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

Percentage Accurate: 79.5% → 88.8%

Time: 18.0s

Alternatives: 17

Speedup: 0.8×

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

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 79.5% 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: 88.8% accurate, 0.1× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;c \leq -3 \cdot 10^{-41} \lor \neg \left(c \leq 2.5 \cdot 10^{+14}\right):\\ \;\;\;\;\mathsf{fma}\left(-4, \frac{a}{\frac{c}{t}}, \mathsf{fma}\left(9, \frac{x}{c} \cdot \frac{y}{z}, \frac{b}{c \cdot z}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(-4 \cdot \left(a \cdot t\right) + \left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right)\right) \cdot \frac{1}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= c -3e-41) (not (<= c 2.5e+14)))
   (fma -4.0 (/ a (/ c t)) (fma 9.0 (* (/ x c) (/ y z)) (/ b (* c z))))
   (* (+ (* -4.0 (* a t)) (+ (* 9.0 (/ (* x y) z)) (/ b z))) (/ 1.0 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 ((c <= -3e-41) || !(c <= 2.5e+14)) {
		tmp = fma(-4.0, (a / (c / t)), fma(9.0, ((x / c) * (y / z)), (b / (c * z))));
	} else {
		tmp = ((-4.0 * (a * t)) + ((9.0 * ((x * y) / z)) + (b / z))) * (1.0 / 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 ((c <= -3e-41) || !(c <= 2.5e+14))
		tmp = fma(-4.0, Float64(a / Float64(c / t)), fma(9.0, Float64(Float64(x / c) * Float64(y / z)), Float64(b / Float64(c * z))));
	else
		tmp = Float64(Float64(Float64(-4.0 * Float64(a * t)) + Float64(Float64(9.0 * Float64(Float64(x * y) / z)) + Float64(b / z))) * Float64(1.0 / c));
	end
	return tmp
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[c, -3e-41], N[Not[LessEqual[c, 2.5e+14]], $MachinePrecision]], N[(-4.0 * N[(a / N[(c / t), $MachinePrecision]), $MachinePrecision] + N[(9.0 * N[(N[(x / c), $MachinePrecision] * N[(y / z), $MachinePrecision]), $MachinePrecision] + N[(b / N[(c * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision] + N[(N[(9.0 * N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] + N[(b / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(1.0 / c), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -2.99999999999999989e-41 or 2.5e14 < c

   1. Initial program 69.5%

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

   2. Taylor expanded in x around 0 79.6%

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

      1. cancel-sign-sub-inv 79.6%

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

      2. metadata-eval 79.6%

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

      3. +-commutative 79.6%

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

      4. fma-def 79.6%

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

      5. associate-/l* 84.4%

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

      6. fma-def 84.4%

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

      7. times-frac 89.0%

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

      8. *-commutative 89.0%

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

   4. Simplified 89.0%

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

   if -2.99999999999999989e-41 < c < 2.5e14

   1. Initial program 92.4%

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

      1. associate-/r* 94.0%

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

      2. associate-+l- 94.0%

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

      3. associate-*r* 94.0%

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

      4. associate-*r* 94.8%

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

      5. div-inv 94.8%

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

      6. associate--r- 94.8%

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

      7. fma-neg 94.8%

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

      8. associate-*r* 94.0%

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

      9. distribute-rgt-neg-in 94.0%

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

      10. associate-*l* 94.9%

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

   3. Applied egg-rr 94.9%

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

   4. Taylor expanded in x around 0 96.4%

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

4. Final simplification 92.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -3 \cdot 10^{-41} \lor \neg \left(c \leq 2.5 \cdot 10^{+14}\right):\\ \;\;\;\;\mathsf{fma}\left(-4, \frac{a}{\frac{c}{t}}, \mathsf{fma}\left(9, \frac{x}{c} \cdot \frac{y}{z}, \frac{b}{c \cdot z}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(-4 \cdot \left(a \cdot t\right) + \left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right)\right) \cdot \frac{1}{c}\\ \end{array} \]

Alternative 2: 91.5% accurate, 0.1× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -800 \lor \neg \left(z \leq 3.1 \cdot 10^{-71}\right):\\ \;\;\;\;\left(-4 \cdot \left(a \cdot t\right) + \left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right)\right) \cdot \frac{1}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{z} \cdot \frac{\mathsf{fma}\left(x, 9 \cdot y, \mathsf{fma}\left(t, z \cdot \left(-4 \cdot a\right), b\right)\right)}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= z -800.0) (not (<= z 3.1e-71)))
   (* (+ (* -4.0 (* a t)) (+ (* 9.0 (/ (* x y) z)) (/ b z))) (/ 1.0 c))
   (* (/ 1.0 z) (/ (fma x (* 9.0 y) (fma t (* z (* -4.0 a)) 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 ((z <= -800.0) || !(z <= 3.1e-71)) {
		tmp = ((-4.0 * (a * t)) + ((9.0 * ((x * y) / z)) + (b / z))) * (1.0 / c);
	} else {
		tmp = (1.0 / z) * (fma(x, (9.0 * y), fma(t, (z * (-4.0 * a)), 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 ((z <= -800.0) || !(z <= 3.1e-71))
		tmp = Float64(Float64(Float64(-4.0 * Float64(a * t)) + Float64(Float64(9.0 * Float64(Float64(x * y) / z)) + Float64(b / z))) * Float64(1.0 / c));
	else
		tmp = Float64(Float64(1.0 / z) * Float64(fma(x, Float64(9.0 * y), fma(t, Float64(z * Float64(-4.0 * a)), b)) / c));
	end
	return tmp
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[z, -800.0], N[Not[LessEqual[z, 3.1e-71]], $MachinePrecision]], N[(N[(N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision] + N[(N[(9.0 * N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] + N[(b / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(1.0 / c), $MachinePrecision]), $MachinePrecision], N[(N[(1.0 / z), $MachinePrecision] * N[(N[(x * N[(9.0 * y), $MachinePrecision] + N[(t * N[(z * N[(-4.0 * a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -800 or 3.10000000000000002e-71 < z

   1. Initial program 66.1%

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

      1. associate-/r* 73.4%

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

      2. associate-+l- 73.3%

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

      3. associate-*r* 73.4%

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

      4. associate-*r* 77.5%

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

      5. div-inv 77.5%

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

      6. associate--r- 77.5%

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

      7. fma-neg 77.5%

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

      8. associate-*r* 73.4%

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

      9. distribute-rgt-neg-in 73.4%

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

      10. associate-*l* 74.1%

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

   3. Applied egg-rr 74.1%

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

   4. Taylor expanded in x around 0 86.9%

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

   if -800 < z < 3.10000000000000002e-71

   1. Initial program 96.4%

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

   3. Simplified 95.6%

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

      1. *-un-lft-identity 95.6%

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

      2. times-frac 95.9%

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

      3. +-commutative 95.9%

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

      4. fma-def 95.9%

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

   5. Applied egg-rr 95.9%

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

4. Final simplification 90.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -800 \lor \neg \left(z \leq 3.1 \cdot 10^{-71}\right):\\ \;\;\;\;\left(-4 \cdot \left(a \cdot t\right) + \left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right)\right) \cdot \frac{1}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{z} \cdot \frac{\mathsf{fma}\left(x, 9 \cdot y, \mathsf{fma}\left(t, z \cdot \left(-4 \cdot a\right), b\right)\right)}{c}\\ \end{array} \]

Alternative 3: 90.1% accurate, 0.2× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+157} \lor \neg \left(z \leq 10^{-13}\right):\\ \;\;\;\;\left(-4 \cdot \left(a \cdot t\right) + \left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right)\right) \cdot \frac{1}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, 9 \cdot y, b + t \cdot \left(z \cdot \left(-4 \cdot a\right)\right)\right)}{c \cdot z}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= z -2.5e+157) (not (<= z 1e-13)))
   (* (+ (* -4.0 (* a t)) (+ (* 9.0 (/ (* x y) z)) (/ b z))) (/ 1.0 c))
   (/ (fma x (* 9.0 y) (+ b (* t (* z (* -4.0 a))))) (* c z))))

C

assert(x < y);
assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((z <= -2.5e+157) || !(z <= 1e-13)) {
		tmp = ((-4.0 * (a * t)) + ((9.0 * ((x * y) / z)) + (b / z))) * (1.0 / c);
	} else {
		tmp = fma(x, (9.0 * y), (b + (t * (z * (-4.0 * a))))) / (c * z);
	}
	return tmp;
}

Julia

x, y = sort([x, y])
t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((z <= -2.5e+157) || !(z <= 1e-13))
		tmp = Float64(Float64(Float64(-4.0 * Float64(a * t)) + Float64(Float64(9.0 * Float64(Float64(x * y) / z)) + Float64(b / z))) * Float64(1.0 / c));
	else
		tmp = Float64(fma(x, Float64(9.0 * y), Float64(b + Float64(t * Float64(z * Float64(-4.0 * a))))) / Float64(c * z));
	end
	return tmp
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[z, -2.5e+157], N[Not[LessEqual[z, 1e-13]], $MachinePrecision]], N[(N[(N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision] + N[(N[(9.0 * N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] + N[(b / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(1.0 / c), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(9.0 * y), $MachinePrecision] + N[(b + N[(t * N[(z * N[(-4.0 * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(c * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.49999999999999988e157 or 1e-13 < z

