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

Percentage Accurate: 79.6% → 84.2%

Time: 16.0s

Alternatives: 14

Speedup: 0.8×

• 37.1% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 79.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 84.2% accurate, 0.2× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{+102} \lor \neg \left(z \leq 4.4 \cdot 10^{+197}\right):\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right) + 9 \cdot \frac{x \cdot y}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{z} \cdot \frac{\mathsf{fma}\left(x, 9 \cdot y, b + \left(z \cdot -4\right) \cdot \left(a \cdot t\right)\right)}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= z -1.45e+102) (not (<= z 4.4e+197)))
   (/ (+ (* -4.0 (* a t)) (* 9.0 (/ (* x y) z))) c)
   (* (/ 1.0 z) (/ (fma x (* 9.0 y) (+ b (* (* z -4.0) (* a t)))) c))))

C

assert(x < y);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((z <= -1.45e+102) || !(z <= 4.4e+197)) {
		tmp = ((-4.0 * (a * t)) + (9.0 * ((x * y) / z))) / c;
	} else {
		tmp = (1.0 / z) * (fma(x, (9.0 * y), (b + ((z * -4.0) * (a * t)))) / c);
	}
	return tmp;
}

Julia

x, y = sort([x, y])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((z <= -1.45e+102) || !(z <= 4.4e+197))
		tmp = Float64(Float64(Float64(-4.0 * Float64(a * t)) + Float64(9.0 * Float64(Float64(x * y) / z))) / c);
	else
		tmp = Float64(Float64(1.0 / z) * Float64(fma(x, Float64(9.0 * y), Float64(b + Float64(Float64(z * -4.0) * Float64(a * t)))) / c));
	end
	return tmp
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[z, -1.45e+102], N[Not[LessEqual[z, 4.4e+197]], $MachinePrecision]], N[(N[(N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision] + N[(9.0 * N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], N[(N[(1.0 / z), $MachinePrecision] * N[(N[(x * N[(9.0 * y), $MachinePrecision] + N[(b + N[(N[(z * -4.0), $MachinePrecision] * N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.4500000000000001e102 or 4.39999999999999979e197 < z

   1. Initial program 49.0%

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

      1. associate-+l- 49.0%

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

      2. associate-*l* 49.0%

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

      3. associate-*l* 52.7%

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

   3. Simplified 52.7%

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

   4. Taylor expanded in b around 0 45.4%

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

   5. Taylor expanded in x around 0 77.6%

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

   6. Taylor expanded in c around 0 83.4%

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

   if -1.4500000000000001e102 < z < 4.39999999999999979e197

   1. Initial program 86.7%

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

      1. associate-+l- 86.7%

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

      2. associate-*l* 86.7%

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

      3. fma-neg 87.8%

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

      4. sub-neg 87.8%

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

      5. distribute-neg-in 87.8%

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

      6. remove-double-neg 87.8%

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

      7. +-commutative 87.8%

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

      8. unsub-neg 87.8%

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

      9. associate-*l* 91.2%

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

      10. *-commutative 91.2%

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

      11. associate-*l* 91.2%

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

   3. Simplified 91.2%

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

      1. *-un-lft-identity 91.2%

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

      2. times-frac 91.6%

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

      3. cancel-sign-sub-inv 91.6%

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

      4. associate-*r* 91.6%

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

      5. metadata-eval 91.6%

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

   5. Applied egg-rr 91.6%

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

4. Final simplification 89.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{+102} \lor \neg \left(z \leq 4.4 \cdot 10^{+197}\right):\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right) + 9 \cdot \frac{x \cdot y}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{z} \cdot \frac{\mathsf{fma}\left(x, 9 \cdot y, b + \left(z \cdot -4\right) \cdot \left(a \cdot t\right)\right)}{c}\\ \end{array} \]

Alternative 2: 84.0% accurate, 0.2× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -9.8 \cdot 10^{+101} \lor \neg \left(z \leq 2.5 \cdot 10^{+197}\right):\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right) + 9 \cdot \frac{x \cdot y}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, 9 \cdot y, b - 4 \cdot \left(z \cdot \left(a \cdot t\right)\right)\right)}{z \cdot c}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= z -9.8e+101) (not (<= z 2.5e+197)))
   (/ (+ (* -4.0 (* a t)) (* 9.0 (/ (* x y) z))) c)
   (/ (fma x (* 9.0 y) (- b (* 4.0 (* z (* a t))))) (* z c))))

C

assert(x < y);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((z <= -9.8e+101) || !(z <= 2.5e+197)) {
		tmp = ((-4.0 * (a * t)) + (9.0 * ((x * y) / z))) / c;
	} else {
		tmp = fma(x, (9.0 * y), (b - (4.0 * (z * (a * t))))) / (z * c);
	}
	return tmp;
}

Julia

x, y = sort([x, y])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((z <= -9.8e+101) || !(z <= 2.5e+197))
		tmp = Float64(Float64(Float64(-4.0 * Float64(a * t)) + Float64(9.0 * Float64(Float64(x * y) / z))) / c);
	else
		tmp = Float64(fma(x, Float64(9.0 * y), Float64(b - Float64(4.0 * Float64(z * Float64(a * t))))) / Float64(z * c));
	end
	return tmp
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[z, -9.8e+101], N[Not[LessEqual[z, 2.5e+197]], $MachinePrecision]], N[(N[(N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision] + N[(9.0 * N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], N[(N[(x * N[(9.0 * y), $MachinePrecision] + N[(b - N[(4.0 * N[(z * N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -9.79999999999999965e101 or 2.50000000000000004e197 < z

   1. Initial program 49.0%

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

      1. associate-+l- 49.0%

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

      2. associate-*l* 49.0%

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

      3. associate-*l* 52.7%

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

   3. Simplified 52.7%

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

   4. Taylor expanded in b around 0 45.4%

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

   5. Taylor expanded in x around 0 77.6%

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

   6. Taylor expanded in c around 0 83.4%

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

   if -9.79999999999999965e101 < z < 2.50000000000000004e197

   1. Initial program 86.7%

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

      1. associate-+l- 86.7%

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

      2. associate-*l* 86.7%

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

      3. fma-neg 87.8%

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

      4. sub-neg 87.8%

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

      5. distribute-neg-in 87.8%

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

      6. remove-double-neg 87.8%

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

      7. +-commutative 87.8%

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

      8. unsub-neg 87.8%

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

      9. associate-*l* 91.2%

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

      10. *-commutative 91.2%

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

      11. associate-*l* 91.2%

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

   3. Simplified 91.2%

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

4. Final simplification 88.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.8 \cdot 10^{+101} \lor \neg \left(z \leq 2.5 \cdot 10^{+197}\right):\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right) + 9 \cdot \frac{x \cdot y}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, 9 \cdot y, b - 4 \cdot \left(z \cdot \left(a \cdot t\right)\right)\right)}{z \cdot c}\\ \end{array} \]

Alternative 3: 73.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} t_1 := \frac{-4 \cdot \left(a \cdot t\right) + 9 \cdot \frac{x \cdot y}{z}}{c}\\ t_2 := \frac{b - 4 \cdot \left(a \cdot \left(z \cdot t\right)\right)}{z \cdot c}\\ \mathbf{if}\;z \leq -1.8 \cdot 10^{+73}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.16 \cdot 10^{-85}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-13}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{+55}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

NOTE: x and y 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)) (* 9.0 (/ (* x y) z))) c))
        (t_2 (/ (- b (* 4.0 (* a (* z t)))) (* z c))))
   (if (<= z -1.8e+73)
     t_1
     (if (<= z -1.16e-85)
       t_2
       (if (<= z 7e-13)
         (/ (+ b (* 9.0 (* x y))) (* z c))
         (if (<= z 9.5e+55) t_2 t_1))))))

