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

Percentage Accurate: 95.2% → 98.8%

Time: 15.9s

Alternatives: 15

Speedup: 0.9×

• Unsound rule application detected in e-graph. Results may not be sound.

• 28.0% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ \left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (+ (- (* x 2.0) (* (* (* y 9.0) z) t)) (* (* a 27.0) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	return ((x * 2.0) - (((y * 9.0) * z) * t)) + ((a * 27.0) * b);
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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
    code = ((x * 2.0d0) - (((y * 9.0d0) * z) * t)) + ((a * 27.0d0) * b)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return ((x * 2.0) - (((y * 9.0) * z) * t)) + ((a * 27.0) * b);
}

Python

def code(x, y, z, t, a, b):
	return ((x * 2.0) - (((y * 9.0) * z) * t)) + ((a * 27.0) * b)

Julia

function code(x, y, z, t, a, b)
	return Float64(Float64(Float64(x * 2.0) - Float64(Float64(Float64(y * 9.0) * z) * t)) + Float64(Float64(a * 27.0) * b))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = ((x * 2.0) - (((y * 9.0) * z) * t)) + ((a * 27.0) * b);
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(N[(x * 2.0), $MachinePrecision] - N[(N[(N[(y * 9.0), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision] + N[(N[(a * 27.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]

Initial Program: 95.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (+ (- (* x 2.0) (* (* (* y 9.0) z) t)) (* (* a 27.0) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	return ((x * 2.0) - (((y * 9.0) * z) * t)) + ((a * 27.0) * b);
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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
    code = ((x * 2.0d0) - (((y * 9.0d0) * z) * t)) + ((a * 27.0d0) * b)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return ((x * 2.0) - (((y * 9.0) * z) * t)) + ((a * 27.0) * b);
}

Python

def code(x, y, z, t, a, b):
	return ((x * 2.0) - (((y * 9.0) * z) * t)) + ((a * 27.0) * b)

Julia

function code(x, y, z, t, a, b)
	return Float64(Float64(Float64(x * 2.0) - Float64(Float64(Float64(y * 9.0) * z) * t)) + Float64(Float64(a * 27.0) * b))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = ((x * 2.0) - (((y * 9.0) * z) * t)) + ((a * 27.0) * b);
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(N[(x * 2.0), $MachinePrecision] - N[(N[(N[(y * 9.0), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision] + N[(N[(a * 27.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]

Alternative 1: 98.8% accurate, 0.1× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq 2 \cdot 10^{-88}:\\ \;\;\;\;\mathsf{fma}\left(a, 27 \cdot b, x \cdot 2 - 9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, 2, \mathsf{fma}\left(t, \left(z \cdot y\right) \cdot -9, b \cdot \left(a \cdot 27\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= z 2e-88)
   (fma a (* 27.0 b) (- (* x 2.0) (* 9.0 (* y (* z t)))))
   (fma x 2.0 (fma t (* (* z y) -9.0) (* b (* a 27.0))))))

C

assert(y < z && z < t);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= 2e-88) {
		tmp = fma(a, (27.0 * b), ((x * 2.0) - (9.0 * (y * (z * t)))));
	} else {
		tmp = fma(x, 2.0, fma(t, ((z * y) * -9.0), (b * (a * 27.0))));
	}
	return tmp;
}

Julia

y, z, t = sort([y, z, t])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= 2e-88)
		tmp = fma(a, Float64(27.0 * b), Float64(Float64(x * 2.0) - Float64(9.0 * Float64(y * Float64(z * t)))));
	else
		tmp = fma(x, 2.0, fma(t, Float64(Float64(z * y) * -9.0), Float64(b * Float64(a * 27.0))));
	end
	return tmp
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, 2e-88], N[(a * N[(27.0 * b), $MachinePrecision] + N[(N[(x * 2.0), $MachinePrecision] - N[(9.0 * N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * 2.0 + N[(t * N[(N[(z * y), $MachinePrecision] * -9.0), $MachinePrecision] + N[(b * N[(a * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 1.99999999999999987e-88

   1. Initial program 97.3%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Step-by-step derivation

      1. +-commutative 97.3%

         \[\leadsto \color{blue}{\left(a \cdot 27\right) \cdot b + \left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)} \]

      2. associate-*l* 97.2%

         \[\leadsto \color{blue}{a \cdot \left(27 \cdot b\right)} + \left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) \]

      3. fma-def 97.2%

         \[\leadsto \color{blue}{\mathsf{fma}\left(a, 27 \cdot b, x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)} \]

      4. associate-*l* 95.6%

         \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, x \cdot 2 - \color{blue}{\left(y \cdot 9\right) \cdot \left(z \cdot t\right)}\right) \]

      5. *-commutative 95.6%

         \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, x \cdot 2 - \color{blue}{\left(9 \cdot y\right)} \cdot \left(z \cdot t\right)\right) \]

      6. associate-*l* 95.6%

         \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, x \cdot 2 - \color{blue}{9 \cdot \left(y \cdot \left(z \cdot t\right)\right)}\right) \]

   3. Simplified 95.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(a, 27 \cdot b, x \cdot 2 - 9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\right)} \]

   if 1.99999999999999987e-88 < z

   1. Initial program 90.0%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l- 90.0%

         \[\leadsto \color{blue}{x \cdot 2 - \left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t - \left(a \cdot 27\right) \cdot b\right)} \]

      2. fma-neg 90.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, 2, -\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t - \left(a \cdot 27\right) \cdot b\right)\right)} \]

      3. neg-sub0 90.0%

         \[\leadsto \mathsf{fma}\left(x, 2, \color{blue}{0 - \left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t - \left(a \cdot 27\right) \cdot b\right)}\right) \]

      4. associate-+l- 90.0%

         \[\leadsto \mathsf{fma}\left(x, 2, \color{blue}{\left(0 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b}\right) \]

      5. neg-sub0 90.0%

         \[\leadsto \mathsf{fma}\left(x, 2, \color{blue}{\left(-\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)} + \left(a \cdot 27\right) \cdot b\right) \]

      6. *-commutative 90.0%

         \[\leadsto \mathsf{fma}\left(x, 2, \left(-\color{blue}{t \cdot \left(\left(y \cdot 9\right) \cdot z\right)}\right) + \left(a \cdot 27\right) \cdot b\right) \]

      7. distribute-rgt-neg-in 90.0%

         \[\leadsto \mathsf{fma}\left(x, 2, \color{blue}{t \cdot \left(-\left(y \cdot 9\right) \cdot z\right)} + \left(a \cdot 27\right) \cdot b\right) \]

      8. fma-def 91.3%

         \[\leadsto \mathsf{fma}\left(x, 2, \color{blue}{\mathsf{fma}\left(t, -\left(y \cdot 9\right) \cdot z, \left(a \cdot 27\right) \cdot b\right)}\right) \]

      9. *-commutative 91.3%

         \[\leadsto \mathsf{fma}\left(x, 2, \mathsf{fma}\left(t, -\color{blue}{z \cdot \left(y \cdot 9\right)}, \left(a \cdot 27\right) \cdot b\right)\right) \]

      10. associate-*r* 91.3%

          \[\leadsto \mathsf{fma}\left(x, 2, \mathsf{fma}\left(t, -\color{blue}{\left(z \cdot y\right) \cdot 9}, \left(a \cdot 27\right) \cdot b\right)\right) \]

      11. distribute-rgt-neg-in 91.3%

          \[\leadsto \mathsf{fma}\left(x, 2, \mathsf{fma}\left(t, \color{blue}{\left(z \cdot y\right) \cdot \left(-9\right)}, \left(a \cdot 27\right) \cdot b\right)\right) \]

      12. *-commutative 91.3%

          \[\leadsto \mathsf{fma}\left(x, 2, \mathsf{fma}\left(t, \color{blue}{\left(y \cdot z\right)} \cdot \left(-9\right), \left(a \cdot 27\right) \cdot b\right)\right) \]

      13. metadata-eval 91.3%

          \[\leadsto \mathsf{fma}\left(x, 2, \mathsf{fma}\left(t, \left(y \cdot z\right) \cdot \color{blue}{-9}, \left(a \cdot 27\right) \cdot b\right)\right) \]

   3. Simplified 91.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, 2, \mathsf{fma}\left(t, \left(y \cdot z\right) \cdot -9, \left(a \cdot 27\right) \cdot b\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 94.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 2 \cdot 10^{-88}:\\ \;\;\;\;\mathsf{fma}\left(a, 27 \cdot b, x \cdot 2 - 9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, 2, \mathsf{fma}\left(t, \left(z \cdot y\right) \cdot -9, b \cdot \left(a \cdot 27\right)\right)\right)\\ \end{array} \]

Alternative 2: 98.6% accurate, 0.1× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq 4.1 \cdot 10^{-86}:\\ \;\;\;\;\mathsf{fma}\left(a, 27 \cdot b, x \cdot 2 - 9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot 27\right) + \left(x \cdot 2 - t \cdot \left(y \cdot \left(z \cdot 9\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= z 4.1e-86)
   (fma a (* 27.0 b) (- (* x 2.0) (* 9.0 (* y (* z t)))))
   (+ (* b (* a 27.0)) (- (* x 2.0) (* t (* y (* z 9.0)))))))