   1. Initial program 59.7%

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

      1. associate-/r* 69.1%

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

      2. associate-+l- 69.1%

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

      3. associate-*r* 69.1%

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

      4. associate-*r* 74.4%

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

      5. div-inv 74.4%

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

      6. associate--r- 74.5%

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

      7. fma-neg 74.5%

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

      8. associate-*r* 69.1%

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

      9. distribute-rgt-neg-in 69.1%

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

      10. associate-*l* 70.0%

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

   3. Applied egg-rr 70.0%

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

   4. Taylor expanded in x around 0 86.6%

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

   if -2.49999999999999988e157 < z < 1e-13

   1. Initial program 94.6%

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

   3. Simplified 94.0%

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

4. Final simplification 90.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+157} \lor \neg \left(z \leq 10^{-13}\right):\\ \;\;\;\;\left(-4 \cdot \left(a \cdot t\right) + \left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right)\right) \cdot \frac{1}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, 9 \cdot y, b + t \cdot \left(z \cdot \left(-4 \cdot a\right)\right)\right)}{c \cdot z}\\ \end{array} \]

Alternative 4: 91.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{+102} \lor \neg \left(z \leq 2.2 \cdot 10^{-13}\right):\\ \;\;\;\;\left(-4 \cdot \left(a \cdot t\right) + \left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right)\right) \cdot \frac{1}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(9 \cdot x\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{c \cdot z}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= z -3.2e+102) (not (<= z 2.2e-13)))
   (* (+ (* -4.0 (* a t)) (+ (* 9.0 (/ (* x y) z)) (/ b z))) (/ 1.0 c))
   (/ (+ b (- (* y (* 9.0 x)) (* a (* t (* z 4.0))))) (* c z))))

C

assert(x < y);
assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((z <= -3.2e+102) || !(z <= 2.2e-13)) {
		tmp = ((-4.0 * (a * t)) + ((9.0 * ((x * y) / z)) + (b / z))) * (1.0 / c);
	} else {
		tmp = (b + ((y * (9.0 * x)) - (a * (t * (z * 4.0))))) / (c * z);
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if ((z <= (-3.2d+102)) .or. (.not. (z <= 2.2d-13))) then
        tmp = (((-4.0d0) * (a * t)) + ((9.0d0 * ((x * y) / z)) + (b / z))) * (1.0d0 / c)
    else
        tmp = (b + ((y * (9.0d0 * x)) - (a * (t * (z * 4.0d0))))) / (c * z)
    end if
    code = tmp
end function

Java

assert x < y;
assert t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((z <= -3.2e+102) || !(z <= 2.2e-13)) {
		tmp = ((-4.0 * (a * t)) + ((9.0 * ((x * y) / z)) + (b / z))) * (1.0 / c);
	} else {
		tmp = (b + ((y * (9.0 * x)) - (a * (t * (z * 4.0))))) / (c * z);
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if (z <= -3.2e+102) or not (z <= 2.2e-13):
		tmp = ((-4.0 * (a * t)) + ((9.0 * ((x * y) / z)) + (b / z))) * (1.0 / c)
	else:
		tmp = (b + ((y * (9.0 * x)) - (a * (t * (z * 4.0))))) / (c * z)
	return tmp

Julia

x, y = sort([x, y])
t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((z <= -3.2e+102) || !(z <= 2.2e-13))
		tmp = Float64(Float64(Float64(-4.0 * Float64(a * t)) + Float64(Float64(9.0 * Float64(Float64(x * y) / z)) + Float64(b / z))) * Float64(1.0 / c));
	else
		tmp = Float64(Float64(b + Float64(Float64(y * Float64(9.0 * x)) - Float64(a * Float64(t * Float64(z * 4.0))))) / Float64(c * z));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((z <= -3.2e+102) || ~((z <= 2.2e-13)))
		tmp = ((-4.0 * (a * t)) + ((9.0 * ((x * y) / z)) + (b / z))) * (1.0 / c);
	else
		tmp = (b + ((y * (9.0 * x)) - (a * (t * (z * 4.0))))) / (c * z);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[z, -3.2e+102], N[Not[LessEqual[z, 2.2e-13]], $MachinePrecision]], N[(N[(N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision] + N[(N[(9.0 * N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] + N[(b / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(1.0 / c), $MachinePrecision]), $MachinePrecision], N[(N[(b + N[(N[(y * N[(9.0 * x), $MachinePrecision]), $MachinePrecision] - N[(a * N[(t * N[(z * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(c * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.1999999999999999e102 or 2.19999999999999997e-13 < z

   1. Initial program 62.2%

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

      1. associate-/r* 70.9%

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

      2. associate-+l- 70.9%

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

      3. associate-*r* 70.9%

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

      4. associate-*r* 75.8%

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

      5. div-inv 75.8%

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

      6. associate--r- 75.8%

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

      7. fma-neg 75.8%

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

      8. associate-*r* 70.9%

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

      9. distribute-rgt-neg-in 70.9%

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

      10. associate-*l* 71.7%

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

   3. Applied egg-rr 71.7%

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

   4. Taylor expanded in x around 0 86.9%

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

   if -3.1999999999999999e102 < z < 2.19999999999999997e-13

   1. Initial program 94.9%

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

4. Final simplification 91.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{+102} \lor \neg \left(z \leq 2.2 \cdot 10^{-13}\right):\\ \;\;\;\;\left(-4 \cdot \left(a \cdot t\right) + \left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right)\right) \cdot \frac{1}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(9 \cdot x\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{c \cdot z}\\ \end{array} \]

Alternative 5: 85.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} t_1 := -4 \cdot \left(a \cdot t\right)\\ \mathbf{if}\;z \leq -2 \cdot 10^{+186}:\\ \;\;\;\;\frac{t_1 + \frac{b}{z}}{c}\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{+106}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(9 \cdot x\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t_1 + 9 \cdot \frac{x \cdot y}{z}}{c}\\ \end{array} \end{array} \]

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 (* -4.0 (* a t))))
   (if (<= z -2e+186)
     (/ (+ t_1 (/ b z)) c)
     (if (<= z 1.3e+106)
       (/ (+ b (- (* y (* 9.0 x)) (* a (* t (* z 4.0))))) (* c z))
       (/ (+ t_1 (* 9.0 (/ (* x y) 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 = -4.0 * (a * t);
	double tmp;
	if (z <= -2e+186) {
		tmp = (t_1 + (b / z)) / c;
	} else if (z <= 1.3e+106) {
		tmp = (b + ((y * (9.0 * x)) - (a * (t * (z * 4.0))))) / (c * z);
	} else {
		tmp = (t_1 + (9.0 * ((x * y) / 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) :: tmp
    t_1 = (-4.0d0) * (a * t)
    if (z <= (-2d+186)) then
        tmp = (t_1 + (b / z)) / c
    else if (z <= 1.3d+106) then
        tmp = (b + ((y * (9.0d0 * x)) - (a * (t * (z * 4.0d0))))) / (c * z)
    else
        tmp = (t_1 + (9.0d0 * ((x * y) / 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 = -4.0 * (a * t);
	double tmp;
	if (z <= -2e+186) {
		tmp = (t_1 + (b / z)) / c;
	} else if (z <= 1.3e+106) {
		tmp = (b + ((y * (9.0 * x)) - (a * (t * (z * 4.0))))) / (c * z);
	} else {
		tmp = (t_1 + (9.0 * ((x * y) / 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 = -4.0 * (a * t)
	tmp = 0
	if z <= -2e+186:
		tmp = (t_1 + (b / z)) / c
	elif z <= 1.3e+106:
		tmp = (b + ((y * (9.0 * x)) - (a * (t * (z * 4.0))))) / (c * z)
	else:
		tmp = (t_1 + (9.0 * ((x * y) / 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(-4.0 * Float64(a * t))
	tmp = 0.0
	if (z <= -2e+186)
		tmp = Float64(Float64(t_1 + Float64(b / z)) / c);
	elseif (z <= 1.3e+106)
		tmp = Float64(Float64(b + Float64(Float64(y * Float64(9.0 * x)) - Float64(a * Float64(t * Float64(z * 4.0))))) / Float64(c * z));
	else
		tmp = Float64(Float64(t_1 + Float64(9.0 * Float64(Float64(x * y) / 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 = -4.0 * (a * t);
	tmp = 0.0;
	if (z <= -2e+186)
		tmp = (t_1 + (b / z)) / c;
	elseif (z <= 1.3e+106)
		tmp = (b + ((y * (9.0 * x)) - (a * (t * (z * 4.0))))) / (c * z);
	else
		tmp = (t_1 + (9.0 * ((x * y) / 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[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2e+186], N[(N[(t$95$1 + N[(b / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[z, 1.3e+106], N[(N[(b + N[(N[(y * N[(9.0 * x), $MachinePrecision]), $MachinePrecision] - N[(a * N[(t * N[(z * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(c * z), $MachinePrecision]), $MachinePrecision], N[(N[(t$95$1 + N[(9.0 * N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.99999999999999996e186

   1. Initial program 51.1%

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

      1. associate-/r* 77.7%

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

      2. associate-+l- 77.7%

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

      3. associate-*r* 77.7%

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

      4. associate-*r* 81.0%

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

      5. div-inv 81.0%

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

      6. associate--r- 81.0%

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

      7. fma-neg 81.0%

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

      8. associate-*r* 77.7%

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

      9. distribute-rgt-neg-in 77.7%

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

      10. associate-*l* 77.7%

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

   3. Applied egg-rr 77.7%

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

   4. Taylor expanded in x around 0 93.4%

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

   5. Taylor expanded in x around 0 81.3%

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

   if -1.99999999999999996e186 < z < 1.3000000000000001e106

   1. Initial program 90.4%

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

   if 1.3000000000000001e106 < z

   1. Initial program 53.6%

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

      1. associate-/r* 58.6%

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

      2. associate-+l- 58.6%

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

      3. associate-*r* 58.7%

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

      4. associate-*r* 63.3%

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

      5. div-inv 63.3%

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

      6. associate--r- 63.3%

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

      7. fma-neg 63.3%

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

      8. associate-*r* 58.7%

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

      9. distribute-rgt-neg-in 58.7%

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

      10. associate-*l* 61.0%

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

   3. Applied egg-rr 61.0%

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

   4. Taylor expanded in x around 0 81.5%

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

   5. Taylor expanded in b around 0 72.4%

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

4. Final simplification 86.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+186}:\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right) + \frac{b}{z}}{c}\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{+106}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(9 \cdot x\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right) + 9 \cdot \frac{x \cdot y}{z}}{c}\\ \end{array} \]