C

assert(x < y);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = ((-4.0 * (a * t)) + (9.0 * ((x * y) / z))) / c;
	double t_2 = (b - (4.0 * (a * (z * t)))) / (z * c);
	double tmp;
	if (z <= -1.8e+73) {
		tmp = t_1;
	} else if (z <= -1.16e-85) {
		tmp = t_2;
	} else if (z <= 7e-13) {
		tmp = (b + (9.0 * (x * y))) / (z * c);
	} else if (z <= 9.5e+55) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (((-4.0d0) * (a * t)) + (9.0d0 * ((x * y) / z))) / c
    t_2 = (b - (4.0d0 * (a * (z * t)))) / (z * c)
    if (z <= (-1.8d+73)) then
        tmp = t_1
    else if (z <= (-1.16d-85)) then
        tmp = t_2
    else if (z <= 7d-13) then
        tmp = (b + (9.0d0 * (x * y))) / (z * c)
    else if (z <= 9.5d+55) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y;
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)) + (9.0 * ((x * y) / z))) / c;
	double t_2 = (b - (4.0 * (a * (z * t)))) / (z * c);
	double tmp;
	if (z <= -1.8e+73) {
		tmp = t_1;
	} else if (z <= -1.16e-85) {
		tmp = t_2;
	} else if (z <= 7e-13) {
		tmp = (b + (9.0 * (x * y))) / (z * c);
	} else if (z <= 9.5e+55) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y, z, t, a, b, c):
	t_1 = ((-4.0 * (a * t)) + (9.0 * ((x * y) / z))) / c
	t_2 = (b - (4.0 * (a * (z * t)))) / (z * c)
	tmp = 0
	if z <= -1.8e+73:
		tmp = t_1
	elif z <= -1.16e-85:
		tmp = t_2
	elif z <= 7e-13:
		tmp = (b + (9.0 * (x * y))) / (z * c)
	elif z <= 9.5e+55:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

x, y = sort([x, y])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(Float64(-4.0 * Float64(a * t)) + Float64(9.0 * Float64(Float64(x * y) / z))) / c)
	t_2 = Float64(Float64(b - Float64(4.0 * Float64(a * Float64(z * t)))) / Float64(z * c))
	tmp = 0.0
	if (z <= -1.8e+73)
		tmp = t_1;
	elseif (z <= -1.16e-85)
		tmp = t_2;
	elseif (z <= 7e-13)
		tmp = Float64(Float64(b + Float64(9.0 * Float64(x * y))) / Float64(z * c));
	elseif (z <= 9.5e+55)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = ((-4.0 * (a * t)) + (9.0 * ((x * y) / z))) / c;
	t_2 = (b - (4.0 * (a * (z * t)))) / (z * c);
	tmp = 0.0;
	if (z <= -1.8e+73)
		tmp = t_1;
	elseif (z <= -1.16e-85)
		tmp = t_2;
	elseif (z <= 7e-13)
		tmp = (b + (9.0 * (x * y))) / (z * c);
	elseif (z <= 9.5e+55)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision] + N[(9.0 * N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b - N[(4.0 * N[(a * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.8e+73], t$95$1, If[LessEqual[z, -1.16e-85], t$95$2, If[LessEqual[z, 7e-13], N[(N[(b + N[(9.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9.5e+55], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.7999999999999999e73 or 9.49999999999999989e55 < z

   1. Initial program 55.2%

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

      1. associate-+l- 55.2%

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

      2. associate-*l* 55.2%

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

      3. associate-*l* 62.8%

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

   3. Simplified 62.8%

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

   4. Taylor expanded in b around 0 49.2%

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

   5. Taylor expanded in x around 0 75.4%

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

   6. Taylor expanded in c around 0 81.2%

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

   if -1.7999999999999999e73 < z < -1.16e-85 or 7.0000000000000005e-13 < z < 9.49999999999999989e55

   1. Initial program 84.1%

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

      1. associate-+l- 84.1%

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

      2. associate-*l* 84.2%

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

      3. associate-*l* 84.4%

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

   3. Simplified 84.4%

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

   4. Taylor expanded in x around 0 77.5%

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

   if -1.16e-85 < z < 7.0000000000000005e-13

   1. Initial program 93.8%

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

   2. Taylor expanded in x around inf 81.8%

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

4. Final simplification 80.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+73}:\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right) + 9 \cdot \frac{x \cdot y}{z}}{c}\\ \mathbf{elif}\;z \leq -1.16 \cdot 10^{-85}:\\ \;\;\;\;\frac{b - 4 \cdot \left(a \cdot \left(z \cdot t\right)\right)}{z \cdot c}\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-13}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{+55}:\\ \;\;\;\;\frac{b - 4 \cdot \left(a \cdot \left(z \cdot t\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right) + 9 \cdot \frac{x \cdot y}{z}}{c}\\ \end{array} \]

Alternative 4: 73.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} t_1 := \frac{-4 \cdot \left(a \cdot t\right) + 9 \cdot \frac{x \cdot y}{z}}{c}\\ \mathbf{if}\;z \leq -2.8 \cdot 10^{+70}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.25 \cdot 10^{-35}:\\ \;\;\;\;\frac{b}{z \cdot c} - \frac{a \cdot 4}{z} \cdot \frac{z \cdot t}{c}\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{-10}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \mathbf{elif}\;z \leq 7.4 \cdot 10^{+55}:\\ \;\;\;\;\frac{b - 4 \cdot \left(a \cdot \left(z \cdot t\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

NOTE: x and y 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)) (* 9.0 (/ (* x y) z))) c)))
   (if (<= z -2.8e+70)
     t_1
     (if (<= z -2.25e-35)
       (- (/ b (* z c)) (* (/ (* a 4.0) z) (/ (* z t) c)))
       (if (<= z 1.35e-10)
         (/ (+ b (* 9.0 (* x y))) (* z c))
         (if (<= z 7.4e+55) (/ (- b (* 4.0 (* a (* z t)))) (* z c)) t_1))))))

C

assert(x < y);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = ((-4.0 * (a * t)) + (9.0 * ((x * y) / z))) / c;
	double tmp;
	if (z <= -2.8e+70) {
		tmp = t_1;
	} else if (z <= -2.25e-35) {
		tmp = (b / (z * c)) - (((a * 4.0) / z) * ((z * t) / c));
	} else if (z <= 1.35e-10) {
		tmp = (b + (9.0 * (x * y))) / (z * c);
	} else if (z <= 7.4e+55) {
		tmp = (b - (4.0 * (a * (z * t)))) / (z * c);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x and y 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)) + (9.0d0 * ((x * y) / z))) / c
    if (z <= (-2.8d+70)) then
        tmp = t_1
    else if (z <= (-2.25d-35)) then
        tmp = (b / (z * c)) - (((a * 4.0d0) / z) * ((z * t) / c))
    else if (z <= 1.35d-10) then
        tmp = (b + (9.0d0 * (x * y))) / (z * c)
    else if (z <= 7.4d+55) then
        tmp = (b - (4.0d0 * (a * (z * t)))) / (z * c)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y;
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)) + (9.0 * ((x * y) / z))) / c;
	double tmp;
	if (z <= -2.8e+70) {
		tmp = t_1;
	} else if (z <= -2.25e-35) {
		tmp = (b / (z * c)) - (((a * 4.0) / z) * ((z * t) / c));
	} else if (z <= 1.35e-10) {
		tmp = (b + (9.0 * (x * y))) / (z * c);
	} else if (z <= 7.4e+55) {
		tmp = (b - (4.0 * (a * (z * t)))) / (z * c);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y, z, t, a, b, c):
	t_1 = ((-4.0 * (a * t)) + (9.0 * ((x * y) / z))) / c
	tmp = 0
	if z <= -2.8e+70:
		tmp = t_1
	elif z <= -2.25e-35:
		tmp = (b / (z * c)) - (((a * 4.0) / z) * ((z * t) / c))
	elif z <= 1.35e-10:
		tmp = (b + (9.0 * (x * y))) / (z * c)
	elif z <= 7.4e+55:
		tmp = (b - (4.0 * (a * (z * t)))) / (z * c)
	else:
		tmp = t_1
	return tmp

Julia

x, y = sort([x, y])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(Float64(-4.0 * Float64(a * t)) + Float64(9.0 * Float64(Float64(x * y) / z))) / c)
	tmp = 0.0
	if (z <= -2.8e+70)
		tmp = t_1;
	elseif (z <= -2.25e-35)
		tmp = Float64(Float64(b / Float64(z * c)) - Float64(Float64(Float64(a * 4.0) / z) * Float64(Float64(z * t) / c)));
	elseif (z <= 1.35e-10)
		tmp = Float64(Float64(b + Float64(9.0 * Float64(x * y))) / Float64(z * c));
	elseif (z <= 7.4e+55)
		tmp = Float64(Float64(b - Float64(4.0 * Float64(a * Float64(z * t)))) / Float64(z * c));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = ((-4.0 * (a * t)) + (9.0 * ((x * y) / z))) / c;
	tmp = 0.0;
	if (z <= -2.8e+70)
		tmp = t_1;
	elseif (z <= -2.25e-35)
		tmp = (b / (z * c)) - (((a * 4.0) / z) * ((z * t) / c));
	elseif (z <= 1.35e-10)
		tmp = (b + (9.0 * (x * y))) / (z * c);
	elseif (z <= 7.4e+55)
		tmp = (b - (4.0 * (a * (z * t)))) / (z * c);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision] + N[(9.0 * N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]}, If[LessEqual[z, -2.8e+70], t$95$1, If[LessEqual[z, -2.25e-35], N[(N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(a * 4.0), $MachinePrecision] / z), $MachinePrecision] * N[(N[(z * t), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.35e-10], N[(N[(b + N[(9.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.4e+55], N[(N[(b - N[(4.0 * N[(a * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.7999999999999999e70 or 7.4000000000000004e55 < z