C

assert(y < z && z < t);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= 4.1e-86) {
		tmp = fma(a, (27.0 * b), ((x * 2.0) - (9.0 * (y * (z * t)))));
	} else {
		tmp = (b * (a * 27.0)) + ((x * 2.0) - (t * (y * (z * 9.0))));
	}
	return tmp;
}

Julia

y, z, t = sort([y, z, t])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= 4.1e-86)
		tmp = fma(a, Float64(27.0 * b), Float64(Float64(x * 2.0) - Float64(9.0 * Float64(y * Float64(z * t)))));
	else
		tmp = Float64(Float64(b * Float64(a * 27.0)) + Float64(Float64(x * 2.0) - Float64(t * Float64(y * Float64(z * 9.0)))));
	end
	return tmp
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, 4.1e-86], N[(a * N[(27.0 * b), $MachinePrecision] + N[(N[(x * 2.0), $MachinePrecision] - N[(9.0 * N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * N[(a * 27.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x * 2.0), $MachinePrecision] - N[(t * N[(y * N[(z * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 4.09999999999999979e-86

   1. Initial program 97.3%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Step-by-step derivation

      1. +-commutative 97.3%

         \[\leadsto \color{blue}{\left(a \cdot 27\right) \cdot b + \left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)} \]

      2. associate-*l* 97.2%

         \[\leadsto \color{blue}{a \cdot \left(27 \cdot b\right)} + \left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) \]

      3. fma-def 97.2%

         \[\leadsto \color{blue}{\mathsf{fma}\left(a, 27 \cdot b, x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)} \]

      4. associate-*l* 95.6%

         \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, x \cdot 2 - \color{blue}{\left(y \cdot 9\right) \cdot \left(z \cdot t\right)}\right) \]

      5. *-commutative 95.6%

         \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, x \cdot 2 - \color{blue}{\left(9 \cdot y\right)} \cdot \left(z \cdot t\right)\right) \]

      6. associate-*l* 95.6%

         \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, x \cdot 2 - \color{blue}{9 \cdot \left(y \cdot \left(z \cdot t\right)\right)}\right) \]

   3. Simplified 95.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(a, 27 \cdot b, x \cdot 2 - 9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\right)} \]

   if 4.09999999999999979e-86 < z

   1. Initial program 90.0%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

   2. Taylor expanded in y around 0 90.0%

      \[\leadsto \left(x \cdot 2 - \color{blue}{\left(9 \cdot \left(y \cdot z\right)\right)} \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   3. Step-by-step derivation

      1. expm1-log1p-u 51.5%

         \[\leadsto \left(x \cdot 2 - \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(9 \cdot \left(y \cdot z\right)\right)\right)} \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

      2. expm1-udef 48.4%

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(e^{\mathsf{log1p}\left(9 \cdot \left(y \cdot z\right)\right)} - 1\right)} \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

   4. Applied egg-rr 48.4%

      \[\leadsto \left(x \cdot 2 - \color{blue}{\left(e^{\mathsf{log1p}\left(9 \cdot \left(y \cdot z\right)\right)} - 1\right)} \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   5. Step-by-step derivation

      1. expm1-def 51.5%

         \[\leadsto \left(x \cdot 2 - \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(9 \cdot \left(y \cdot z\right)\right)\right)} \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

      2. expm1-log1p 90.0%

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(9 \cdot \left(y \cdot z\right)\right)} \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

      3. associate-*r* 90.0%

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(\left(9 \cdot y\right) \cdot z\right)} \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

      4. *-commutative 90.0%

         \[\leadsto \left(x \cdot 2 - \left(\color{blue}{\left(y \cdot 9\right)} \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

      5. associate-*l* 90.0%

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(y \cdot \left(9 \cdot z\right)\right)} \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

   6. Simplified 90.0%

      \[\leadsto \left(x \cdot 2 - \color{blue}{\left(y \cdot \left(9 \cdot z\right)\right)} \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
3. Recombined 2 regimes into one program.

4. Final simplification 93.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 4.1 \cdot 10^{-86}:\\ \;\;\;\;\mathsf{fma}\left(a, 27 \cdot b, x \cdot 2 - 9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot 27\right) + \left(x \cdot 2 - t \cdot \left(y \cdot \left(z \cdot 9\right)\right)\right)\\ \end{array} \]

Alternative 3: 43.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ \\ \begin{array}{l} t_1 := -9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ t_2 := 27 \cdot \left(a \cdot b\right)\\ \mathbf{if}\;b \leq -5.5 \cdot 10^{-106}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 2.4 \cdot 10^{-239}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;b \leq 1.6 \cdot 10^{-58}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 8 \cdot 10^{+46}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;b \leq 4 \cdot 10^{+93}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 9.2 \cdot 10^{+159}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;b \leq 3.3 \cdot 10^{+196}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* -9.0 (* y (* z t)))) (t_2 (* 27.0 (* a b))))
   (if (<= b -5.5e-106)
     t_2
     (if (<= b 2.4e-239)
       (* x 2.0)
       (if (<= b 1.6e-58)
         t_1
         (if (<= b 8e+46)
           (* x 2.0)
           (if (<= b 4e+93)
             t_1
             (if (<= b 9.2e+159) (* x 2.0) (if (<= b 3.3e+196) t_1 t_2)))))))))

C

assert(y < z && z < t);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = -9.0 * (y * (z * t));
	double t_2 = 27.0 * (a * b);
	double tmp;
	if (b <= -5.5e-106) {
		tmp = t_2;
	} else if (b <= 2.4e-239) {
		tmp = x * 2.0;
	} else if (b <= 1.6e-58) {
		tmp = t_1;
	} else if (b <= 8e+46) {
		tmp = x * 2.0;
	} else if (b <= 4e+93) {
		tmp = t_1;
	} else if (b <= 9.2e+159) {
		tmp = x * 2.0;
	} else if (b <= 3.3e+196) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (-9.0d0) * (y * (z * t))
    t_2 = 27.0d0 * (a * b)
    if (b <= (-5.5d-106)) then
        tmp = t_2
    else if (b <= 2.4d-239) then
        tmp = x * 2.0d0
    else if (b <= 1.6d-58) then
        tmp = t_1
    else if (b <= 8d+46) then
        tmp = x * 2.0d0
    else if (b <= 4d+93) then
        tmp = t_1
    else if (b <= 9.2d+159) then
        tmp = x * 2.0d0
    else if (b <= 3.3d+196) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

assert y < z && z < t;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = -9.0 * (y * (z * t));
	double t_2 = 27.0 * (a * b);
	double tmp;
	if (b <= -5.5e-106) {
		tmp = t_2;
	} else if (b <= 2.4e-239) {
		tmp = x * 2.0;
	} else if (b <= 1.6e-58) {
		tmp = t_1;
	} else if (b <= 8e+46) {
		tmp = x * 2.0;
	} else if (b <= 4e+93) {
		tmp = t_1;
	} else if (b <= 9.2e+159) {
		tmp = x * 2.0;
	} else if (b <= 3.3e+196) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
def code(x, y, z, t, a, b):
	t_1 = -9.0 * (y * (z * t))
	t_2 = 27.0 * (a * b)
	tmp = 0
	if b <= -5.5e-106:
		tmp = t_2
	elif b <= 2.4e-239:
		tmp = x * 2.0
	elif b <= 1.6e-58:
		tmp = t_1
	elif b <= 8e+46:
		tmp = x * 2.0
	elif b <= 4e+93:
		tmp = t_1
	elif b <= 9.2e+159:
		tmp = x * 2.0
	elif b <= 3.3e+196:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

y, z, t = sort([y, z, t])
function code(x, y, z, t, a, b)
	t_1 = Float64(-9.0 * Float64(y * Float64(z * t)))
	t_2 = Float64(27.0 * Float64(a * b))
	tmp = 0.0
	if (b <= -5.5e-106)
		tmp = t_2;
	elseif (b <= 2.4e-239)
		tmp = Float64(x * 2.0);
	elseif (b <= 1.6e-58)
		tmp = t_1;
	elseif (b <= 8e+46)
		tmp = Float64(x * 2.0);
	elseif (b <= 4e+93)
		tmp = t_1;
	elseif (b <= 9.2e+159)
		tmp = Float64(x * 2.0);
	elseif (b <= 3.3e+196)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = -9.0 * (y * (z * t));
	t_2 = 27.0 * (a * b);
	tmp = 0.0;
	if (b <= -5.5e-106)
		tmp = t_2;
	elseif (b <= 2.4e-239)
		tmp = x * 2.0;
	elseif (b <= 1.6e-58)
		tmp = t_1;
	elseif (b <= 8e+46)
		tmp = x * 2.0;
	elseif (b <= 4e+93)
		tmp = t_1;
	elseif (b <= 9.2e+159)
		tmp = x * 2.0;
	elseif (b <= 3.3e+196)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(-9.0 * N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -5.5e-106], t$95$2, If[LessEqual[b, 2.4e-239], N[(x * 2.0), $MachinePrecision], If[LessEqual[b, 1.6e-58], t$95$1, If[LessEqual[b, 8e+46], N[(x * 2.0), $MachinePrecision], If[LessEqual[b, 4e+93], t$95$1, If[LessEqual[b, 9.2e+159], N[(x * 2.0), $MachinePrecision], If[LessEqual[b, 3.3e+196], t$95$1, t$95$2]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -5.5000000000000001e-106 or 3.3000000000000002e196 < b