Alternative 6: 74.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} t_1 := -4 \cdot \left(a \cdot t\right)\\ \mathbf{if}\;b \leq -7 \cdot 10^{+69}:\\ \;\;\;\;\frac{b + y \cdot \left(9 \cdot x\right)}{c \cdot z}\\ \mathbf{elif}\;b \leq 4.2 \cdot 10^{-33}:\\ \;\;\;\;\frac{t_1 + 9 \cdot \frac{x \cdot y}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{t_1 + \frac{b}{z}}{c}\\ \end{array} \end{array} \]

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 (* -4.0 (* a t))))
   (if (<= b -7e+69)
     (/ (+ b (* y (* 9.0 x))) (* c z))
     (if (<= b 4.2e-33)
       (/ (+ t_1 (* 9.0 (/ (* x y) z))) c)
       (/ (+ t_1 (/ b z)) c)))))

C

assert(x < y);
assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = -4.0 * (a * t);
	double tmp;
	if (b <= -7e+69) {
		tmp = (b + (y * (9.0 * x))) / (c * z);
	} else if (b <= 4.2e-33) {
		tmp = (t_1 + (9.0 * ((x * y) / z))) / c;
	} else {
		tmp = (t_1 + (b / z)) / c;
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (-4.0d0) * (a * t)
    if (b <= (-7d+69)) then
        tmp = (b + (y * (9.0d0 * x))) / (c * z)
    else if (b <= 4.2d-33) then
        tmp = (t_1 + (9.0d0 * ((x * y) / z))) / c
    else
        tmp = (t_1 + (b / z)) / c
    end if
    code = tmp
end function

Java

assert x < y;
assert t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = -4.0 * (a * t);
	double tmp;
	if (b <= -7e+69) {
		tmp = (b + (y * (9.0 * x))) / (c * z);
	} else if (b <= 4.2e-33) {
		tmp = (t_1 + (9.0 * ((x * y) / z))) / c;
	} else {
		tmp = (t_1 + (b / z)) / c;
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	t_1 = -4.0 * (a * t)
	tmp = 0
	if b <= -7e+69:
		tmp = (b + (y * (9.0 * x))) / (c * z)
	elif b <= 4.2e-33:
		tmp = (t_1 + (9.0 * ((x * y) / z))) / c
	else:
		tmp = (t_1 + (b / z)) / c
	return tmp

Julia

x, y = sort([x, y])
t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(-4.0 * Float64(a * t))
	tmp = 0.0
	if (b <= -7e+69)
		tmp = Float64(Float64(b + Float64(y * Float64(9.0 * x))) / Float64(c * z));
	elseif (b <= 4.2e-33)
		tmp = Float64(Float64(t_1 + Float64(9.0 * Float64(Float64(x * y) / z))) / c);
	else
		tmp = Float64(Float64(t_1 + Float64(b / 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 = -4.0 * (a * t);
	tmp = 0.0;
	if (b <= -7e+69)
		tmp = (b + (y * (9.0 * x))) / (c * z);
	elseif (b <= 4.2e-33)
		tmp = (t_1 + (9.0 * ((x * y) / z))) / c;
	else
		tmp = (t_1 + (b / z)) / c;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -7e+69], N[(N[(b + N[(y * N[(9.0 * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(c * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 4.2e-33], N[(N[(t$95$1 + N[(9.0 * N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], N[(N[(t$95$1 + N[(b / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if b < -6.99999999999999974e69

   1. Initial program 84.6%

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

   2. Taylor expanded in z around 0 80.2%

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

      1. associate-*r* 80.3%

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

      2. *-commutative 80.3%

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

   4. Simplified 80.3%

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

   if -6.99999999999999974e69 < b < 4.2e-33

   1. Initial program 81.1%

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

      1. associate-/r* 83.5%

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

      2. associate-+l- 83.5%

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

      3. associate-*r* 83.5%

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

      4. associate-*r* 85.6%

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

      5. div-inv 85.6%

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

      6. associate--r- 85.6%

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

      7. fma-neg 85.6%

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

      8. associate-*r* 83.5%

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

      9. distribute-rgt-neg-in 83.5%

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

      10. associate-*l* 83.5%

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

   3. Applied egg-rr 83.5%

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

   4. Taylor expanded in x around 0 89.6%

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

   5. Taylor expanded in b around 0 81.3%

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

   if 4.2e-33 < b

   1. Initial program 74.1%

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

      1. associate-/r* 69.4%

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

      2. associate-+l- 69.4%

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

      3. associate-*r* 69.4%

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

      4. associate-*r* 73.4%

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

      5. div-inv 73.3%

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

      6. associate--r- 73.3%

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

      7. fma-neg 73.3%

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

      8. associate-*r* 69.3%

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

      9. distribute-rgt-neg-in 69.3%

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

      10. associate-*l* 70.6%

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

   3. Applied egg-rr 70.6%

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

   4. Taylor expanded in x around 0 78.6%

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

   5. Taylor expanded in x around 0 74.6%

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

4. Final simplification 79.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -7 \cdot 10^{+69}:\\ \;\;\;\;\frac{b + y \cdot \left(9 \cdot x\right)}{c \cdot z}\\ \mathbf{elif}\;b \leq 4.2 \cdot 10^{-33}:\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right) + 9 \cdot \frac{x \cdot y}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right) + \frac{b}{z}}{c}\\ \end{array} \]

Alternative 7: 46.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} t_1 := 9 \cdot \left(\frac{x}{c} \cdot \frac{y}{z}\right)\\ \mathbf{if}\;a \leq 3.4 \cdot 10^{-242}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 5.2 \cdot 10^{-163}:\\ \;\;\;\;b \cdot \frac{1}{c \cdot z}\\ \mathbf{elif}\;a \leq 1.18 \cdot 10^{-17}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* 9.0 (* (/ x c) (/ y z)))))
   (if (<= a 3.4e-242)
     t_1
     (if (<= a 5.2e-163)
       (* b (/ 1.0 (* c z)))
       (if (<= a 1.18e-17) t_1 (* -4.0 (/ a (/ c t))))))))

C

assert(x < y);
assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = 9.0 * ((x / c) * (y / z));
	double tmp;
	if (a <= 3.4e-242) {
		tmp = t_1;
	} else if (a <= 5.2e-163) {
		tmp = b * (1.0 / (c * z));
	} else if (a <= 1.18e-17) {
		tmp = t_1;
	} else {
		tmp = -4.0 * (a / (c / t));
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 9.0d0 * ((x / c) * (y / z))
    if (a <= 3.4d-242) then
        tmp = t_1
    else if (a <= 5.2d-163) then
        tmp = b * (1.0d0 / (c * z))
    else if (a <= 1.18d-17) then
        tmp = t_1
    else
        tmp = (-4.0d0) * (a / (c / t))
    end if
    code = tmp
end function

Java

assert x < y;
assert t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = 9.0 * ((x / c) * (y / z));
	double tmp;
	if (a <= 3.4e-242) {
		tmp = t_1;
	} else if (a <= 5.2e-163) {
		tmp = b * (1.0 / (c * z));
	} else if (a <= 1.18e-17) {
		tmp = t_1;
	} else {
		tmp = -4.0 * (a / (c / t));
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	t_1 = 9.0 * ((x / c) * (y / z))
	tmp = 0
	if a <= 3.4e-242:
		tmp = t_1
	elif a <= 5.2e-163:
		tmp = b * (1.0 / (c * z))
	elif a <= 1.18e-17:
		tmp = t_1
	else:
		tmp = -4.0 * (a / (c / t))
	return tmp

Julia

x, y = sort([x, y])
t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(9.0 * Float64(Float64(x / c) * Float64(y / z)))
	tmp = 0.0
	if (a <= 3.4e-242)
		tmp = t_1;
	elseif (a <= 5.2e-163)
		tmp = Float64(b * Float64(1.0 / Float64(c * z)));
	elseif (a <= 1.18e-17)
		tmp = t_1;
	else
		tmp = Float64(-4.0 * Float64(a / Float64(c / t)));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = 9.0 * ((x / c) * (y / z));
	tmp = 0.0;
	if (a <= 3.4e-242)
		tmp = t_1;
	elseif (a <= 5.2e-163)
		tmp = b * (1.0 / (c * z));
	elseif (a <= 1.18e-17)
		tmp = t_1;
	else
		tmp = -4.0 * (a / (c / t));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(9.0 * N[(N[(x / c), $MachinePrecision] * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, 3.4e-242], t$95$1, If[LessEqual[a, 5.2e-163], N[(b * N[(1.0 / N[(c * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.18e-17], t$95$1, N[(-4.0 * N[(a / N[(c / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if a < 3.4000000000000001e-242 or 5.20000000000000003e-163 < a < 1.18000000000000004e-17

   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. Taylor expanded in x around inf 44.9%

