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

Percentage Accurate: 79.6% → 88.5%

Time: 19.8s

Alternatives: 18

Speedup: 0.2×

• 36.6% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 79.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 88.5% accurate, 0.1× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} t_1 := \frac{\left(y \cdot \left(x \cdot 9\right) - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\\ \mathbf{if}\;t_1 \leq -2 \cdot 10^{-32}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq 0:\\ \;\;\;\;\frac{b + \mathsf{fma}\left(x, 9 \cdot y, a \cdot \left(z \cdot \left(t \cdot \left(-4\right)\right)\right)\right)}{z} \cdot \frac{1}{c}\\ \mathbf{elif}\;t_1 \leq \infty:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{\frac{c}{t}} \cdot -4\\ \end{array} \end{array} \]

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 (/ (+ (- (* y (* x 9.0)) (* (* (* z 4.0) t) a)) b) (* z c))))
   (if (<= t_1 -2e-32)
     t_1
     (if (<= t_1 0.0)
       (* (/ (+ b (fma x (* 9.0 y) (* a (* z (* t (- 4.0)))))) z) (/ 1.0 c))
       (if (<= t_1 INFINITY) t_1 (* (/ a (/ c t)) -4.0))))))

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 = (((y * (x * 9.0)) - (((z * 4.0) * t) * a)) + b) / (z * c);
	double tmp;
	if (t_1 <= -2e-32) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = ((b + fma(x, (9.0 * y), (a * (z * (t * -4.0))))) / z) * (1.0 / c);
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = (a / (c / t)) * -4.0;
	}
	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(Float64(Float64(y * Float64(x * 9.0)) - Float64(Float64(Float64(z * 4.0) * t) * a)) + b) / Float64(z * c))
	tmp = 0.0
	if (t_1 <= -2e-32)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = Float64(Float64(Float64(b + fma(x, Float64(9.0 * y), Float64(a * Float64(z * Float64(t * Float64(-4.0)))))) / z) * Float64(1.0 / c));
	elseif (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = Float64(Float64(a / Float64(c / t)) * -4.0);
	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_] := Block[{t$95$1 = N[(N[(N[(N[(y * N[(x * 9.0), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(z * 4.0), $MachinePrecision] * t), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e-32], t$95$1, If[LessEqual[t$95$1, 0.0], N[(N[(N[(b + N[(x * N[(9.0 * y), $MachinePrecision] + N[(a * N[(z * N[(t * (-4.0)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] * N[(1.0 / c), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, Infinity], t$95$1, N[(N[(a / N[(c / t), $MachinePrecision]), $MachinePrecision] * -4.0), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)) b) (*.f64 z c)) < -2.00000000000000011e-32 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 89.4%

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

   if -2.00000000000000011e-32 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)) b) (*.f64 z c)) < -0.0

   1. Initial program 68.0%

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

      1. associate-/r* 99.7%

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

      2. associate-+l- 99.7%

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

      3. associate-*r* 99.6%

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

      4. associate-*r* 99.6%

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

      5. div-inv 99.7%

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

      6. associate--r- 99.7%

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

      7. fma-neg 99.7%

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

      8. associate-*r* 99.7%

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

      9. distribute-rgt-neg-in 99.7%

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

      10. associate-*l* 99.7%

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

   3. Applied egg-rr 99.7%

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

   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 z around inf 64.7%

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

      1. *-commutative 64.7%

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

      2. associate-/l* 77.3%

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

   4. Simplified 77.3%

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

4. Final simplification 89.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(y \cdot \left(x \cdot 9\right) - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \leq -2 \cdot 10^{-32}:\\ \;\;\;\;\frac{\left(y \cdot \left(x \cdot 9\right) - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\\ \mathbf{elif}\;\frac{\left(y \cdot \left(x \cdot 9\right) - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \leq 0:\\ \;\;\;\;\frac{b + \mathsf{fma}\left(x, 9 \cdot y, a \cdot \left(z \cdot \left(t \cdot \left(-4\right)\right)\right)\right)}{z} \cdot \frac{1}{c}\\ \mathbf{elif}\;\frac{\left(y \cdot \left(x \cdot 9\right) - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \leq \infty:\\ \;\;\;\;\frac{\left(y \cdot \left(x \cdot 9\right) - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{\frac{c}{t}} \cdot -4\\ \end{array} \]

Alternative 2: 88.0% accurate, 0.1× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} t_1 := \frac{\left(y \cdot \left(x \cdot 9\right) - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\\ \mathbf{if}\;t_1 \leq -2:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{-225}:\\ \;\;\;\;\frac{1}{z} \cdot \frac{b + \mathsf{fma}\left(x, 9 \cdot y, a \cdot \left(z \cdot \left(t \cdot \left(-4\right)\right)\right)\right)}{c}\\ \mathbf{elif}\;t_1 \leq \infty:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{\frac{c}{t}} \cdot -4\\ \end{array} \end{array} \]

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 (/ (+ (- (* y (* x 9.0)) (* (* (* z 4.0) t) a)) b) (* z c))))
   (if (<= t_1 -2.0)
     t_1
     (if (<= t_1 2e-225)
       (* (/ 1.0 z) (/ (+ b (fma x (* 9.0 y) (* a (* z (* t (- 4.0)))))) c))
       (if (<= t_1 INFINITY) t_1 (* (/ a (/ c t)) -4.0))))))

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 = (((y * (x * 9.0)) - (((z * 4.0) * t) * a)) + b) / (z * c);
	double tmp;
	if (t_1 <= -2.0) {
		tmp = t_1;
	} else if (t_1 <= 2e-225) {
		tmp = (1.0 / z) * ((b + fma(x, (9.0 * y), (a * (z * (t * -4.0))))) / c);
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = (a / (c / t)) * -4.0;
	}
	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(Float64(Float64(y * Float64(x * 9.0)) - Float64(Float64(Float64(z * 4.0) * t) * a)) + b) / Float64(z * c))
	tmp = 0.0
	if (t_1 <= -2.0)
		tmp = t_1;
	elseif (t_1 <= 2e-225)
		tmp = Float64(Float64(1.0 / z) * Float64(Float64(b + fma(x, Float64(9.0 * y), Float64(a * Float64(z * Float64(t * Float64(-4.0)))))) / c));
	elseif (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = Float64(Float64(a / Float64(c / t)) * -4.0);
	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_] := Block[{t$95$1 = N[(N[(N[(N[(y * N[(x * 9.0), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(z * 4.0), $MachinePrecision] * t), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2.0], t$95$1, If[LessEqual[t$95$1, 2e-225], N[(N[(1.0 / z), $MachinePrecision] * N[(N[(b + N[(x * N[(9.0 * y), $MachinePrecision] + N[(a * N[(z * N[(t * (-4.0)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, Infinity], t$95$1, N[(N[(a / N[(c / t), $MachinePrecision]), $MachinePrecision] * -4.0), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)) b) (*.f64 z c)) < -2 or 1.9999999999999999e-225 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)) b) (*.f64 z c)) < +inf.0

   1. Initial program 89.2%

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

   if -2 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)) b) (*.f64 z c)) < 1.9999999999999999e-225

   1. Initial program 72.9%

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

      1. associate-+l- 72.9%

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

      2. associate-*r* 72.9%

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

      3. associate-*r* 73.0%

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

      4. *-un-lft-identity 73.0%

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

      5. times-frac 99.7%

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

      6. associate--r- 99.7%

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

      7. fma-neg 99.7%

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

      8. associate-*r* 99.5%

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

      9. distribute-rgt-neg-in 99.5%

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

      10. associate-*l* 99.5%

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

   3. Applied egg-rr 99.5%

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

   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 z around inf 64.7%

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

      1. *-commutative 64.7%

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

      2. associate-/l* 77.3%

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

   4. Simplified 77.3%

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

4. Final simplification 89.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(y \cdot \left(x \cdot 9\right) - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \leq -2:\\ \;\;\;\;\frac{\left(y \cdot \left(x \cdot 9\right) - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\\ \mathbf{elif}\;\frac{\left(y \cdot \left(x \cdot 9\right) - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \leq 2 \cdot 10^{-225}:\\ \;\;\;\;\frac{1}{z} \cdot \frac{b + \mathsf{fma}\left(x, 9 \cdot y, a \cdot \left(z \cdot \left(t \cdot \left(-4\right)\right)\right)\right)}{c}\\ \mathbf{elif}\;\frac{\left(y \cdot \left(x \cdot 9\right) - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \leq \infty:\\ \;\;\;\;\frac{\left(y \cdot \left(x \cdot 9\right) - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{\frac{c}{t}} \cdot -4\\ \end{array} \]

Alternative 3: 87.4% accurate, 0.2× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} t_1 := \frac{\left(y \cdot \left(x \cdot 9\right) - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\\ \mathbf{if}\;t_1 \leq -2 \cdot 10^{-263}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq 0:\\ \;\;\;\;\frac{1}{c} \cdot \frac{b + -4 \cdot \left(a \cdot \left(z \cdot t\right)\right)}{z}\\ \mathbf{elif}\;t_1 \leq \infty:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{\frac{c}{t}} \cdot -4\\ \end{array} \end{array} \]

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 (/ (+ (- (* y (* x 9.0)) (* (* (* z 4.0) t) a)) b) (* z c))))
   (if (<= t_1 -2e-263)
     t_1
     (if (<= t_1 0.0)
       (* (/ 1.0 c) (/ (+ b (* -4.0 (* a (* z t)))) z))
       (if (<= t_1 INFINITY) t_1 (* (/ a (/ c t)) -4.0))))))

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 = (((y * (x * 9.0)) - (((z * 4.0) * t) * a)) + b) / (z * c);
	double tmp;
	if (t_1 <= -2e-263) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = (1.0 / c) * ((b + (-4.0 * (a * (z * t)))) / z);
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = (a / (c / t)) * -4.0;
	}
	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 = (((y * (x * 9.0)) - (((z * 4.0) * t) * a)) + b) / (z * c);
	double tmp;
	if (t_1 <= -2e-263) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = (1.0 / c) * ((b + (-4.0 * (a * (z * t)))) / z);
	} else if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else {
		tmp = (a / (c / t)) * -4.0;
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	t_1 = (((y * (x * 9.0)) - (((z * 4.0) * t) * a)) + b) / (z * c)
	tmp = 0
	if t_1 <= -2e-263:
		tmp = t_1
	elif t_1 <= 0.0:
		tmp = (1.0 / c) * ((b + (-4.0 * (a * (z * t)))) / z)
	elif t_1 <= math.inf:
		tmp = t_1
	else:
		tmp = (a / (c / t)) * -4.0
	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(Float64(Float64(y * Float64(x * 9.0)) - Float64(Float64(Float64(z * 4.0) * t) * a)) + b) / Float64(z * c))
	tmp = 0.0
	if (t_1 <= -2e-263)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = Float64(Float64(1.0 / c) * Float64(Float64(b + Float64(-4.0 * Float64(a * Float64(z * t)))) / z));
	elseif (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = Float64(Float64(a / Float64(c / t)) * -4.0);
	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 = (((y * (x * 9.0)) - (((z * 4.0) * t) * a)) + b) / (z * c);
	tmp = 0.0;
	if (t_1 <= -2e-263)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = (1.0 / c) * ((b + (-4.0 * (a * (z * t)))) / z);
	elseif (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = (a / (c / t)) * -4.0;
	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[(N[(N[(y * N[(x * 9.0), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(z * 4.0), $MachinePrecision] * t), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e-263], t$95$1, If[LessEqual[t$95$1, 0.0], N[(N[(1.0 / c), $MachinePrecision] * N[(N[(b + N[(-4.0 * N[(a * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, Infinity], t$95$1, N[(N[(a / N[(c / t), $MachinePrecision]), $MachinePrecision] * -4.0), $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)) < -2e-263 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 90.0%

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

   if -2e-263 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)) b) (*.f64 z c)) < -0.0

   1. Initial program 39.1%

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

      1. associate-/r* 99.7%

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

      2. associate-+l- 99.7%

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

      3. associate-*r* 99.7%

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

      4. associate-*r* 99.7%

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

      5. div-inv 99.8%

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

      6. associate--r- 99.8%

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

      7. fma-neg 99.8%

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

      8. associate-*r* 99.8%

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

      9. distribute-rgt-neg-in 99.8%

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

      10. associate-*l* 99.8%

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

   3. Applied egg-rr 99.8%

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

   4. Taylor expanded in x around 0 86.6%

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

      1. *-commutative 86.6%

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

   6. Simplified 86.6%

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

   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 z around inf 64.7%

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

      1. *-commutative 64.7%

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

      2. associate-/l* 77.3%

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

   4. Simplified 77.3%

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

4. Final simplification 88.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(y \cdot \left(x \cdot 9\right) - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \leq -2 \cdot 10^{-263}:\\ \;\;\;\;\frac{\left(y \cdot \left(x \cdot 9\right) - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\\ \mathbf{elif}\;\frac{\left(y \cdot \left(x \cdot 9\right) - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \leq 0:\\ \;\;\;\;\frac{1}{c} \cdot \frac{b + -4 \cdot \left(a \cdot \left(z \cdot t\right)\right)}{z}\\ \mathbf{elif}\;\frac{\left(y \cdot \left(x \cdot 9\right) - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \leq \infty:\\ \;\;\;\;\frac{\left(y \cdot \left(x \cdot 9\right) - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{\frac{c}{t}} \cdot -4\\ \end{array} \]