   1. Initial program 96.7%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

   2. Taylor expanded in a around inf 48.5%

      \[\leadsto \color{blue}{27 \cdot \left(a \cdot b\right)} \]

   if -5.5000000000000001e-106 < b < 2.39999999999999993e-239 or 1.6e-58 < b < 7.9999999999999999e46 or 4.00000000000000017e93 < b < 9.19999999999999981e159

   1. Initial program 93.3%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

   2. Taylor expanded in x around inf 55.5%

      \[\leadsto \color{blue}{2 \cdot x} \]

   if 2.39999999999999993e-239 < b < 1.6e-58 or 7.9999999999999999e46 < b < 4.00000000000000017e93 or 9.19999999999999981e159 < b < 3.3000000000000002e196

   1. Initial program 94.2%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

   2. Taylor expanded in y around inf 46.0%

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

4. Final simplification 50.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5.5 \cdot 10^{-106}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;b \leq 2.4 \cdot 10^{-239}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;b \leq 1.6 \cdot 10^{-58}:\\ \;\;\;\;-9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;b \leq 8 \cdot 10^{+46}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;b \leq 4 \cdot 10^{+93}:\\ \;\;\;\;-9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;b \leq 9.2 \cdot 10^{+159}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;b \leq 3.3 \cdot 10^{+196}:\\ \;\;\;\;-9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \end{array} \]

Alternative 4: 43.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ \\ \begin{array}{l} t_1 := -9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ t_2 := 27 \cdot \left(a \cdot b\right)\\ \mathbf{if}\;b \leq -5.5 \cdot 10^{-106}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 8.5 \cdot 10^{-242}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;b \leq 3.8 \cdot 10^{-58}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 10^{+47}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;b \leq 10^{+94}:\\ \;\;\;\;-9 \cdot \left(t \cdot \left(z \cdot y\right)\right)\\ \mathbf{elif}\;b \leq 7.5 \cdot 10^{+160}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;b \leq 8.2 \cdot 10^{+194}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* -9.0 (* y (* z t)))) (t_2 (* 27.0 (* a b))))
   (if (<= b -5.5e-106)
     t_2
     (if (<= b 8.5e-242)
       (* x 2.0)
       (if (<= b 3.8e-58)
         t_1
         (if (<= b 1e+47)
           (* x 2.0)
           (if (<= b 1e+94)
             (* -9.0 (* t (* z y)))
             (if (<= b 7.5e+160) (* x 2.0) (if (<= b 8.2e+194) t_1 t_2)))))))))

C

assert(y < z && z < t);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = -9.0 * (y * (z * t));
	double t_2 = 27.0 * (a * b);
	double tmp;
	if (b <= -5.5e-106) {
		tmp = t_2;
	} else if (b <= 8.5e-242) {
		tmp = x * 2.0;
	} else if (b <= 3.8e-58) {
		tmp = t_1;
	} else if (b <= 1e+47) {
		tmp = x * 2.0;
	} else if (b <= 1e+94) {
		tmp = -9.0 * (t * (z * y));
	} else if (b <= 7.5e+160) {
		tmp = x * 2.0;
	} else if (b <= 8.2e+194) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (-9.0d0) * (y * (z * t))
    t_2 = 27.0d0 * (a * b)
    if (b <= (-5.5d-106)) then
        tmp = t_2
    else if (b <= 8.5d-242) then
        tmp = x * 2.0d0
    else if (b <= 3.8d-58) then
        tmp = t_1
    else if (b <= 1d+47) then
        tmp = x * 2.0d0
    else if (b <= 1d+94) then
        tmp = (-9.0d0) * (t * (z * y))
    else if (b <= 7.5d+160) then
        tmp = x * 2.0d0
    else if (b <= 8.2d+194) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

assert y < z && z < t;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = -9.0 * (y * (z * t));
	double t_2 = 27.0 * (a * b);
	double tmp;
	if (b <= -5.5e-106) {
		tmp = t_2;
	} else if (b <= 8.5e-242) {
		tmp = x * 2.0;
	} else if (b <= 3.8e-58) {
		tmp = t_1;
	} else if (b <= 1e+47) {
		tmp = x * 2.0;
	} else if (b <= 1e+94) {
		tmp = -9.0 * (t * (z * y));
	} else if (b <= 7.5e+160) {
		tmp = x * 2.0;
	} else if (b <= 8.2e+194) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
def code(x, y, z, t, a, b):
	t_1 = -9.0 * (y * (z * t))
	t_2 = 27.0 * (a * b)
	tmp = 0
	if b <= -5.5e-106:
		tmp = t_2
	elif b <= 8.5e-242:
		tmp = x * 2.0
	elif b <= 3.8e-58:
		tmp = t_1
	elif b <= 1e+47:
		tmp = x * 2.0
	elif b <= 1e+94:
		tmp = -9.0 * (t * (z * y))
	elif b <= 7.5e+160:
		tmp = x * 2.0
	elif b <= 8.2e+194:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

y, z, t = sort([y, z, t])
function code(x, y, z, t, a, b)
	t_1 = Float64(-9.0 * Float64(y * Float64(z * t)))
	t_2 = Float64(27.0 * Float64(a * b))
	tmp = 0.0
	if (b <= -5.5e-106)
		tmp = t_2;
	elseif (b <= 8.5e-242)
		tmp = Float64(x * 2.0);
	elseif (b <= 3.8e-58)
		tmp = t_1;
	elseif (b <= 1e+47)
		tmp = Float64(x * 2.0);
	elseif (b <= 1e+94)
		tmp = Float64(-9.0 * Float64(t * Float64(z * y)));
	elseif (b <= 7.5e+160)
		tmp = Float64(x * 2.0);
	elseif (b <= 8.2e+194)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = -9.0 * (y * (z * t));
	t_2 = 27.0 * (a * b);
	tmp = 0.0;
	if (b <= -5.5e-106)
		tmp = t_2;
	elseif (b <= 8.5e-242)
		tmp = x * 2.0;
	elseif (b <= 3.8e-58)
		tmp = t_1;
	elseif (b <= 1e+47)
		tmp = x * 2.0;
	elseif (b <= 1e+94)
		tmp = -9.0 * (t * (z * y));
	elseif (b <= 7.5e+160)
		tmp = x * 2.0;
	elseif (b <= 8.2e+194)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(-9.0 * N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -5.5e-106], t$95$2, If[LessEqual[b, 8.5e-242], N[(x * 2.0), $MachinePrecision], If[LessEqual[b, 3.8e-58], t$95$1, If[LessEqual[b, 1e+47], N[(x * 2.0), $MachinePrecision], If[LessEqual[b, 1e+94], N[(-9.0 * N[(t * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 7.5e+160], N[(x * 2.0), $MachinePrecision], If[LessEqual[b, 8.2e+194], t$95$1, t$95$2]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -5.5000000000000001e-106 or 8.2000000000000001e194 < b

   1. Initial program 96.7%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

   2. Taylor expanded in a around inf 48.5%

      \[\leadsto \color{blue}{27 \cdot \left(a \cdot b\right)} \]

   if -5.5000000000000001e-106 < b < 8.4999999999999997e-242 or 3.7999999999999997e-58 < b < 1e47 or 1e94 < b < 7.50000000000000028e160

   1. Initial program 93.3%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

   2. Taylor expanded in x around inf 55.5%

      \[\leadsto \color{blue}{2 \cdot x} \]

   if 8.4999999999999997e-242 < b < 3.7999999999999997e-58 or 7.50000000000000028e160 < b < 8.2000000000000001e194

   1. Initial program 94.7%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

   2. Taylor expanded in y around inf 50.5%

      \[\leadsto \color{blue}{-9 \cdot \left(y \cdot \left(t \cdot z\right)\right)} \]

   if 1e47 < b < 1e94

   1. Initial program 92.8%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

   2. Taylor expanded in y around 0 92.8%

      \[\leadsto \left(x \cdot 2 - \color{blue}{\left(9 \cdot \left(y \cdot z\right)\right)} \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

   3. Taylor expanded in y around inf 33.1%

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

      1. *-commutative 33.1%

         \[\leadsto -9 \cdot \left(y \cdot \color{blue}{\left(z \cdot t\right)}\right) \]

      2. associate-*r* 40.9%

         \[\leadsto -9 \cdot \color{blue}{\left(\left(y \cdot z\right) \cdot t\right)} \]

   5. Simplified 40.9%

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

4. Final simplification 50.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5.5 \cdot 10^{-106}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;b \leq 8.5 \cdot 10^{-242}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;b \leq 3.8 \cdot 10^{-58}:\\ \;\;\;\;-9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;b \leq 10^{+47}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;b \leq 10^{+94}:\\ \;\;\;\;-9 \cdot \left(t \cdot \left(z \cdot y\right)\right)\\ \mathbf{elif}\;b \leq 7.5 \cdot 10^{+160}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;b \leq 8.2 \cdot 10^{+194}:\\ \;\;\;\;-9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \end{array} \]