   1. Initial program 55.2%

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

      1. associate-+l- 55.2%

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

      2. associate-*l* 55.2%

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

      3. associate-*l* 62.8%

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

   3. Simplified 62.8%

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

   4. Taylor expanded in b around 0 49.2%

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

   5. Taylor expanded in x around 0 75.4%

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

   6. Taylor expanded in c around 0 81.2%

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

   if -2.7999999999999999e70 < z < -2.25000000000000005e-35

   1. Initial program 78.2%

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

      1. associate-+l- 78.2%

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

      2. associate-*l* 78.2%

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

      3. associate-*l* 82.6%

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

   3. Simplified 82.6%

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

   4. Taylor expanded in x around 0 81.0%

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

      1. div-sub 81.0%

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

      2. associate-*r* 81.0%

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

      3. times-frac 81.2%

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

   6. Applied egg-rr 81.2%

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

   if -2.25000000000000005e-35 < z < 1.35e-10

   1. Initial program 93.6%

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

   2. Taylor expanded in x around inf 79.2%

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

   if 1.35e-10 < z < 7.4000000000000004e55

   1. Initial program 87.1%

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

      1. associate-+l- 87.1%

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

      2. associate-*l* 87.1%

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

      3. associate-*l* 87.2%

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

   3. Simplified 87.2%

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

   4. Taylor expanded in x around 0 86.0%

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

4. Final simplification 80.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+70}:\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right) + 9 \cdot \frac{x \cdot y}{z}}{c}\\ \mathbf{elif}\;z \leq -2.25 \cdot 10^{-35}:\\ \;\;\;\;\frac{b}{z \cdot c} - \frac{a \cdot 4}{z} \cdot \frac{z \cdot t}{c}\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{-10}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \mathbf{elif}\;z \leq 7.4 \cdot 10^{+55}:\\ \;\;\;\;\frac{b - 4 \cdot \left(a \cdot \left(z \cdot t\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right) + 9 \cdot \frac{x \cdot y}{z}}{c}\\ \end{array} \]

Alternative 5: 84.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -2.65 \cdot 10^{+54} \lor \neg \left(z \leq 1.2 \cdot 10^{+56}\right):\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right) + 9 \cdot \frac{x \cdot y}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(9 \cdot x\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= z -2.65e+54) (not (<= z 1.2e+56)))
   (/ (+ (* -4.0 (* a t)) (* 9.0 (/ (* x y) z))) c)
   (/ (+ b (- (* y (* 9.0 x)) (* a (* t (* z 4.0))))) (* z c))))

C

assert(x < y);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((z <= -2.65e+54) || !(z <= 1.2e+56)) {
		tmp = ((-4.0 * (a * t)) + (9.0 * ((x * y) / z))) / c;
	} else {
		tmp = (b + ((y * (9.0 * x)) - (a * (t * (z * 4.0))))) / (z * c);
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
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 <= (-2.65d+54)) .or. (.not. (z <= 1.2d+56))) then
        tmp = (((-4.0d0) * (a * t)) + (9.0d0 * ((x * y) / z))) / c
    else
        tmp = (b + ((y * (9.0d0 * x)) - (a * (t * (z * 4.0d0))))) / (z * c)
    end if
    code = tmp
end function

Java

assert x < y;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((z <= -2.65e+54) || !(z <= 1.2e+56)) {
		tmp = ((-4.0 * (a * t)) + (9.0 * ((x * y) / z))) / c;
	} else {
		tmp = (b + ((y * (9.0 * x)) - (a * (t * (z * 4.0))))) / (z * c);
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if (z <= -2.65e+54) or not (z <= 1.2e+56):
		tmp = ((-4.0 * (a * t)) + (9.0 * ((x * y) / z))) / c
	else:
		tmp = (b + ((y * (9.0 * x)) - (a * (t * (z * 4.0))))) / (z * c)
	return tmp

Julia

x, y = sort([x, y])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((z <= -2.65e+54) || !(z <= 1.2e+56))
		tmp = Float64(Float64(Float64(-4.0 * Float64(a * t)) + Float64(9.0 * Float64(Float64(x * y) / z))) / c);
	else
		tmp = Float64(Float64(b + Float64(Float64(y * Float64(9.0 * x)) - Float64(a * Float64(t * Float64(z * 4.0))))) / Float64(z * c));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((z <= -2.65e+54) || ~((z <= 1.2e+56)))
		tmp = ((-4.0 * (a * t)) + (9.0 * ((x * y) / z))) / c;
	else
		tmp = (b + ((y * (9.0 * x)) - (a * (t * (z * 4.0))))) / (z * c);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[z, -2.65e+54], N[Not[LessEqual[z, 1.2e+56]], $MachinePrecision]], N[(N[(N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision] + N[(9.0 * N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], N[(N[(b + N[(N[(y * N[(9.0 * x), $MachinePrecision]), $MachinePrecision] - N[(a * N[(t * N[(z * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.65000000000000009e54 or 1.20000000000000007e56 < z

   1. Initial program 54.2%

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

      1. associate-+l- 54.2%

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

      2. associate-*l* 54.2%

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

      3. associate-*l* 62.4%

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

   3. Simplified 62.4%

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

   4. Taylor expanded in b around 0 48.4%

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

   5. Taylor expanded in x around 0 74.6%

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

   6. Taylor expanded in c around 0 81.0%

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

   if -2.65000000000000009e54 < z < 1.20000000000000007e56

   1. Initial program 92.2%

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

4. Final simplification 87.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.65 \cdot 10^{+54} \lor \neg \left(z \leq 1.2 \cdot 10^{+56}\right):\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right) + 9 \cdot \frac{x \cdot y}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(9 \cdot x\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c}\\ \end{array} \]

Alternative 6: 83.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -2.65 \cdot 10^{+54} \lor \neg \left(z \leq 3.2 \cdot 10^{+197}\right):\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right) + 9 \cdot \frac{x \cdot y}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(9 \cdot y\right) + \left(b - \left(a \cdot t\right) \cdot \left(z \cdot 4\right)\right)}{z \cdot c}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= z -2.65e+54) (not (<= z 3.2e+197)))
   (/ (+ (* -4.0 (* a t)) (* 9.0 (/ (* x y) z))) c)
   (/ (+ (* x (* 9.0 y)) (- b (* (* a t) (* z 4.0)))) (* z c))))

C

assert(x < y);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((z <= -2.65e+54) || !(z <= 3.2e+197)) {
		tmp = ((-4.0 * (a * t)) + (9.0 * ((x * y) / z))) / c;
	} else {
		tmp = ((x * (9.0 * y)) + (b - ((a * t) * (z * 4.0)))) / (z * c);
	}
	return tmp;
}

Fortran

NOTE: x and y 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 <= (-2.65d+54)) .or. (.not. (z <= 3.2d+197))) then
        tmp = (((-4.0d0) * (a * t)) + (9.0d0 * ((x * y) / z))) / c
    else
        tmp = ((x * (9.0d0 * y)) + (b - ((a * t) * (z * 4.0d0)))) / (z * c)
    end if
    code = tmp
end function

Java

assert x < y;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((z <= -2.65e+54) || !(z <= 3.2e+197)) {
		tmp = ((-4.0 * (a * t)) + (9.0 * ((x * y) / z))) / c;
	} else {
		tmp = ((x * (9.0 * y)) + (b - ((a * t) * (z * 4.0)))) / (z * c);
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if (z <= -2.65e+54) or not (z <= 3.2e+197):
		tmp = ((-4.0 * (a * t)) + (9.0 * ((x * y) / z))) / c
	else:
		tmp = ((x * (9.0 * y)) + (b - ((a * t) * (z * 4.0)))) / (z * c)
	return tmp

