)
    else
        tmp = (-4.0d0) * (t * (a / c))
    end if
    code = tmp
end function

Java

assert x < y;
assert t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (t <= -1.2e+141) {
		tmp = -4.0 * (a / (c / t));
	} else if (t <= 2e-6) {
		tmp = (b + (y * (9.0 * x))) / (z * c);
	} else {
		tmp = -4.0 * (t * (a / c));
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if t <= -1.2e+141:
		tmp = -4.0 * (a / (c / t))
	elif t <= 2e-6:
		tmp = (b + (y * (9.0 * x))) / (z * c)
	else:
		tmp = -4.0 * (t * (a / c))
	return tmp

Julia

x, y = sort([x, y])
t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (t <= -1.2e+141)
		tmp = Float64(-4.0 * Float64(a / Float64(c / t)));
	elseif (t <= 2e-6)
		tmp = Float64(Float64(b + Float64(y * Float64(9.0 * x))) / Float64(z * c));
	else
		tmp = Float64(-4.0 * Float64(t * Float64(a / c)));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (t <= -1.2e+141)
		tmp = -4.0 * (a / (c / t));
	elseif (t <= 2e-6)
		tmp = (b + (y * (9.0 * x))) / (z * c);
	else
		tmp = -4.0 * (t * (a / c));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[t, -1.2e+141], N[(-4.0 * N[(a / N[(c / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2e-6], N[(N[(b + N[(y * N[(9.0 * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.19999999999999999e141

   1. Initial program 69.2%

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

   2. Taylor expanded in z around inf 52.0%

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

      1. *-commutative 52.0%

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

      2. associate-/l* 64.6%

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

   4. Simplified 64.6%

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

   if -1.19999999999999999e141 < t < 1.99999999999999991e-6

   1. Initial program 85.7%

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

      1. associate-+l- 85.7%

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

      2. associate-*r* 85.7%

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

      3. associate-*r* 85.7%

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

      4. *-un-lft-identity 85.7%

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

      5. times-frac 88.9%

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

      6. associate--r- 88.9%

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

      7. fma-neg 88.9%

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

      8. associate-*r* 88.3%

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

      9. distribute-rgt-neg-in 88.3%

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

      10. associate-*l* 88.3%

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

   3. Applied egg-rr 88.3%

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

   4. Taylor expanded in c around 0 88.3%

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

   5. Taylor expanded in z around 0 69.3%

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

      1. associate-*r* 69.3%

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

   7. Simplified 69.3%

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

   if 1.99999999999999991e-6 < t

   1. Initial program 71.9%

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

   2. Taylor expanded in x around 0 73.8%

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

   3. Taylor expanded in z around inf 47.9%

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

      1. associate-*l/ 56.5%

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

   5. Simplified 56.5%

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

4. Final simplification 65.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.2 \cdot 10^{+141}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;t \leq 2 \cdot 10^{-6}:\\ \;\;\;\;\frac{b + y \cdot \left(9 \cdot x\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \end{array} \]

Alternative 15: 68.4% accurate, 1.3× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -5.8 \cdot 10^{+140}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{-10}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= t -5.8e+140)
   (* -4.0 (/ a (/ c t)))
   (if (<= t 1.9e-10)
     (/ (+ b (* 9.0 (* x y))) (* z c))
     (* -4.0 (* t (/ a c))))))

C

assert(x < y);
assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (t <= -5.8e+140) {
		tmp = -4.0 * (a / (c / t));
	} else if (t <= 1.9e-10) {
		tmp = (b + (9.0 * (x * y))) / (z * c);
	} else {
		tmp = -4.0 * (t * (a / c));
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (t <= (-5.8d+140)) then
        tmp = (-4.0d0) * (a / (c / t))
    else if (t <= 1.9d-10) then
        tmp = (b + (9.0d0 * (x * y))) / (z * c)
    else
        tmp = (-4.0d0) * (t * (a / c))
    end if
    code = tmp
end function

Java

assert x < y;
assert t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (t <= -5.8e+140) {
		tmp = -4.0 * (a / (c / t));
	} else if (t <= 1.9e-10) {
		tmp = (b + (9.0 * (x * y))) / (z * c);
	} else {
		tmp = -4.0 * (t * (a / c));
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if t <= -5.8e+140:
		tmp = -4.0 * (a / (c / t))
	elif t <= 1.9e-10:
		tmp = (b + (9.0 * (x * y))) / (z * c)
	else:
		tmp = -4.0 * (t * (a / c))
	return tmp