Alternative 5: 43.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ \\ \begin{array}{l} t_1 := 27 \cdot \left(a \cdot b\right)\\ \mathbf{if}\;b \leq -5.5 \cdot 10^{-106}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 1.8 \cdot 10^{-238}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;b \leq 1.2 \cdot 10^{-58}:\\ \;\;\;\;y \cdot \left(\left(z \cdot t\right) \cdot -9\right)\\ \mathbf{elif}\;b \leq 3 \cdot 10^{+46}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;b \leq 1.25 \cdot 10^{+97}:\\ \;\;\;\;-9 \cdot \left(t \cdot \left(z \cdot y\right)\right)\\ \mathbf{elif}\;b \leq 7.8 \cdot 10^{+159}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;b \leq 8.2 \cdot 10^{+194}:\\ \;\;\;\;-9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* 27.0 (* a b))))
   (if (<= b -5.5e-106)
     t_1
     (if (<= b 1.8e-238)
       (* x 2.0)
       (if (<= b 1.2e-58)
         (* y (* (* z t) -9.0))
         (if (<= b 3e+46)
           (* x 2.0)
           (if (<= b 1.25e+97)
             (* -9.0 (* t (* z y)))
             (if (<= b 7.8e+159)
               (* x 2.0)
               (if (<= b 8.2e+194) (* -9.0 (* y (* z t))) t_1)))))))))

C

assert(y < z && z < t);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 27.0 * (a * b);
	double tmp;
	if (b <= -5.5e-106) {
		tmp = t_1;
	} else if (b <= 1.8e-238) {
		tmp = x * 2.0;
	} else if (b <= 1.2e-58) {
		tmp = y * ((z * t) * -9.0);
	} else if (b <= 3e+46) {
		tmp = x * 2.0;
	} else if (b <= 1.25e+97) {
		tmp = -9.0 * (t * (z * y));
	} else if (b <= 7.8e+159) {
		tmp = x * 2.0;
	} else if (b <= 8.2e+194) {
		tmp = -9.0 * (y * (z * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    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) :: t_1
    real(8) :: tmp
    t_1 = 27.0d0 * (a * b)
    if (b <= (-5.5d-106)) then
        tmp = t_1
    else if (b <= 1.8d-238) then
        tmp = x * 2.0d0
    else if (b <= 1.2d-58) then
        tmp = y * ((z * t) * (-9.0d0))
    else if (b <= 3d+46) then
        tmp = x * 2.0d0
    else if (b <= 1.25d+97) then
        tmp = (-9.0d0) * (t * (z * y))
    else if (b <= 7.8d+159) then
        tmp = x * 2.0d0
    else if (b <= 8.2d+194) then
        tmp = (-9.0d0) * (y * (z * t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert y < z && z < t;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 27.0 * (a * b);
	double tmp;
	if (b <= -5.5e-106) {
		tmp = t_1;
	} else if (b <= 1.8e-238) {
		tmp = x * 2.0;
	} else if (b <= 1.2e-58) {
		tmp = y * ((z * t) * -9.0);
	} else if (b <= 3e+46) {
		tmp = x * 2.0;
	} else if (b <= 1.25e+97) {
		tmp = -9.0 * (t * (z * y));
	} else if (b <= 7.8e+159) {
		tmp = x * 2.0;
	} else if (b <= 8.2e+194) {
		tmp = -9.0 * (y * (z * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
def code(x, y, z, t, a, b):
	t_1 = 27.0 * (a * b)
	tmp = 0
	if b <= -5.5e-106:
		tmp = t_1
	elif b <= 1.8e-238:
		tmp = x * 2.0
	elif b <= 1.2e-58:
		tmp = y * ((z * t) * -9.0)
	elif b <= 3e+46:
		tmp = x * 2.0
	elif b <= 1.25e+97:
		tmp = -9.0 * (t * (z * y))
	elif b <= 7.8e+159:
		tmp = x * 2.0
	elif b <= 8.2e+194:
		tmp = -9.0 * (y * (z * t))
	else:
		tmp = t_1
	return tmp

Julia

y, z, t = sort([y, z, t])
function code(x, y, z, t, a, b)
	t_1 = Float64(27.0 * Float64(a * b))
	tmp = 0.0
	if (b <= -5.5e-106)
		tmp = t_1;
	elseif (b <= 1.8e-238)
		tmp = Float64(x * 2.0);
	elseif (b <= 1.2e-58)
		tmp = Float64(y * Float64(Float64(z * t) * -9.0));
	elseif (b <= 3e+46)
		tmp = Float64(x * 2.0);
	elseif (b <= 1.25e+97)
		tmp = Float64(-9.0 * Float64(t * Float64(z * y)));
	elseif (b <= 7.8e+159)
		tmp = Float64(x * 2.0);
	elseif (b <= 8.2e+194)
		tmp = Float64(-9.0 * Float64(y * Float64(z * t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = 27.0 * (a * b);
	tmp = 0.0;
	if (b <= -5.5e-106)
		tmp = t_1;
	elseif (b <= 1.8e-238)
		tmp = x * 2.0;
	elseif (b <= 1.2e-58)
		tmp = y * ((z * t) * -9.0);
	elseif (b <= 3e+46)
		tmp = x * 2.0;
	elseif (b <= 1.25e+97)
		tmp = -9.0 * (t * (z * y));
	elseif (b <= 7.8e+159)
		tmp = x * 2.0;
	elseif (b <= 8.2e+194)
		tmp = -9.0 * (y * (z * t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -5.5e-106], t$95$1, If[LessEqual[b, 1.8e-238], N[(x * 2.0), $MachinePrecision], If[LessEqual[b, 1.2e-58], N[(y * N[(N[(z * t), $MachinePrecision] * -9.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3e+46], N[(x * 2.0), $MachinePrecision], If[LessEqual[b, 1.25e+97], N[(-9.0 * N[(t * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 7.8e+159], N[(x * 2.0), $MachinePrecision], If[LessEqual[b, 8.2e+194], N[(-9.0 * N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -5.5000000000000001e-106 or 8.2000000000000001e194 < b

   1. Initial program 96.7%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

   2. Taylor expanded in a around inf 48.5%

      \[\leadsto \color{blue}{27 \cdot \left(a \cdot b\right)} \]

   if -5.5000000000000001e-106 < b < 1.80000000000000005e-238 or 1.2e-58 < b < 3.00000000000000023e46 or 1.25e97 < b < 7.8000000000000001e159

   1. Initial program 93.3%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

   2. Taylor expanded in x around inf 55.5%

      \[\leadsto \color{blue}{2 \cdot x} \]

   if 1.80000000000000005e-238 < b < 1.2e-58

   1. Initial program 91.9%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

   2. Taylor expanded in y around inf 47.8%

      \[\leadsto \color{blue}{-9 \cdot \left(y \cdot \left(t \cdot z\right)\right)} \]
   3. Step-by-step derivation

      1. *-commutative 47.8%

         \[\leadsto \color{blue}{\left(y \cdot \left(t \cdot z\right)\right) \cdot -9} \]

      2. *-commutative 47.8%

         \[\leadsto \left(y \cdot \color{blue}{\left(z \cdot t\right)}\right) \cdot -9 \]

      3. associate-*l* 47.7%

         \[\leadsto \color{blue}{y \cdot \left(\left(z \cdot t\right) \cdot -9\right)} \]

      4. *-commutative 47.7%

         \[\leadsto y \cdot \color{blue}{\left(-9 \cdot \left(z \cdot t\right)\right)} \]

      5. *-commutative 47.7%

         \[\leadsto y \cdot \left(-9 \cdot \color{blue}{\left(t \cdot z\right)}\right) \]

   4. Simplified 47.7%

      \[\leadsto \color{blue}{y \cdot \left(-9 \cdot \left(t \cdot z\right)\right)} \]

   if 3.00000000000000023e46 < b < 1.25e97

   1. Initial program 92.8%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

   2. Taylor expanded in y around 0 92.8%

      \[\leadsto \left(x \cdot 2 - \color{blue}{\left(9 \cdot \left(y \cdot z\right)\right)} \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

   3. Taylor expanded in y around inf 33.1%

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

      1. *-commutative 33.1%

         \[\leadsto -9 \cdot \left(y \cdot \color{blue}{\left(z \cdot t\right)}\right) \]

      2. associate-*r* 40.9%

         \[\leadsto -9 \cdot \color{blue}{\left(\left(y \cdot z\right) \cdot t\right)} \]

   5. Simplified 40.9%

      \[\leadsto \color{blue}{-9 \cdot \left(\left(y \cdot z\right) \cdot t\right)} \]

   if 7.8000000000000001e159 < b < 8.2000000000000001e194

   1. Initial program 100.0%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

   2. Taylor expanded in y around inf 55.6%

      \[\leadsto \color{blue}{-9 \cdot \left(y \cdot \left(t \cdot z\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 50.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5.5 \cdot 10^{-106}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;b \leq 1.8 \cdot 10^{-238}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;b \leq 1.2 \cdot 10^{-58}:\\ \;\;\;\;y \cdot \left(\left(z \cdot t\right) \cdot -9\right)\\ \mathbf{elif}\;b \leq 3 \cdot 10^{+46}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;b \leq 1.25 \cdot 10^{+97}:\\ \;\;\;\;-9 \cdot \left(t \cdot \left(z \cdot y\right)\right)\\ \mathbf{elif}\;b \leq 7.8 \cdot 10^{+159}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;b \leq 8.2 \cdot 10^{+194}:\\ \;\;\;\;-9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \end{array} \]