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

      1. times-frac 47.7%

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

   4. Simplified 47.7%

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

   if 3.4000000000000001e-242 < a < 5.20000000000000003e-163

   1. Initial program 81.5%

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

   2. Taylor expanded in b around inf 43.7%

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

      1. *-commutative 43.7%

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

   4. Simplified 43.7%

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

      1. div-inv 48.2%

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

   6. Applied egg-rr 48.2%

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

   if 1.18000000000000004e-17 < a

   1. Initial program 80.8%

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

   2. Taylor expanded in z around inf 58.0%

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

      1. *-commutative 58.0%

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

      2. associate-/l* 66.0%

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

   4. Simplified 66.0%

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

4. Final simplification 52.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 3.4 \cdot 10^{-242}:\\ \;\;\;\;9 \cdot \left(\frac{x}{c} \cdot \frac{y}{z}\right)\\ \mathbf{elif}\;a \leq 5.2 \cdot 10^{-163}:\\ \;\;\;\;b \cdot \frac{1}{c \cdot z}\\ \mathbf{elif}\;a \leq 1.18 \cdot 10^{-17}:\\ \;\;\;\;9 \cdot \left(\frac{x}{c} \cdot \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \end{array} \]

Alternative 8: 46.5% accurate, 1.3× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq 3.55 \cdot 10^{-237}:\\ \;\;\;\;9 \cdot \left(y \cdot \frac{\frac{x}{c}}{z}\right)\\ \mathbf{elif}\;a \leq 3 \cdot 10^{-163}:\\ \;\;\;\;b \cdot \frac{1}{c \cdot z}\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{-19}:\\ \;\;\;\;9 \cdot \left(\frac{x}{c} \cdot \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= a 3.55e-237)
   (* 9.0 (* y (/ (/ x c) z)))
   (if (<= a 3e-163)
     (* b (/ 1.0 (* c z)))
     (if (<= a 9.5e-19) (* 9.0 (* (/ x c) (/ y z))) (* -4.0 (/ a (/ c t)))))))

C

assert(x < y);
assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (a <= 3.55e-237) {
		tmp = 9.0 * (y * ((x / c) / z));
	} else if (a <= 3e-163) {
		tmp = b * (1.0 / (c * z));
	} else if (a <= 9.5e-19) {
		tmp = 9.0 * ((x / c) * (y / z));
	} else {
		tmp = -4.0 * (a / (c / t));
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (a <= 3.55d-237) then
        tmp = 9.0d0 * (y * ((x / c) / z))
    else if (a <= 3d-163) then
        tmp = b * (1.0d0 / (c * z))
    else if (a <= 9.5d-19) then
        tmp = 9.0d0 * ((x / c) * (y / z))
    else
        tmp = (-4.0d0) * (a / (c / t))
    end if
    code = tmp
end function

Java

assert x < y;
assert t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (a <= 3.55e-237) {
		tmp = 9.0 * (y * ((x / c) / z));
	} else if (a <= 3e-163) {
		tmp = b * (1.0 / (c * z));
	} else if (a <= 9.5e-19) {
		tmp = 9.0 * ((x / c) * (y / z));
	} else {
		tmp = -4.0 * (a / (c / t));
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if a <= 3.55e-237:
		tmp = 9.0 * (y * ((x / c) / z))
	elif a <= 3e-163:
		tmp = b * (1.0 / (c * z))
	elif a <= 9.5e-19:
		tmp = 9.0 * ((x / c) * (y / z))
	else:
		tmp = -4.0 * (a / (c / t))
	return tmp

Julia

x, y = sort([x, y])
t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (a <= 3.55e-237)
		tmp = Float64(9.0 * Float64(y * Float64(Float64(x / c) / z)));
	elseif (a <= 3e-163)
		tmp = Float64(b * Float64(1.0 / Float64(c * z)));
	elseif (a <= 9.5e-19)
		tmp = Float64(9.0 * Float64(Float64(x / c) * Float64(y / z)));
	else
		tmp = Float64(-4.0 * Float64(a / Float64(c / t)));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (a <= 3.55e-237)
		tmp = 9.0 * (y * ((x / c) / z));
	elseif (a <= 3e-163)
		tmp = b * (1.0 / (c * z));
	elseif (a <= 9.5e-19)
		tmp = 9.0 * ((x / c) * (y / z));
	else
		tmp = -4.0 * (a / (c / t));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[a, 3.55e-237], N[(9.0 * N[(y * N[(N[(x / c), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3e-163], N[(b * N[(1.0 / N[(c * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 9.5e-19], N[(9.0 * N[(N[(x / c), $MachinePrecision] * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-4.0 * N[(a / N[(c / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if a < 3.5499999999999999e-237

   1. Initial program 80.6%

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

   3. Simplified 80.0%

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

      1. *-un-lft-identity 80.0%

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

      2. times-frac 82.4%

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

      3. +-commutative 82.4%

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

      4. fma-def 82.4%

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

   5. Applied egg-rr 82.4%

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

   6. Taylor expanded in x around inf 46.7%

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

      1. times-frac 47.3%

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

      2. associate-*r/ 48.8%

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

      3. associate-/l* 47.4%

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

      4. associate-/r/ 48.3%

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

   8. Simplified 48.3%

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

   if 3.5499999999999999e-237 < a < 3.0000000000000002e-163

   1. Initial program 81.5%

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

   2. Taylor expanded in b around inf 43.7%

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

      1. *-commutative 43.7%

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

   4. Simplified 43.7%

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

      1. div-inv 48.2%

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

   6. Applied egg-rr 48.2%

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

   if 3.0000000000000002e-163 < a < 9.4999999999999995e-19

   1. Initial program 72.6%

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

   2. Taylor expanded in x around inf 37.9%

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

      1. times-frac 49.4%

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

   4. Simplified 49.4%

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

   if 9.4999999999999995e-19 < a

   1. Initial program 80.8%

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

   2. Taylor expanded in z around inf 58.0%

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

      1. *-commutative 58.0%

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

      2. associate-/l* 66.0%

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

   4. Simplified 66.0%

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

4. Final simplification 53.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 3.55 \cdot 10^{-237}:\\ \;\;\;\;9 \cdot \left(y \cdot \frac{\frac{x}{c}}{z}\right)\\ \mathbf{elif}\;a \leq 3 \cdot 10^{-163}:\\ \;\;\;\;b \cdot \frac{1}{c \cdot z}\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{-19}:\\ \;\;\;\;9 \cdot \left(\frac{x}{c} \cdot \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \end{array} \]

Alternative 9: 46.5% accurate, 1.3× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq 3.4 \cdot 10^{-237}:\\ \;\;\;\;9 \cdot \left(y \cdot \frac{\frac{x}{c}}{z}\right)\\ \mathbf{elif}\;a \leq 1.02 \cdot 10^{-162}:\\ \;\;\;\;b \cdot \frac{1}{c \cdot z}\\ \mathbf{elif}\;a \leq 1.3 \cdot 10^{-20}:\\ \;\;\;\;9 \cdot \frac{x}{c \cdot \frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= a 3.4e-237)
   (* 9.0 (* y (/ (/ x c) z)))
   (if (<= a 1.02e-162)
     (* b (/ 1.0 (* c z)))
     (if (<= a 1.3e-20) (* 9.0 (/ x (* c (/ z y)))) (* -4.0 (/ a (/ c t)))))))

C

assert(x < y);
assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (a <= 3.4e-237) {
		tmp = 9.0 * (y * ((x / c) / z));
	} else if (a <= 1.02e-162) {
		tmp = b * (1.0 / (c * z));
	} else if (a <= 1.3e-20) {
		tmp = 9.0 * (x / (c * (z / y)));
	} else {
		tmp = -4.0 * (a / (c / t));
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (a <= 3.4d-237) then
        tmp = 9.0d0 * (y * ((x / c) / z))
    else if (a <= 1.02d-162) then
        tmp = b * (1.0d0 / (c * z))
    else if (a <= 1.3d-20) then
        tmp = 9.0d0 * (x / (c * (z / y)))
    else
        tmp = (-4.0d0) * (a / (c / t))
    end if
    code = tmp
end function

Java

assert x < y;
assert t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (a <= 3.4e-237) {
		tmp = 9.0 * (y * ((x / c) / z));
	} else if (a <= 1.02e-162) {
		tmp = b * (1.0 / (c * z));
	} else if (a <= 1.3e-20) {
		tmp = 9.0 * (x / (c * (z / y)));
	} else {
		tmp = -4.0 * (a / (c / t));
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if a <= 3.4e-237:
		tmp = 9.0 * (y * ((x / c) / z))
	elif a <= 1.02e-162:
		tmp = b * (1.0 / (c * z))
	elif a <= 1.3e-20:
		tmp = 9.0 * (x / (c * (z / y)))
	else:
		tmp = -4.0 * (a / (c / t))
	return tmp

Julia

x, y = sort([x, y])
t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (a <= 3.4e-237)
		tmp = Float64(9.0 * Float64(y * Float64(Float64(x / c) / z)));
	elseif (a <= 1.02e-162)
		tmp = Float64(b * Float64(1.0 / Float64(c * z)));
	elseif (a <= 1.3e-20)
		tmp = Float64(9.0 * Float64(x / Float64(c * Float64(z / y))));
	else
		tmp = Float64(-4.0 * Float64(a / Float64(c / t)));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (a <= 3.4e-237)
		tmp = 9.0 * (y * ((x / c) / z));
	elseif (a <= 1.02e-162)
		tmp = b * (1.0 / (c * z));
	elseif (a <= 1.3e-20)
		tmp = 9.0 * (x / (c * (z / y)));
	else
		tmp = -4.0 * (a / (c / t));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[a, 3.4e-237], N[(9.0 * N[(y * N[(N[(x / c), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.02e-162], N[(b * N[(1.0 / N[(c * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.3e-20], N[(9.0 * N[(x / N[(c * N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-4.0 * N[(a / N[(c / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if a < 3.4000000000000002e-237