Julia

x, y = sort([x, y])
t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (t <= -5.8e+140)
		tmp = Float64(-4.0 * Float64(a / Float64(c / t)));
	elseif (t <= 1.9e-10)
		tmp = Float64(Float64(b + Float64(9.0 * Float64(x * y))) / Float64(z * c));
	else
		tmp = Float64(-4.0 * Float64(t * Float64(a / c)));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (t <= -5.8e+140)
		tmp = -4.0 * (a / (c / t));
	elseif (t <= 1.9e-10)
		tmp = (b + (9.0 * (x * y))) / (z * c);
	else
		tmp = -4.0 * (t * (a / c));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[t, -5.8e+140], N[(-4.0 * N[(a / N[(c / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.9e-10], N[(N[(b + N[(9.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -5.7999999999999998e140

   1. Initial program 69.2%

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

   2. Taylor expanded in z around inf 52.0%

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

      1. *-commutative 52.0%

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

      2. associate-/l* 64.6%

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

   4. Simplified 64.6%

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

   if -5.7999999999999998e140 < t < 1.8999999999999999e-10

   1. Initial program 85.7%

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

   2. Taylor expanded in x around inf 69.3%

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

   if 1.8999999999999999e-10 < t

   1. Initial program 71.9%

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

   2. Taylor expanded in x around 0 73.8%

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

   3. Taylor expanded in z around inf 47.9%

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

      1. associate-*l/ 56.5%

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

   5. Simplified 56.5%

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

4. Final simplification 65.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.8 \cdot 10^{+140}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{-10}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \end{array} \]

Alternative 16: 49.8% accurate, 1.7× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -1.65 \cdot 10^{+74} \lor \neg \left(t \leq 3 \cdot 10^{-125}\right):\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= t -1.65e+74) (not (<= t 3e-125)))
   (* -4.0 (* t (/ a c)))
   (/ b (* z c))))

C

assert(x < y);
assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((t <= -1.65e+74) || !(t <= 3e-125)) {
		tmp = -4.0 * (t * (a / c));
	} else {
		tmp = b / (z * c);
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if ((t <= (-1.65d+74)) .or. (.not. (t <= 3d-125))) then
        tmp = (-4.0d0) * (t * (a / c))
    else
        tmp = b / (z * c)
    end if
    code = tmp
end function

Java

assert x < y;
assert t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((t <= -1.65e+74) || !(t <= 3e-125)) {
		tmp = -4.0 * (t * (a / c));
	} else {
		tmp = b / (z * c);
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if (t <= -1.65e+74) or not (t <= 3e-125):
		tmp = -4.0 * (t * (a / c))
	else:
		tmp = b / (z * c)
	return tmp

Julia

x, y = sort([x, y])
t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((t <= -1.65e+74) || !(t <= 3e-125))
		tmp = Float64(-4.0 * Float64(t * Float64(a / c)));
	else
		tmp = Float64(b / Float64(z * c));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((t <= -1.65e+74) || ~((t <= 3e-125)))
		tmp = -4.0 * (t * (a / c));
	else
		tmp = b / (z * c);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[t, -1.65e+74], N[Not[LessEqual[t, 3e-125]], $MachinePrecision]], N[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.6500000000000001e74 or 2.9999999999999999e-125 < t

   1. Initial program 73.5%

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

   2. Taylor expanded in x around 0 72.3%

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

   3. Taylor expanded in z around inf 46.9%

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

      1. associate-*l/ 51.5%

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

   5. Simplified 51.5%

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

   if -1.6500000000000001e74 < t < 2.9999999999999999e-125

   1. Initial program 88.9%

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

   2. Taylor expanded in b around inf 41.5%

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

      1. *-commutative 41.5%

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

   4. Simplified 41.5%

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

4. Final simplification 47.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.65 \cdot 10^{+74} \lor \neg \left(t \leq 3 \cdot 10^{-125}\right):\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \end{array} \]

Alternative 17: 50.6% accurate, 1.7× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -9.2 \cdot 10^{+24}:\\ \;\;\;\;a \cdot \left(-4 \cdot \frac{t}{c}\right)\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{-125}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= t -9.2e+24)
   (* a (* -4.0 (/ t c)))
   (if (<= t 5.8e-125) (/ b (* z c)) (* -4.0 (* t (/ a c))))))