Alternative 4: 68.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} t_1 := \frac{1}{c} \cdot \frac{b + -4 \cdot \left(a \cdot \left(z \cdot t\right)\right)}{z}\\ t_2 := \frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \mathbf{if}\;z \leq -6.7 \cdot 10^{+118}:\\ \;\;\;\;\frac{1}{c} \cdot \left(t \cdot \left(a \cdot -4\right)\right)\\ \mathbf{elif}\;z \leq -7 \cdot 10^{+53}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.9:\\ \;\;\;\;9 \cdot \frac{y}{z \cdot \frac{c}{x}}\\ \mathbf{elif}\;z \leq 9.6 \cdot 10^{-57}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 4.3 \cdot 10^{+61}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 9 \cdot 10^{+106}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{t}{\frac{c}{a}}\\ \end{array} \end{array} \]

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
 (let* ((t_1 (* (/ 1.0 c) (/ (+ b (* -4.0 (* a (* z t)))) z)))
        (t_2 (/ (+ b (* 9.0 (* x y))) (* z c))))
   (if (<= z -6.7e+118)
     (* (/ 1.0 c) (* t (* a -4.0)))
     (if (<= z -7e+53)
       t_1
       (if (<= z -2.9)
         (* 9.0 (/ y (* z (/ c x))))
         (if (<= z 9.6e-57)
           t_2
           (if (<= z 4.3e+61)
             t_1
             (if (<= z 9e+106) t_2 (* -4.0 (/ t (/ 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 t_1 = (1.0 / c) * ((b + (-4.0 * (a * (z * t)))) / z);
	double t_2 = (b + (9.0 * (x * y))) / (z * c);
	double tmp;
	if (z <= -6.7e+118) {
		tmp = (1.0 / c) * (t * (a * -4.0));
	} else if (z <= -7e+53) {
		tmp = t_1;
	} else if (z <= -2.9) {
		tmp = 9.0 * (y / (z * (c / x)));
	} else if (z <= 9.6e-57) {
		tmp = t_2;
	} else if (z <= 4.3e+61) {
		tmp = t_1;
	} else if (z <= 9e+106) {
		tmp = t_2;
	} else {
		tmp = -4.0 * (t / (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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (1.0d0 / c) * ((b + ((-4.0d0) * (a * (z * t)))) / z)
    t_2 = (b + (9.0d0 * (x * y))) / (z * c)
    if (z <= (-6.7d+118)) then
        tmp = (1.0d0 / c) * (t * (a * (-4.0d0)))
    else if (z <= (-7d+53)) then
        tmp = t_1
    else if (z <= (-2.9d0)) then
        tmp = 9.0d0 * (y / (z * (c / x)))
    else if (z <= 9.6d-57) then
        tmp = t_2
    else if (z <= 4.3d+61) then
        tmp = t_1
    else if (z <= 9d+106) then
        tmp = t_2
    else
        tmp = (-4.0d0) * (t / (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 t_1 = (1.0 / c) * ((b + (-4.0 * (a * (z * t)))) / z);
	double t_2 = (b + (9.0 * (x * y))) / (z * c);
	double tmp;
	if (z <= -6.7e+118) {
		tmp = (1.0 / c) * (t * (a * -4.0));
	} else if (z <= -7e+53) {
		tmp = t_1;
	} else if (z <= -2.9) {
		tmp = 9.0 * (y / (z * (c / x)));
	} else if (z <= 9.6e-57) {
		tmp = t_2;
	} else if (z <= 4.3e+61) {
		tmp = t_1;
	} else if (z <= 9e+106) {
		tmp = t_2;
	} else {
		tmp = -4.0 * (t / (c / a));
	}
	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 / c) * ((b + (-4.0 * (a * (z * t)))) / z)
	t_2 = (b + (9.0 * (x * y))) / (z * c)
	tmp = 0
	if z <= -6.7e+118:
		tmp = (1.0 / c) * (t * (a * -4.0))
	elif z <= -7e+53:
		tmp = t_1
	elif z <= -2.9:
		tmp = 9.0 * (y / (z * (c / x)))
	elif z <= 9.6e-57:
		tmp = t_2
	elif z <= 4.3e+61:
		tmp = t_1
	elif z <= 9e+106:
		tmp = t_2
	else:
		tmp = -4.0 * (t / (c / a))
	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 / c) * Float64(Float64(b + Float64(-4.0 * Float64(a * Float64(z * t)))) / z))
	t_2 = Float64(Float64(b + Float64(9.0 * Float64(x * y))) / Float64(z * c))
	tmp = 0.0
	if (z <= -6.7e+118)
		tmp = Float64(Float64(1.0 / c) * Float64(t * Float64(a * -4.0)));
	elseif (z <= -7e+53)
		tmp = t_1;
	elseif (z <= -2.9)
		tmp = Float64(9.0 * Float64(y / Float64(z * Float64(c / x))));
	elseif (z <= 9.6e-57)
		tmp = t_2;
	elseif (z <= 4.3e+61)
		tmp = t_1;
	elseif (z <= 9e+106)
		tmp = t_2;
	else
		tmp = Float64(-4.0 * Float64(t / 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)
	t_1 = (1.0 / c) * ((b + (-4.0 * (a * (z * t)))) / z);
	t_2 = (b + (9.0 * (x * y))) / (z * c);
	tmp = 0.0;
	if (z <= -6.7e+118)
		tmp = (1.0 / c) * (t * (a * -4.0));
	elseif (z <= -7e+53)
		tmp = t_1;
	elseif (z <= -2.9)
		tmp = 9.0 * (y / (z * (c / x)));
	elseif (z <= 9.6e-57)
		tmp = t_2;
	elseif (z <= 4.3e+61)
		tmp = t_1;
	elseif (z <= 9e+106)
		tmp = t_2;
	else
		tmp = -4.0 * (t / (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_] := Block[{t$95$1 = N[(N[(1.0 / c), $MachinePrecision] * N[(N[(b + N[(-4.0 * N[(a * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b + N[(9.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6.7e+118], N[(N[(1.0 / c), $MachinePrecision] * N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -7e+53], t$95$1, If[LessEqual[z, -2.9], N[(9.0 * N[(y / N[(z * N[(c / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9.6e-57], t$95$2, If[LessEqual[z, 4.3e+61], t$95$1, If[LessEqual[z, 9e+106], t$95$2, N[(-4.0 * N[(t / N[(c / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -6.7000000000000003e118

   1. Initial program 33.3%

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

      1. associate-/r* 48.8%

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

      2. associate-+l- 48.8%

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

      3. associate-*r* 48.8%

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

      4. associate-*r* 66.6%

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

      5. div-inv 66.6%

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

      6. associate--r- 66.6%

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

      7. fma-neg 69.9%

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

      8. associate-*r* 52.0%

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

      9. distribute-rgt-neg-in 52.0%

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

      10. associate-*l* 52.0%

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

   3. Applied egg-rr 52.0%

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

   4. Taylor expanded in z around inf 76.4%

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

      1. associate-*r* 76.4%

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

   6. Simplified 76.4%

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

   if -6.7000000000000003e118 < z < -7.00000000000000038e53 or 9.60000000000000025e-57 < z < 4.3000000000000001e61

   1. Initial program 83.0%

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

      1. associate-/r* 89.4%

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

      2. associate-+l- 89.4%

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

      3. associate-*r* 89.4%

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

      4. associate-*r* 91.6%

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

      5. div-inv 91.5%

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

      6. associate--r- 91.5%

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

      7. fma-neg 91.5%

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

      8. associate-*r* 89.4%

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

      9. distribute-rgt-neg-in 89.4%

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

      10. associate-*l* 89.4%

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

   3. Applied egg-rr 89.4%

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

   4. Taylor expanded in x around 0 78.6%

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

      1. *-commutative 78.6%

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

   6. Simplified 78.6%

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

   if -7.00000000000000038e53 < z < -2.89999999999999991

   1. Initial program 56.6%

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

   2. Taylor expanded in x around inf 41.1%

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

      1. associate-*r/ 41.2%

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

      2. associate-*r* 41.1%

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

      3. *-commutative 41.1%

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

      4. times-frac 76.7%

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

      5. *-commutative 76.7%

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

   4. Simplified 76.7%

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

      1. clear-num 76.7%

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

      2. frac-times 76.8%

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

      3. *-un-lft-identity 76.8%

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

      4. *-un-lft-identity 76.8%

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

      5. times-frac 76.7%

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

      6. metadata-eval 76.7%

         \[\leadsto \frac{y}{\left(\color{blue}{0.1111111111111111} \cdot \frac{c}{x}\right) \cdot z} \]

   6. Applied egg-rr 76.7%

      \[\leadsto \color{blue}{\frac{y}{\left(0.1111111111111111 \cdot \frac{c}{x}\right) \cdot z}} \]
   7. Step-by-step derivation

      1. *-rgt-identity 76.7%

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

      2. associate-*l* 76.8%

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

      3. *-commutative 76.8%

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

      4. times-frac 76.8%

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

      5. metadata-eval 76.8%

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

      6. *-commutative 76.8%

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

   8. Simplified 76.8%

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

   if -2.89999999999999991 < z < 9.60000000000000025e-57 or 4.3000000000000001e61 < z < 8.9999999999999994e106

   1. Initial program 95.7%

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

   2. Taylor expanded in x around inf 84.8%

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

   if 8.9999999999999994e106 < z

   1. Initial program 61.4%

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

   2. Taylor expanded in z around inf 57.4%

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

      1. *-commutative 57.4%

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

      2. associate-/l* 63.4%

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

   4. Simplified 63.4%

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

   5. Taylor expanded in a around 0 57.4%

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

      1. *-commutative 57.4%

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

      2. associate-/l* 54.5%

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

   7. Simplified 54.5%

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

4. Final simplification 78.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.7 \cdot 10^{+118}:\\ \;\;\;\;\frac{1}{c} \cdot \left(t \cdot \left(a \cdot -4\right)\right)\\ \mathbf{elif}\;z \leq -7 \cdot 10^{+53}:\\ \;\;\;\;\frac{1}{c} \cdot \frac{b + -4 \cdot \left(a \cdot \left(z \cdot t\right)\right)}{z}\\ \mathbf{elif}\;z \leq -2.9:\\ \;\;\;\;9 \cdot \frac{y}{z \cdot \frac{c}{x}}\\ \mathbf{elif}\;z \leq 9.6 \cdot 10^{-57}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \mathbf{elif}\;z \leq 4.3 \cdot 10^{+61}:\\ \;\;\;\;\frac{1}{c} \cdot \frac{b + -4 \cdot \left(a \cdot \left(z \cdot t\right)\right)}{z}\\ \mathbf{elif}\;z \leq 9 \cdot 10^{+106}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{t}{\frac{c}{a}}\\ \end{array} \]

Alternative 5: 67.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} t_1 := \frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \mathbf{if}\;z \leq -2 \cdot 10^{+117}:\\ \;\;\;\;\frac{1}{c} \cdot \left(t \cdot \left(a \cdot -4\right)\right)\\ \mathbf{elif}\;z \leq -3 \cdot 10^{+54}:\\ \;\;\;\;\frac{b - z \cdot \left(a \cdot \left(4 \cdot t\right)\right)}{z \cdot c}\\ \mathbf{elif}\;z \leq -2.9:\\ \;\;\;\;9 \cdot \frac{y}{z \cdot \frac{c}{x}}\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-54}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{+58}:\\ \;\;\;\;\frac{b - 4 \cdot \left(a \cdot \left(z \cdot t\right)\right)}{z \cdot c}\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{+107}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{t}{\frac{c}{a}}\\ \end{array} \end{array} \]