Alternative 6: 98.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot 27\right)\\ \mathbf{if}\;z \leq -2600:\\ \;\;\;\;t_1 + \left(x \cdot 2 - \left(z \cdot 9\right) \cdot \left(y \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1 + \left(x \cdot 2 - t \cdot \left(9 \cdot \left(z \cdot y\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (* a 27.0))))
   (if (<= z -2600.0)
     (+ t_1 (- (* x 2.0) (* (* z 9.0) (* y t))))
     (+ t_1 (- (* x 2.0) (* t (* 9.0 (* z y))))))))

C

assert(y < z && z < t);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a * 27.0);
	double tmp;
	if (z <= -2600.0) {
		tmp = t_1 + ((x * 2.0) - ((z * 9.0) * (y * t)));
	} else {
		tmp = t_1 + ((x * 2.0) - (t * (9.0 * (z * y))));
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    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) :: t_1
    real(8) :: tmp
    t_1 = b * (a * 27.0d0)
    if (z <= (-2600.0d0)) then
        tmp = t_1 + ((x * 2.0d0) - ((z * 9.0d0) * (y * t)))
    else
        tmp = t_1 + ((x * 2.0d0) - (t * (9.0d0 * (z * y))))
    end if
    code = tmp
end function

Java

assert y < z && z < t;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a * 27.0);
	double tmp;
	if (z <= -2600.0) {
		tmp = t_1 + ((x * 2.0) - ((z * 9.0) * (y * t)));
	} else {
		tmp = t_1 + ((x * 2.0) - (t * (9.0 * (z * y))));
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
def code(x, y, z, t, a, b):
	t_1 = b * (a * 27.0)
	tmp = 0
	if z <= -2600.0:
		tmp = t_1 + ((x * 2.0) - ((z * 9.0) * (y * t)))
	else:
		tmp = t_1 + ((x * 2.0) - (t * (9.0 * (z * y))))
	return tmp

Julia

y, z, t = sort([y, z, t])
function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(a * 27.0))
	tmp = 0.0
	if (z <= -2600.0)
		tmp = Float64(t_1 + Float64(Float64(x * 2.0) - Float64(Float64(z * 9.0) * Float64(y * t))));
	else
		tmp = Float64(t_1 + Float64(Float64(x * 2.0) - Float64(t * Float64(9.0 * Float64(z * y)))));
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * (a * 27.0);
	tmp = 0.0;
	if (z <= -2600.0)
		tmp = t_1 + ((x * 2.0) - ((z * 9.0) * (y * t)));
	else
		tmp = t_1 + ((x * 2.0) - (t * (9.0 * (z * y))));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(a * 27.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2600.0], N[(t$95$1 + N[(N[(x * 2.0), $MachinePrecision] - N[(N[(z * 9.0), $MachinePrecision] * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + N[(N[(x * 2.0), $MachinePrecision] - N[(t * N[(9.0 * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -2600

   1. Initial program 91.8%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

   2. Taylor expanded in y around 0 86.6%

      \[\leadsto \left(x \cdot 2 - \color{blue}{9 \cdot \left(y \cdot \left(t \cdot z\right)\right)}\right) + \left(a \cdot 27\right) \cdot b \]
   3. Step-by-step derivation

      1. *-commutative 86.6%

         \[\leadsto \left(x \cdot 2 - 9 \cdot \color{blue}{\left(\left(t \cdot z\right) \cdot y\right)}\right) + \left(a \cdot 27\right) \cdot b \]

      2. *-commutative 86.6%

         \[\leadsto \left(x \cdot 2 - 9 \cdot \left(\color{blue}{\left(z \cdot t\right)} \cdot y\right)\right) + \left(a \cdot 27\right) \cdot b \]

      3. associate-*l* 86.5%

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(9 \cdot \left(z \cdot t\right)\right) \cdot y}\right) + \left(a \cdot 27\right) \cdot b \]

      4. associate-*r* 86.5%

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(\left(9 \cdot z\right) \cdot t\right)} \cdot y\right) + \left(a \cdot 27\right) \cdot b \]

      5. associate-*l* 99.7%

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(9 \cdot z\right) \cdot \left(t \cdot y\right)}\right) + \left(a \cdot 27\right) \cdot b \]

      6. *-commutative 99.7%

         \[\leadsto \left(x \cdot 2 - \left(9 \cdot z\right) \cdot \color{blue}{\left(y \cdot t\right)}\right) + \left(a \cdot 27\right) \cdot b \]

   4. Simplified 99.7%

      \[\leadsto \left(x \cdot 2 - \color{blue}{\left(9 \cdot z\right) \cdot \left(y \cdot t\right)}\right) + \left(a \cdot 27\right) \cdot b \]

   if -2600 < z

   1. Initial program 96.0%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

   2. Taylor expanded in y around 0 96.0%

      \[\leadsto \left(x \cdot 2 - \color{blue}{\left(9 \cdot \left(y \cdot z\right)\right)} \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
3. Recombined 2 regimes into one program.

4. Final simplification 96.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2600:\\ \;\;\;\;b \cdot \left(a \cdot 27\right) + \left(x \cdot 2 - \left(z \cdot 9\right) \cdot \left(y \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot 27\right) + \left(x \cdot 2 - t \cdot \left(9 \cdot \left(z \cdot y\right)\right)\right)\\ \end{array} \]

Alternative 7: 98.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot 27\right)\\ \mathbf{if}\;z \leq -500000:\\ \;\;\;\;t_1 + \left(x \cdot 2 - \left(z \cdot 9\right) \cdot \left(y \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1 + \left(x \cdot 2 - t \cdot \left(y \cdot \left(z \cdot 9\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (* a 27.0))))
   (if (<= z -500000.0)
     (+ t_1 (- (* x 2.0) (* (* z 9.0) (* y t))))
     (+ t_1 (- (* x 2.0) (* t (* y (* z 9.0))))))))

C

assert(y < z && z < t);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a * 27.0);
	double tmp;
	if (z <= -500000.0) {
		tmp = t_1 + ((x * 2.0) - ((z * 9.0) * (y * t)));
	} else {
		tmp = t_1 + ((x * 2.0) - (t * (y * (z * 9.0))));
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    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) :: t_1
    real(8) :: tmp
    t_1 = b * (a * 27.0d0)
    if (z <= (-500000.0d0)) then
        tmp = t_1 + ((x * 2.0d0) - ((z * 9.0d0) * (y * t)))
    else
        tmp = t_1 + ((x * 2.0d0) - (t * (y * (z * 9.0d0))))
    end if
    code = tmp
end function

Java

assert y < z && z < t;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a * 27.0);
	double tmp;
	if (z <= -500000.0) {
		tmp = t_1 + ((x * 2.0) - ((z * 9.0) * (y * t)));
	} else {
		tmp = t_1 + ((x * 2.0) - (t * (y * (z * 9.0))));
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
def code(x, y, z, t, a, b):
	t_1 = b * (a * 27.0)
	tmp = 0
	if z <= -500000.0:
		tmp = t_1 + ((x * 2.0) - ((z * 9.0) * (y * t)))
	else:
		tmp = t_1 + ((x * 2.0) - (t * (y * (z * 9.0))))
	return tmp

Julia

y, z, t = sort([y, z, t])
function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(a * 27.0))
	tmp = 0.0
	if (z <= -500000.0)
		tmp = Float64(t_1 + Float64(Float64(x * 2.0) - Float64(Float64(z * 9.0) * Float64(y * t))));
	else
		tmp = Float64(t_1 + Float64(Float64(x * 2.0) - Float64(t * Float64(y * Float64(z * 9.0)))));
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * (a * 27.0);
	tmp = 0.0;
	if (z <= -500000.0)
		tmp = t_1 + ((x * 2.0) - ((z * 9.0) * (y * t)));
	else
		tmp = t_1 + ((x * 2.0) - (t * (y * (z * 9.0))));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(a * 27.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -500000.0], N[(t$95$1 + N[(N[(x * 2.0), $MachinePrecision] - N[(N[(z * 9.0), $MachinePrecision] * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + N[(N[(x * 2.0), $MachinePrecision] - N[(t * N[(y * N[(z * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -5e5

   1. Initial program 91.8%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

   2. Taylor expanded in y around 0 86.6%

      \[\leadsto \left(x \cdot 2 - \color{blue}{9 \cdot \left(y \cdot \left(t \cdot z\right)\right)}\right) + \left(a \cdot 27\right) \cdot b \]
   3. Step-by-step derivation

      1. *-commutative 86.6%

         \[\leadsto \left(x \cdot 2 - 9 \cdot \color{blue}{\left(\left(t \cdot z\right) \cdot y\right)}\right) + \left(a \cdot 27\right) \cdot b \]

      2. *-commutative 86.6%

         \[\leadsto \left(x \cdot 2 - 9 \cdot \left(\color{blue}{\left(z \cdot t\right)} \cdot y\right)\right) + \left(a \cdot 27\right) \cdot b \]

      3. associate-*l* 86.5%

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(9 \cdot \left(z \cdot t\right)\right) \cdot y}\right) + \left(a \cdot 27\right) \cdot b \]

      4. associate-*r* 86.5%

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(\left(9 \cdot z\right) \cdot t\right)} \cdot y\right) + \left(a \cdot 27\right) \cdot b \]

      5. associate-*l* 99.7%

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(9 \cdot z\right) \cdot \left(t \cdot y\right)}\right) + \left(a \cdot 27\right) \cdot b \]