   1. Initial program 80.6%

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

   3. Simplified 80.0%

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

      1. *-un-lft-identity 80.0%

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

      2. times-frac 82.4%

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

      3. +-commutative 82.4%

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

      4. fma-def 82.4%

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

   5. Applied egg-rr 82.4%

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

   6. Taylor expanded in x around inf 46.7%

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

      1. times-frac 47.3%

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

      2. associate-*r/ 48.8%

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

      3. associate-/l* 47.4%

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

      4. associate-/r/ 48.3%

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

   8. Simplified 48.3%

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

   if 3.4000000000000002e-237 < a < 1.01999999999999998e-162

   1. Initial program 81.5%

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

   2. Taylor expanded in b around inf 43.7%

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

      1. *-commutative 43.7%

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

   4. Simplified 43.7%

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

      1. div-inv 48.2%

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

   6. Applied egg-rr 48.2%

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

   if 1.01999999999999998e-162 < a < 1.29999999999999997e-20

   1. Initial program 72.6%

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

      1. associate-/r* 68.0%

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

      2. associate-+l- 68.0%

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

      3. associate-*r* 68.1%

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

      4. associate-*r* 71.0%

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

      5. div-inv 71.2%

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

      6. associate--r- 71.2%

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

      7. fma-neg 71.2%

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

      8. associate-*r* 68.2%

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

      9. distribute-rgt-neg-in 68.2%

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

      10. associate-*l* 68.2%

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

   3. Applied egg-rr 68.2%

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

   4. Taylor expanded in x around 0 77.1%

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

   5. Taylor expanded in x around inf 37.9%

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

      1. associate-/l* 52.1%

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

      2. associate-*r/ 55.1%

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

   7. Simplified 55.1%

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

   if 1.29999999999999997e-20 < a

   1. Initial program 80.8%

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

   2. Taylor expanded in z around inf 58.0%

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

      1. *-commutative 58.0%

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

      2. associate-/l* 66.0%

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

   4. Simplified 66.0%

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

4. Final simplification 54.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 3.4 \cdot 10^{-237}:\\ \;\;\;\;9 \cdot \left(y \cdot \frac{\frac{x}{c}}{z}\right)\\ \mathbf{elif}\;a \leq 1.02 \cdot 10^{-162}:\\ \;\;\;\;b \cdot \frac{1}{c \cdot z}\\ \mathbf{elif}\;a \leq 1.3 \cdot 10^{-20}:\\ \;\;\;\;9 \cdot \frac{x}{c \cdot \frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \end{array} \]

Alternative 10: 46.4% accurate, 1.3× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq 5.3 \cdot 10^{-239}:\\ \;\;\;\;9 \cdot \left(y \cdot \frac{\frac{x}{c}}{z}\right)\\ \mathbf{elif}\;a \leq 2.3 \cdot 10^{-163}:\\ \;\;\;\;b \cdot \frac{1}{c \cdot z}\\ \mathbf{elif}\;a \leq 5.5 \cdot 10^{-22}:\\ \;\;\;\;\frac{9 \cdot x}{c \cdot \frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= a 5.3e-239)
   (* 9.0 (* y (/ (/ x c) z)))
   (if (<= a 2.3e-163)
     (* b (/ 1.0 (* c z)))
     (if (<= a 5.5e-22) (/ (* 9.0 x) (* c (/ z y))) (* -4.0 (/ a (/ c t)))))))

C

assert(x < y);
assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (a <= 5.3e-239) {
		tmp = 9.0 * (y * ((x / c) / z));
	} else if (a <= 2.3e-163) {
		tmp = b * (1.0 / (c * z));
	} else if (a <= 5.5e-22) {
		tmp = (9.0 * x) / (c * (z / y));
	} else {
		tmp = -4.0 * (a / (c / t));
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (a <= 5.3d-239) then
        tmp = 9.0d0 * (y * ((x / c) / z))
    else if (a <= 2.3d-163) then
        tmp = b * (1.0d0 / (c * z))
    else if (a <= 5.5d-22) then
        tmp = (9.0d0 * x) / (c * (z / y))
    else
        tmp = (-4.0d0) * (a / (c / t))
    end if
    code = tmp
end function

Java

assert x < y;
assert t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (a <= 5.3e-239) {
		tmp = 9.0 * (y * ((x / c) / z));
	} else if (a <= 2.3e-163) {
		tmp = b * (1.0 / (c * z));
	} else if (a <= 5.5e-22) {
		tmp = (9.0 * x) / (c * (z / y));
	} else {
		tmp = -4.0 * (a / (c / t));
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if a <= 5.3e-239:
		tmp = 9.0 * (y * ((x / c) / z))
	elif a <= 2.3e-163:
		tmp = b * (1.0 / (c * z))
	elif a <= 5.5e-22:
		tmp = (9.0 * x) / (c * (z / y))
	else:
		tmp = -4.0 * (a / (c / t))
	return tmp

Julia

x, y = sort([x, y])
t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (a <= 5.3e-239)
		tmp = Float64(9.0 * Float64(y * Float64(Float64(x / c) / z)));
	elseif (a <= 2.3e-163)
		tmp = Float64(b * Float64(1.0 / Float64(c * z)));
	elseif (a <= 5.5e-22)
		tmp = Float64(Float64(9.0 * x) / Float64(c * Float64(z / y)));
	else
		tmp = Float64(-4.0 * Float64(a / Float64(c / t)));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (a <= 5.3e-239)
		tmp = 9.0 * (y * ((x / c) / z));
	elseif (a <= 2.3e-163)
		tmp = b * (1.0 / (c * z));
	elseif (a <= 5.5e-22)
		tmp = (9.0 * x) / (c * (z / y));
	else
		tmp = -4.0 * (a / (c / t));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[a, 5.3e-239], N[(9.0 * N[(y * N[(N[(x / c), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.3e-163], N[(b * N[(1.0 / N[(c * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 5.5e-22], N[(N[(9.0 * x), $MachinePrecision] / N[(c * N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-4.0 * N[(a / N[(c / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if a < 5.2999999999999997e-239

   1. Initial program 80.6%

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

   3. Simplified 80.0%

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

      1. *-un-lft-identity 80.0%

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

      2. times-frac 82.4%

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

      3. +-commutative 82.4%

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

      4. fma-def 82.4%

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

   5. Applied egg-rr 82.4%

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

   6. Taylor expanded in x around inf 46.7%

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

      1. times-frac 47.3%

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

      2. associate-*r/ 48.8%

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

      3. associate-/l* 47.4%

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

      4. associate-/r/ 48.3%

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

   8. Simplified 48.3%

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

   if 5.2999999999999997e-239 < a < 2.2999999999999999e-163

   1. Initial program 81.5%

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

   2. Taylor expanded in b around inf 43.7%

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

      1. *-commutative 43.7%

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

   4. Simplified 43.7%

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

      1. div-inv 48.2%

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

   6. Applied egg-rr 48.2%

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

   if 2.2999999999999999e-163 < a < 5.5000000000000001e-22

   1. Initial program 72.6%

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

      1. associate-/r* 68.0%

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

      2. associate-+l- 68.0%

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

      3. associate-*r* 68.1%

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

      4. associate-*r* 71.0%

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

      5. div-inv 71.2%

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

      6. associate--r- 71.2%

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

      7. fma-neg 71.2%

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

      8. associate-*r* 68.2%

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

      9. distribute-rgt-neg-in 68.2%

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

      10. associate-*l* 68.2%

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

   3. Applied egg-rr 68.2%

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

   4. Taylor expanded in x around 0 77.1%

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

   5. Taylor expanded in x around inf 37.9%

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

      1. associate-/l* 52.1%

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

      2. associate-*r/ 55.1%

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

   7. Simplified 55.1%

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

      1. associate-*r/ 55.2%

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

   9. Applied egg-rr 55.2%

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

   if 5.5000000000000001e-22 < a

   1. Initial program 80.8%

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

   2. Taylor expanded in z around inf 58.0%

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

      1. *-commutative 58.0%

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

      2. associate-/l* 66.0%

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

   4. Simplified 66.0%

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

4. Final simplification 54.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 5.3 \cdot 10^{-239}:\\ \;\;\;\;9 \cdot \left(y \cdot \frac{\frac{x}{c}}{z}\right)\\ \mathbf{elif}\;a \leq 2.3 \cdot 10^{-163}:\\ \;\;\;\;b \cdot \frac{1}{c \cdot z}\\ \mathbf{elif}\;a \leq 5.5 \cdot 10^{-22}:\\ \;\;\;\;\frac{9 \cdot x}{c \cdot \frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \end{array} \]

Alternative 11: 76.1% accurate, 1.3× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{+35} \lor \neg \left(z \leq 3.6 \cdot 10^{-13}\right):\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right) + \frac{b}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + y \cdot \left(9 \cdot x\right)}{c \cdot z}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= z -3.5e+35) (not (<= z 3.6e-13)))
   (/ (+ (* -4.0 (* a t)) (/ b z)) c)
   (/ (+ b (* y (* 9.0 x))) (* c z))))

C

assert(x < y);
assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((z <= -3.5e+35) || !(z <= 3.6e-13)) {
		tmp = ((-4.0 * (a * t)) + (b / z)) / c;
	} else {
		tmp = (b + (y * (9.0 * x))) / (c * z);
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if ((z <= (-3.5d+35)) .or. (.not. (z <= 3.6d-13))) then
        tmp = (((-4.0d0) * (a * t)) + (b / z)) / c
    else
        tmp = (b + (y * (9.0d0 * x))) / (c * z)
    end if
    code = tmp
end function