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
 (let* ((t_1 (/ (+ b (* 9.0 (* x y))) (* z c))))
   (if (<= z -2e+117)
     (* (/ 1.0 c) (* t (* a -4.0)))
     (if (<= z -3e+54)
       (/ (- b (* z (* a (* 4.0 t)))) (* z c))
       (if (<= z -2.9)
         (* 9.0 (/ y (* z (/ c x))))
         (if (<= z 1.4e-54)
           t_1
           (if (<= z 2.2e+58)
             (/ (- b (* 4.0 (* a (* z t)))) (* z c))
             (if (<= z 1.8e+107) t_1 (* -4.0 (/ t (/ 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 t_1 = (b + (9.0 * (x * y))) / (z * c);
	double tmp;
	if (z <= -2e+117) {
		tmp = (1.0 / c) * (t * (a * -4.0));
	} else if (z <= -3e+54) {
		tmp = (b - (z * (a * (4.0 * t)))) / (z * c);
	} else if (z <= -2.9) {
		tmp = 9.0 * (y / (z * (c / x)));
	} else if (z <= 1.4e-54) {
		tmp = t_1;
	} else if (z <= 2.2e+58) {
		tmp = (b - (4.0 * (a * (z * t)))) / (z * c);
	} else if (z <= 1.8e+107) {
		tmp = t_1;
	} else {
		tmp = -4.0 * (t / (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) :: t_1
    real(8) :: tmp
    t_1 = (b + (9.0d0 * (x * y))) / (z * c)
    if (z <= (-2d+117)) then
        tmp = (1.0d0 / c) * (t * (a * (-4.0d0)))
    else if (z <= (-3d+54)) then
        tmp = (b - (z * (a * (4.0d0 * t)))) / (z * c)
    else if (z <= (-2.9d0)) then
        tmp = 9.0d0 * (y / (z * (c / x)))
    else if (z <= 1.4d-54) then
        tmp = t_1
    else if (z <= 2.2d+58) then
        tmp = (b - (4.0d0 * (a * (z * t)))) / (z * c)
    else if (z <= 1.8d+107) then
        tmp = t_1
    else
        tmp = (-4.0d0) * (t / (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 t_1 = (b + (9.0 * (x * y))) / (z * c);
	double tmp;
	if (z <= -2e+117) {
		tmp = (1.0 / c) * (t * (a * -4.0));
	} else if (z <= -3e+54) {
		tmp = (b - (z * (a * (4.0 * t)))) / (z * c);
	} else if (z <= -2.9) {
		tmp = 9.0 * (y / (z * (c / x)));
	} else if (z <= 1.4e-54) {
		tmp = t_1;
	} else if (z <= 2.2e+58) {
		tmp = (b - (4.0 * (a * (z * t)))) / (z * c);
	} else if (z <= 1.8e+107) {
		tmp = t_1;
	} else {
		tmp = -4.0 * (t / (c / a));
	}
	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))) / (z * c)
	tmp = 0
	if z <= -2e+117:
		tmp = (1.0 / c) * (t * (a * -4.0))
	elif z <= -3e+54:
		tmp = (b - (z * (a * (4.0 * t)))) / (z * c)
	elif z <= -2.9:
		tmp = 9.0 * (y / (z * (c / x)))
	elif z <= 1.4e-54:
		tmp = t_1
	elif z <= 2.2e+58:
		tmp = (b - (4.0 * (a * (z * t)))) / (z * c)
	elif z <= 1.8e+107:
		tmp = t_1
	else:
		tmp = -4.0 * (t / (c / a))
	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(9.0 * Float64(x * y))) / Float64(z * c))
	tmp = 0.0
	if (z <= -2e+117)
		tmp = Float64(Float64(1.0 / c) * Float64(t * Float64(a * -4.0)));
	elseif (z <= -3e+54)
		tmp = Float64(Float64(b - Float64(z * Float64(a * Float64(4.0 * t)))) / Float64(z * c));
	elseif (z <= -2.9)
		tmp = Float64(9.0 * Float64(y / Float64(z * Float64(c / x))));
	elseif (z <= 1.4e-54)
		tmp = t_1;
	elseif (z <= 2.2e+58)
		tmp = Float64(Float64(b - Float64(4.0 * Float64(a * Float64(z * t)))) / Float64(z * c));
	elseif (z <= 1.8e+107)
		tmp = t_1;
	else
		tmp = Float64(-4.0 * Float64(t / 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)
	t_1 = (b + (9.0 * (x * y))) / (z * c);
	tmp = 0.0;
	if (z <= -2e+117)
		tmp = (1.0 / c) * (t * (a * -4.0));
	elseif (z <= -3e+54)
		tmp = (b - (z * (a * (4.0 * t)))) / (z * c);
	elseif (z <= -2.9)
		tmp = 9.0 * (y / (z * (c / x)));
	elseif (z <= 1.4e-54)
		tmp = t_1;
	elseif (z <= 2.2e+58)
		tmp = (b - (4.0 * (a * (z * t)))) / (z * c);
	elseif (z <= 1.8e+107)
		tmp = t_1;
	else
		tmp = -4.0 * (t / (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_] := Block[{t$95$1 = N[(N[(b + N[(9.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2e+117], N[(N[(1.0 / c), $MachinePrecision] * N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -3e+54], N[(N[(b - N[(z * N[(a * N[(4.0 * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.9], N[(9.0 * N[(y / N[(z * N[(c / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.4e-54], t$95$1, If[LessEqual[z, 2.2e+58], N[(N[(b - N[(4.0 * N[(a * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.8e+107], t$95$1, N[(-4.0 * N[(t / N[(c / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -2.0000000000000001e117

   1. Initial program 33.3%

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

      1. associate-/r* 48.8%

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

      2. associate-+l- 48.8%

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

      3. associate-*r* 48.8%

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

      4. associate-*r* 66.6%

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

      5. div-inv 66.6%

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

      6. associate--r- 66.6%

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

      7. fma-neg 69.9%

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

      8. associate-*r* 52.0%

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

      9. distribute-rgt-neg-in 52.0%

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

      10. associate-*l* 52.0%

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

   3. Applied egg-rr 52.0%

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

   4. Taylor expanded in z around inf 76.4%

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

      1. associate-*r* 76.4%

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

   6. Simplified 76.4%

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

   if -2.0000000000000001e117 < z < -2.9999999999999999e54

   1. Initial program 73.9%

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

   2. Taylor expanded in x around 0 69.4%

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

      1. associate-*r* 73.7%

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

      2. *-commutative 73.7%

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

      3. associate-*l* 73.7%

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

      4. *-commutative 73.7%

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

      5. associate-*r* 73.7%

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

      6. *-commutative 73.7%

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

   4. Simplified 73.7%

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

   if -2.9999999999999999e54 < z < -2.89999999999999991

   1. Initial program 56.6%

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

   2. Taylor expanded in x around inf 41.1%

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

      1. associate-*r/ 41.2%

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

      2. associate-*r* 41.1%

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

      3. *-commutative 41.1%

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

      4. times-frac 76.7%

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

      5. *-commutative 76.7%

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

   4. Simplified 76.7%

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

      1. clear-num 76.7%

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

      2. frac-times 76.8%

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

      3. *-un-lft-identity 76.8%

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

      4. *-un-lft-identity 76.8%

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

      5. times-frac 76.7%

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

      6. metadata-eval 76.7%

         \[\leadsto \frac{y}{\left(\color{blue}{0.1111111111111111} \cdot \frac{c}{x}\right) \cdot z} \]

   6. Applied egg-rr 76.7%

      \[\leadsto \color{blue}{\frac{y}{\left(0.1111111111111111 \cdot \frac{c}{x}\right) \cdot z}} \]
   7. Step-by-step derivation

      1. *-rgt-identity 76.7%

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

      2. associate-*l* 76.8%

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

      3. *-commutative 76.8%

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

      4. times-frac 76.8%

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

      5. metadata-eval 76.8%

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

      6. *-commutative 76.8%

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

   8. Simplified 76.8%

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

   if -2.89999999999999991 < z < 1.4000000000000001e-54 or 2.2000000000000001e58 < z < 1.7999999999999999e107

   1. Initial program 95.7%

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

   2. Taylor expanded in x around inf 84.8%

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

   if 1.4000000000000001e-54 < z < 2.2000000000000001e58

   1. Initial program 91.4%

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

      1. associate-+l- 91.4%

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

      2. associate-*l* 91.4%

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

      3. associate-*l* 91.5%

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

   3. Simplified 91.5%

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

   4. Taylor expanded in x around 0 75.0%

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

   if 1.7999999999999999e107 < z

   1. Initial program 61.4%

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

   2. Taylor expanded in z around inf 57.4%

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

      1. *-commutative 57.4%

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

      2. associate-/l* 63.4%

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

   4. Simplified 63.4%

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

   5. Taylor expanded in a around 0 57.4%

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

      1. *-commutative 57.4%

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

      2. associate-/l* 54.5%

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

   7. Simplified 54.5%

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

4. Final simplification 77.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+117}:\\ \;\;\;\;\frac{1}{c} \cdot \left(t \cdot \left(a \cdot -4\right)\right)\\ \mathbf{elif}\;z \leq -3 \cdot 10^{+54}:\\ \;\;\;\;\frac{b - z \cdot \left(a \cdot \left(4 \cdot t\right)\right)}{z \cdot c}\\ \mathbf{elif}\;z \leq -2.9:\\ \;\;\;\;9 \cdot \frac{y}{z \cdot \frac{c}{x}}\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-54}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{+58}:\\ \;\;\;\;\frac{b - 4 \cdot \left(a \cdot \left(z \cdot t\right)\right)}{z \cdot c}\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{+107}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{t}{\frac{c}{a}}\\ \end{array} \]

Alternative 6: 47.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} t_1 := 9 \cdot \frac{x}{z \cdot \frac{c}{y}}\\ t_2 := \frac{1}{z} \cdot \frac{b}{c}\\ \mathbf{if}\;a \leq -7.6 \cdot 10^{-44}:\\ \;\;\;\;\frac{a}{\frac{c}{t}} \cdot -4\\ \mathbf{elif}\;a \leq 3 \cdot 10^{-256}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 5.2 \cdot 10^{+15}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 2.9 \cdot 10^{+75}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 5.8 \cdot 10^{+142}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 1.55 \cdot 10^{+172}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{t}{\frac{c}{a}}\\ \end{array} \end{array} \]

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
 (let* ((t_1 (* 9.0 (/ x (* z (/ c y))))) (t_2 (* (/ 1.0 z) (/ b c))))
   (if (<= a -7.6e-44)
     (* (/ a (/ c t)) -4.0)
     (if (<= a 3e-256)
       t_1
       (if (<= a 5.2e+15)
         t_2
         (if (<= a 2.9e+75)
           t_1
           (if (<= a 5.8e+142)
             t_2
             (if (<= a 1.55e+172) t_1 (* -4.0 (/ t (/ 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 t_1 = 9.0 * (x / (z * (c / y)));
	double t_2 = (1.0 / z) * (b / c);
	double tmp;
	if (a <= -7.6e-44) {
		tmp = (a / (c / t)) * -4.0;
	} else if (a <= 3e-256) {
		tmp = t_1;
	} else if (a <= 5.2e+15) {
		tmp = t_2;
	} else if (a <= 2.9e+75) {
		tmp = t_1;
	} else if (a <= 5.8e+142) {
		tmp = t_2;
	} else if (a <= 1.55e+172) {
		tmp = t_1;
	} else {
		tmp = -4.0 * (t / (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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = 9.0d0 * (x / (z * (c / y)))
    t_2 = (1.0d0 / z) * (b / c)
    if (a <= (-7.6d-44)) then
        tmp = (a / (c / t)) * (-4.0d0)
    else if (a <= 3d-256) then
        tmp = t_1
    else if (a <= 5.2d+15) then
        tmp = t_2
    else if (a <= 2.9d+75) then
        tmp = t_1
    else if (a <= 5.8d+142) then
        tmp = t_2
    else if (a <= 1.55d+172) then
        tmp = t_1
    else
        tmp = (-4.0d0) * (t / (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 t_1 = 9.0 * (x / (z * (c / y)));
	double t_2 = (1.0 / z) * (b / c);
	double tmp;
	if (a <= -7.6e-44) {
		tmp = (a / (c / t)) * -4.0;
	} else if (a <= 3e-256) {
		tmp = t_1;
	} else if (a <= 5.2e+15) {
		tmp = t_2;
	} else if (a <= 2.9e+75) {
		tmp = t_1;
	} else if (a <= 5.8e+142) {
		tmp = t_2;
	} else if (a <= 1.55e+172) {
		tmp = t_1;
	} else {
		tmp = -4.0 * (t / (c / a));
	}
	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 * (x / (z * (c / y)))
	t_2 = (1.0 / z) * (b / c)
	tmp = 0
	if a <= -7.6e-44:
		tmp = (a / (c / t)) * -4.0
	elif a <= 3e-256:
		tmp = t_1
	elif a <= 5.2e+15:
		tmp = t_2
	elif a <= 2.9e+75:
		tmp = t_1
	elif a <= 5.8e+142:
		tmp = t_2
	elif a <= 1.55e+172:
		tmp = t_1
	else:
		tmp = -4.0 * (t / (c / a))
	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(x / Float64(z * Float64(c / y))))
	t_2 = Float64(Float64(1.0 / z) * Float64(b / c))
	tmp = 0.0
	if (a <= -7.6e-44)
		tmp = Float64(Float64(a / Float64(c / t)) * -4.0);
	elseif (a <= 3e-256)
		tmp = t_1;
	elseif (a <= 5.2e+15)
		tmp = t_2;
	elseif (a <= 2.9e+75)
		tmp = t_1;
	elseif (a <= 5.8e+142)
		tmp = t_2;
	elseif (a <= 1.55e+172)
		tmp = t_1;
	else
		tmp = Float64(-4.0 * Float64(t / 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)
	t_1 = 9.0 * (x / (z * (c / y)));
	t_2 = (1.0 / z) * (b / c);
	tmp = 0.0;
	if (a <= -7.6e-44)
		tmp = (a / (c / t)) * -4.0;
	elseif (a <= 3e-256)
		tmp = t_1;
	elseif (a <= 5.2e+15)
		tmp = t_2;
	elseif (a <= 2.9e+75)
		tmp = t_1;
	elseif (a <= 5.8e+142)
		tmp = t_2;
	elseif (a <= 1.55e+172)
		tmp = t_1;
	else
		tmp = -4.0 * (t / (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_] := Block[{t$95$1 = N[(9.0 * N[(x / N[(z * N[(c / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(1.0 / z), $MachinePrecision] * N[(b / c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -7.6e-44], N[(N[(a / N[(c / t), $MachinePrecision]), $MachinePrecision] * -4.0), $MachinePrecision], If[LessEqual[a, 3e-256], t$95$1, If[LessEqual[a, 5.2e+15], t$95$2, If[LessEqual[a, 2.9e+75], t$95$1, If[LessEqual[a, 5.8e+142], t$95$2, If[LessEqual[a, 1.55e+172], t$95$1, N[(-4.0 * N[(t / N[(c / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -7.6000000000000002e-44