Julia

x, y = sort([x, y])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((z <= -2.65e+54) || !(z <= 3.2e+197))
		tmp = Float64(Float64(Float64(-4.0 * Float64(a * t)) + Float64(9.0 * Float64(Float64(x * y) / z))) / c);
	else
		tmp = Float64(Float64(Float64(x * Float64(9.0 * y)) + Float64(b - Float64(Float64(a * t) * Float64(z * 4.0)))) / Float64(z * c));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((z <= -2.65e+54) || ~((z <= 3.2e+197)))
		tmp = ((-4.0 * (a * t)) + (9.0 * ((x * y) / z))) / c;
	else
		tmp = ((x * (9.0 * y)) + (b - ((a * t) * (z * 4.0)))) / (z * c);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[z, -2.65e+54], N[Not[LessEqual[z, 3.2e+197]], $MachinePrecision]], N[(N[(N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision] + N[(9.0 * N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], N[(N[(N[(x * N[(9.0 * y), $MachinePrecision]), $MachinePrecision] + N[(b - N[(N[(a * t), $MachinePrecision] * N[(z * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.65000000000000009e54 or 3.1999999999999998e197 < z

   1. Initial program 50.2%

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

      1. associate-+l- 50.2%

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

      2. associate-*l* 50.2%

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

      3. associate-*l* 54.7%

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

   3. Simplified 54.7%

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

   4. Taylor expanded in b around 0 45.9%

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

   5. Taylor expanded in x around 0 76.3%

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

   6. Taylor expanded in c around 0 82.7%

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

   if -2.65000000000000009e54 < z < 3.1999999999999998e197

   1. Initial program 87.8%

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

      1. associate-+l- 87.8%

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

      2. associate-*l* 87.8%

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

      3. associate-*l* 90.7%

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

   3. Simplified 90.7%

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

4. Final simplification 87.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.65 \cdot 10^{+54} \lor \neg \left(z \leq 3.2 \cdot 10^{+197}\right):\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right) + 9 \cdot \frac{x \cdot y}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(9 \cdot y\right) + \left(b - \left(a \cdot t\right) \cdot \left(z \cdot 4\right)\right)}{z \cdot c}\\ \end{array} \]

Alternative 7: 68.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} t_1 := \frac{b - 4 \cdot \left(a \cdot \left(z \cdot t\right)\right)}{z \cdot c}\\ \mathbf{if}\;z \leq -2.15 \cdot 10^{+54}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;z \leq -5.6 \cdot 10^{-86}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{-13}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{+197}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{a \cdot t}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (- b (* 4.0 (* a (* z t)))) (* z c))))
   (if (<= z -2.15e+54)
     (* -4.0 (/ a (/ c t)))
     (if (<= z -5.6e-86)
       t_1
       (if (<= z 4.8e-13)
         (/ (+ b (* 9.0 (* x y))) (* z c))
         (if (<= z 2.5e+197) t_1 (* -4.0 (/ (* a t) c))))))))

C

assert(x < y);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (b - (4.0 * (a * (z * t)))) / (z * c);
	double tmp;
	if (z <= -2.15e+54) {
		tmp = -4.0 * (a / (c / t));
	} else if (z <= -5.6e-86) {
		tmp = t_1;
	} else if (z <= 4.8e-13) {
		tmp = (b + (9.0 * (x * y))) / (z * c);
	} else if (z <= 2.5e+197) {
		tmp = t_1;
	} else {
		tmp = -4.0 * ((a * t) / c);
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (b - (4.0d0 * (a * (z * t)))) / (z * c)
    if (z <= (-2.15d+54)) then
        tmp = (-4.0d0) * (a / (c / t))
    else if (z <= (-5.6d-86)) then
        tmp = t_1
    else if (z <= 4.8d-13) then
        tmp = (b + (9.0d0 * (x * y))) / (z * c)
    else if (z <= 2.5d+197) then
        tmp = t_1
    else
        tmp = (-4.0d0) * ((a * t) / c)
    end if
    code = tmp
end function

Java

assert x < y;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (b - (4.0 * (a * (z * t)))) / (z * c);
	double tmp;
	if (z <= -2.15e+54) {
		tmp = -4.0 * (a / (c / t));
	} else if (z <= -5.6e-86) {
		tmp = t_1;
	} else if (z <= 4.8e-13) {
		tmp = (b + (9.0 * (x * y))) / (z * c);
	} else if (z <= 2.5e+197) {
		tmp = t_1;
	} else {
		tmp = -4.0 * ((a * t) / c);
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y, z, t, a, b, c):
	t_1 = (b - (4.0 * (a * (z * t)))) / (z * c)
	tmp = 0
	if z <= -2.15e+54:
		tmp = -4.0 * (a / (c / t))
	elif z <= -5.6e-86:
		tmp = t_1
	elif z <= 4.8e-13:
		tmp = (b + (9.0 * (x * y))) / (z * c)
	elif z <= 2.5e+197:
		tmp = t_1
	else:
		tmp = -4.0 * ((a * t) / c)
	return tmp

Julia

x, y = sort([x, y])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(b - Float64(4.0 * Float64(a * Float64(z * t)))) / Float64(z * c))
	tmp = 0.0
	if (z <= -2.15e+54)
		tmp = Float64(-4.0 * Float64(a / Float64(c / t)));
	elseif (z <= -5.6e-86)
		tmp = t_1;
	elseif (z <= 4.8e-13)
		tmp = Float64(Float64(b + Float64(9.0 * Float64(x * y))) / Float64(z * c));
	elseif (z <= 2.5e+197)
		tmp = t_1;
	else
		tmp = Float64(-4.0 * Float64(Float64(a * t) / c));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (b - (4.0 * (a * (z * t)))) / (z * c);
	tmp = 0.0;
	if (z <= -2.15e+54)
		tmp = -4.0 * (a / (c / t));
	elseif (z <= -5.6e-86)
		tmp = t_1;
	elseif (z <= 4.8e-13)
		tmp = (b + (9.0 * (x * y))) / (z * c);
	elseif (z <= 2.5e+197)
		tmp = t_1;
	else
		tmp = -4.0 * ((a * t) / c);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(b - N[(4.0 * N[(a * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.15e+54], N[(-4.0 * N[(a / N[(c / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -5.6e-86], t$95$1, If[LessEqual[z, 4.8e-13], N[(N[(b + N[(9.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.5e+197], t$95$1, N[(-4.0 * N[(N[(a * t), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.14999999999999988e54

   1. Initial program 56.8%

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

   2. Taylor expanded in z around inf 69.8%

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

      1. *-commutative 69.8%

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

      2. associate-/l* 72.8%

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

   4. Simplified 72.8%

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

   if -2.14999999999999988e54 < z < -5.60000000000000019e-86 or 4.7999999999999997e-13 < z < 2.50000000000000004e197

   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

      1. associate-+l- 80.6%

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

      2. associate-*l* 80.6%

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

      3. associate-*l* 86.9%

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

   3. Simplified 86.9%

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

   4. Taylor expanded in x around 0 72.2%

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

   if -5.60000000000000019e-86 < z < 4.7999999999999997e-13

   1. Initial program 93.8%

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

   2. Taylor expanded in x around inf 81.8%

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

   if 2.50000000000000004e197 < z

   1. Initial program 36.2%

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

   2. Taylor expanded in z around inf 73.0%

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

4. Final simplification 75.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.15 \cdot 10^{+54}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;z \leq -5.6 \cdot 10^{-86}:\\ \;\;\;\;\frac{b - 4 \cdot \left(a \cdot \left(z \cdot t\right)\right)}{z \cdot c}\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{-13}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{+197}:\\ \;\;\;\;\frac{b - 4 \cdot \left(a \cdot \left(z \cdot t\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{a \cdot t}{c}\\ \end{array} \]

Alternative 8: 48.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} t_1 := 9 \cdot \left(\frac{x}{c} \cdot \frac{y}{z}\right)\\ \mathbf{if}\;a \leq -1 \cdot 10^{-100}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;a \leq -4 \cdot 10^{-200}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.32 \cdot 10^{-140}:\\ \;\;\;\;b \cdot \frac{1}{z \cdot c}\\ \mathbf{elif}\;a \leq 3.9 \cdot 10^{-33}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* 9.0 (* (/ x c) (/ y z)))))
   (if (<= a -1e-100)
     (* -4.0 (/ a (/ c t)))
     (if (<= a -4e-200)
       t_1
       (if (<= a 1.32e-140)
         (* b (/ 1.0 (* z c)))
         (if (<= a 3.9e-33) t_1 (* -4.0 (* t (/ a c)))))))))