C

assert(x < y);
assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (t <= -9.2e+24) {
		tmp = a * (-4.0 * (t / c));
	} else if (t <= 5.8e-125) {
		tmp = b / (z * c);
	} else {
		tmp = -4.0 * (t * (a / c));
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (t <= (-9.2d+24)) then
        tmp = a * ((-4.0d0) * (t / c))
    else if (t <= 5.8d-125) then
        tmp = b / (z * c)
    else
        tmp = (-4.0d0) * (t * (a / c))
    end if
    code = tmp
end function

Java

assert x < y;
assert t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (t <= -9.2e+24) {
		tmp = a * (-4.0 * (t / c));
	} else if (t <= 5.8e-125) {
		tmp = b / (z * c);
	} else {
		tmp = -4.0 * (t * (a / c));
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if t <= -9.2e+24:
		tmp = a * (-4.0 * (t / c))
	elif t <= 5.8e-125:
		tmp = b / (z * c)
	else:
		tmp = -4.0 * (t * (a / c))
	return tmp

Julia

x, y = sort([x, y])
t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (t <= -9.2e+24)
		tmp = Float64(a * Float64(-4.0 * Float64(t / c)));
	elseif (t <= 5.8e-125)
		tmp = Float64(b / Float64(z * c));
	else
		tmp = Float64(-4.0 * Float64(t * Float64(a / c)));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (t <= -9.2e+24)
		tmp = a * (-4.0 * (t / c));
	elseif (t <= 5.8e-125)
		tmp = b / (z * c);
	else
		tmp = -4.0 * (t * (a / c));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[t, -9.2e+24], N[(a * N[(-4.0 * N[(t / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.8e-125], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -9.1999999999999996e24

   1. Initial program 75.8%

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

   2. Taylor expanded in x around 0 67.1%

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

   3. Taylor expanded in z around inf 52.7%

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

      1. associate-*r/ 52.7%

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

      2. *-commutative 52.7%

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

      3. associate-/l* 52.7%

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

      4. associate-*r/ 60.6%

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

      5. associate-/r/ 60.6%

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

   5. Simplified 60.6%

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

   if -9.1999999999999996e24 < t < 5.8000000000000004e-125

   1. Initial program 89.1%

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

   2. Taylor expanded in b around inf 44.8%

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

      1. *-commutative 44.8%

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

   4. Simplified 44.8%

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

   if 5.8000000000000004e-125 < t

   1. Initial program 73.3%

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

   2. Taylor expanded in x around 0 76.3%

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

   3. Taylor expanded in z around inf 45.0%

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

      1. associate-*l/ 49.5%

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

   5. Simplified 49.5%

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

4. Final simplification 50.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9.2 \cdot 10^{+24}:\\ \;\;\;\;a \cdot \left(-4 \cdot \frac{t}{c}\right)\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{-125}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \end{array} \]

Alternative 18: 50.4% accurate, 1.7× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -1.56 \cdot 10^{+74}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;t \leq 3.9 \cdot 10^{-124}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= t -1.56e+74)
   (* -4.0 (/ a (/ c t)))
   (if (<= t 3.9e-124) (/ b (* z c)) (* -4.0 (* t (/ a c))))))

C

assert(x < y);
assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (t <= -1.56e+74) {
		tmp = -4.0 * (a / (c / t));
	} else if (t <= 3.9e-124) {
		tmp = b / (z * c);
	} else {
		tmp = -4.0 * (t * (a / c));
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (t <= (-1.56d+74)) then
        tmp = (-4.0d0) * (a / (c / t))
    else if (t <= 3.9d-124) then
        tmp = b / (z * c)
    else
        tmp = (-4.0d0) * (t * (a / c))
    end if
    code = tmp
end function

Java

assert x < y;
assert t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (t <= -1.56e+74) {
		tmp = -4.0 * (a / (c / t));
	} else if (t <= 3.9e-124) {
		tmp = b / (z * c);
	} else {
		tmp = -4.0 * (t * (a / c));
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if t <= -1.56e+74:
		tmp = -4.0 * (a / (c / t))
	elif t <= 3.9e-124:
		tmp = b / (z * c)
	else:
		tmp = -4.0 * (t * (a / c))
	return tmp