   1. Initial program 83.5%

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

   2. Taylor expanded in z around inf 54.3%

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

      1. *-commutative 54.3%

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

      2. associate-/l* 58.0%

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

   4. Simplified 58.0%

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

   if -7.6000000000000002e-44 < a < 2.9999999999999998e-256 or 5.2e15 < a < 2.8999999999999998e75 or 5.80000000000000027e142 < a < 1.54999999999999994e172

   1. Initial program 79.0%

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

      1. associate-+l- 79.0%

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

      2. associate-*r* 79.0%

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

      3. associate-*r* 84.6%

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

      4. *-un-lft-identity 84.6%

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

      5. times-frac 80.2%

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

      6. associate--r- 80.2%

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

      7. fma-neg 80.2%

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

      8. associate-*r* 75.7%

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

      9. distribute-rgt-neg-in 75.7%

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

      10. associate-*l* 74.5%

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

   3. Applied egg-rr 74.5%

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

   4. Taylor expanded in x around inf 52.8%

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

      1. associate-/l* 58.0%

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

      2. *-commutative 58.0%

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

      3. *-lft-identity 58.0%

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

      4. times-frac 57.0%

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

      5. /-rgt-identity 57.0%

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

   6. Simplified 57.0%

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

   if 2.9999999999999998e-256 < a < 5.2e15 or 2.8999999999999998e75 < a < 5.80000000000000027e142

   1. Initial program 76.1%

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

      1. associate-+l- 76.1%

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

      2. associate-*r* 74.7%

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

      3. associate-*r* 77.8%

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

      4. *-un-lft-identity 77.8%

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

      5. times-frac 90.1%

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

      6. associate--r- 90.1%

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

      7. fma-neg 90.1%

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

      8. associate-*r* 81.6%

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

      9. distribute-rgt-neg-in 81.6%

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

      10. associate-*l* 81.6%

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

   3. Applied egg-rr 81.6%

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

   4. Taylor expanded in b around inf 51.3%

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

   if 1.54999999999999994e172 < a

   1. Initial program 77.4%

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

   2. Taylor expanded in z around inf 71.9%

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

      1. *-commutative 71.9%

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

      2. associate-/l* 71.4%

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

   4. Simplified 71.4%

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

   5. Taylor expanded in a around 0 71.9%

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

      1. *-commutative 71.9%

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

      2. associate-/l* 83.9%

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

   7. Simplified 83.9%

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

4. Final simplification 58.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7.6 \cdot 10^{-44}:\\ \;\;\;\;\frac{a}{\frac{c}{t}} \cdot -4\\ \mathbf{elif}\;a \leq 3 \cdot 10^{-256}:\\ \;\;\;\;9 \cdot \frac{x}{z \cdot \frac{c}{y}}\\ \mathbf{elif}\;a \leq 5.2 \cdot 10^{+15}:\\ \;\;\;\;\frac{1}{z} \cdot \frac{b}{c}\\ \mathbf{elif}\;a \leq 2.9 \cdot 10^{+75}:\\ \;\;\;\;9 \cdot \frac{x}{z \cdot \frac{c}{y}}\\ \mathbf{elif}\;a \leq 5.8 \cdot 10^{+142}:\\ \;\;\;\;\frac{1}{z} \cdot \frac{b}{c}\\ \mathbf{elif}\;a \leq 1.55 \cdot 10^{+172}:\\ \;\;\;\;9 \cdot \frac{x}{z \cdot \frac{c}{y}}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{t}{\frac{c}{a}}\\ \end{array} \]

Alternative 7: 47.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} t_1 := 9 \cdot \frac{x}{z \cdot \frac{c}{y}}\\ t_2 := \frac{1}{z} \cdot \frac{b}{c}\\ \mathbf{if}\;a \leq -3.4 \cdot 10^{-43}:\\ \;\;\;\;\frac{a}{\frac{c}{t}} \cdot -4\\ \mathbf{elif}\;a \leq 1.22 \cdot 10^{-256}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 8.8 \cdot 10^{+15}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 4.8 \cdot 10^{+76}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2.3 \cdot 10^{+143}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 1.55 \cdot 10^{+172}:\\ \;\;\;\;9 \cdot \frac{y}{z \cdot \frac{c}{x}}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{t}{\frac{c}{a}}\\ \end{array} \end{array} \]

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
 (let* ((t_1 (* 9.0 (/ x (* z (/ c y))))) (t_2 (* (/ 1.0 z) (/ b c))))
   (if (<= a -3.4e-43)
     (* (/ a (/ c t)) -4.0)
     (if (<= a 1.22e-256)
       t_1
       (if (<= a 8.8e+15)
         t_2
         (if (<= a 4.8e+76)
           t_1
           (if (<= a 2.3e+143)
             t_2
             (if (<= a 1.55e+172)
               (* 9.0 (/ y (* z (/ c x))))
               (* -4.0 (/ t (/ 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 t_1 = 9.0 * (x / (z * (c / y)));
	double t_2 = (1.0 / z) * (b / c);
	double tmp;
	if (a <= -3.4e-43) {
		tmp = (a / (c / t)) * -4.0;
	} else if (a <= 1.22e-256) {
		tmp = t_1;
	} else if (a <= 8.8e+15) {
		tmp = t_2;
	} else if (a <= 4.8e+76) {
		tmp = t_1;
	} else if (a <= 2.3e+143) {
		tmp = t_2;
	} else if (a <= 1.55e+172) {
		tmp = 9.0 * (y / (z * (c / x)));
	} else {
		tmp = -4.0 * (t / (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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = 9.0d0 * (x / (z * (c / y)))
    t_2 = (1.0d0 / z) * (b / c)
    if (a <= (-3.4d-43)) then
        tmp = (a / (c / t)) * (-4.0d0)
    else if (a <= 1.22d-256) then
        tmp = t_1
    else if (a <= 8.8d+15) then
        tmp = t_2
    else if (a <= 4.8d+76) then
        tmp = t_1
    else if (a <= 2.3d+143) then
        tmp = t_2
    else if (a <= 1.55d+172) then
        tmp = 9.0d0 * (y / (z * (c / x)))
    else
        tmp = (-4.0d0) * (t / (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 t_1 = 9.0 * (x / (z * (c / y)));
	double t_2 = (1.0 / z) * (b / c);
	double tmp;
	if (a <= -3.4e-43) {
		tmp = (a / (c / t)) * -4.0;
	} else if (a <= 1.22e-256) {
		tmp = t_1;
	} else if (a <= 8.8e+15) {
		tmp = t_2;
	} else if (a <= 4.8e+76) {
		tmp = t_1;
	} else if (a <= 2.3e+143) {
		tmp = t_2;
	} else if (a <= 1.55e+172) {
		tmp = 9.0 * (y / (z * (c / x)));
	} else {
		tmp = -4.0 * (t / (c / a));
	}
	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 * (x / (z * (c / y)))
	t_2 = (1.0 / z) * (b / c)
	tmp = 0
	if a <= -3.4e-43:
		tmp = (a / (c / t)) * -4.0
	elif a <= 1.22e-256:
		tmp = t_1
	elif a <= 8.8e+15:
		tmp = t_2
	elif a <= 4.8e+76:
		tmp = t_1
	elif a <= 2.3e+143:
		tmp = t_2
	elif a <= 1.55e+172:
		tmp = 9.0 * (y / (z * (c / x)))
	else:
		tmp = -4.0 * (t / (c / a))
	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(x / Float64(z * Float64(c / y))))
	t_2 = Float64(Float64(1.0 / z) * Float64(b / c))
	tmp = 0.0
	if (a <= -3.4e-43)
		tmp = Float64(Float64(a / Float64(c / t)) * -4.0);
	elseif (a <= 1.22e-256)
		tmp = t_1;
	elseif (a <= 8.8e+15)
		tmp = t_2;
	elseif (a <= 4.8e+76)
		tmp = t_1;
	elseif (a <= 2.3e+143)
		tmp = t_2;
	elseif (a <= 1.55e+172)
		tmp = Float64(9.0 * Float64(y / Float64(z * Float64(c / x))));
	else
		tmp = Float64(-4.0 * Float64(t / 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)
	t_1 = 9.0 * (x / (z * (c / y)));
	t_2 = (1.0 / z) * (b / c);
	tmp = 0.0;
	if (a <= -3.4e-43)
		tmp = (a / (c / t)) * -4.0;
	elseif (a <= 1.22e-256)
		tmp = t_1;
	elseif (a <= 8.8e+15)
		tmp = t_2;
	elseif (a <= 4.8e+76)
		tmp = t_1;
	elseif (a <= 2.3e+143)
		tmp = t_2;
	elseif (a <= 1.55e+172)
		tmp = 9.0 * (y / (z * (c / x)));
	else
		tmp = -4.0 * (t / (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_] := Block[{t$95$1 = N[(9.0 * N[(x / N[(z * N[(c / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(1.0 / z), $MachinePrecision] * N[(b / c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -3.4e-43], N[(N[(a / N[(c / t), $MachinePrecision]), $MachinePrecision] * -4.0), $MachinePrecision], If[LessEqual[a, 1.22e-256], t$95$1, If[LessEqual[a, 8.8e+15], t$95$2, If[LessEqual[a, 4.8e+76], t$95$1, If[LessEqual[a, 2.3e+143], t$95$2, If[LessEqual[a, 1.55e+172], N[(9.0 * N[(y / N[(z * N[(c / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-4.0 * N[(t / N[(c / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -3.4000000000000001e-43

   1. Initial program 83.5%

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

   2. Taylor expanded in z around inf 54.3%

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

      1. *-commutative 54.3%

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

      2. associate-/l* 58.0%

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

   4. Simplified 58.0%

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

   if -3.4000000000000001e-43 < a < 1.2199999999999999e-256 or 8.8e15 < a < 4.8e76

   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* 78.5%

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

      3. associate-*r* 84.5%

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

      4. *-un-lft-identity 84.5%

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

      5. times-frac 79.7%

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

      6. associate--r- 79.7%

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

      7. fma-neg 79.7%

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

      8. associate-*r* 74.8%

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

      9. distribute-rgt-neg-in 74.8%

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

      10. associate-*l* 73.6%

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

   3. Applied egg-rr 73.6%

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

   4. Taylor expanded in x around inf 49.9%

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

      1. associate-/l* 55.6%

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

      2. *-commutative 55.6%

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

      3. *-lft-identity 55.6%

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

      4. times-frac 54.5%

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

      5. /-rgt-identity 54.5%

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

   6. Simplified 54.5%

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

   if 1.2199999999999999e-256 < a < 8.8e15 or 4.8e76 < a < 2.3e143

   1. Initial program 76.1%

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

      1. associate-+l- 76.1%

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

      2. associate-*r* 74.7%

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

      3. associate-*r* 77.8%

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

      4. *-un-lft-identity 77.8%

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

      5. times-frac 90.1%

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

      6. associate--r- 90.1%

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

      7. fma-neg 90.1%

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

      8. associate-*r* 81.6%

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

      9. distribute-rgt-neg-in 81.6%

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

      10. associate-*l* 81.6%

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

   3. Applied egg-rr 81.6%

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

   4. Taylor expanded in b around inf 51.3%

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

   if 2.3e143 < a < 1.54999999999999994e172

   1. Initial program 85.5%

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

   2. Taylor expanded in x around inf 85.7%

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

      1. associate-*r/ 85.5%

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

      2. associate-*r* 85.5%

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

      3. *-commutative 85.5%

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

      4. times-frac 85.5%

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

      5. *-commutative 85.5%

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

   4. Simplified 85.5%

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

      1. clear-num 85.5%

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

      2. frac-times 85.5%

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

      3. *-un-lft-identity 85.5%

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

      4. *-un-lft-identity 85.5%

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

      5. times-frac 85.7%

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

      6. metadata-eval 85.7%

         \[\leadsto \frac{y}{\left(\color{blue}{0.1111111111111111} \cdot \frac{c}{x}\right) \cdot z} \]

   6. Applied egg-rr 85.7%

      \[\leadsto \color{blue}{\frac{y}{\left(0.1111111111111111 \cdot \frac{c}{x}\right) \cdot z}} \]
   7. Step-by-step derivation

      1. *-rgt-identity 85.7%

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

      2. associate-*l* 85.7%

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

      3. *-commutative 85.7%

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

      4. times-frac 85.7%

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

      5. metadata-eval 85.7%

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

      6. *-commutative 85.7%

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

   8. Simplified 85.7%

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

   if 1.54999999999999994e172 < a

   1. Initial program 77.4%

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

   2. Taylor expanded in z around inf 71.9%

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

      1. *-commutative 71.9%

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

      2. associate-/l* 71.4%

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

   4. Simplified 71.4%

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

   5. Taylor expanded in a around 0 71.9%

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

      1. *-commutative 71.9%

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

      2. associate-/l* 83.9%

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

   7. Simplified 83.9%

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

4. Final simplification 58.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.4 \cdot 10^{-43}:\\ \;\;\;\;\frac{a}{\frac{c}{t}} \cdot -4\\ \mathbf{elif}\;a \leq 1.22 \cdot 10^{-256}:\\ \;\;\;\;9 \cdot \frac{x}{z \cdot \frac{c}{y}}\\ \mathbf{elif}\;a \leq 8.8 \cdot 10^{+15}:\\ \;\;\;\;\frac{1}{z} \cdot \frac{b}{c}\\ \mathbf{elif}\;a \leq 4.8 \cdot 10^{+76}:\\ \;\;\;\;9 \cdot \frac{x}{z \cdot \frac{c}{y}}\\ \mathbf{elif}\;a \leq 2.3 \cdot 10^{+143}:\\ \;\;\;\;\frac{1}{z} \cdot \frac{b}{c}\\ \mathbf{elif}\;a \leq 1.55 \cdot 10^{+172}:\\ \;\;\;\;9 \cdot \frac{y}{z \cdot \frac{c}{x}}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{t}{\frac{c}{a}}\\ \end{array} \]