C

assert(x < y);
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 <= -1e-100) {
		tmp = -4.0 * (a / (c / t));
	} else if (a <= -4e-200) {
		tmp = t_1;
	} else if (a <= 1.32e-140) {
		tmp = b * (1.0 / (z * c));
	} else if (a <= 3.9e-33) {
		tmp = t_1;
	} else {
		tmp = -4.0 * (t * (a / c));
	}
	return tmp;
}

Fortran

NOTE: x and y 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 <= (-1d-100)) then
        tmp = (-4.0d0) * (a / (c / t))
    else if (a <= (-4d-200)) then
        tmp = t_1
    else if (a <= 1.32d-140) then
        tmp = b * (1.0d0 / (z * c))
    else if (a <= 3.9d-33) then
        tmp = t_1
    else
        tmp = (-4.0d0) * (t * (a / c))
    end if
    code = tmp
end function

Java

assert x < y;
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 <= -1e-100) {
		tmp = -4.0 * (a / (c / t));
	} else if (a <= -4e-200) {
		tmp = t_1;
	} else if (a <= 1.32e-140) {
		tmp = b * (1.0 / (z * c));
	} else if (a <= 3.9e-33) {
		tmp = t_1;
	} else {
		tmp = -4.0 * (t * (a / c));
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y, z, t, a, b, c):
	t_1 = 9.0 * ((x / c) * (y / z))
	tmp = 0
	if a <= -1e-100:
		tmp = -4.0 * (a / (c / t))
	elif a <= -4e-200:
		tmp = t_1
	elif a <= 1.32e-140:
		tmp = b * (1.0 / (z * c))
	elif a <= 3.9e-33:
		tmp = t_1
	else:
		tmp = -4.0 * (t * (a / c))
	return tmp

Julia

x, y = sort([x, y])
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 <= -1e-100)
		tmp = Float64(-4.0 * Float64(a / Float64(c / t)));
	elseif (a <= -4e-200)
		tmp = t_1;
	elseif (a <= 1.32e-140)
		tmp = Float64(b * Float64(1.0 / Float64(z * c)));
	elseif (a <= 3.9e-33)
		tmp = t_1;
	else
		tmp = Float64(-4.0 * Float64(t * Float64(a / c)));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = 9.0 * ((x / c) * (y / z));
	tmp = 0.0;
	if (a <= -1e-100)
		tmp = -4.0 * (a / (c / t));
	elseif (a <= -4e-200)
		tmp = t_1;
	elseif (a <= 1.32e-140)
		tmp = b * (1.0 / (z * c));
	elseif (a <= 3.9e-33)
		tmp = t_1;
	else
		tmp = -4.0 * (t * (a / c));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
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, -1e-100], N[(-4.0 * N[(a / N[(c / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -4e-200], t$95$1, If[LessEqual[a, 1.32e-140], N[(b * N[(1.0 / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.9e-33], t$95$1, N[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1e-100

   1. Initial program 81.6%

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

   2. Taylor expanded in z around inf 57.8%

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

      1. *-commutative 57.8%

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

      2. associate-/l* 60.2%

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

   4. Simplified 60.2%

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

   if -1e-100 < a < -3.9999999999999999e-200 or 1.32e-140 < a < 3.89999999999999974e-33

   1. Initial program 60.5%

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

   2. Taylor expanded in x around inf 25.4%

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

      1. times-frac 36.2%

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

   4. Simplified 36.2%

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

   if -3.9999999999999999e-200 < a < 1.32e-140

   1. Initial program 77.4%

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

      1. associate-+l- 77.4%

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

      2. associate-*l* 77.4%

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

      3. fma-neg 77.4%

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

      4. sub-neg 77.4%

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

      5. distribute-neg-in 77.4%

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

      6. remove-double-neg 77.4%

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

      7. +-commutative 77.4%

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

      8. unsub-neg 77.4%

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

      9. associate-*l* 85.4%

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

      10. *-commutative 85.4%

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

      11. associate-*l* 85.4%

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

   3. Simplified 85.4%

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

      1. div-inv 85.2%

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

      2. cancel-sign-sub-inv 85.2%

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

      3. associate-*r* 85.2%

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

      4. metadata-eval 85.2%

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

   5. Applied egg-rr 85.2%

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

   6. Taylor expanded in b around inf 46.0%

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

   if 3.89999999999999974e-33 < a

   1. Initial program 73.2%

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

      1. associate-+l- 73.2%

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

      2. associate-*l* 73.3%

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

      3. fma-neg 77.4%

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

      4. sub-neg 77.4%

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

      5. distribute-neg-in 77.4%

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

      6. remove-double-neg 77.4%

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

      7. +-commutative 77.4%

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

      8. unsub-neg 77.4%

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

      9. associate-*l* 77.5%

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

      10. *-commutative 77.5%

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

      11. associate-*l* 77.5%

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

   3. Simplified 77.5%

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

      1. associate-/r* 74.0%

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

      2. div-inv 74.0%

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

      3. cancel-sign-sub-inv 74.0%

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

      4. associate-*r* 74.0%

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

      5. metadata-eval 74.0%

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

   5. Applied egg-rr 74.0%

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

   6. Taylor expanded in z around inf 63.1%

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

      1. associate-/l* 69.4%

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

      2. associate-/r/ 69.5%

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

   8. Simplified 69.5%

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

4. Final simplification 55.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1 \cdot 10^{-100}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;a \leq -4 \cdot 10^{-200}:\\ \;\;\;\;9 \cdot \left(\frac{x}{c} \cdot \frac{y}{z}\right)\\ \mathbf{elif}\;a \leq 1.32 \cdot 10^{-140}:\\ \;\;\;\;b \cdot \frac{1}{z \cdot c}\\ \mathbf{elif}\;a \leq 3.9 \cdot 10^{-33}:\\ \;\;\;\;9 \cdot \left(\frac{x}{c} \cdot \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \end{array} \]

Alternative 9: 48.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq -7.4 \cdot 10^{-101}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;a \leq -5.5 \cdot 10^{-200}:\\ \;\;\;\;\frac{\frac{9 \cdot x}{\frac{z}{y}}}{c}\\ \mathbf{elif}\;a \leq 10^{-140}:\\ \;\;\;\;b \cdot \frac{1}{z \cdot c}\\ \mathbf{elif}\;a \leq 2.5 \cdot 10^{-29}:\\ \;\;\;\;9 \cdot \left(\frac{x}{c} \cdot \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= a -7.4e-101)
   (* -4.0 (/ a (/ c t)))
   (if (<= a -5.5e-200)
     (/ (/ (* 9.0 x) (/ z y)) c)
     (if (<= a 1e-140)
       (* b (/ 1.0 (* z c)))
       (if (<= a 2.5e-29)
         (* 9.0 (* (/ x c) (/ y z)))
         (* -4.0 (* t (/ a c))))))))

C

assert(x < y);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (a <= -7.4e-101) {
		tmp = -4.0 * (a / (c / t));
	} else if (a <= -5.5e-200) {
		tmp = ((9.0 * x) / (z / y)) / c;
	} else if (a <= 1e-140) {
		tmp = b * (1.0 / (z * c));
	} else if (a <= 2.5e-29) {
		tmp = 9.0 * ((x / c) * (y / z));
	} else {
		tmp = -4.0 * (t * (a / c));
	}
	return tmp;
}

Fortran

NOTE: x and y 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 <= (-7.4d-101)) then
        tmp = (-4.0d0) * (a / (c / t))
    else if (a <= (-5.5d-200)) then
        tmp = ((9.0d0 * x) / (z / y)) / c
    else if (a <= 1d-140) then
        tmp = b * (1.0d0 / (z * c))
    else if (a <= 2.5d-29) then
        tmp = 9.0d0 * ((x / c) * (y / z))
    else
        tmp = (-4.0d0) * (t * (a / c))
    end if
    code = tmp
end function

Java

assert x < y;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (a <= -7.4e-101) {
		tmp = -4.0 * (a / (c / t));
	} else if (a <= -5.5e-200) {
		tmp = ((9.0 * x) / (z / y)) / c;
	} else if (a <= 1e-140) {
		tmp = b * (1.0 / (z * c));
	} else if (a <= 2.5e-29) {
		tmp = 9.0 * ((x / c) * (y / z));
	} else {
		tmp = -4.0 * (t * (a / c));
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if a <= -7.4e-101:
		tmp = -4.0 * (a / (c / t))
	elif a <= -5.5e-200:
		tmp = ((9.0 * x) / (z / y)) / c
	elif a <= 1e-140:
		tmp = b * (1.0 / (z * c))
	elif a <= 2.5e-29:
		tmp = 9.0 * ((x / c) * (y / z))
	else:
		tmp = -4.0 * (t * (a / c))
	return tmp