      6. *-commutative 99.7%

         \[\leadsto \left(x \cdot 2 - \left(9 \cdot z\right) \cdot \color{blue}{\left(y \cdot t\right)}\right) + \left(a \cdot 27\right) \cdot b \]

   4. Simplified 99.7%

      \[\leadsto \left(x \cdot 2 - \color{blue}{\left(9 \cdot z\right) \cdot \left(y \cdot t\right)}\right) + \left(a \cdot 27\right) \cdot b \]

   if -5e5 < z

   1. Initial program 96.0%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

   2. Taylor expanded in y around 0 96.0%

      \[\leadsto \left(x \cdot 2 - \color{blue}{\left(9 \cdot \left(y \cdot z\right)\right)} \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   3. Step-by-step derivation

      1. expm1-log1p-u 73.0%

         \[\leadsto \left(x \cdot 2 - \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(9 \cdot \left(y \cdot z\right)\right)\right)} \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

      2. expm1-udef 64.6%

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(e^{\mathsf{log1p}\left(9 \cdot \left(y \cdot z\right)\right)} - 1\right)} \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

   4. Applied egg-rr 64.6%

      \[\leadsto \left(x \cdot 2 - \color{blue}{\left(e^{\mathsf{log1p}\left(9 \cdot \left(y \cdot z\right)\right)} - 1\right)} \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   5. Step-by-step derivation

      1. expm1-def 73.0%

         \[\leadsto \left(x \cdot 2 - \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(9 \cdot \left(y \cdot z\right)\right)\right)} \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

      2. expm1-log1p 96.0%

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(9 \cdot \left(y \cdot z\right)\right)} \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

      3. associate-*r* 96.0%

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(\left(9 \cdot y\right) \cdot z\right)} \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

      4. *-commutative 96.0%

         \[\leadsto \left(x \cdot 2 - \left(\color{blue}{\left(y \cdot 9\right)} \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

      5. associate-*l* 96.0%

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(y \cdot \left(9 \cdot z\right)\right)} \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

   6. Simplified 96.0%

      \[\leadsto \left(x \cdot 2 - \color{blue}{\left(y \cdot \left(9 \cdot z\right)\right)} \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
3. Recombined 2 regimes into one program.

4. Final simplification 96.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -500000:\\ \;\;\;\;b \cdot \left(a \cdot 27\right) + \left(x \cdot 2 - \left(z \cdot 9\right) \cdot \left(y \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot 27\right) + \left(x \cdot 2 - t \cdot \left(y \cdot \left(z \cdot 9\right)\right)\right)\\ \end{array} \]

Alternative 8: 98.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq 4.5 \cdot 10^{-87}:\\ \;\;\;\;x \cdot 2 + \left(a \cdot \left(27 \cdot b\right) - \left(z \cdot t\right) \cdot \left(9 \cdot y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot 27\right) + \left(x \cdot 2 - t \cdot \left(y \cdot \left(z \cdot 9\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= z 4.5e-87)
   (+ (* x 2.0) (- (* a (* 27.0 b)) (* (* z t) (* 9.0 y))))
   (+ (* b (* a 27.0)) (- (* x 2.0) (* t (* y (* z 9.0)))))))

C

assert(y < z && z < t);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= 4.5e-87) {
		tmp = (x * 2.0) + ((a * (27.0 * b)) - ((z * t) * (9.0 * y)));
	} else {
		tmp = (b * (a * 27.0)) + ((x * 2.0) - (t * (y * (z * 9.0))));
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    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) :: tmp
    if (z <= 4.5d-87) then
        tmp = (x * 2.0d0) + ((a * (27.0d0 * b)) - ((z * t) * (9.0d0 * y)))
    else
        tmp = (b * (a * 27.0d0)) + ((x * 2.0d0) - (t * (y * (z * 9.0d0))))
    end if
    code = tmp
end function

Java

assert y < z && z < t;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= 4.5e-87) {
		tmp = (x * 2.0) + ((a * (27.0 * b)) - ((z * t) * (9.0 * y)));
	} else {
		tmp = (b * (a * 27.0)) + ((x * 2.0) - (t * (y * (z * 9.0))));
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
def code(x, y, z, t, a, b):
	tmp = 0
	if z <= 4.5e-87:
		tmp = (x * 2.0) + ((a * (27.0 * b)) - ((z * t) * (9.0 * y)))
	else:
		tmp = (b * (a * 27.0)) + ((x * 2.0) - (t * (y * (z * 9.0))))
	return tmp

Julia

y, z, t = sort([y, z, t])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= 4.5e-87)
		tmp = Float64(Float64(x * 2.0) + Float64(Float64(a * Float64(27.0 * b)) - Float64(Float64(z * t) * Float64(9.0 * y))));
	else
		tmp = Float64(Float64(b * Float64(a * 27.0)) + Float64(Float64(x * 2.0) - Float64(t * Float64(y * Float64(z * 9.0)))));
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= 4.5e-87)
		tmp = (x * 2.0) + ((a * (27.0 * b)) - ((z * t) * (9.0 * y)));
	else
		tmp = (b * (a * 27.0)) + ((x * 2.0) - (t * (y * (z * 9.0))));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, 4.5e-87], N[(N[(x * 2.0), $MachinePrecision] + N[(N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision] - N[(N[(z * t), $MachinePrecision] * N[(9.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * N[(a * 27.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x * 2.0), $MachinePrecision] - N[(t * N[(y * N[(z * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 4.49999999999999958e-87

   1. Initial program 97.3%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l- 97.3%

         \[\leadsto \color{blue}{x \cdot 2 - \left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t - \left(a \cdot 27\right) \cdot b\right)} \]

      2. sub-neg 97.3%

         \[\leadsto \color{blue}{x \cdot 2 + \left(-\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t - \left(a \cdot 27\right) \cdot b\right)\right)} \]

      3. neg-mul-1 97.3%

         \[\leadsto x \cdot 2 + \color{blue}{-1 \cdot \left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t - \left(a \cdot 27\right) \cdot b\right)} \]

      4. metadata-eval 97.3%

         \[\leadsto x \cdot 2 + \color{blue}{\left(-1\right)} \cdot \left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t - \left(a \cdot 27\right) \cdot b\right) \]

      5. metadata-eval 97.3%

         \[\leadsto x \cdot 2 + \left(-\color{blue}{\left(--1\right)}\right) \cdot \left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t - \left(a \cdot 27\right) \cdot b\right) \]

      6. cancel-sign-sub-inv 97.3%

         \[\leadsto \color{blue}{x \cdot 2 - \left(--1\right) \cdot \left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t - \left(a \cdot 27\right) \cdot b\right)} \]

      7. metadata-eval 97.3%

         \[\leadsto x \cdot 2 - \color{blue}{1} \cdot \left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t - \left(a \cdot 27\right) \cdot b\right) \]

      8. *-lft-identity 97.3%

         \[\leadsto x \cdot 2 - \color{blue}{\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t - \left(a \cdot 27\right) \cdot b\right)} \]

      9. associate-*l* 95.6%

         \[\leadsto x \cdot 2 - \left(\color{blue}{\left(y \cdot 9\right) \cdot \left(z \cdot t\right)} - \left(a \cdot 27\right) \cdot b\right) \]

      10. associate-*l* 95.6%

          \[\leadsto x \cdot 2 - \left(\left(y \cdot 9\right) \cdot \left(z \cdot t\right) - \color{blue}{a \cdot \left(27 \cdot b\right)}\right) \]

   3. Simplified 95.6%

      \[\leadsto \color{blue}{x \cdot 2 - \left(\left(y \cdot 9\right) \cdot \left(z \cdot t\right) - a \cdot \left(27 \cdot b\right)\right)} \]

   if 4.49999999999999958e-87 < z

   1. Initial program 90.0%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

   2. Taylor expanded in y around 0 90.0%

      \[\leadsto \left(x \cdot 2 - \color{blue}{\left(9 \cdot \left(y \cdot z\right)\right)} \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   3. Step-by-step derivation

      1. expm1-log1p-u 51.5%

         \[\leadsto \left(x \cdot 2 - \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(9 \cdot \left(y \cdot z\right)\right)\right)} \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

      2. expm1-udef 48.4%

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(e^{\mathsf{log1p}\left(9 \cdot \left(y \cdot z\right)\right)} - 1\right)} \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

   4. Applied egg-rr 48.4%

      \[\leadsto \left(x \cdot 2 - \color{blue}{\left(e^{\mathsf{log1p}\left(9 \cdot \left(y \cdot z\right)\right)} - 1\right)} \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   5. Step-by-step derivation

      1. expm1-def 51.5%

         \[\leadsto \left(x \cdot 2 - \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(9 \cdot \left(y \cdot z\right)\right)\right)} \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

      2. expm1-log1p 90.0%

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(9 \cdot \left(y \cdot z\right)\right)} \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

      3. associate-*r* 90.0%

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(\left(9 \cdot y\right) \cdot z\right)} \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

      4. *-commutative 90.0%

         \[\leadsto \left(x \cdot 2 - \left(\color{blue}{\left(y \cdot 9\right)} \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

      5. associate-*l* 90.0%

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(y \cdot \left(9 \cdot z\right)\right)} \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

   6. Simplified 90.0%

      \[\leadsto \left(x \cdot 2 - \color{blue}{\left(y \cdot \left(9 \cdot z\right)\right)} \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
3. Recombined 2 regimes into one program.