Java

assert x < y;
assert t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((z <= -3.5e+35) || !(z <= 3.6e-13)) {
		tmp = ((-4.0 * (a * t)) + (b / z)) / c;
	} else {
		tmp = (b + (y * (9.0 * x))) / (c * z);
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if (z <= -3.5e+35) or not (z <= 3.6e-13):
		tmp = ((-4.0 * (a * t)) + (b / z)) / c
	else:
		tmp = (b + (y * (9.0 * x))) / (c * z)
	return tmp

Julia

x, y = sort([x, y])
t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((z <= -3.5e+35) || !(z <= 3.6e-13))
		tmp = Float64(Float64(Float64(-4.0 * Float64(a * t)) + Float64(b / z)) / c);
	else
		tmp = Float64(Float64(b + Float64(y * Float64(9.0 * x))) / Float64(c * z));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((z <= -3.5e+35) || ~((z <= 3.6e-13)))
		tmp = ((-4.0 * (a * t)) + (b / z)) / c;
	else
		tmp = (b + (y * (9.0 * x))) / (c * z);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[z, -3.5e+35], N[Not[LessEqual[z, 3.6e-13]], $MachinePrecision]], N[(N[(N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision] + N[(b / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], N[(N[(b + N[(y * N[(9.0 * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(c * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.5000000000000001e35 or 3.5999999999999998e-13 < z

   1. Initial program 63.5%

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

      1. associate-/r* 71.8%

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

      2. associate-+l- 71.8%

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

      3. associate-*r* 71.8%

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

      4. associate-*r* 76.5%

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

      5. div-inv 76.5%

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

      6. associate--r- 76.5%

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

      7. fma-neg 76.5%

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

      8. associate-*r* 71.8%

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

      9. distribute-rgt-neg-in 71.8%

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

      10. associate-*l* 72.6%

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

   3. Applied egg-rr 72.6%

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

   4. Taylor expanded in x around 0 87.3%

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

   5. Taylor expanded in x around 0 73.4%

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

   if -3.5000000000000001e35 < z < 3.5999999999999998e-13

   1. Initial program 94.8%

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

   2. Taylor expanded in z around 0 81.9%

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

      1. associate-*r* 81.9%

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

      2. *-commutative 81.9%

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

   4. Simplified 81.9%

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

4. Final simplification 77.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{+35} \lor \neg \left(z \leq 3.6 \cdot 10^{-13}\right):\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right) + \frac{b}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + y \cdot \left(9 \cdot x\right)}{c \cdot z}\\ \end{array} \]

Alternative 12: 66.9% accurate, 1.3× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.28 \cdot 10^{+39}:\\ \;\;\;\;\frac{-4 \cdot a}{\frac{c}{t}}\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{-13}:\\ \;\;\;\;\frac{b + y \cdot \left(9 \cdot x\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= z -1.28e+39)
   (/ (* -4.0 a) (/ c t))
   (if (<= z 6.8e-13)
     (/ (+ b (* y (* 9.0 x))) (* c z))
     (* -4.0 (/ a (/ c t))))))

C

assert(x < y);
assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (z <= -1.28e+39) {
		tmp = (-4.0 * a) / (c / t);
	} else if (z <= 6.8e-13) {
		tmp = (b + (y * (9.0 * x))) / (c * z);
	} else {
		tmp = -4.0 * (a / (c / t));
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (z <= (-1.28d+39)) then
        tmp = ((-4.0d0) * a) / (c / t)
    else if (z <= 6.8d-13) then
        tmp = (b + (y * (9.0d0 * x))) / (c * z)
    else
        tmp = (-4.0d0) * (a / (c / t))
    end if
    code = tmp
end function

Java

assert x < y;
assert t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (z <= -1.28e+39) {
		tmp = (-4.0 * a) / (c / t);
	} else if (z <= 6.8e-13) {
		tmp = (b + (y * (9.0 * x))) / (c * z);
	} else {
		tmp = -4.0 * (a / (c / t));
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if z <= -1.28e+39:
		tmp = (-4.0 * a) / (c / t)
	elif z <= 6.8e-13:
		tmp = (b + (y * (9.0 * x))) / (c * z)
	else:
		tmp = -4.0 * (a / (c / t))
	return tmp

Julia

x, y = sort([x, y])
t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (z <= -1.28e+39)
		tmp = Float64(Float64(-4.0 * a) / Float64(c / t));
	elseif (z <= 6.8e-13)
		tmp = Float64(Float64(b + Float64(y * Float64(9.0 * x))) / Float64(c * z));
	else
		tmp = Float64(-4.0 * Float64(a / Float64(c / t)));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (z <= -1.28e+39)
		tmp = (-4.0 * a) / (c / t);
	elseif (z <= 6.8e-13)
		tmp = (b + (y * (9.0 * x))) / (c * z);
	else
		tmp = -4.0 * (a / (c / t));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[z, -1.28e+39], N[(N[(-4.0 * a), $MachinePrecision] / N[(c / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.8e-13], N[(N[(b + N[(y * N[(9.0 * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(c * z), $MachinePrecision]), $MachinePrecision], N[(-4.0 * N[(a / N[(c / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.27999999999999994e39

   1. Initial program 64.1%

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

   2. Taylor expanded in z around inf 57.1%

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

      1. *-commutative 57.1%

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

      2. associate-/l* 61.0%

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

   4. Simplified 61.0%

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

      1. associate-*l/ 61.0%

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

   6. Applied egg-rr 61.0%

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

   if -1.27999999999999994e39 < z < 6.80000000000000031e-13

   1. Initial program 94.8%

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

   2. Taylor expanded in z around 0 81.9%

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

      1. associate-*r* 81.9%

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

      2. *-commutative 81.9%

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

   4. Simplified 81.9%

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

   if 6.80000000000000031e-13 < z

   1. Initial program 63.0%

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

   2. Taylor expanded in z around inf 55.1%

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

      1. *-commutative 55.1%

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

      2. associate-/l* 57.7%

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

   4. Simplified 57.7%

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

4. Final simplification 70.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.28 \cdot 10^{+39}:\\ \;\;\;\;\frac{-4 \cdot a}{\frac{c}{t}}\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{-13}:\\ \;\;\;\;\frac{b + y \cdot \left(9 \cdot x\right)}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \end{array} \]

Alternative 13: 49.5% accurate, 1.7× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;b \leq -1.7 \cdot 10^{+24}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;b \leq 4 \cdot 10^{+121}:\\ \;\;\;\;-4 \cdot \frac{a \cdot t}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \end{array} \end{array} \]

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 -1.7e+24)
   (/ (/ b c) z)
   (if (<= b 4e+121) (* -4.0 (/ (* a t) c)) (/ b (* c z)))))

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 <= -1.7e+24) {
		tmp = (b / c) / z;
	} else if (b <= 4e+121) {
		tmp = -4.0 * ((a * t) / c);
	} else {
		tmp = b / (c * z);
	}
	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 <= (-1.7d+24)) then
        tmp = (b / c) / z
    else if (b <= 4d+121) then
        tmp = (-4.0d0) * ((a * t) / c)
    else
        tmp = b / (c * z)
    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 <= -1.7e+24) {
		tmp = (b / c) / z;
	} else if (b <= 4e+121) {
		tmp = -4.0 * ((a * t) / c);
	} else {
		tmp = b / (c * z);
	}
	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 <= -1.7e+24:
		tmp = (b / c) / z
	elif b <= 4e+121:
		tmp = -4.0 * ((a * t) / c)
	else:
		tmp = b / (c * z)
	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 <= -1.7e+24)
		tmp = Float64(Float64(b / c) / z);
	elseif (b <= 4e+121)
		tmp = Float64(-4.0 * Float64(Float64(a * t) / c));
	else
		tmp = Float64(b / Float64(c * z));
	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 <= -1.7e+24)
		tmp = (b / c) / z;
	elseif (b <= 4e+121)
		tmp = -4.0 * ((a * t) / c);
	else
		tmp = b / (c * z);
	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, -1.7e+24], N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[b, 4e+121], N[(-4.0 * N[(N[(a * t), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision], N[(b / N[(c * z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.7e24

   1. Initial program 82.3%

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

      1. associate-/r* 74.8%

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

      2. associate-+l- 74.8%

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

      3. associate-*r* 74.8%

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

      4. associate-*r* 72.8%

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

      5. div-inv 72.7%

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

      6. associate--r- 72.7%

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

      7. fma-neg 72.7%

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

      8. associate-*r* 74.7%

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

      9. distribute-rgt-neg-in 74.7%

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

      10. associate-*l* 74.7%

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

   3. Applied egg-rr 74.7%

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

   4. Taylor expanded in b around inf 55.4%

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

      1. associate-*l/ 65.3%

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

      2. un-div-inv 65.3%

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

   6. Applied egg-rr 65.3%

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

   if -1.7e24 < b < 4.00000000000000015e121

   1. Initial program 79.4%

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

   2. Taylor expanded in z around inf 45.6%

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

   if 4.00000000000000015e121 < b

   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 b around inf 59.0%

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

      1. *-commutative 59.0%

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

   4. Simplified 59.0%

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

4. Final simplification 51.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.7 \cdot 10^{+24}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;b \leq 4 \cdot 10^{+121}:\\ \;\;\;\;-4 \cdot \frac{a \cdot t}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \end{array} \]

Alternative 14: 50.1% accurate, 1.7× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;b \leq -3 \cdot 10^{+28}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;b \leq 6.4 \cdot 10^{+103}:\\ \;\;\;\;\frac{a}{c} \cdot \left(-4 \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \end{array} \end{array} \]

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 -3e+28)
   (/ (/ b c) z)
   (if (<= b 6.4e+103) (* (/ a c) (* -4.0 t)) (/ b (* c z)))))