Julia

x, y = sort([x, y])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (a <= -7.4e-101)
		tmp = Float64(-4.0 * Float64(a / Float64(c / t)));
	elseif (a <= -5.5e-200)
		tmp = Float64(Float64(Float64(9.0 * x) / Float64(z / y)) / c);
	elseif (a <= 1e-140)
		tmp = Float64(b * Float64(1.0 / Float64(z * c)));
	elseif (a <= 2.5e-29)
		tmp = Float64(9.0 * Float64(Float64(x / c) * Float64(y / z)));
	else
		tmp = Float64(-4.0 * Float64(t * Float64(a / c)));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (a <= -7.4e-101)
		tmp = -4.0 * (a / (c / t));
	elseif (a <= -5.5e-200)
		tmp = ((9.0 * x) / (z / y)) / c;
	elseif (a <= 1e-140)
		tmp = b * (1.0 / (z * c));
	elseif (a <= 2.5e-29)
		tmp = 9.0 * ((x / c) * (y / z));
	else
		tmp = -4.0 * (t * (a / c));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[a, -7.4e-101], N[(-4.0 * N[(a / N[(c / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -5.5e-200], N[(N[(N[(9.0 * x), $MachinePrecision] / N[(z / y), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[a, 1e-140], N[(b * N[(1.0 / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.5e-29], N[(9.0 * N[(N[(x / c), $MachinePrecision] * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -7.4000000000000001e-101

   1. Initial program 81.6%

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

   2. Taylor expanded in z around inf 57.8%

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

      1. *-commutative 57.8%

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

      2. associate-/l* 60.2%

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

   4. Simplified 60.2%

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

   if -7.4000000000000001e-101 < a < -5.4999999999999996e-200

   1. Initial program 70.9%

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

      1. associate-+l- 70.9%

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

      2. associate-*l* 70.9%

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

      3. associate-*l* 76.8%

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

   3. Simplified 76.8%

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

   4. Taylor expanded in b around 0 30.5%

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

   5. Taylor expanded in x around 0 53.2%

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

   6. Taylor expanded in c around 0 53.5%

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

   7. Taylor expanded in a around 0 19.9%

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

      1. associate-/l* 25.5%

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

      2. associate-*r/ 25.5%

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

   9. Simplified 25.5%

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

   if -5.4999999999999996e-200 < a < 9.9999999999999998e-141

   1. Initial program 77.4%

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

      1. associate-+l- 77.4%

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

      2. associate-*l* 77.4%

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

      3. fma-neg 77.4%

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

      4. sub-neg 77.4%

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

      5. distribute-neg-in 77.4%

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

      6. remove-double-neg 77.4%

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

      7. +-commutative 77.4%

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

      8. unsub-neg 77.4%

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

      9. associate-*l* 85.4%

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

      10. *-commutative 85.4%

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

      11. associate-*l* 85.4%

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

   3. Simplified 85.4%

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

      1. div-inv 85.2%

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

      2. cancel-sign-sub-inv 85.2%

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

      3. associate-*r* 85.2%

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

      4. metadata-eval 85.2%

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

   5. Applied egg-rr 85.2%

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

   6. Taylor expanded in b around inf 46.0%

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

   if 9.9999999999999998e-141 < a < 2.49999999999999993e-29

   1. Initial program 55.5%

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

   2. Taylor expanded in x around inf 28.0%

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

      1. times-frac 41.4%

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

   4. Simplified 41.4%

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

   if 2.49999999999999993e-29 < a

   1. Initial program 72.9%

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

      1. associate-+l- 72.9%

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

      2. associate-*l* 72.9%

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

      3. fma-neg 77.0%

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

      4. sub-neg 77.0%

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

      5. distribute-neg-in 77.0%

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

      6. remove-double-neg 77.0%

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

      7. +-commutative 77.0%

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

      8. unsub-neg 77.0%

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

      9. associate-*l* 77.2%

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

      10. *-commutative 77.2%

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

      11. associate-*l* 77.2%

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

   3. Simplified 77.2%

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

      1. associate-/r* 73.7%

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

      2. div-inv 73.6%

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

      3. cancel-sign-sub-inv 73.6%

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

      4. associate-*r* 73.6%

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

      5. metadata-eval 73.6%

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

   5. Applied egg-rr 73.6%

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

   6. Taylor expanded in z around inf 62.6%

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

      1. associate-/l* 68.9%

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

      2. associate-/r/ 69.1%

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

   8. Simplified 69.1%

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

4. Final simplification 55.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7.4 \cdot 10^{-101}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;a \leq -5.5 \cdot 10^{-200}:\\ \;\;\;\;\frac{\frac{9 \cdot x}{\frac{z}{y}}}{c}\\ \mathbf{elif}\;a \leq 10^{-140}:\\ \;\;\;\;b \cdot \frac{1}{z \cdot c}\\ \mathbf{elif}\;a \leq 2.5 \cdot 10^{-29}:\\ \;\;\;\;9 \cdot \left(\frac{x}{c} \cdot \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \end{array} \]

Alternative 10: 50.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} t_1 := -4 \cdot \left(t \cdot \frac{a}{c}\right)\\ t_2 := \frac{\frac{b}{c}}{z}\\ \mathbf{if}\;b \leq -8.5 \cdot 10^{+78}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 5.5 \cdot 10^{-26}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 2.95 \cdot 10^{+146}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 1.85 \cdot 10^{+198}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* -4.0 (* t (/ a c)))) (t_2 (/ (/ b c) z)))
   (if (<= b -8.5e+78)
     t_2
     (if (<= b 5.5e-26)
       t_1
       (if (<= b 2.95e+146) t_2 (if (<= b 1.85e+198) t_1 (/ b (* z c))))))))

C

assert(x < y);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = -4.0 * (t * (a / c));
	double t_2 = (b / c) / z;
	double tmp;
	if (b <= -8.5e+78) {
		tmp = t_2;
	} else if (b <= 5.5e-26) {
		tmp = t_1;
	} else if (b <= 2.95e+146) {
		tmp = t_2;
	} else if (b <= 1.85e+198) {
		tmp = t_1;
	} else {
		tmp = b / (z * c);
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (-4.0d0) * (t * (a / c))
    t_2 = (b / c) / z
    if (b <= (-8.5d+78)) then
        tmp = t_2
    else if (b <= 5.5d-26) then
        tmp = t_1
    else if (b <= 2.95d+146) then
        tmp = t_2
    else if (b <= 1.85d+198) then
        tmp = t_1
    else
        tmp = b / (z * c)
    end if
    code = tmp
end function

Java

assert x < y;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = -4.0 * (t * (a / c));
	double t_2 = (b / c) / z;
	double tmp;
	if (b <= -8.5e+78) {
		tmp = t_2;
	} else if (b <= 5.5e-26) {
		tmp = t_1;
	} else if (b <= 2.95e+146) {
		tmp = t_2;
	} else if (b <= 1.85e+198) {
		tmp = t_1;
	} else {
		tmp = b / (z * c);
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y, z, t, a, b, c):
	t_1 = -4.0 * (t * (a / c))
	t_2 = (b / c) / z
	tmp = 0
	if b <= -8.5e+78:
		tmp = t_2
	elif b <= 5.5e-26:
		tmp = t_1
	elif b <= 2.95e+146:
		tmp = t_2
	elif b <= 1.85e+198:
		tmp = t_1
	else:
		tmp = b / (z * c)
	return tmp

Julia

x, y = sort([x, y])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(-4.0 * Float64(t * Float64(a / c)))
	t_2 = Float64(Float64(b / c) / z)
	tmp = 0.0
	if (b <= -8.5e+78)
		tmp = t_2;
	elseif (b <= 5.5e-26)
		tmp = t_1;
	elseif (b <= 2.95e+146)
		tmp = t_2;
	elseif (b <= 1.85e+198)
		tmp = t_1;
	else
		tmp = Float64(b / Float64(z * c));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = -4.0 * (t * (a / c));
	t_2 = (b / c) / z;
	tmp = 0.0;
	if (b <= -8.5e+78)
		tmp = t_2;
	elseif (b <= 5.5e-26)
		tmp = t_1;
	elseif (b <= 2.95e+146)
		tmp = t_2;
	elseif (b <= 1.85e+198)
		tmp = t_1;
	else
		tmp = b / (z * c);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision]}, If[LessEqual[b, -8.5e+78], t$95$2, If[LessEqual[b, 5.5e-26], t$95$1, If[LessEqual[b, 2.95e+146], t$95$2, If[LessEqual[b, 1.85e+198], t$95$1, N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -8.50000000000000079e78 or 5.5000000000000005e-26 < b < 2.95000000000000015e146