Alternative 8: 47.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} t_1 := \frac{1}{z} \cdot \frac{b}{c}\\ \mathbf{if}\;a \leq -3.8 \cdot 10^{-43}:\\ \;\;\;\;\frac{a}{\frac{c}{t}} \cdot -4\\ \mathbf{elif}\;a \leq 3.1 \cdot 10^{-251}:\\ \;\;\;\;\frac{x \cdot 9}{c} \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 6.8 \cdot 10^{+15}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{+77}:\\ \;\;\;\;9 \cdot \frac{x}{z \cdot \frac{c}{y}}\\ \mathbf{elif}\;a \leq 8.8 \cdot 10^{+142}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.55 \cdot 10^{+172}:\\ \;\;\;\;9 \cdot \frac{y}{z \cdot \frac{c}{x}}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{t}{\frac{c}{a}}\\ \end{array} \end{array} \]

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
 (let* ((t_1 (* (/ 1.0 z) (/ b c))))
   (if (<= a -3.8e-43)
     (* (/ a (/ c t)) -4.0)
     (if (<= a 3.1e-251)
       (* (/ (* x 9.0) c) (/ y z))
       (if (<= a 6.8e+15)
         t_1
         (if (<= a 1.8e+77)
           (* 9.0 (/ x (* z (/ c y))))
           (if (<= a 8.8e+142)
             t_1
             (if (<= a 1.55e+172)
               (* 9.0 (/ y (* z (/ c x))))
               (* -4.0 (/ t (/ 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 t_1 = (1.0 / z) * (b / c);
	double tmp;
	if (a <= -3.8e-43) {
		tmp = (a / (c / t)) * -4.0;
	} else if (a <= 3.1e-251) {
		tmp = ((x * 9.0) / c) * (y / z);
	} else if (a <= 6.8e+15) {
		tmp = t_1;
	} else if (a <= 1.8e+77) {
		tmp = 9.0 * (x / (z * (c / y)));
	} else if (a <= 8.8e+142) {
		tmp = t_1;
	} else if (a <= 1.55e+172) {
		tmp = 9.0 * (y / (z * (c / x)));
	} else {
		tmp = -4.0 * (t / (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) :: t_1
    real(8) :: tmp
    t_1 = (1.0d0 / z) * (b / c)
    if (a <= (-3.8d-43)) then
        tmp = (a / (c / t)) * (-4.0d0)
    else if (a <= 3.1d-251) then
        tmp = ((x * 9.0d0) / c) * (y / z)
    else if (a <= 6.8d+15) then
        tmp = t_1
    else if (a <= 1.8d+77) then
        tmp = 9.0d0 * (x / (z * (c / y)))
    else if (a <= 8.8d+142) then
        tmp = t_1
    else if (a <= 1.55d+172) then
        tmp = 9.0d0 * (y / (z * (c / x)))
    else
        tmp = (-4.0d0) * (t / (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 t_1 = (1.0 / z) * (b / c);
	double tmp;
	if (a <= -3.8e-43) {
		tmp = (a / (c / t)) * -4.0;
	} else if (a <= 3.1e-251) {
		tmp = ((x * 9.0) / c) * (y / z);
	} else if (a <= 6.8e+15) {
		tmp = t_1;
	} else if (a <= 1.8e+77) {
		tmp = 9.0 * (x / (z * (c / y)));
	} else if (a <= 8.8e+142) {
		tmp = t_1;
	} else if (a <= 1.55e+172) {
		tmp = 9.0 * (y / (z * (c / x)));
	} else {
		tmp = -4.0 * (t / (c / a));
	}
	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 / c)
	tmp = 0
	if a <= -3.8e-43:
		tmp = (a / (c / t)) * -4.0
	elif a <= 3.1e-251:
		tmp = ((x * 9.0) / c) * (y / z)
	elif a <= 6.8e+15:
		tmp = t_1
	elif a <= 1.8e+77:
		tmp = 9.0 * (x / (z * (c / y)))
	elif a <= 8.8e+142:
		tmp = t_1
	elif a <= 1.55e+172:
		tmp = 9.0 * (y / (z * (c / x)))
	else:
		tmp = -4.0 * (t / (c / a))
	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(b / c))
	tmp = 0.0
	if (a <= -3.8e-43)
		tmp = Float64(Float64(a / Float64(c / t)) * -4.0);
	elseif (a <= 3.1e-251)
		tmp = Float64(Float64(Float64(x * 9.0) / c) * Float64(y / z));
	elseif (a <= 6.8e+15)
		tmp = t_1;
	elseif (a <= 1.8e+77)
		tmp = Float64(9.0 * Float64(x / Float64(z * Float64(c / y))));
	elseif (a <= 8.8e+142)
		tmp = t_1;
	elseif (a <= 1.55e+172)
		tmp = Float64(9.0 * Float64(y / Float64(z * Float64(c / x))));
	else
		tmp = Float64(-4.0 * Float64(t / 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)
	t_1 = (1.0 / z) * (b / c);
	tmp = 0.0;
	if (a <= -3.8e-43)
		tmp = (a / (c / t)) * -4.0;
	elseif (a <= 3.1e-251)
		tmp = ((x * 9.0) / c) * (y / z);
	elseif (a <= 6.8e+15)
		tmp = t_1;
	elseif (a <= 1.8e+77)
		tmp = 9.0 * (x / (z * (c / y)));
	elseif (a <= 8.8e+142)
		tmp = t_1;
	elseif (a <= 1.55e+172)
		tmp = 9.0 * (y / (z * (c / x)));
	else
		tmp = -4.0 * (t / (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_] := Block[{t$95$1 = N[(N[(1.0 / z), $MachinePrecision] * N[(b / c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -3.8e-43], N[(N[(a / N[(c / t), $MachinePrecision]), $MachinePrecision] * -4.0), $MachinePrecision], If[LessEqual[a, 3.1e-251], N[(N[(N[(x * 9.0), $MachinePrecision] / c), $MachinePrecision] * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 6.8e+15], t$95$1, If[LessEqual[a, 1.8e+77], N[(9.0 * N[(x / N[(z * N[(c / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 8.8e+142], t$95$1, If[LessEqual[a, 1.55e+172], N[(9.0 * N[(y / N[(z * N[(c / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-4.0 * N[(t / N[(c / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if a < -3.7999999999999997e-43

   1. Initial program 83.5%

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

   2. Taylor expanded in z around inf 54.3%

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

      1. *-commutative 54.3%

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

      2. associate-/l* 58.0%

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

   4. Simplified 58.0%

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

   if -3.7999999999999997e-43 < a < 3.10000000000000003e-251

   1. Initial program 76.5%

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

   2. Taylor expanded in x around inf 47.5%

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

      1. associate-*r/ 47.5%

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

      2. associate-*r* 47.5%

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

      3. *-commutative 47.5%

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

      4. times-frac 51.9%

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

      5. *-commutative 51.9%

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

   4. Simplified 51.9%

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

   if 3.10000000000000003e-251 < a < 6.8e15 or 1.7999999999999999e77 < a < 8.79999999999999947e142

   1. Initial program 77.1%

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

      1. associate-+l- 77.1%

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

      2. associate-*r* 75.7%

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

      3. associate-*r* 77.5%

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

      4. *-un-lft-identity 77.5%

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

      5. times-frac 89.9%

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

      6. associate--r- 89.9%

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

      7. fma-neg 89.9%

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

      8. associate-*r* 82.7%

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

      9. distribute-rgt-neg-in 82.7%

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

      10. associate-*l* 82.7%

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

   3. Applied egg-rr 82.7%

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

   4. Taylor expanded in b around inf 52.0%

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

   if 6.8e15 < a < 1.7999999999999999e77

   1. Initial program 81.0%

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

      1. associate-+l- 81.0%

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

      2. associate-*r* 81.1%

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

      3. associate-*r* 81.0%

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

      4. *-un-lft-identity 81.0%

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

      5. times-frac 65.0%

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

      6. associate--r- 65.0%

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

      7. fma-neg 65.0%

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

      8. associate-*r* 65.0%

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

      9. distribute-rgt-neg-in 65.0%

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

      10. associate-*l* 65.0%

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

   3. Applied egg-rr 65.0%

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

   4. Taylor expanded in x around inf 55.5%

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

      1. associate-/l* 59.5%

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

      2. *-commutative 59.5%

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

      3. *-lft-identity 59.5%

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

      4. times-frac 54.8%

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

      5. /-rgt-identity 54.8%

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

   6. Simplified 54.8%

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

   if 8.79999999999999947e142 < a < 1.54999999999999994e172

   1. Initial program 85.5%

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

   2. Taylor expanded in x around inf 85.7%

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

      1. associate-*r/ 85.5%

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

      2. associate-*r* 85.5%

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

      3. *-commutative 85.5%

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

      4. times-frac 85.5%

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

      5. *-commutative 85.5%

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

   4. Simplified 85.5%

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

      1. clear-num 85.5%

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

      2. frac-times 85.5%

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

      3. *-un-lft-identity 85.5%

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

      4. *-un-lft-identity 85.5%

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

      5. times-frac 85.7%

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

      6. metadata-eval 85.7%

         \[\leadsto \frac{y}{\left(\color{blue}{0.1111111111111111} \cdot \frac{c}{x}\right) \cdot z} \]

   6. Applied egg-rr 85.7%

      \[\leadsto \color{blue}{\frac{y}{\left(0.1111111111111111 \cdot \frac{c}{x}\right) \cdot z}} \]
   7. Step-by-step derivation

      1. *-rgt-identity 85.7%

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

      2. associate-*l* 85.7%

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

      3. *-commutative 85.7%

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

      4. times-frac 85.7%

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

      5. metadata-eval 85.7%

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

      6. *-commutative 85.7%

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

   8. Simplified 85.7%

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

   if 1.54999999999999994e172 < a

   1. Initial program 77.4%

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

   2. Taylor expanded in z around inf 71.9%

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

      1. *-commutative 71.9%

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

      2. associate-/l* 71.4%

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

   4. Simplified 71.4%

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

   5. Taylor expanded in a around 0 71.9%

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

      1. *-commutative 71.9%

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

      2. associate-/l* 83.9%

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

   7. Simplified 83.9%

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

4. Final simplification 57.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.8 \cdot 10^{-43}:\\ \;\;\;\;\frac{a}{\frac{c}{t}} \cdot -4\\ \mathbf{elif}\;a \leq 3.1 \cdot 10^{-251}:\\ \;\;\;\;\frac{x \cdot 9}{c} \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 6.8 \cdot 10^{+15}:\\ \;\;\;\;\frac{1}{z} \cdot \frac{b}{c}\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{+77}:\\ \;\;\;\;9 \cdot \frac{x}{z \cdot \frac{c}{y}}\\ \mathbf{elif}\;a \leq 8.8 \cdot 10^{+142}:\\ \;\;\;\;\frac{1}{z} \cdot \frac{b}{c}\\ \mathbf{elif}\;a \leq 1.55 \cdot 10^{+172}:\\ \;\;\;\;9 \cdot \frac{y}{z \cdot \frac{c}{x}}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{t}{\frac{c}{a}}\\ \end{array} \]

Alternative 9: 47.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} t_1 := \frac{1}{z} \cdot \frac{b}{c}\\ \mathbf{if}\;a \leq -1.65 \cdot 10^{-43}:\\ \;\;\;\;\frac{a}{\frac{c}{t}} \cdot -4\\ \mathbf{elif}\;a \leq 2.6 \cdot 10^{-254}:\\ \;\;\;\;\frac{9}{\frac{c}{x} \cdot \frac{z}{y}}\\ \mathbf{elif}\;a \leq 8 \cdot 10^{+16}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.5 \cdot 10^{+77}:\\ \;\;\;\;9 \cdot \frac{x}{z \cdot \frac{c}{y}}\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{+143}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.55 \cdot 10^{+172}:\\ \;\;\;\;9 \cdot \frac{y}{z \cdot \frac{c}{x}}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{t}{\frac{c}{a}}\\ \end{array} \end{array} \]