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 <= -3e+28) {
		tmp = (b / c) / z;
	} else if (b <= 6.4e+103) {
		tmp = (a / c) * (-4.0 * t);
	} else {
		tmp = b / (c * z);
	}
	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 <= (-3d+28)) then
        tmp = (b / c) / z
    else if (b <= 6.4d+103) then
        tmp = (a / c) * ((-4.0d0) * t)
    else
        tmp = b / (c * z)
    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 <= -3e+28) {
		tmp = (b / c) / z;
	} else if (b <= 6.4e+103) {
		tmp = (a / c) * (-4.0 * t);
	} else {
		tmp = b / (c * z);
	}
	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 <= -3e+28:
		tmp = (b / c) / z
	elif b <= 6.4e+103:
		tmp = (a / c) * (-4.0 * t)
	else:
		tmp = b / (c * z)
	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 <= -3e+28)
		tmp = Float64(Float64(b / c) / z);
	elseif (b <= 6.4e+103)
		tmp = Float64(Float64(a / c) * Float64(-4.0 * t));
	else
		tmp = Float64(b / Float64(c * z));
	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 <= -3e+28)
		tmp = (b / c) / z;
	elseif (b <= 6.4e+103)
		tmp = (a / c) * (-4.0 * t);
	else
		tmp = b / (c * z);
	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, -3e+28], N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[b, 6.4e+103], N[(N[(a / c), $MachinePrecision] * N[(-4.0 * t), $MachinePrecision]), $MachinePrecision], N[(b / N[(c * z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -3.0000000000000001e28

   1. Initial program 82.3%

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

      1. associate-/r* 74.8%

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

      2. associate-+l- 74.8%

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

      3. associate-*r* 74.8%

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

      4. associate-*r* 72.8%

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

      5. div-inv 72.7%

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

      6. associate--r- 72.7%

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

      7. fma-neg 72.7%

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

      8. associate-*r* 74.7%

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

      9. distribute-rgt-neg-in 74.7%

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

      10. associate-*l* 74.7%

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

   3. Applied egg-rr 74.7%

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

   4. Taylor expanded in b around inf 55.4%

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

      1. associate-*l/ 65.3%

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

      2. un-div-inv 65.3%

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

   6. Applied egg-rr 65.3%

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

   if -3.0000000000000001e28 < b < 6.39999999999999985e103

   1. Initial program 79.3%

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

      1. associate-/r* 79.2%

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

      2. associate-+l- 79.1%

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

      3. associate-*r* 79.2%

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

      4. associate-*r* 81.7%

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

      5. div-inv 81.7%

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

      6. associate--r- 81.7%

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

      7. fma-neg 81.7%

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

      8. associate-*r* 79.2%

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

      9. distribute-rgt-neg-in 79.2%

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

      10. associate-*l* 79.2%

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

   3. Applied egg-rr 79.2%

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

   4. Taylor expanded in x around 0 87.1%

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

   5. Taylor expanded in a around inf 44.9%

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

      1. associate-/l* 48.5%

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

      2. *-commutative 48.5%

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

      3. associate-/r/ 46.7%

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

      4. associate-*l* 46.7%

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

   7. Simplified 46.7%

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

   if 6.39999999999999985e103 < b

   1. Initial program 78.6%

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

   2. Taylor expanded in b around inf 58.2%

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

      1. *-commutative 58.2%

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

   4. Simplified 58.2%

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

4. Final simplification 52.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3 \cdot 10^{+28}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;b \leq 6.4 \cdot 10^{+103}:\\ \;\;\;\;\frac{a}{c} \cdot \left(-4 \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \end{array} \]

Alternative 15: 49.9% accurate, 1.7× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;b \leq -1 \cdot 10^{+28}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;b \leq 3.8 \cdot 10^{+121}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \end{array} \end{array} \]

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 -1e+28)
   (/ (/ b c) z)
   (if (<= b 3.8e+121) (* -4.0 (/ a (/ c t))) (/ b (* c z)))))

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 <= -1e+28) {
		tmp = (b / c) / z;
	} else if (b <= 3.8e+121) {
		tmp = -4.0 * (a / (c / t));
	} else {
		tmp = b / (c * z);
	}
	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 <= (-1d+28)) then
        tmp = (b / c) / z
    else if (b <= 3.8d+121) then
        tmp = (-4.0d0) * (a / (c / t))
    else
        tmp = b / (c * z)
    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 <= -1e+28) {
		tmp = (b / c) / z;
	} else if (b <= 3.8e+121) {
		tmp = -4.0 * (a / (c / t));
	} else {
		tmp = b / (c * z);
	}
	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 <= -1e+28:
		tmp = (b / c) / z
	elif b <= 3.8e+121:
		tmp = -4.0 * (a / (c / t))
	else:
		tmp = b / (c * z)
	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 <= -1e+28)
		tmp = Float64(Float64(b / c) / z);
	elseif (b <= 3.8e+121)
		tmp = Float64(-4.0 * Float64(a / Float64(c / t)));
	else
		tmp = Float64(b / Float64(c * z));
	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 <= -1e+28)
		tmp = (b / c) / z;
	elseif (b <= 3.8e+121)
		tmp = -4.0 * (a / (c / t));
	else
		tmp = b / (c * z);
	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, -1e+28], N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[b, 3.8e+121], N[(-4.0 * N[(a / N[(c / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b / N[(c * z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -9.99999999999999958e27

   1. Initial program 82.3%

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

      1. associate-/r* 74.8%

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

      2. associate-+l- 74.8%

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

      3. associate-*r* 74.8%

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

      4. associate-*r* 72.8%

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

      5. div-inv 72.7%

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

      6. associate--r- 72.7%

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

      7. fma-neg 72.7%

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

      8. associate-*r* 74.7%

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

      9. distribute-rgt-neg-in 74.7%

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

      10. associate-*l* 74.7%

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

   3. Applied egg-rr 74.7%

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

   4. Taylor expanded in b around inf 55.4%

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

      1. associate-*l/ 65.3%

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

      2. un-div-inv 65.3%

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

   6. Applied egg-rr 65.3%

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

   if -9.99999999999999958e27 < b < 3.8e121

   1. Initial program 79.4%

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

   2. Taylor expanded in z around inf 45.6%

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

      1. *-commutative 45.6%

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

      2. associate-/l* 49.1%

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

   4. Simplified 49.1%

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

   if 3.8e121 < b

   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 b around inf 59.0%

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

      1. *-commutative 59.0%

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

   4. Simplified 59.0%

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

4. Final simplification 53.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1 \cdot 10^{+28}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;b \leq 3.8 \cdot 10^{+121}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \end{array} \]

Alternative 16: 49.8% accurate, 1.7× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;b \leq -1.25 \cdot 10^{+27}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;b \leq 2.8 \cdot 10^{+121}:\\ \;\;\;\;\frac{-4 \cdot a}{\frac{c}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \end{array} \end{array} \]

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 -1.25e+27)
   (/ (/ b c) z)
   (if (<= b 2.8e+121) (/ (* -4.0 a) (/ c t)) (/ b (* c z)))))

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 <= -1.25e+27) {
		tmp = (b / c) / z;
	} else if (b <= 2.8e+121) {
		tmp = (-4.0 * a) / (c / t);
	} else {
		tmp = b / (c * z);
	}
	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 <= (-1.25d+27)) then
        tmp = (b / c) / z
    else if (b <= 2.8d+121) then
        tmp = ((-4.0d0) * a) / (c / t)
    else
        tmp = b / (c * z)
    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 <= -1.25e+27) {
		tmp = (b / c) / z;
	} else if (b <= 2.8e+121) {
		tmp = (-4.0 * a) / (c / t);
	} else {
		tmp = b / (c * z);
	}
	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 <= -1.25e+27:
		tmp = (b / c) / z
	elif b <= 2.8e+121:
		tmp = (-4.0 * a) / (c / t)
	else:
		tmp = b / (c * z)
	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 <= -1.25e+27)
		tmp = Float64(Float64(b / c) / z);
	elseif (b <= 2.8e+121)
		tmp = Float64(Float64(-4.0 * a) / Float64(c / t));
	else
		tmp = Float64(b / Float64(c * z));
	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 <= -1.25e+27)
		tmp = (b / c) / z;
	elseif (b <= 2.8e+121)
		tmp = (-4.0 * a) / (c / t);
	else
		tmp = b / (c * z);
	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, -1.25e+27], N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[b, 2.8e+121], N[(N[(-4.0 * a), $MachinePrecision] / N[(c / t), $MachinePrecision]), $MachinePrecision], N[(b / N[(c * z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.24999999999999995e27

   1. Initial program 82.3%

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

      1. associate-/r* 74.8%

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

      2. associate-+l- 74.8%

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

      3. associate-*r* 74.8%

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

      4. associate-*r* 72.8%

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

      5. div-inv 72.7%

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

      6. associate--r- 72.7%

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

      7. fma-neg 72.7%

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

      8. associate-*r* 74.7%

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

      9. distribute-rgt-neg-in 74.7%

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

      10. associate-*l* 74.7%

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

   3. Applied egg-rr 74.7%

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

   4. Taylor expanded in b around inf 55.4%

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

      1. associate-*l/ 65.3%

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

      2. un-div-inv 65.3%

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

   6. Applied egg-rr 65.3%

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

   if -1.24999999999999995e27 < b < 2.80000000000000006e121

   1. Initial program 79.4%

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

   2. Taylor expanded in z around inf 45.6%

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

      1. *-commutative 45.6%

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

      2. associate-/l* 49.1%

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

   4. Simplified 49.1%

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

      1. associate-*l/ 49.1%

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

   6. Applied egg-rr 49.1%

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

   if 2.80000000000000006e121 < b

   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 b around inf 59.0%

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

      1. *-commutative 59.0%

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

   4. Simplified 59.0%

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

4. Final simplification 53.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.25 \cdot 10^{+27}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;b \leq 2.8 \cdot 10^{+121}:\\ \;\;\;\;\frac{-4 \cdot a}{\frac{c}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{c \cdot z}\\ \end{array} \]