   1. Initial program 72.2%

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

      1. associate-+l- 72.2%

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

      2. associate-*l* 72.3%

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

      3. fma-neg 74.8%

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

      4. sub-neg 74.8%

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

      5. distribute-neg-in 74.8%

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

      6. remove-double-neg 74.8%

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

      7. +-commutative 74.8%

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

      8. unsub-neg 74.8%

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

      9. associate-*l* 77.1%

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

      10. *-commutative 77.1%

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

      11. associate-*l* 77.1%

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

   3. Simplified 77.1%

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

      1. div-inv 77.0%

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

      2. cancel-sign-sub-inv 77.0%

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

      3. associate-*r* 77.0%

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

      4. metadata-eval 77.0%

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

   5. Applied egg-rr 77.0%

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

   6. Taylor expanded in b around inf 50.7%

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

      1. associate-*r/ 50.7%

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

      2. frac-times 50.7%

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

      3. associate-*l/ 56.7%

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

      4. un-div-inv 56.7%

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

   8. Applied egg-rr 56.7%

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

   if -8.50000000000000079e78 < b < 5.5000000000000005e-26 or 2.95000000000000015e146 < b < 1.8499999999999999e198

   1. Initial program 72.7%

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

      1. associate-+l- 72.7%

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

      2. associate-*l* 72.8%

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

      3. fma-neg 74.1%

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

      4. sub-neg 74.1%

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

      5. distribute-neg-in 74.1%

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

      6. remove-double-neg 74.1%

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

      7. +-commutative 74.1%

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

      8. unsub-neg 74.1%

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

      9. associate-*l* 78.7%

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

      10. *-commutative 78.7%

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

      11. associate-*l* 78.7%

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

   3. Simplified 78.7%

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

      1. associate-/r* 82.8%

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

      2. div-inv 82.8%

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

      3. cancel-sign-sub-inv 82.8%

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

      4. associate-*r* 82.8%

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

      5. metadata-eval 82.8%

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

   5. Applied egg-rr 82.8%

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

   6. Taylor expanded in z around inf 60.0%

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

      1. associate-/l* 63.7%

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

      2. associate-/r/ 61.4%

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

   8. Simplified 61.4%

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

   if 1.8499999999999999e198 < b

   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. Taylor expanded in b around inf 73.7%

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

      1. *-commutative 73.7%

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

   4. Simplified 73.7%

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

4. Final simplification 61.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -8.5 \cdot 10^{+78}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;b \leq 5.5 \cdot 10^{-26}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;b \leq 2.95 \cdot 10^{+146}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;b \leq 1.85 \cdot 10^{+198}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \end{array} \]

Alternative 11: 50.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} t_1 := -4 \cdot \left(t \cdot \frac{a}{c}\right)\\ t_2 := \frac{\frac{b}{c}}{z}\\ \mathbf{if}\;b \leq -2.25 \cdot 10^{+79}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 2.15 \cdot 10^{-32}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 1.85 \cdot 10^{+146}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 3.8 \cdot 10^{+195}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot \frac{\frac{1}{z}}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y 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 (* t (/ a c)))) (t_2 (/ (/ b c) z)))
   (if (<= b -2.25e+79)
     t_2
     (if (<= b 2.15e-32)
       t_1
       (if (<= b 1.85e+146)
         t_2
         (if (<= b 3.8e+195) t_1 (* b (/ (/ 1.0 z) c))))))))

C

assert(x < y);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = -4.0 * (t * (a / c));
	double t_2 = (b / c) / z;
	double tmp;
	if (b <= -2.25e+79) {
		tmp = t_2;
	} else if (b <= 2.15e-32) {
		tmp = t_1;
	} else if (b <= 1.85e+146) {
		tmp = t_2;
	} else if (b <= 3.8e+195) {
		tmp = t_1;
	} else {
		tmp = b * ((1.0 / z) / c);
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (-4.0d0) * (t * (a / c))
    t_2 = (b / c) / z
    if (b <= (-2.25d+79)) then
        tmp = t_2
    else if (b <= 2.15d-32) then
        tmp = t_1
    else if (b <= 1.85d+146) then
        tmp = t_2
    else if (b <= 3.8d+195) then
        tmp = t_1
    else
        tmp = b * ((1.0d0 / z) / c)
    end if
    code = tmp
end function

Java

assert x < y;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = -4.0 * (t * (a / c));
	double t_2 = (b / c) / z;
	double tmp;
	if (b <= -2.25e+79) {
		tmp = t_2;
	} else if (b <= 2.15e-32) {
		tmp = t_1;
	} else if (b <= 1.85e+146) {
		tmp = t_2;
	} else if (b <= 3.8e+195) {
		tmp = t_1;
	} else {
		tmp = b * ((1.0 / z) / c);
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y, z, t, a, b, c):
	t_1 = -4.0 * (t * (a / c))
	t_2 = (b / c) / z
	tmp = 0
	if b <= -2.25e+79:
		tmp = t_2
	elif b <= 2.15e-32:
		tmp = t_1
	elif b <= 1.85e+146:
		tmp = t_2
	elif b <= 3.8e+195:
		tmp = t_1
	else:
		tmp = b * ((1.0 / z) / c)
	return tmp

Julia

x, y = sort([x, y])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(-4.0 * Float64(t * Float64(a / c)))
	t_2 = Float64(Float64(b / c) / z)
	tmp = 0.0
	if (b <= -2.25e+79)
		tmp = t_2;
	elseif (b <= 2.15e-32)
		tmp = t_1;
	elseif (b <= 1.85e+146)
		tmp = t_2;
	elseif (b <= 3.8e+195)
		tmp = t_1;
	else
		tmp = Float64(b * Float64(Float64(1.0 / z) / c));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = -4.0 * (t * (a / c));
	t_2 = (b / c) / z;
	tmp = 0.0;
	if (b <= -2.25e+79)
		tmp = t_2;
	elseif (b <= 2.15e-32)
		tmp = t_1;
	elseif (b <= 1.85e+146)
		tmp = t_2;
	elseif (b <= 3.8e+195)
		tmp = t_1;
	else
		tmp = b * ((1.0 / z) / c);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision]}, If[LessEqual[b, -2.25e+79], t$95$2, If[LessEqual[b, 2.15e-32], t$95$1, If[LessEqual[b, 1.85e+146], t$95$2, If[LessEqual[b, 3.8e+195], t$95$1, N[(b * N[(N[(1.0 / z), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -2.24999999999999997e79 or 2.14999999999999995e-32 < b < 1.85000000000000002e146

   1. Initial program 72.2%

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

      1. associate-+l- 72.2%

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

      2. associate-*l* 72.3%

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

      3. fma-neg 74.8%

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

      4. sub-neg 74.8%

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

      5. distribute-neg-in 74.8%

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

      6. remove-double-neg 74.8%

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

      7. +-commutative 74.8%

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

      8. unsub-neg 74.8%

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

      9. associate-*l* 77.1%

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

      10. *-commutative 77.1%

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

      11. associate-*l* 77.1%

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

   3. Simplified 77.1%

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

      1. div-inv 77.0%

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

      2. cancel-sign-sub-inv 77.0%

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

      3. associate-*r* 77.0%

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

      4. metadata-eval 77.0%

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

   5. Applied egg-rr 77.0%

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

   6. Taylor expanded in b around inf 50.7%

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

      1. associate-*r/ 50.7%

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

      2. frac-times 50.7%

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

      3. associate-*l/ 56.7%

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

      4. un-div-inv 56.7%

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

   8. Applied egg-rr 56.7%

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

   if -2.24999999999999997e79 < b < 2.14999999999999995e-32 or 1.85000000000000002e146 < b < 3.8e195