4. Final simplification 93.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 4.5 \cdot 10^{-87}:\\ \;\;\;\;x \cdot 2 + \left(a \cdot \left(27 \cdot b\right) - \left(z \cdot t\right) \cdot \left(9 \cdot y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot 27\right) + \left(x \cdot 2 - t \cdot \left(y \cdot \left(z \cdot 9\right)\right)\right)\\ \end{array} \]

Alternative 9: 72.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ \\ \begin{array}{l} t_1 := x \cdot 2 - a \cdot \left(b \cdot -27\right)\\ \mathbf{if}\;z \leq -3.4 \cdot 10^{+72}:\\ \;\;\;\;y \cdot \left(z \cdot \left(t \cdot -9\right)\right)\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-70}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-35}:\\ \;\;\;\;-9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{+115}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;-9 \cdot \left(t \cdot \left(z \cdot y\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (* x 2.0) (* a (* b -27.0)))))
   (if (<= z -3.4e+72)
     (* y (* z (* t -9.0)))
     (if (<= z 2.2e-70)
       t_1
       (if (<= z 1.8e-35)
         (* -9.0 (* y (* z t)))
         (if (<= z 2.2e+115) t_1 (* -9.0 (* t (* z y)))))))))

C

assert(y < z && z < t);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * 2.0) - (a * (b * -27.0));
	double tmp;
	if (z <= -3.4e+72) {
		tmp = y * (z * (t * -9.0));
	} else if (z <= 2.2e-70) {
		tmp = t_1;
	} else if (z <= 1.8e-35) {
		tmp = -9.0 * (y * (z * t));
	} else if (z <= 2.2e+115) {
		tmp = t_1;
	} else {
		tmp = -9.0 * (t * (z * y));
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    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) :: t_1
    real(8) :: tmp
    t_1 = (x * 2.0d0) - (a * (b * (-27.0d0)))
    if (z <= (-3.4d+72)) then
        tmp = y * (z * (t * (-9.0d0)))
    else if (z <= 2.2d-70) then
        tmp = t_1
    else if (z <= 1.8d-35) then
        tmp = (-9.0d0) * (y * (z * t))
    else if (z <= 2.2d+115) then
        tmp = t_1
    else
        tmp = (-9.0d0) * (t * (z * y))
    end if
    code = tmp
end function

Java

assert y < z && z < t;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * 2.0) - (a * (b * -27.0));
	double tmp;
	if (z <= -3.4e+72) {
		tmp = y * (z * (t * -9.0));
	} else if (z <= 2.2e-70) {
		tmp = t_1;
	} else if (z <= 1.8e-35) {
		tmp = -9.0 * (y * (z * t));
	} else if (z <= 2.2e+115) {
		tmp = t_1;
	} else {
		tmp = -9.0 * (t * (z * y));
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
def code(x, y, z, t, a, b):
	t_1 = (x * 2.0) - (a * (b * -27.0))
	tmp = 0
	if z <= -3.4e+72:
		tmp = y * (z * (t * -9.0))
	elif z <= 2.2e-70:
		tmp = t_1
	elif z <= 1.8e-35:
		tmp = -9.0 * (y * (z * t))
	elif z <= 2.2e+115:
		tmp = t_1
	else:
		tmp = -9.0 * (t * (z * y))
	return tmp

Julia

y, z, t = sort([y, z, t])
function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x * 2.0) - Float64(a * Float64(b * -27.0)))
	tmp = 0.0
	if (z <= -3.4e+72)
		tmp = Float64(y * Float64(z * Float64(t * -9.0)));
	elseif (z <= 2.2e-70)
		tmp = t_1;
	elseif (z <= 1.8e-35)
		tmp = Float64(-9.0 * Float64(y * Float64(z * t)));
	elseif (z <= 2.2e+115)
		tmp = t_1;
	else
		tmp = Float64(-9.0 * Float64(t * Float64(z * y)));
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x * 2.0) - (a * (b * -27.0));
	tmp = 0.0;
	if (z <= -3.4e+72)
		tmp = y * (z * (t * -9.0));
	elseif (z <= 2.2e-70)
		tmp = t_1;
	elseif (z <= 1.8e-35)
		tmp = -9.0 * (y * (z * t));
	elseif (z <= 2.2e+115)
		tmp = t_1;
	else
		tmp = -9.0 * (t * (z * y));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x * 2.0), $MachinePrecision] - N[(a * N[(b * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.4e+72], N[(y * N[(z * N[(t * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.2e-70], t$95$1, If[LessEqual[z, 1.8e-35], N[(-9.0 * N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.2e+115], t$95$1, N[(-9.0 * N[(t * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.3999999999999998e72

   1. Initial program 90.1%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

   2. Taylor expanded in y around 0 90.2%

      \[\leadsto \left(x \cdot 2 - \color{blue}{\left(9 \cdot \left(y \cdot z\right)\right)} \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

   3. Taylor expanded in y around inf 44.7%

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

      1. *-commutative 44.7%

         \[\leadsto -9 \cdot \color{blue}{\left(\left(t \cdot z\right) \cdot y\right)} \]

      2. *-commutative 44.7%

         \[\leadsto -9 \cdot \left(\color{blue}{\left(z \cdot t\right)} \cdot y\right) \]

      3. *-commutative 44.7%

         \[\leadsto -9 \cdot \color{blue}{\left(y \cdot \left(z \cdot t\right)\right)} \]

      4. *-commutative 44.7%

         \[\leadsto \color{blue}{\left(y \cdot \left(z \cdot t\right)\right) \cdot -9} \]

      5. associate-*r* 44.7%

         \[\leadsto \color{blue}{y \cdot \left(\left(z \cdot t\right) \cdot -9\right)} \]

      6. associate-*l* 44.7%

         \[\leadsto y \cdot \color{blue}{\left(z \cdot \left(t \cdot -9\right)\right)} \]

   5. Simplified 44.7%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot \left(t \cdot -9\right)\right)} \]

   if -3.3999999999999998e72 < z < 2.1999999999999999e-70 or 1.80000000000000009e-35 < z < 2.2e115

   1. Initial program 99.8%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l- 99.8%

         \[\leadsto \color{blue}{x \cdot 2 - \left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t - \left(a \cdot 27\right) \cdot b\right)} \]

      2. sub-neg 99.8%

         \[\leadsto \color{blue}{x \cdot 2 + \left(-\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t - \left(a \cdot 27\right) \cdot b\right)\right)} \]

      3. neg-mul-1 99.8%

         \[\leadsto x \cdot 2 + \color{blue}{-1 \cdot \left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t - \left(a \cdot 27\right) \cdot b\right)} \]

      4. metadata-eval 99.8%

         \[\leadsto x \cdot 2 + \color{blue}{\left(-1\right)} \cdot \left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t - \left(a \cdot 27\right) \cdot b\right) \]

      5. metadata-eval 99.8%

         \[\leadsto x \cdot 2 + \left(-\color{blue}{\left(--1\right)}\right) \cdot \left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t - \left(a \cdot 27\right) \cdot b\right) \]

      6. cancel-sign-sub-inv 99.8%

         \[\leadsto \color{blue}{x \cdot 2 - \left(--1\right) \cdot \left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t - \left(a \cdot 27\right) \cdot b\right)} \]

      7. metadata-eval 99.8%

         \[\leadsto x \cdot 2 - \color{blue}{1} \cdot \left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t - \left(a \cdot 27\right) \cdot b\right) \]

      8. *-lft-identity 99.8%

         \[\leadsto x \cdot 2 - \color{blue}{\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t - \left(a \cdot 27\right) \cdot b\right)} \]

      9. associate-*l* 98.0%

         \[\leadsto x \cdot 2 - \left(\color{blue}{\left(y \cdot 9\right) \cdot \left(z \cdot t\right)} - \left(a \cdot 27\right) \cdot b\right) \]

      10. associate-*l* 98.0%

          \[\leadsto x \cdot 2 - \left(\left(y \cdot 9\right) \cdot \left(z \cdot t\right) - \color{blue}{a \cdot \left(27 \cdot b\right)}\right) \]

   3. Simplified 98.0%

      \[\leadsto \color{blue}{x \cdot 2 - \left(\left(y \cdot 9\right) \cdot \left(z \cdot t\right) - a \cdot \left(27 \cdot b\right)\right)} \]

   4. Taylor expanded in y around 0 73.7%

      \[\leadsto x \cdot 2 - \color{blue}{-27 \cdot \left(a \cdot b\right)} \]
   5. Step-by-step derivation

      1. *-commutative 73.7%

         \[\leadsto x \cdot 2 - \color{blue}{\left(a \cdot b\right) \cdot -27} \]

      2. associate-*r* 73.7%

         \[\leadsto x \cdot 2 - \color{blue}{a \cdot \left(b \cdot -27\right)} \]

   6. Simplified 73.7%

      \[\leadsto x \cdot 2 - \color{blue}{a \cdot \left(b \cdot -27\right)} \]

   if 2.1999999999999999e-70 < z < 1.80000000000000009e-35

   1. Initial program 99.6%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

   2. Taylor expanded in y around inf 38.6%

      \[\leadsto \color{blue}{-9 \cdot \left(y \cdot \left(t \cdot z\right)\right)} \]

   if 2.2e115 < z

   1. Initial program 82.3%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

   2. Taylor expanded in y around 0 82.3%

      \[\leadsto \left(x \cdot 2 - \color{blue}{\left(9 \cdot \left(y \cdot z\right)\right)} \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