Julia

x, y = sort([x, y])
t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (t <= -1.56e+74)
		tmp = Float64(-4.0 * Float64(a / Float64(c / t)));
	elseif (t <= 3.9e-124)
		tmp = Float64(b / Float64(z * c));
	else
		tmp = Float64(-4.0 * Float64(t * Float64(a / c)));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (t <= -1.56e+74)
		tmp = -4.0 * (a / (c / t));
	elseif (t <= 3.9e-124)
		tmp = b / (z * c);
	else
		tmp = -4.0 * (t * (a / c));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[t, -1.56e+74], N[(-4.0 * N[(a / N[(c / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.9e-124], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.56e74

   1. Initial program 74.0%

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

   2. Taylor expanded in z around inf 50.9%

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

      1. *-commutative 50.9%

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

      2. associate-/l* 60.7%

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

   4. Simplified 60.7%

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

   if -1.56e74 < t < 3.89999999999999993e-124

   1. Initial program 88.9%

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

   2. Taylor expanded in b around inf 41.5%

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

      1. *-commutative 41.5%

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

   4. Simplified 41.5%

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

   if 3.89999999999999993e-124 < t

   1. Initial program 73.3%

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

   2. Taylor expanded in x around 0 76.3%

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

   3. Taylor expanded in z around inf 45.0%

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

      1. associate-*l/ 49.5%

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

   5. Simplified 49.5%

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

4. Final simplification 48.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.56 \cdot 10^{+74}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;t \leq 3.9 \cdot 10^{-124}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \end{array} \]

Alternative 19: 50.4% accurate, 1.7× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -3.7 \cdot 10^{+74}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;t \leq 3.9 \cdot 10^{-124}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot -4}{\frac{c}{a}}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= t -3.7e+74)
   (* -4.0 (/ a (/ c t)))
   (if (<= t 3.9e-124) (/ b (* z c)) (/ (* t -4.0) (/ c a)))))

C

assert(x < y);
assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (t <= -3.7e+74) {
		tmp = -4.0 * (a / (c / t));
	} else if (t <= 3.9e-124) {
		tmp = b / (z * c);
	} else {
		tmp = (t * -4.0) / (c / a);
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (t <= (-3.7d+74)) then
        tmp = (-4.0d0) * (a / (c / t))
    else if (t <= 3.9d-124) then
        tmp = b / (z * c)
    else
        tmp = (t * (-4.0d0)) / (c / a)
    end if
    code = tmp
end function

Java

assert x < y;
assert t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (t <= -3.7e+74) {
		tmp = -4.0 * (a / (c / t));
	} else if (t <= 3.9e-124) {
		tmp = b / (z * c);
	} else {
		tmp = (t * -4.0) / (c / a);
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if t <= -3.7e+74:
		tmp = -4.0 * (a / (c / t))
	elif t <= 3.9e-124:
		tmp = b / (z * c)
	else:
		tmp = (t * -4.0) / (c / a)
	return tmp

Julia

x, y = sort([x, y])
t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (t <= -3.7e+74)
		tmp = Float64(-4.0 * Float64(a / Float64(c / t)));
	elseif (t <= 3.9e-124)
		tmp = Float64(b / Float64(z * c));
	else
		tmp = Float64(Float64(t * -4.0) / Float64(c / a));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (t <= -3.7e+74)
		tmp = -4.0 * (a / (c / t));
	elseif (t <= 3.9e-124)
		tmp = b / (z * c);
	else
		tmp = (t * -4.0) / (c / a);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[t, -3.7e+74], N[(-4.0 * N[(a / N[(c / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.9e-124], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(N[(t * -4.0), $MachinePrecision] / N[(c / a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.7000000000000001e74