   1. Initial program 72.7%

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

      1. associate-+l- 72.7%

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

      2. associate-*l* 72.8%

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

      3. fma-neg 74.1%

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

      4. sub-neg 74.1%

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

      5. distribute-neg-in 74.1%

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

      6. remove-double-neg 74.1%

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

      7. +-commutative 74.1%

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

      8. unsub-neg 74.1%

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

      9. associate-*l* 78.7%

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

      10. *-commutative 78.7%

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

      11. associate-*l* 78.7%

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

   3. Simplified 78.7%

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

      1. associate-/r* 82.8%

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

      2. div-inv 82.8%

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

      3. cancel-sign-sub-inv 82.8%

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

      4. associate-*r* 82.8%

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

      5. metadata-eval 82.8%

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

   5. Applied egg-rr 82.8%

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

   6. Taylor expanded in z around inf 60.0%

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

      1. associate-/l* 63.7%

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

      2. associate-/r/ 61.4%

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

   8. Simplified 61.4%

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

   if 3.8e195 < b

   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-+l- 92.4%

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

      2. associate-*l* 92.4%

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

      3. fma-neg 92.4%

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

      4. sub-neg 92.4%

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

      5. distribute-neg-in 92.4%

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

      6. remove-double-neg 92.4%

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

      7. +-commutative 92.4%

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

      8. unsub-neg 92.4%

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

      9. associate-*l* 92.4%

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

      10. *-commutative 92.4%

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

      11. associate-*l* 92.4%

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

   3. Simplified 92.4%

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

      1. div-inv 92.3%

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

      2. cancel-sign-sub-inv 92.3%

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

      3. associate-*r* 92.3%

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

      4. metadata-eval 92.3%

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

   5. Applied egg-rr 92.3%

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

   6. Taylor expanded in b around inf 73.6%

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

   7. Taylor expanded in z around 0 73.6%

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

      1. associate-/l/ 73.8%

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

   9. Simplified 73.8%

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

4. Final simplification 61.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.25 \cdot 10^{+79}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;b \leq 2.15 \cdot 10^{-32}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;b \leq 1.85 \cdot 10^{+146}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;b \leq 3.8 \cdot 10^{+195}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \frac{\frac{1}{z}}{c}\\ \end{array} \]

Alternative 12: 68.2% accurate, 1.3× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{+53}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;z \leq 8.8 \cdot 10^{+55}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{-4}{\frac{c}{a \cdot t}}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= z -6e+53)
   (* -4.0 (/ a (/ c t)))
   (if (<= z 8.8e+55)
     (/ (+ b (* 9.0 (* x y))) (* z c))
     (/ -4.0 (/ c (* a t))))))

C

assert(x < y);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (z <= -6e+53) {
		tmp = -4.0 * (a / (c / t));
	} else if (z <= 8.8e+55) {
		tmp = (b + (9.0 * (x * y))) / (z * c);
	} else {
		tmp = -4.0 / (c / (a * t));
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (z <= (-6d+53)) then
        tmp = (-4.0d0) * (a / (c / t))
    else if (z <= 8.8d+55) then
        tmp = (b + (9.0d0 * (x * y))) / (z * c)
    else
        tmp = (-4.0d0) / (c / (a * t))
    end if
    code = tmp
end function

Java

assert x < y;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (z <= -6e+53) {
		tmp = -4.0 * (a / (c / t));
	} else if (z <= 8.8e+55) {
		tmp = (b + (9.0 * (x * y))) / (z * c);
	} else {
		tmp = -4.0 / (c / (a * t));
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if z <= -6e+53:
		tmp = -4.0 * (a / (c / t))
	elif z <= 8.8e+55:
		tmp = (b + (9.0 * (x * y))) / (z * c)
	else:
		tmp = -4.0 / (c / (a * t))
	return tmp

Julia

x, y = sort([x, y])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (z <= -6e+53)
		tmp = Float64(-4.0 * Float64(a / Float64(c / t)));
	elseif (z <= 8.8e+55)
		tmp = Float64(Float64(b + Float64(9.0 * Float64(x * y))) / Float64(z * c));
	else
		tmp = Float64(-4.0 / Float64(c / Float64(a * t)));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (z <= -6e+53)
		tmp = -4.0 * (a / (c / t));
	elseif (z <= 8.8e+55)
		tmp = (b + (9.0 * (x * y))) / (z * c);
	else
		tmp = -4.0 / (c / (a * t));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[z, -6e+53], N[(-4.0 * N[(a / N[(c / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8.8e+55], N[(N[(b + N[(9.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(-4.0 / N[(c / N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.99999999999999996e53

   1. Initial program 56.8%

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

   2. Taylor expanded in z around inf 69.8%

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

      1. *-commutative 69.8%

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

      2. associate-/l* 72.8%

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

   4. Simplified 72.8%

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

   if -5.99999999999999996e53 < z < 8.80000000000000042e55

   1. Initial program 92.2%

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

   2. Taylor expanded in x around inf 74.5%

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

   if 8.80000000000000042e55 < z

   1. Initial program 51.6%

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

      1. associate-+l- 51.6%

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

      2. associate-*l* 51.6%

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

      3. fma-neg 53.3%

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

      4. sub-neg 53.3%

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

      5. distribute-neg-in 53.3%

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

      6. remove-double-neg 53.3%

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

      7. +-commutative 53.3%

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

      8. unsub-neg 53.3%

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

      9. associate-*l* 64.9%

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

      10. *-commutative 64.9%

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

      11. associate-*l* 64.9%

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

   3. Simplified 64.9%

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

      1. div-inv 64.8%

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

      2. cancel-sign-sub-inv 64.8%

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

      3. associate-*r* 64.8%

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

      4. metadata-eval 64.8%

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

   5. Applied egg-rr 64.8%

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

   6. Taylor expanded in z around 0 64.8%

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

      1. associate-/r* 64.8%

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

   8. Simplified 64.8%

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

   9. Taylor expanded in z around inf 64.5%

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

       1. associate-/l* 63.1%

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

       2. associate-*r/ 63.1%

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

       3. associate-/l* 63.0%

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

       4. associate-/l/ 64.5%

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

   11. Simplified 64.5%

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

4. Final simplification 71.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{+53}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;z \leq 8.8 \cdot 10^{+55}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{-4}{\frac{c}{a \cdot t}}\\ \end{array} \]

Alternative 13: 36.2% accurate, 2.7× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+14}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= z -1e+14) (/ (/ b c) z) (/ b (* z c))))

C

assert(x < y);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (z <= -1e+14) {
		tmp = (b / c) / z;
	} else {
		tmp = b / (z * c);
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
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 <= (-1d+14)) then
        tmp = (b / c) / z
    else
        tmp = b / (z * c)
    end if
    code = tmp
end function

Java

assert x < y;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (z <= -1e+14) {
		tmp = (b / c) / z;
	} else {
		tmp = b / (z * c);
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if z <= -1e+14:
		tmp = (b / c) / z
	else:
		tmp = b / (z * c)
	return tmp

Julia

x, y = sort([x, y])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (z <= -1e+14)
		tmp = Float64(Float64(b / c) / z);
	else
		tmp = Float64(b / Float64(z * c));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (z <= -1e+14)
		tmp = (b / c) / z;
	else
		tmp = b / (z * c);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[z, -1e+14], N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1e14

   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-+l- 62.2%

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

      2. associate-*l* 62.2%

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

      3. fma-neg 65.1%

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

      4. sub-neg 65.1%

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

      5. distribute-neg-in 65.1%

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

      6. remove-double-neg 65.1%

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

      7. +-commutative 65.1%

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

      8. unsub-neg 65.1%

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

      9. associate-*l* 69.3%

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

      10. *-commutative 69.3%

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

      11. associate-*l* 69.3%

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

   3. Simplified 69.3%

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

      1. div-inv 69.2%

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

      2. cancel-sign-sub-inv 69.2%

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

      3. associate-*r* 69.2%

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

      4. metadata-eval 69.2%

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

   5. Applied egg-rr 69.2%

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

   6. Taylor expanded in b around inf 18.1%

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

      1. associate-*r/ 18.1%

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

      2. frac-times 20.7%

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

      3. associate-*l/ 24.8%

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

      4. un-div-inv 24.8%

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

   8. Applied egg-rr 24.8%

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

   if -1e14 < z

   1. Initial program 79.2%

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

   2. Taylor expanded in b around inf 38.3%

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

      1. *-commutative 38.3%

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

   4. Simplified 38.3%

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

4. Final simplification 34.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+14}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \end{array} \]

Alternative 14: 35.4% accurate, 3.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 74.6%

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

2. Taylor expanded in b around inf 32.8%

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

   1. *-commutative 32.8%

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

4. Simplified 32.8%

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

5. Final simplification 32.8%

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

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 2023306 
(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)))