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
 (let* ((t_1 (* (/ 1.0 z) (/ b c))))
   (if (<= a -1.65e-43)
     (* (/ a (/ c t)) -4.0)
     (if (<= a 2.6e-254)
       (/ 9.0 (* (/ c x) (/ z y)))
       (if (<= a 8e+16)
         t_1
         (if (<= a 1.5e+77)
           (* 9.0 (/ x (* z (/ c y))))
           (if (<= a 1.25e+143)
             t_1
             (if (<= a 1.55e+172)
               (* 9.0 (/ y (* z (/ c x))))
               (* -4.0 (/ t (/ 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 t_1 = (1.0 / z) * (b / c);
	double tmp;
	if (a <= -1.65e-43) {
		tmp = (a / (c / t)) * -4.0;
	} else if (a <= 2.6e-254) {
		tmp = 9.0 / ((c / x) * (z / y));
	} else if (a <= 8e+16) {
		tmp = t_1;
	} else if (a <= 1.5e+77) {
		tmp = 9.0 * (x / (z * (c / y)));
	} else if (a <= 1.25e+143) {
		tmp = t_1;
	} else if (a <= 1.55e+172) {
		tmp = 9.0 * (y / (z * (c / x)));
	} else {
		tmp = -4.0 * (t / (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) :: t_1
    real(8) :: tmp
    t_1 = (1.0d0 / z) * (b / c)
    if (a <= (-1.65d-43)) then
        tmp = (a / (c / t)) * (-4.0d0)
    else if (a <= 2.6d-254) then
        tmp = 9.0d0 / ((c / x) * (z / y))
    else if (a <= 8d+16) then
        tmp = t_1
    else if (a <= 1.5d+77) then
        tmp = 9.0d0 * (x / (z * (c / y)))
    else if (a <= 1.25d+143) then
        tmp = t_1
    else if (a <= 1.55d+172) then
        tmp = 9.0d0 * (y / (z * (c / x)))
    else
        tmp = (-4.0d0) * (t / (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 t_1 = (1.0 / z) * (b / c);
	double tmp;
	if (a <= -1.65e-43) {
		tmp = (a / (c / t)) * -4.0;
	} else if (a <= 2.6e-254) {
		tmp = 9.0 / ((c / x) * (z / y));
	} else if (a <= 8e+16) {
		tmp = t_1;
	} else if (a <= 1.5e+77) {
		tmp = 9.0 * (x / (z * (c / y)));
	} else if (a <= 1.25e+143) {
		tmp = t_1;
	} else if (a <= 1.55e+172) {
		tmp = 9.0 * (y / (z * (c / x)));
	} else {
		tmp = -4.0 * (t / (c / a));
	}
	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 / c)
	tmp = 0
	if a <= -1.65e-43:
		tmp = (a / (c / t)) * -4.0
	elif a <= 2.6e-254:
		tmp = 9.0 / ((c / x) * (z / y))
	elif a <= 8e+16:
		tmp = t_1
	elif a <= 1.5e+77:
		tmp = 9.0 * (x / (z * (c / y)))
	elif a <= 1.25e+143:
		tmp = t_1
	elif a <= 1.55e+172:
		tmp = 9.0 * (y / (z * (c / x)))
	else:
		tmp = -4.0 * (t / (c / a))
	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(b / c))
	tmp = 0.0
	if (a <= -1.65e-43)
		tmp = Float64(Float64(a / Float64(c / t)) * -4.0);
	elseif (a <= 2.6e-254)
		tmp = Float64(9.0 / Float64(Float64(c / x) * Float64(z / y)));
	elseif (a <= 8e+16)
		tmp = t_1;
	elseif (a <= 1.5e+77)
		tmp = Float64(9.0 * Float64(x / Float64(z * Float64(c / y))));
	elseif (a <= 1.25e+143)
		tmp = t_1;
	elseif (a <= 1.55e+172)
		tmp = Float64(9.0 * Float64(y / Float64(z * Float64(c / x))));
	else
		tmp = Float64(-4.0 * Float64(t / 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)
	t_1 = (1.0 / z) * (b / c);
	tmp = 0.0;
	if (a <= -1.65e-43)
		tmp = (a / (c / t)) * -4.0;
	elseif (a <= 2.6e-254)
		tmp = 9.0 / ((c / x) * (z / y));
	elseif (a <= 8e+16)
		tmp = t_1;
	elseif (a <= 1.5e+77)
		tmp = 9.0 * (x / (z * (c / y)));
	elseif (a <= 1.25e+143)
		tmp = t_1;
	elseif (a <= 1.55e+172)
		tmp = 9.0 * (y / (z * (c / x)));
	else
		tmp = -4.0 * (t / (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_] := Block[{t$95$1 = N[(N[(1.0 / z), $MachinePrecision] * N[(b / c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.65e-43], N[(N[(a / N[(c / t), $MachinePrecision]), $MachinePrecision] * -4.0), $MachinePrecision], If[LessEqual[a, 2.6e-254], N[(9.0 / N[(N[(c / x), $MachinePrecision] * N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 8e+16], t$95$1, If[LessEqual[a, 1.5e+77], N[(9.0 * N[(x / N[(z * N[(c / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.25e+143], t$95$1, If[LessEqual[a, 1.55e+172], N[(9.0 * N[(y / N[(z * N[(c / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-4.0 * N[(t / N[(c / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if a < -1.65000000000000008e-43

   1. Initial program 83.5%

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

   2. Taylor expanded in z around inf 54.3%

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

      1. *-commutative 54.3%

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

      2. associate-/l* 58.0%

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

   4. Simplified 58.0%

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

   if -1.65000000000000008e-43 < a < 2.6e-254

   1. Initial program 77.7%

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

   2. Taylor expanded in x around inf 48.2%

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

      1. associate-*r/ 48.3%

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

      2. associate-*r* 48.2%

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

      3. *-commutative 48.2%

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

      4. times-frac 52.7%

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

      5. *-commutative 52.7%

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

   4. Simplified 52.7%

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

      1. *-commutative 52.7%

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

      2. clear-num 52.6%

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

      3. associate-/l* 52.6%

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

      4. frac-times 53.2%

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

      5. metadata-eval 53.2%

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

   6. Applied egg-rr 53.2%

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

   if 2.6e-254 < a < 8e16 or 1.4999999999999999e77 < a < 1.25000000000000003e143

   1. Initial program 76.1%

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

      1. associate-+l- 76.1%

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

      2. associate-*r* 74.7%

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

      3. associate-*r* 77.8%

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

      4. *-un-lft-identity 77.8%

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

      5. times-frac 90.1%

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

      6. associate--r- 90.1%

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

      7. fma-neg 90.1%

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

      8. associate-*r* 81.6%

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

      9. distribute-rgt-neg-in 81.6%

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

      10. associate-*l* 81.6%

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

   3. Applied egg-rr 81.6%

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

   4. Taylor expanded in b around inf 51.3%

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

   if 8e16 < a < 1.4999999999999999e77

   1. Initial program 81.0%

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

      1. associate-+l- 81.0%

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

      2. associate-*r* 81.1%

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

      3. associate-*r* 81.0%

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

      4. *-un-lft-identity 81.0%

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

      5. times-frac 65.0%

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

      6. associate--r- 65.0%

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

      7. fma-neg 65.0%

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

      8. associate-*r* 65.0%

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

      9. distribute-rgt-neg-in 65.0%

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

      10. associate-*l* 65.0%

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

   3. Applied egg-rr 65.0%

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

   4. Taylor expanded in x around inf 55.5%

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

      1. associate-/l* 59.5%

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

      2. *-commutative 59.5%

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

      3. *-lft-identity 59.5%

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

      4. times-frac 54.8%

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

      5. /-rgt-identity 54.8%

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

   6. Simplified 54.8%

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

   if 1.25000000000000003e143 < a < 1.54999999999999994e172

   1. Initial program 85.5%

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

   2. Taylor expanded in x around inf 85.7%

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

      1. associate-*r/ 85.5%

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

      2. associate-*r* 85.5%

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

      3. *-commutative 85.5%

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

      4. times-frac 85.5%

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

      5. *-commutative 85.5%

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

   4. Simplified 85.5%

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

      1. clear-num 85.5%

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

      2. frac-times 85.5%

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

      3. *-un-lft-identity 85.5%

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

      4. *-un-lft-identity 85.5%

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

      5. times-frac 85.7%

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

      6. metadata-eval 85.7%

         \[\leadsto \frac{y}{\left(\color{blue}{0.1111111111111111} \cdot \frac{c}{x}\right) \cdot z} \]

   6. Applied egg-rr 85.7%

      \[\leadsto \color{blue}{\frac{y}{\left(0.1111111111111111 \cdot \frac{c}{x}\right) \cdot z}} \]
   7. Step-by-step derivation

      1. *-rgt-identity 85.7%

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

      2. associate-*l* 85.7%

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

      3. *-commutative 85.7%

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

      4. times-frac 85.7%

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

      5. metadata-eval 85.7%

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

      6. *-commutative 85.7%

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

   8. Simplified 85.7%

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

   if 1.54999999999999994e172 < a

   1. Initial program 77.4%

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

   2. Taylor expanded in z around inf 71.9%

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

      1. *-commutative 71.9%

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

      2. associate-/l* 71.4%

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

   4. Simplified 71.4%

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

   5. Taylor expanded in a around 0 71.9%

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

      1. *-commutative 71.9%

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

      2. associate-/l* 83.9%

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

   7. Simplified 83.9%

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

4. Final simplification 57.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.65 \cdot 10^{-43}:\\ \;\;\;\;\frac{a}{\frac{c}{t}} \cdot -4\\ \mathbf{elif}\;a \leq 2.6 \cdot 10^{-254}:\\ \;\;\;\;\frac{9}{\frac{c}{x} \cdot \frac{z}{y}}\\ \mathbf{elif}\;a \leq 8 \cdot 10^{+16}:\\ \;\;\;\;\frac{1}{z} \cdot \frac{b}{c}\\ \mathbf{elif}\;a \leq 1.5 \cdot 10^{+77}:\\ \;\;\;\;9 \cdot \frac{x}{z \cdot \frac{c}{y}}\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{+143}:\\ \;\;\;\;\frac{1}{z} \cdot \frac{b}{c}\\ \mathbf{elif}\;a \leq 1.55 \cdot 10^{+172}:\\ \;\;\;\;9 \cdot \frac{y}{z \cdot \frac{c}{x}}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{t}{\frac{c}{a}}\\ \end{array} \]

Alternative 10: 68.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} t_1 := a \cdot \left(z \cdot t\right)\\ t_2 := 9 \cdot \left(x \cdot y\right)\\ \mathbf{if}\;b \leq -3.15 \cdot 10^{-19}:\\ \;\;\;\;\frac{1}{c} \cdot \frac{b + -4 \cdot t_1}{z}\\ \mathbf{elif}\;b \leq 4.3 \cdot 10^{+48}:\\ \;\;\;\;\frac{t_2 - 4 \cdot t_1}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + t_2}{z \cdot c}\\ \end{array} \end{array} \]

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
 (let* ((t_1 (* a (* z t))) (t_2 (* 9.0 (* x y))))
   (if (<= b -3.15e-19)
     (* (/ 1.0 c) (/ (+ b (* -4.0 t_1)) z))
     (if (<= b 4.3e+48)
       (/ (- t_2 (* 4.0 t_1)) (* z c))
       (/ (+ b t_2) (* 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 t_1 = a * (z * t);
	double t_2 = 9.0 * (x * y);
	double tmp;
	if (b <= -3.15e-19) {
		tmp = (1.0 / c) * ((b + (-4.0 * t_1)) / z);
	} else if (b <= 4.3e+48) {
		tmp = (t_2 - (4.0 * t_1)) / (z * c);
	} else {
		tmp = (b + t_2) / (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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a * (z * t)
    t_2 = 9.0d0 * (x * y)
    if (b <= (-3.15d-19)) then
        tmp = (1.0d0 / c) * ((b + ((-4.0d0) * t_1)) / z)
    else if (b <= 4.3d+48) then
        tmp = (t_2 - (4.0d0 * t_1)) / (z * c)
    else
        tmp = (b + t_2) / (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 t_1 = a * (z * t);
	double t_2 = 9.0 * (x * y);
	double tmp;
	if (b <= -3.15e-19) {
		tmp = (1.0 / c) * ((b + (-4.0 * t_1)) / z);
	} else if (b <= 4.3e+48) {
		tmp = (t_2 - (4.0 * t_1)) / (z * c);
	} else {
		tmp = (b + t_2) / (z * 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 = a * (z * t)
	t_2 = 9.0 * (x * y)
	tmp = 0
	if b <= -3.15e-19:
		tmp = (1.0 / c) * ((b + (-4.0 * t_1)) / z)
	elif b <= 4.3e+48:
		tmp = (t_2 - (4.0 * t_1)) / (z * c)
	else:
		tmp = (b + t_2) / (z * 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(a * Float64(z * t))
	t_2 = Float64(9.0 * Float64(x * y))
	tmp = 0.0
	if (b <= -3.15e-19)
		tmp = Float64(Float64(1.0 / c) * Float64(Float64(b + Float64(-4.0 * t_1)) / z));
	elseif (b <= 4.3e+48)
		tmp = Float64(Float64(t_2 - Float64(4.0 * t_1)) / Float64(z * c));
	else
		tmp = Float64(Float64(b + t_2) / 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)
	t_1 = a * (z * t);
	t_2 = 9.0 * (x * y);
	tmp = 0.0;
	if (b <= -3.15e-19)
		tmp = (1.0 / c) * ((b + (-4.0 * t_1)) / z);
	elseif (b <= 4.3e+48)
		tmp = (t_2 - (4.0 * t_1)) / (z * c);
	else
		tmp = (b + t_2) / (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_] := Block[{t$95$1 = N[(a * N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(9.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -3.15e-19], N[(N[(1.0 / c), $MachinePrecision] * N[(N[(b + N[(-4.0 * t$95$1), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 4.3e+48], N[(N[(t$95$2 - N[(4.0 * t$95$1), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(N[(b + t$95$2), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -3.15000000000000009e-19