   1. Initial program 74.0%

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

   2. Taylor expanded in z around inf 50.9%

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

      1. *-commutative 50.9%

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

      2. associate-/l* 60.7%

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

   4. Simplified 60.7%

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

   if -3.7000000000000001e74 < t < 3.89999999999999993e-124

   1. Initial program 88.9%

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

   2. Taylor expanded in b around inf 41.5%

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

      1. *-commutative 41.5%

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

   4. Simplified 41.5%

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

   if 3.89999999999999993e-124 < t

   1. Initial program 73.3%

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

   2. Taylor expanded in z around inf 45.0%

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

      1. associate-*r/ 45.0%

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

      2. *-commutative 45.0%

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

      3. associate-*r* 45.0%

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

   4. Simplified 45.0%

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

      1. *-un-lft-identity 45.0%

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

      2. associate-/l* 49.5%

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

   6. Applied egg-rr 49.5%

      \[\leadsto \color{blue}{1 \cdot \frac{-4 \cdot t}{\frac{c}{a}}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 48.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.7 \cdot 10^{+74}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;t \leq 3.9 \cdot 10^{-124}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot -4}{\frac{c}{a}}\\ \end{array} \]

Alternative 20: 35.0% accurate, 2.7× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -1.55 \cdot 10^{+76}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= t -1.55e+76) (/ (/ b c) z) (/ b (* z c))))

C

assert(x < y);
assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (t <= -1.55e+76) {
		tmp = (b / c) / z;
	} else {
		tmp = b / (z * c);
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (t <= (-1.55d+76)) then
        tmp = (b / c) / z
    else
        tmp = b / (z * c)
    end if
    code = tmp
end function

Java

assert x < y;
assert t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (t <= -1.55e+76) {
		tmp = (b / c) / z;
	} else {
		tmp = b / (z * c);
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if t <= -1.55e+76:
		tmp = (b / c) / z
	else:
		tmp = b / (z * c)
	return tmp

Julia

x, y = sort([x, y])
t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (t <= -1.55e+76)
		tmp = Float64(Float64(b / c) / z);
	else
		tmp = Float64(b / Float64(z * c));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (t <= -1.55e+76)
		tmp = (b / c) / z;
	else
		tmp = b / (z * c);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[t, -1.55e+76], N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.55000000000000006e76

   1. Initial program 74.0%

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

   2. Taylor expanded in b around inf 16.5%

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

      1. *-commutative 16.5%

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

   4. Simplified 16.5%

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

      1. div-inv 16.4%

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

   6. Applied egg-rr 16.4%

      \[\leadsto \color{blue}{b \cdot \frac{1}{z \cdot c}} \]
   7. Step-by-step derivation

      1. un-div-inv 16.5%

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

      2. *-commutative 16.5%

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

      3. associate-/r* 23.8%

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

   8. Applied egg-rr 23.8%

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

   if -1.55000000000000006e76 < t

   1. Initial program 81.2%

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

   2. Taylor expanded in b around inf 32.5%

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

      1. *-commutative 32.5%

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

   4. Simplified 32.5%

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

4. Final simplification 30.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.55 \cdot 10^{+76}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \end{array} \]

Alternative 21: 35.1% accurate, 3.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 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. Taylor expanded in b around inf 29.4%