Alternative 17: 34.8% accurate, 3.8× speedup

Math

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

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 (* c z)))

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 / (c * z);
}

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 / (c * z)
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 / (c * z);
}

Python

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

Julia

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

Derivation

1. Initial program 79.7%

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

2. Taylor expanded in b around inf 35.1%

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

   1. *-commutative 35.1%

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

4. Simplified 35.1%

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

5. Final simplification 35.1%

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

Developer target: 80.1% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{b}{c \cdot z}\\ t_2 := 4 \cdot \frac{a \cdot t}{c}\\ t_3 := \left(x \cdot 9\right) \cdot y\\ t_4 := \left(t_3 - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b\\ t_5 := \frac{t_4}{z \cdot c}\\ t_6 := \frac{\left(t_3 - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}\\ \mathbf{if}\;t_5 < -1.100156740804105 \cdot 10^{-171}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;t_5 < 0:\\ \;\;\;\;\frac{\frac{t_4}{z}}{c}\\ \mathbf{elif}\;t_5 < 1.1708877911747488 \cdot 10^{-53}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;t_5 < 2.876823679546137 \cdot 10^{+130}:\\ \;\;\;\;\left(\left(9 \cdot \frac{y}{c}\right) \cdot \frac{x}{z} + t_1\right) - t_2\\ \mathbf{elif}\;t_5 < 1.3838515042456319 \cdot 10^{+158}:\\ \;\;\;\;t_6\\ \mathbf{else}:\\ \;\;\;\;\left(9 \cdot \left(\frac{y}{c \cdot z} \cdot x\right) + t_1\right) - t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ b (* c z)))
        (t_2 (* 4.0 (/ (* a t) c)))
        (t_3 (* (* x 9.0) y))
        (t_4 (+ (- t_3 (* (* (* z 4.0) t) a)) b))
        (t_5 (/ t_4 (* z c)))
        (t_6 (/ (+ (- t_3 (* (* z 4.0) (* t a))) b) (* z c))))
   (if (< t_5 -1.100156740804105e-171)
     t_6
     (if (< t_5 0.0)
       (/ (/ t_4 z) c)
       (if (< t_5 1.1708877911747488e-53)
         t_6
         (if (< t_5 2.876823679546137e+130)
           (- (+ (* (* 9.0 (/ y c)) (/ x z)) t_1) t_2)
           (if (< t_5 1.3838515042456319e+158)
             t_6
             (- (+ (* 9.0 (* (/ y (* c z)) x)) t_1) t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = b / (c * z);
	double t_2 = 4.0 * ((a * t) / c);
	double t_3 = (x * 9.0) * y;
	double t_4 = (t_3 - (((z * 4.0) * t) * a)) + b;
	double t_5 = t_4 / (z * c);
	double t_6 = ((t_3 - ((z * 4.0) * (t * a))) + b) / (z * c);
	double tmp;
	if (t_5 < -1.100156740804105e-171) {
		tmp = t_6;
	} else if (t_5 < 0.0) {
		tmp = (t_4 / z) / c;
	} else if (t_5 < 1.1708877911747488e-53) {
		tmp = t_6;
	} else if (t_5 < 2.876823679546137e+130) {
		tmp = (((9.0 * (y / c)) * (x / z)) + t_1) - t_2;
	} else if (t_5 < 1.3838515042456319e+158) {
		tmp = t_6;
	} else {
		tmp = ((9.0 * ((y / (c * z)) * x)) + t_1) - t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: tmp
    t_1 = b / (c * z)
    t_2 = 4.0d0 * ((a * t) / c)
    t_3 = (x * 9.0d0) * y
    t_4 = (t_3 - (((z * 4.0d0) * t) * a)) + b
    t_5 = t_4 / (z * c)
    t_6 = ((t_3 - ((z * 4.0d0) * (t * a))) + b) / (z * c)
    if (t_5 < (-1.100156740804105d-171)) then
        tmp = t_6
    else if (t_5 < 0.0d0) then
        tmp = (t_4 / z) / c
    else if (t_5 < 1.1708877911747488d-53) then
        tmp = t_6
    else if (t_5 < 2.876823679546137d+130) then
        tmp = (((9.0d0 * (y / c)) * (x / z)) + t_1) - t_2
    else if (t_5 < 1.3838515042456319d+158) then
        tmp = t_6
    else
        tmp = ((9.0d0 * ((y / (c * z)) * x)) + t_1) - t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = b / (c * z);
	double t_2 = 4.0 * ((a * t) / c);
	double t_3 = (x * 9.0) * y;
	double t_4 = (t_3 - (((z * 4.0) * t) * a)) + b;
	double t_5 = t_4 / (z * c);
	double t_6 = ((t_3 - ((z * 4.0) * (t * a))) + b) / (z * c);
	double tmp;
	if (t_5 < -1.100156740804105e-171) {
		tmp = t_6;
	} else if (t_5 < 0.0) {
		tmp = (t_4 / z) / c;
	} else if (t_5 < 1.1708877911747488e-53) {
		tmp = t_6;
	} else if (t_5 < 2.876823679546137e+130) {
		tmp = (((9.0 * (y / c)) * (x / z)) + t_1) - t_2;
	} else if (t_5 < 1.3838515042456319e+158) {
		tmp = t_6;
	} else {
		tmp = ((9.0 * ((y / (c * z)) * x)) + t_1) - t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = b / (c * z)
	t_2 = 4.0 * ((a * t) / c)
	t_3 = (x * 9.0) * y
	t_4 = (t_3 - (((z * 4.0) * t) * a)) + b
	t_5 = t_4 / (z * c)
	t_6 = ((t_3 - ((z * 4.0) * (t * a))) + b) / (z * c)
	tmp = 0
	if t_5 < -1.100156740804105e-171:
		tmp = t_6
	elif t_5 < 0.0:
		tmp = (t_4 / z) / c
	elif t_5 < 1.1708877911747488e-53:
		tmp = t_6
	elif t_5 < 2.876823679546137e+130:
		tmp = (((9.0 * (y / c)) * (x / z)) + t_1) - t_2
	elif t_5 < 1.3838515042456319e+158:
		tmp = t_6
	else:
		tmp = ((9.0 * ((y / (c * z)) * x)) + t_1) - t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(b / Float64(c * z))
	t_2 = Float64(4.0 * Float64(Float64(a * t) / c))
	t_3 = Float64(Float64(x * 9.0) * y)
	t_4 = Float64(Float64(t_3 - Float64(Float64(Float64(z * 4.0) * t) * a)) + b)
	t_5 = Float64(t_4 / Float64(z * c))
	t_6 = Float64(Float64(Float64(t_3 - Float64(Float64(z * 4.0) * Float64(t * a))) + b) / Float64(z * c))
	tmp = 0.0
	if (t_5 < -1.100156740804105e-171)
		tmp = t_6;
	elseif (t_5 < 0.0)
		tmp = Float64(Float64(t_4 / z) / c);
	elseif (t_5 < 1.1708877911747488e-53)
		tmp = t_6;
	elseif (t_5 < 2.876823679546137e+130)
		tmp = Float64(Float64(Float64(Float64(9.0 * Float64(y / c)) * Float64(x / z)) + t_1) - t_2);
	elseif (t_5 < 1.3838515042456319e+158)
		tmp = t_6;
	else
		tmp = Float64(Float64(Float64(9.0 * Float64(Float64(y / Float64(c * z)) * x)) + t_1) - t_2);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = b / (c * z);
	t_2 = 4.0 * ((a * t) / c);
	t_3 = (x * 9.0) * y;
	t_4 = (t_3 - (((z * 4.0) * t) * a)) + b;
	t_5 = t_4 / (z * c);
	t_6 = ((t_3 - ((z * 4.0) * (t * a))) + b) / (z * c);
	tmp = 0.0;
	if (t_5 < -1.100156740804105e-171)
		tmp = t_6;
	elseif (t_5 < 0.0)
		tmp = (t_4 / z) / c;
	elseif (t_5 < 1.1708877911747488e-53)
		tmp = t_6;
	elseif (t_5 < 2.876823679546137e+130)
		tmp = (((9.0 * (y / c)) * (x / z)) + t_1) - t_2;
	elseif (t_5 < 1.3838515042456319e+158)
		tmp = t_6;
	else
		tmp = ((9.0 * ((y / (c * z)) * x)) + t_1) - t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(b / N[(c * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(4.0 * N[(N[(a * t), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision]}, Block[{t$95$4 = N[(N[(t$95$3 - N[(N[(N[(z * 4.0), $MachinePrecision] * t), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]}, Block[{t$95$5 = N[(t$95$4 / N[(z * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(N[(N[(t$95$3 - N[(N[(z * 4.0), $MachinePrecision] * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]}, If[Less[t$95$5, -1.100156740804105e-171], t$95$6, If[Less[t$95$5, 0.0], N[(N[(t$95$4 / z), $MachinePrecision] / c), $MachinePrecision], If[Less[t$95$5, 1.1708877911747488e-53], t$95$6, If[Less[t$95$5, 2.876823679546137e+130], N[(N[(N[(N[(9.0 * N[(y / c), $MachinePrecision]), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision] - t$95$2), $MachinePrecision], If[Less[t$95$5, 1.3838515042456319e+158], t$95$6, N[(N[(N[(9.0 * N[(N[(y / N[(c * z), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision] - t$95$2), $MachinePrecision]]]]]]]]]]]]

Reproduce

herbie shell --seed 2023318 
(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)))