   1. Initial program 75.0%

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

      1. associate-/r* 79.3%

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

      2. associate-+l- 79.3%

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

      3. associate-*r* 77.9%

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

      4. associate-*r* 86.2%

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

      5. div-inv 86.1%

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

      6. associate--r- 86.1%

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

      7. fma-neg 86.1%

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

      8. associate-*r* 77.9%

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

      9. distribute-rgt-neg-in 77.9%

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

      10. associate-*l* 77.9%

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

   3. Applied egg-rr 77.9%

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

   4. Taylor expanded in x around 0 72.3%

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

      1. *-commutative 72.3%

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

   6. Simplified 72.3%

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

   if -3.15000000000000009e-19 < b < 4.29999999999999978e48

   1. Initial program 78.1%

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

      1. associate-+l- 78.1%

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

      2. associate-*l* 78.9%

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

      3. associate-*l* 78.3%

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

   3. Simplified 78.3%

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

   4. Taylor expanded in b around 0 73.7%

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

   if 4.29999999999999978e48 < b

   1. Initial program 89.8%

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

   2. Taylor expanded in x around inf 83.3%

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

4. Final simplification 75.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.15 \cdot 10^{-19}:\\ \;\;\;\;\frac{1}{c} \cdot \frac{b + -4 \cdot \left(a \cdot \left(z \cdot t\right)\right)}{z}\\ \mathbf{elif}\;b \leq 4.3 \cdot 10^{+48}:\\ \;\;\;\;\frac{9 \cdot \left(x \cdot y\right) - 4 \cdot \left(a \cdot \left(z \cdot t\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \end{array} \]

Alternative 11: 67.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq -4.2 \cdot 10^{-43}:\\ \;\;\;\;\frac{a}{\frac{c}{t}} \cdot -4\\ \mathbf{elif}\;a \leq 1.55 \cdot 10^{+172}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b - 4 \cdot \left(a \cdot \left(z \cdot t\right)\right)}{z \cdot c}\\ \end{array} \end{array} \]

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 (<= a -4.2e-43)
   (* (/ a (/ c t)) -4.0)
   (if (<= a 1.55e+172)
     (/ (+ b (* 9.0 (* x y))) (* z c))
     (/ (- b (* 4.0 (* a (* z t)))) (* 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 (a <= -4.2e-43) {
		tmp = (a / (c / t)) * -4.0;
	} else if (a <= 1.55e+172) {
		tmp = (b + (9.0 * (x * y))) / (z * c);
	} else {
		tmp = (b - (4.0 * (a * (z * t)))) / (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 (a <= (-4.2d-43)) then
        tmp = (a / (c / t)) * (-4.0d0)
    else if (a <= 1.55d+172) then
        tmp = (b + (9.0d0 * (x * y))) / (z * c)
    else
        tmp = (b - (4.0d0 * (a * (z * t)))) / (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 (a <= -4.2e-43) {
		tmp = (a / (c / t)) * -4.0;
	} else if (a <= 1.55e+172) {
		tmp = (b + (9.0 * (x * y))) / (z * c);
	} else {
		tmp = (b - (4.0 * (a * (z * t)))) / (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 a <= -4.2e-43:
		tmp = (a / (c / t)) * -4.0
	elif a <= 1.55e+172:
		tmp = (b + (9.0 * (x * y))) / (z * c)
	else:
		tmp = (b - (4.0 * (a * (z * t)))) / (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 (a <= -4.2e-43)
		tmp = Float64(Float64(a / Float64(c / t)) * -4.0);
	elseif (a <= 1.55e+172)
		tmp = Float64(Float64(b + Float64(9.0 * Float64(x * y))) / Float64(z * c));
	else
		tmp = Float64(Float64(b - Float64(4.0 * Float64(a * Float64(z * t)))) / 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 (a <= -4.2e-43)
		tmp = (a / (c / t)) * -4.0;
	elseif (a <= 1.55e+172)
		tmp = (b + (9.0 * (x * y))) / (z * c);
	else
		tmp = (b - (4.0 * (a * (z * t)))) / (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[a, -4.2e-43], N[(N[(a / N[(c / t), $MachinePrecision]), $MachinePrecision] * -4.0), $MachinePrecision], If[LessEqual[a, 1.55e+172], N[(N[(b + N[(9.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(N[(b - N[(4.0 * N[(a * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -4.2000000000000001e-43

   1. Initial program 83.5%

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

   2. Taylor expanded in z around inf 54.3%

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

      1. *-commutative 54.3%

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

      2. associate-/l* 58.0%

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

   4. Simplified 58.0%

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

   if -4.2000000000000001e-43 < a < 1.54999999999999994e172

   1. Initial program 77.7%

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

   2. Taylor expanded in x around inf 70.3%

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

   if 1.54999999999999994e172 < a

   1. Initial program 77.4%

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

      1. associate-+l- 77.4%

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

      2. associate-*l* 77.4%

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

      3. associate-*l* 73.1%

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

   3. Simplified 73.1%

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

   4. Taylor expanded in x around 0 76.6%

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

4. Final simplification 67.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.2 \cdot 10^{-43}:\\ \;\;\;\;\frac{a}{\frac{c}{t}} \cdot -4\\ \mathbf{elif}\;a \leq 1.55 \cdot 10^{+172}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b - 4 \cdot \left(a \cdot \left(z \cdot t\right)\right)}{z \cdot c}\\ \end{array} \]

Alternative 12: 68.1% accurate, 1.3× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq -4.2 \cdot 10^{-43}:\\ \;\;\;\;\frac{a}{\frac{c}{t}} \cdot -4\\ \mathbf{elif}\;a \leq 1.65 \cdot 10^{+172}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{t}{\frac{c}{a}}\\ \end{array} \end{array} \]

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 (<= a -4.2e-43)
   (* (/ a (/ c t)) -4.0)
   (if (<= a 1.65e+172)
     (/ (+ b (* 9.0 (* x y))) (* z c))
     (* -4.0 (/ t (/ 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 (a <= -4.2e-43) {
		tmp = (a / (c / t)) * -4.0;
	} else if (a <= 1.65e+172) {
		tmp = (b + (9.0 * (x * y))) / (z * c);
	} else {
		tmp = -4.0 * (t / (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 (a <= (-4.2d-43)) then
        tmp = (a / (c / t)) * (-4.0d0)
    else if (a <= 1.65d+172) then
        tmp = (b + (9.0d0 * (x * y))) / (z * c)
    else
        tmp = (-4.0d0) * (t / (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 (a <= -4.2e-43) {
		tmp = (a / (c / t)) * -4.0;
	} else if (a <= 1.65e+172) {
		tmp = (b + (9.0 * (x * y))) / (z * c);
	} else {
		tmp = -4.0 * (t / (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 a <= -4.2e-43:
		tmp = (a / (c / t)) * -4.0
	elif a <= 1.65e+172:
		tmp = (b + (9.0 * (x * y))) / (z * c)
	else:
		tmp = -4.0 * (t / (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 (a <= -4.2e-43)
		tmp = Float64(Float64(a / Float64(c / t)) * -4.0);
	elseif (a <= 1.65e+172)
		tmp = Float64(Float64(b + Float64(9.0 * Float64(x * y))) / Float64(z * c));
	else
		tmp = Float64(-4.0 * Float64(t / 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 (a <= -4.2e-43)
		tmp = (a / (c / t)) * -4.0;
	elseif (a <= 1.65e+172)
		tmp = (b + (9.0 * (x * y))) / (z * c);
	else
		tmp = -4.0 * (t / (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[a, -4.2e-43], N[(N[(a / N[(c / t), $MachinePrecision]), $MachinePrecision] * -4.0), $MachinePrecision], If[LessEqual[a, 1.65e+172], N[(N[(b + N[(9.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(-4.0 * N[(t / N[(c / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -4.2000000000000001e-43

   1. Initial program 83.5%

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

   2. Taylor expanded in z around inf 54.3%

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

      1. *-commutative 54.3%

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

      2. associate-/l* 58.0%

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

   4. Simplified 58.0%

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

   if -4.2000000000000001e-43 < a < 1.64999999999999991e172

   1. Initial program 77.7%

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

   2. Taylor expanded in x around inf 70.3%

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

   if 1.64999999999999991e172 < a

   1. Initial program 77.4%

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

   2. Taylor expanded in z around inf 71.9%

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

      1. *-commutative 71.9%

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

      2. associate-/l* 71.4%

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

   4. Simplified 71.4%

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

   5. Taylor expanded in a around 0 71.9%

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

      1. *-commutative 71.9%

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

      2. associate-/l* 83.9%

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

   7. Simplified 83.9%

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

4. Final simplification 67.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.2 \cdot 10^{-43}:\\ \;\;\;\;\frac{a}{\frac{c}{t}} \cdot -4\\ \mathbf{elif}\;a \leq 1.65 \cdot 10^{+172}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{t}{\frac{c}{a}}\\ \end{array} \]

Alternative 13: 49.0% accurate, 1.7× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;b \leq -118:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{elif}\;b \leq 2.5 \cdot 10^{+47}:\\ \;\;\;\;\left(a \cdot -4\right) \cdot \frac{t}{c}\\ \mathbf{else}:\\ \;\;\;\;b \cdot \frac{1}{z \cdot c}\\ \end{array} \end{array} \]

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 (<= b -118.0)
   (/ (/ b z) c)
   (if (<= b 2.5e+47) (* (* a -4.0) (/ t c)) (* b (/ 1.0 (* 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 (b <= -118.0) {
		tmp = (b / z) / c;
	} else if (b <= 2.5e+47) {
		tmp = (a * -4.0) * (t / c);
	} else {
		tmp = b * (1.0 / (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 (b <= (-118.0d0)) then
        tmp = (b / z) / c
    else if (b <= 2.5d+47) then
        tmp = (a * (-4.0d0)) * (t / c)
    else
        tmp = b * (1.0d0 / (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 (b <= -118.0) {
		tmp = (b / z) / c;
	} else if (b <= 2.5e+47) {
		tmp = (a * -4.0) * (t / c);
	} else {
		tmp = b * (1.0 / (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 b <= -118.0:
		tmp = (b / z) / c
	elif b <= 2.5e+47:
		tmp = (a * -4.0) * (t / c)
	else:
		tmp = b * (1.0 / (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 (b <= -118.0)
		tmp = Float64(Float64(b / z) / c);
	elseif (b <= 2.5e+47)
		tmp = Float64(Float64(a * -4.0) * Float64(t / c));
	else
		tmp = Float64(b * Float64(1.0 / 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 (b <= -118.0)
		tmp = (b / z) / c;
	elseif (b <= 2.5e+47)
		tmp = (a * -4.0) * (t / c);
	else
		tmp = b * (1.0 / (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[LessEqual[b, -118.0], N[(N[(b / z), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[b, 2.5e+47], N[(N[(a * -4.0), $MachinePrecision] * N[(t / c), $MachinePrecision]), $MachinePrecision], N[(b * N[(1.0 / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -118

   1. Initial program 75.6%

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

      1. associate-+l- 75.6%

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

      2. associate-*r* 74.1%

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

      3. associate-*r* 78.7%

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

      4. clear-num 78.8%

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

      5. inv-pow 78.8%

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

      6. associate--r- 78.8%

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

      7. fma-neg 78.8%

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

      8. associate-*r* 74.0%

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

      9. distribute-rgt-neg-in 74.0%

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

      10. associate-*l* 74.0%

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

   3. Applied egg-rr 74.0%

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

   5. Simplified 80.4%

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

   6. Taylor expanded in b around inf 57.7%

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

      1. *-commutative 57.7%

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

      2. associate-/r* 62.1%

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

   8. Simplified 62.1%

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

   if -118 < b < 2.50000000000000011e47

   1. Initial program 77.7%

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

      1. associate-+l- 77.7%

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

      2. associate-*r* 78.5%

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

      3. associate-*r* 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. clear-num 77.4%

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

      5. inv-pow 77.4%

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

      6. associate--r- 77.4%

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

      7. fma-neg 77.4%

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

      8. associate-*r* 78.0%

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

      9. distribute-rgt-neg-in 78.0%

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

      10. associate-*l* 77.3%

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

   3. Applied egg-rr 77.3%

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

   5. Simplified 77.4%

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

   6. Taylor expanded in z around inf 48.6%

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

      1. associate-*r/ 48.6%

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

      2. associate-*r* 48.6%

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

      3. associate-*r/ 51.4%

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

      4. *-commutative 51.4%

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

   8. Simplified 51.4%

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

   if 2.50000000000000011e47 < b

   1. Initial program 89.8%

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

   2. Taylor expanded in b around inf 60.0%

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

      1. *-commutative 60.0%

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

   4. Simplified 60.0%

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

      1. div-inv 60.1%

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

   6. Applied egg-rr 60.1%

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

4. Final simplification 55.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -118:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{elif}\;b \leq 2.5 \cdot 10^{+47}:\\ \;\;\;\;\left(a \cdot -4\right) \cdot \frac{t}{c}\\ \mathbf{else}:\\ \;\;\;\;b \cdot \frac{1}{z \cdot c}\\ \end{array} \]

Alternative 14: 49.3% accurate, 1.7× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;b \leq -0.00011:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{elif}\;b \leq 8.2 \cdot 10^{+28}:\\ \;\;\;\;\left(a \cdot -4\right) \cdot \frac{t}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{z} \cdot \frac{b}{c}\\ \end{array} \end{array} \]