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

   1. *-commutative 29.4%

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

4. Simplified 29.4%

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

5. Final simplification 29.4%

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

Developer target: 81.1% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{b}{c \cdot z}\\ t_2 := 4 \cdot \frac{a \cdot t}{c}\\ t_3 := \left(x \cdot 9\right) \cdot y\\ t_4 := \left(t_3 - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b\\ t_5 := \frac{t_4}{z \cdot c}\\ t_6 := \frac{\left(t_3 - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}\\ \mathbf{if}\;t_5 < -1.100156740804105 \cdot 10^{-171}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;t_5 < 0:\\ \;\;\;\;\frac{\frac{t_4}{z}}{c}\\ \mathbf{elif}\;t_5 < 1.1708877911747488 \cdot 10^{-53}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;t_5 < 2.876823679546137 \cdot 10^{+130}:\\ \;\;\;\;\left(\left(9 \cdot \frac{y}{c}\right) \cdot \frac{x}{z} + t_1\right) - t_2\\ \mathbf{elif}\;t_5 < 1.3838515042456319 \cdot 10^{+158}:\\ \;\;\;\;t_6\\ \mathbf{else}:\\ \;\;\;\;\left(9 \cdot \left(\frac{y}{c \cdot z} \cdot x\right) + t_1\right) - t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ b (* c z)))
        (t_2 (* 4.0 (/ (* a t) c)))
        (t_3 (* (* x 9.0) y))
        (t_4 (+ (- t_3 (* (* (* z 4.0) t) a)) b))
        (t_5 (/ t_4 (* z c)))
        (t_6 (/ (+ (- t_3 (* (* z 4.0) (* t a))) b) (* z c))))
   (if (< t_5 -1.100156740804105e-171)
     t_6
     (if (< t_5 0.0)
       (/ (/ t_4 z) c)
       (if (< t_5 1.1708877911747488e-53)
         t_6
         (if (< t_5 2.876823679546137e+130)
           (- (+ (* (* 9.0 (/ y c)) (/ x z)) t_1) t_2)
           (if (< t_5 1.3838515042456319e+158)
             t_6
             (- (+ (* 9.0 (* (/ y (* c z)) x)) t_1) t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = b / (c * z);
	double t_2 = 4.0 * ((a * t) / c);
	double t_3 = (x * 9.0) * y;
	double t_4 = (t_3 - (((z * 4.0) * t) * a)) + b;
	double t_5 = t_4 / (z * c);
	double t_6 = ((t_3 - ((z * 4.0) * (t * a))) + b) / (z * c);
	double tmp;
	if (t_5 < -1.100156740804105e-171) {
		tmp = t_6;
	} else if (t_5 < 0.0) {
		tmp = (t_4 / z) / c;
	} else if (t_5 < 1.1708877911747488e-53) {
		tmp = t_6;
	} else if (t_5 < 2.876823679546137e+130) {
		tmp = (((9.0 * (y / c)) * (x / z)) + t_1) - t_2;
	} else if (t_5 < 1.3838515042456319e+158) {
		tmp = t_6;
	} else {
		tmp = ((9.0 * ((y / (c * z)) * x)) + t_1) - t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: tmp
    t_1 = b / (c * z)
    t_2 = 4.0d0 * ((a * t) / c)
    t_3 = (x * 9.0d0) * y
    t_4 = (t_3 - (((z * 4.0d0) * t) * a)) + b
    t_5 = t_4 / (z * c)
    t_6 = ((t_3 - ((z * 4.0d0) * (t * a))) + b) / (z * c)
    if (t_5 < (-1.100156740804105d-171)) then
        tmp = t_6
    else if (t_5 < 0.0d0) then
        tmp = (t_4 / z) / c
    else if (t_5 < 1.1708877911747488d-53) then
        tmp = t_6
    else if (t_5 < 2.876823679546137d+130) then
        tmp = (((9.0d0 * (y / c)) * (x / z)) + t_1) - t_2
    else if (t_5 < 1.3838515042456319d+158) then
        tmp = t_6
    else
        tmp = ((9.0d0 * ((y / (c * z)) * x)) + t_1) - t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = b / (c * z);
	double t_2 = 4.0 * ((a * t) / c);
	double t_3 = (x * 9.0) * y;
	double t_4 = (t_3 - (((z * 4.0) * t) * a)) + b;
	double t_5 = t_4 / (z * c);
	double t_6 = ((t_3 - ((z * 4.0) * (t * a))) + b) / (z * c);
	double tmp;
	if (t_5 < -1.100156740804105e-171) {
		tmp = t_6;
	} else if (t_5 < 0.0) {
		tmp = (t_4 / z) / c;
	} else if (t_5 < 1.1708877911747488e-53) {
		tmp = t_6;
	} else if (t_5 < 2.876823679546137e+130) {
		tmp = (((9.0 * (y / c)) * (x / z)) + t_1) - t_2;
	} else if (t_5 < 1.3838515042456319e+158) {
		tmp = t_6;
	} else {
		tmp = ((9.0 * ((y / (c * z)) * x)) + t_1) - t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = b / (c * z)
	t_2 = 4.0 * ((a * t) / c)
	t_3 = (x * 9.0) * y