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 -0.00011)
   (/ (/ b z) c)
   (if (<= b 8.2e+28) (* (* a -4.0) (/ t c)) (* (/ 1.0 z) (/ b 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 <= -0.00011) {
		tmp = (b / z) / c;
	} else if (b <= 8.2e+28) {
		tmp = (a * -4.0) * (t / c);
	} else {
		tmp = (1.0 / z) * (b / 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 <= (-0.00011d0)) then
        tmp = (b / z) / c
    else if (b <= 8.2d+28) then
        tmp = (a * (-4.0d0)) * (t / c)
    else
        tmp = (1.0d0 / z) * (b / 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 <= -0.00011) {
		tmp = (b / z) / c;
	} else if (b <= 8.2e+28) {
		tmp = (a * -4.0) * (t / c);
	} else {
		tmp = (1.0 / z) * (b / 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 <= -0.00011:
		tmp = (b / z) / c
	elif b <= 8.2e+28:
		tmp = (a * -4.0) * (t / c)
	else:
		tmp = (1.0 / z) * (b / 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 <= -0.00011)
		tmp = Float64(Float64(b / z) / c);
	elseif (b <= 8.2e+28)
		tmp = Float64(Float64(a * -4.0) * Float64(t / c));
	else
		tmp = Float64(Float64(1.0 / z) * Float64(b / 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 <= -0.00011)
		tmp = (b / z) / c;
	elseif (b <= 8.2e+28)
		tmp = (a * -4.0) * (t / c);
	else
		tmp = (1.0 / z) * (b / 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, -0.00011], N[(N[(b / z), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[b, 8.2e+28], N[(N[(a * -4.0), $MachinePrecision] * N[(t / c), $MachinePrecision]), $MachinePrecision], N[(N[(1.0 / z), $MachinePrecision] * N[(b / c), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.10000000000000004e-4

   1. Initial program 75.6%

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

      1. associate-+l- 75.6%

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

      2. associate-*r* 74.1%

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

      3. associate-*r* 78.7%

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

      4. clear-num 78.8%

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

      5. inv-pow 78.8%

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

      6. associate--r- 78.8%

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

      7. fma-neg 78.8%

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

      8. associate-*r* 74.0%

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

      9. distribute-rgt-neg-in 74.0%

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

      10. associate-*l* 74.0%

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

   3. Applied egg-rr 74.0%

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

   5. Simplified 80.4%

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

   6. Taylor expanded in b around inf 57.7%

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

      1. *-commutative 57.7%

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

      2. associate-/r* 62.1%

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

   8. Simplified 62.1%

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

   if -1.10000000000000004e-4 < b < 8.19999999999999961e28

   1. Initial program 77.3%

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

      1. associate-+l- 77.3%

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

      2. associate-*r* 78.0%

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

      3. associate-*r* 77.4%

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

      4. clear-num 76.9%

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

      5. inv-pow 76.9%

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

      6. associate--r- 76.9%

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

      7. fma-neg 76.9%

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

      8. associate-*r* 77.5%

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

      9. distribute-rgt-neg-in 77.5%

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

      10. associate-*l* 76.8%

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

   3. Applied egg-rr 76.8%

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

   5. Simplified 76.9%

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

   6. Taylor expanded in z around inf 48.8%

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

      1. associate-*r/ 48.8%

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

      2. associate-*r* 48.8%

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

      3. associate-*r/ 51.1%

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

      4. *-commutative 51.1%

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

   8. Simplified 51.1%

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

   if 8.19999999999999961e28 < b

   1. Initial program 89.4%

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

      1. associate-+l- 89.4%

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

      2. associate-*r* 89.4%

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

      3. associate-*r* 87.7%

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

      4. *-un-lft-identity 87.7%

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

      5. times-frac 81.4%

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

      6. associate--r- 81.4%

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

      7. fma-neg 81.4%

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

      8. associate-*r* 84.7%

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

      9. distribute-rgt-neg-in 84.7%

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

      10. associate-*l* 84.7%

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

   3. Applied egg-rr 84.7%

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

   4. Taylor expanded in b around inf 58.2%

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

4. Final simplification 55.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -0.00011:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{elif}\;b \leq 8.2 \cdot 10^{+28}:\\ \;\;\;\;\left(a \cdot -4\right) \cdot \frac{t}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{z} \cdot \frac{b}{c}\\ \end{array} \]

Alternative 15: 49.6% accurate, 1.7× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;b \leq -2 \cdot 10^{+42}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{elif}\;b \leq 3.5 \cdot 10^{+38}:\\ \;\;\;\;-4 \cdot \frac{t}{\frac{c}{a}}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{z} \cdot \frac{b}{c}\\ \end{array} \end{array} \]

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 -2e+42)
   (/ (/ b z) c)
   (if (<= b 3.5e+38) (* -4.0 (/ t (/ c a))) (* (/ 1.0 z) (/ b 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 <= -2e+42) {
		tmp = (b / z) / c;
	} else if (b <= 3.5e+38) {
		tmp = -4.0 * (t / (c / a));
	} else {
		tmp = (1.0 / z) * (b / 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 <= (-2d+42)) then
        tmp = (b / z) / c
    else if (b <= 3.5d+38) then
        tmp = (-4.0d0) * (t / (c / a))
    else
        tmp = (1.0d0 / z) * (b / 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 <= -2e+42) {
		tmp = (b / z) / c;
	} else if (b <= 3.5e+38) {
		tmp = -4.0 * (t / (c / a));
	} else {
		tmp = (1.0 / z) * (b / 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 <= -2e+42:
		tmp = (b / z) / c
	elif b <= 3.5e+38:
		tmp = -4.0 * (t / (c / a))
	else:
		tmp = (1.0 / z) * (b / 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 <= -2e+42)
		tmp = Float64(Float64(b / z) / c);
	elseif (b <= 3.5e+38)
		tmp = Float64(-4.0 * Float64(t / Float64(c / a)));
	else
		tmp = Float64(Float64(1.0 / z) * Float64(b / 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 <= -2e+42)
		tmp = (b / z) / c;
	elseif (b <= 3.5e+38)
		tmp = -4.0 * (t / (c / a));
	else
		tmp = (1.0 / z) * (b / 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, -2e+42], N[(N[(b / z), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[b, 3.5e+38], N[(-4.0 * N[(t / N[(c / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(1.0 / z), $MachinePrecision] * N[(b / c), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -2.00000000000000009e42

   1. Initial program 74.8%

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

      1. associate-+l- 74.8%

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

      2. associate-*r* 72.9%

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

      3. associate-*r* 78.3%

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

      4. clear-num 78.4%

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

      5. inv-pow 78.4%

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

      6. associate--r- 78.4%

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

      7. fma-neg 78.4%

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

      8. associate-*r* 73.0%

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

      9. distribute-rgt-neg-in 73.0%

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

      10. associate-*l* 73.0%

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

   3. Applied egg-rr 73.0%

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

   5. Simplified 80.3%

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

   6. Taylor expanded in b around inf 60.5%

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

      1. *-commutative 60.5%

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

      2. associate-/r* 67.5%

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

   8. Simplified 67.5%

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

   if -2.00000000000000009e42 < b < 3.50000000000000002e38

   1. Initial program 78.0%

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

   2. Taylor expanded in z around inf 48.4%

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

      1. *-commutative 48.4%

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

      2. associate-/l* 51.1%

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

   4. Simplified 51.1%

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

   5. Taylor expanded in a around 0 48.4%

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

      1. *-commutative 48.4%

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

      2. associate-/l* 48.2%

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

   7. Simplified 48.2%

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

   if 3.50000000000000002e38 < b

   1. Initial program 88.6%

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

      1. associate-+l- 88.6%

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

      2. associate-*r* 88.6%

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

      3. associate-*r* 86.8%

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

      4. *-un-lft-identity 86.8%

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

      5. times-frac 79.9%

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

      6. associate--r- 79.9%

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

      7. fma-neg 79.9%

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

      8. associate-*r* 83.5%

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

      9. distribute-rgt-neg-in 83.5%

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

      10. associate-*l* 83.5%

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

   3. Applied egg-rr 83.5%

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

   4. Taylor expanded in b around inf 58.7%

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

4. Final simplification 54.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2 \cdot 10^{+42}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{elif}\;b \leq 3.5 \cdot 10^{+38}:\\ \;\;\;\;-4 \cdot \frac{t}{\frac{c}{a}}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{z} \cdot \frac{b}{c}\\ \end{array} \]

Alternative 16: 50.4% accurate, 1.7× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;b \leq -8.5 \cdot 10^{+21}:\\ \;\;\;\;\frac{1}{\frac{z}{\frac{b}{c}}}\\ \mathbf{elif}\;b \leq 2.9 \cdot 10^{+38}:\\ \;\;\;\;-4 \cdot \frac{t}{\frac{c}{a}}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{z} \cdot \frac{b}{c}\\ \end{array} \end{array} \]

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 -8.5e+21)
   (/ 1.0 (/ z (/ b c)))
   (if (<= b 2.9e+38) (* -4.0 (/ t (/ c a))) (* (/ 1.0 z) (/ b 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 <= -8.5e+21) {
		tmp = 1.0 / (z / (b / c));
	} else if (b <= 2.9e+38) {
		tmp = -4.0 * (t / (c / a));
	} else {
		tmp = (1.0 / z) * (b / 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 <= (-8.5d+21)) then
        tmp = 1.0d0 / (z / (b / c))
    else if (b <= 2.9d+38) then
        tmp = (-4.0d0) * (t / (c / a))
    else
        tmp = (1.0d0 / z) * (b / 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 <= -8.5e+21) {
		tmp = 1.0 / (z / (b / c));
	} else if (b <= 2.9e+38) {
		tmp = -4.0 * (t / (c / a));
	} else {
		tmp = (1.0 / z) * (b / 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 <= -8.5e+21:
		tmp = 1.0 / (z / (b / c))
	elif b <= 2.9e+38:
		tmp = -4.0 * (t / (c / a))
	else:
		tmp = (1.0 / z) * (b / 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 <= -8.5e+21)
		tmp = Float64(1.0 / Float64(z / Float64(b / c)));
	elseif (b <= 2.9e+38)
		tmp = Float64(-4.0 * Float64(t / Float64(c / a)));
	else
		tmp = Float64(Float64(1.0 / z) * Float64(b / 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 <= -8.5e+21)
		tmp = 1.0 / (z / (b / c));
	elseif (b <= 2.9e+38)
		tmp = -4.0 * (t / (c / a));
	else
		tmp = (1.0 / z) * (b / 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, -8.5e+21], N[(1.0 / N[(z / N[(b / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.9e+38], N[(-4.0 * N[(t / N[(c / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(1.0 / z), $MachinePrecision] * N[(b / c), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -8.5e21

   1. Initial program 75.7%

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

   2. Taylor expanded in b around inf 59.6%

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

      1. *-commutative 59.6%

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

   4. Simplified 59.6%

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

      1. clear-num 59.6%

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

      2. inv-pow 59.6%

         \[\leadsto \color{blue}{{\left(\frac{z \cdot c}{b}\right)}^{-1}} \]

   6. Applied egg-rr 59.6%

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

      1. unpow-1 59.6%

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

      2. associate-/l* 64.4%

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

   8. Simplified 64.4%

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

   if -8.5e21 < b < 2.90000000000000007e38

   1. Initial program 77.8%

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

   2. Taylor expanded in z around inf 48.9%

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

      1. *-commutative 48.9%

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

      2. associate-/l* 51.7%

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

   4. Simplified 51.7%

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

   5. Taylor expanded in a around 0 48.9%

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

      1. *-commutative 48.9%

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

      2. associate-/l* 48.7%

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

   7. Simplified 48.7%

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

   if 2.90000000000000007e38 < b

   1. Initial program 88.6%

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

      1. associate-+l- 88.6%

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

      2. associate-*r* 88.6%

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

      3. associate-*r* 86.8%

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

      4. *-un-lft-identity 86.8%

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

      5. times-frac 79.9%

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

      6. associate--r- 79.9%

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

      7. fma-neg 79.9%

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

      8. associate-*r* 83.5%

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

      9. distribute-rgt-neg-in 83.5%

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

      10. associate-*l* 83.5%

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

   3. Applied egg-rr 83.5%

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

   4. Taylor expanded in b around inf 58.7%

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

4. Final simplification 54.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -8.5 \cdot 10^{+21}:\\ \;\;\;\;\frac{1}{\frac{z}{\frac{b}{c}}}\\ \mathbf{elif}\;b \leq 2.9 \cdot 10^{+38}:\\ \;\;\;\;-4 \cdot \frac{t}{\frac{c}{a}}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{z} \cdot \frac{b}{c}\\ \end{array} \]

Alternative 17: 34.8% accurate, 2.7× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ b \cdot \frac{1}{z \cdot c} \end{array} \]

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 (/ 1.0 (* 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) {
	return b * (1.0 / (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 * (1.0d0 / (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 * (1.0 / (z * c));
}

Python

[x, y] = sort([x, y])
[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	return b * (1.0 / (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(1.0 / 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 * (1.0 / (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[(1.0 / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 79.5%

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

2. Taylor expanded in b around inf 35.6%

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

   1. *-commutative 35.6%

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

4. Simplified 35.6%

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

   1. div-inv 36.8%

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

6. Applied egg-rr 36.8%

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

7. Final simplification 36.8%

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

Alternative 18: 34.7% 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 79.5%

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

2. Taylor expanded in b around inf 35.6%

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

   1. *-commutative 35.6%

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

4. Simplified 35.6%

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

5. Final simplification 35.6%

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

Developer target: 80.8% 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 2023336 
(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)))