	t_4 = (t_3 - (((z * 4.0) * t) * a)) + b
	t_5 = t_4 / (z * c)
	t_6 = ((t_3 - ((z * 4.0) * (t * a))) + b) / (z * c)
	tmp = 0
	if t_5 < -1.100156740804105e-171:
		tmp = t_6
	elif t_5 < 0.0:
		tmp = (t_4 / z) / c
	elif t_5 < 1.1708877911747488e-53:
		tmp = t_6
	elif t_5 < 2.876823679546137e+130:
		tmp = (((9.0 * (y / c)) * (x / z)) + t_1) - t_2
	elif t_5 < 1.3838515042456319e+158:
		tmp = t_6
	else:
		tmp = ((9.0 * ((y / (c * z)) * x)) + t_1) - t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(b / Float64(c * z))
	t_2 = Float64(4.0 * Float64(Float64(a * t) / c))
	t_3 = Float64(Float64(x * 9.0) * y)
	t_4 = Float64(Float64(t_3 - Float64(Float64(Float64(z * 4.0) * t) * a)) + b)
	t_5 = Float64(t_4 / Float64(z * c))
	t_6 = Float64(Float64(Float64(t_3 - Float64(Float64(z * 4.0) * Float64(t * a))) + b) / Float64(z * c))
	tmp = 0.0
	if (t_5 < -1.100156740804105e-171)
		tmp = t_6;
	elseif (t_5 < 0.0)
		tmp = Float64(Float64(t_4 / z) / c);
	elseif (t_5 < 1.1708877911747488e-53)
		tmp = t_6;
	elseif (t_5 < 2.876823679546137e+130)
		tmp = Float64(Float64(Float64(Float64(9.0 * Float64(y / c)) * Float64(x / z)) + t_1) - t_2);
	elseif (t_5 < 1.3838515042456319e+158)
		tmp = t_6;
	else
		tmp = Float64(Float64(Float64(9.0 * Float64(Float64(y / Float64(c * z)) * x)) + t_1) - t_2);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = b / (c * z);
	t_2 = 4.0 * ((a * t) / c);
	t_3 = (x * 9.0) * y;
	t_4 = (t_3 - (((z * 4.0) * t) * a)) + b;
	t_5 = t_4 / (z * c);
	t_6 = ((t_3 - ((z * 4.0) * (t * a))) + b) / (z * c);
	tmp = 0.0;
	if (t_5 < -1.100156740804105e-171)
		tmp = t_6;
	elseif (t_5 < 0.0)
		tmp = (t_4 / z) / c;
	elseif (t_5 < 1.1708877911747488e-53)
		tmp = t_6;
	elseif (t_5 < 2.876823679546137e+130)
		tmp = (((9.0 * (y / c)) * (x / z)) + t_1) - t_2;
	elseif (t_5 < 1.3838515042456319e+158)
		tmp = t_6;
	else
		tmp = ((9.0 * ((y / (c * z)) * x)) + t_1) - t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(b / N[(c * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(4.0 * N[(N[(a * t), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision]}, Block[{t$95$4 = N[(N[(t$95$3 - N[(N[(N[(z * 4.0), $MachinePrecision] * t), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]}, Block[{t$95$5 = N[(t$95$4 / N[(z * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(N[(N[(t$95$3 - N[(N[(z * 4.0), $MachinePrecision] * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]}, If[Less[t$95$5, -1.100156740804105e-171], t$95$6, If[Less[t$95$5, 0.0], N[(N[(t$95$4 / z), $MachinePrecision] / c), $MachinePrecision], If[Less[t$95$5, 1.1708877911747488e-53], t$95$6, If[Less[t$95$5, 2.876823679546137e+130], N[(N[(N[(N[(9.0 * N[(y / c), $MachinePrecision]), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision] - t$95$2), $MachinePrecision], If[Less[t$95$5, 1.3838515042456319e+158], t$95$6, N[(N[(N[(9.0 * N[(N[(y / N[(c * z), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision] - t$95$2), $MachinePrecision]]]]]]]]]]]]

Reproduce

herbie shell --seed 2023309 
(FPCore (x y z t a b c)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, J"
  :precision binary64

  :herbie-target
  (if (< (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)) -1.100156740804105e-171) (/ (+ (- (* (* x 9.0) y) (* (* z 4.0) (* t a))) b) (* z c)) (if (< (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)) 0.0) (/ (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) z) c) (if (< (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)) 1.1708877911747488e-53) (/ (+ (- (* (* x 9.0) y) (* (* z 4.0) (* t a))) b) (* z c)) (if (< (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)) 2.876823679546137e+130) (- (+ (* (* 9.0 (/ y c)) (/ x z)) (/ b (* c z))) (* 4.0 (/ (* a t) c))) (if (< (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)) 1.3838515042456319e+158) (/ (+ (- (* (* x 9.0) y) (* (* z 4.0) (* t a))) b) (* z c)) (- (+ (* 9.0 (* (/ y (* c z)) x)) (/ b (* c z))) (* 4.0 (/ (* a t) c))))))))

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