   3. Taylor expanded in y around inf 64.8%

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

      1. *-commutative 64.8%

         \[\leadsto -9 \cdot \left(y \cdot \color{blue}{\left(z \cdot t\right)}\right) \]

      2. associate-*r* 56.2%

         \[\leadsto -9 \cdot \color{blue}{\left(\left(y \cdot z\right) \cdot t\right)} \]

   5. Simplified 56.2%

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

4. Final simplification 64.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{+72}:\\ \;\;\;\;y \cdot \left(z \cdot \left(t \cdot -9\right)\right)\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-70}:\\ \;\;\;\;x \cdot 2 - a \cdot \left(b \cdot -27\right)\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-35}:\\ \;\;\;\;-9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{+115}:\\ \;\;\;\;x \cdot 2 - a \cdot \left(b \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;-9 \cdot \left(t \cdot \left(z \cdot y\right)\right)\\ \end{array} \]

Alternative 10: 72.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.95 \cdot 10^{+77}:\\ \;\;\;\;y \cdot \left(z \cdot \left(t \cdot -9\right)\right)\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-70}:\\ \;\;\;\;x \cdot 2 - b \cdot \left(a \cdot -27\right)\\ \mathbf{elif}\;z \leq 10^{-38}:\\ \;\;\;\;-9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{+115}:\\ \;\;\;\;x \cdot 2 - a \cdot \left(b \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;-9 \cdot \left(t \cdot \left(z \cdot y\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -1.95e+77)
   (* y (* z (* t -9.0)))
   (if (<= z 2.2e-70)
     (- (* x 2.0) (* b (* a -27.0)))
     (if (<= z 1e-38)
       (* -9.0 (* y (* z t)))
       (if (<= z 3.7e+115)
         (- (* x 2.0) (* a (* b -27.0)))
         (* -9.0 (* t (* z y))))))))

C

assert(y < z && z < t);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.95e+77) {
		tmp = y * (z * (t * -9.0));
	} else if (z <= 2.2e-70) {
		tmp = (x * 2.0) - (b * (a * -27.0));
	} else if (z <= 1e-38) {
		tmp = -9.0 * (y * (z * t));
	} else if (z <= 3.7e+115) {
		tmp = (x * 2.0) - (a * (b * -27.0));
	} else {
		tmp = -9.0 * (t * (z * y));
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    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) :: tmp
    if (z <= (-1.95d+77)) then
        tmp = y * (z * (t * (-9.0d0)))
    else if (z <= 2.2d-70) then
        tmp = (x * 2.0d0) - (b * (a * (-27.0d0)))
    else if (z <= 1d-38) then
        tmp = (-9.0d0) * (y * (z * t))
    else if (z <= 3.7d+115) then
        tmp = (x * 2.0d0) - (a * (b * (-27.0d0)))
    else
        tmp = (-9.0d0) * (t * (z * y))
    end if
    code = tmp
end function

Java

assert y < z && z < t;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.95e+77) {
		tmp = y * (z * (t * -9.0));
	} else if (z <= 2.2e-70) {
		tmp = (x * 2.0) - (b * (a * -27.0));
	} else if (z <= 1e-38) {
		tmp = -9.0 * (y * (z * t));
	} else if (z <= 3.7e+115) {
		tmp = (x * 2.0) - (a * (b * -27.0));
	} else {
		tmp = -9.0 * (t * (z * y));
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -1.95e+77:
		tmp = y * (z * (t * -9.0))
	elif z <= 2.2e-70:
		tmp = (x * 2.0) - (b * (a * -27.0))
	elif z <= 1e-38:
		tmp = -9.0 * (y * (z * t))
	elif z <= 3.7e+115:
		tmp = (x * 2.0) - (a * (b * -27.0))
	else:
		tmp = -9.0 * (t * (z * y))
	return tmp

Julia

y, z, t = sort([y, z, t])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -1.95e+77)
		tmp = Float64(y * Float64(z * Float64(t * -9.0)));
	elseif (z <= 2.2e-70)
		tmp = Float64(Float64(x * 2.0) - Float64(b * Float64(a * -27.0)));
	elseif (z <= 1e-38)
		tmp = Float64(-9.0 * Float64(y * Float64(z * t)));
	elseif (z <= 3.7e+115)
		tmp = Float64(Float64(x * 2.0) - Float64(a * Float64(b * -27.0)));
	else
		tmp = Float64(-9.0 * Float64(t * Float64(z * y)));
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -1.95e+77)
		tmp = y * (z * (t * -9.0));
	elseif (z <= 2.2e-70)
		tmp = (x * 2.0) - (b * (a * -27.0));
	elseif (z <= 1e-38)
		tmp = -9.0 * (y * (z * t));
	elseif (z <= 3.7e+115)
		tmp = (x * 2.0) - (a * (b * -27.0));
	else
		tmp = -9.0 * (t * (z * y));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -1.95e+77], N[(y * N[(z * N[(t * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.2e-70], N[(N[(x * 2.0), $MachinePrecision] - N[(b * N[(a * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1e-38], N[(-9.0 * N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.7e+115], N[(N[(x * 2.0), $MachinePrecision] - N[(a * N[(b * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-9.0 * N[(t * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -1.9499999999999999e77

   1. Initial program 89.9%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

   2. Taylor expanded in y around 0 89.9%

      \[\leadsto \left(x \cdot 2 - \color{blue}{\left(9 \cdot \left(y \cdot z\right)\right)} \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

   3. Taylor expanded in y around inf 45.6%

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

      1. *-commutative 45.6%

         \[\leadsto -9 \cdot \color{blue}{\left(\left(t \cdot z\right) \cdot y\right)} \]

      2. *-commutative 45.6%

         \[\leadsto -9 \cdot \left(\color{blue}{\left(z \cdot t\right)} \cdot y\right) \]

      3. *-commutative 45.6%

         \[\leadsto -9 \cdot \color{blue}{\left(y \cdot \left(z \cdot t\right)\right)} \]

      4. *-commutative 45.6%

         \[\leadsto \color{blue}{\left(y \cdot \left(z \cdot t\right)\right) \cdot -9} \]

      5. associate-*r* 45.6%

         \[\leadsto \color{blue}{y \cdot \left(\left(z \cdot t\right) \cdot -9\right)} \]

      6. associate-*l* 45.6%

         \[\leadsto y \cdot \color{blue}{\left(z \cdot \left(t \cdot -9\right)\right)} \]

   5. Simplified 45.6%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot \left(t \cdot -9\right)\right)} \]

   if -1.9499999999999999e77 < z < 2.1999999999999999e-70

   1. Initial program 99.8%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l- 99.8%

         \[\leadsto \color{blue}{x \cdot 2 - \left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t - \left(a \cdot 27\right) \cdot b\right)} \]

      2. sub-neg 99.8%

         \[\leadsto \color{blue}{x \cdot 2 + \left(-\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t - \left(a \cdot 27\right) \cdot b\right)\right)} \]

      3. neg-mul-1 99.8%

         \[\leadsto x \cdot 2 + \color{blue}{-1 \cdot \left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t - \left(a \cdot 27\right) \cdot b\right)} \]

      4. metadata-eval 99.8%

         \[\leadsto x \cdot 2 + \color{blue}{\left(-1\right)} \cdot \left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t - \left(a \cdot 27\right) \cdot b\right) \]

      5. metadata-eval 99.8%

         \[\leadsto x \cdot 2 + \left(-\color{blue}{\left(--1\right)}\right) \cdot \left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t - \left(a \cdot 27\right) \cdot b\right) \]

      6. cancel-sign-sub-inv 99.8%

         \[\leadsto \color{blue}{x \cdot 2 - \left(--1\right) \cdot \left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t - \left(a \cdot 27\right) \cdot b\right)} \]

      7. metadata-eval 99.8%

         \[\leadsto x \cdot 2 - \color{blue}{1} \cdot \left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t - \left(a \cdot 27\right) \cdot b\right) \]

      8. *-lft-identity 99.8%

         \[\leadsto x \cdot 2 - \color{blue}{\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t - \left(a \cdot 27\right) \cdot b\right)} \]

      9. associate-*l* 99.1%

         \[\leadsto x \cdot 2 - \left(\color{blue}{\left(y \cdot 9\right) \cdot \left(z \cdot t\right)} - \left(a \cdot 27\right) \cdot b\right) \]

      10. associate-*l* 99.1%

          \[\leadsto x \cdot 2 - \left(\left(y \cdot 9\right) \cdot \left(z \cdot t\right) - \color{blue}{a \cdot \left(27 \cdot b\right)}\right) \]

   3. Simplified 99.1%

      \[\leadsto \color{blue}{x \cdot 2 - \left(\left(y \cdot 9\right) \cdot \left(z \cdot t\right) - a \cdot \left(27 \cdot b\right)\right)} \]

   4. Taylor expanded in y around 0 76.4%

      \[\leadsto x \cdot 2 - \color{blue}{-27 \cdot \left(a \cdot b\right)} \]
   5. Step-by-step derivation

      1. *-commutative 76.4%

         \[\leadsto x \cdot 2 - \color{blue}{\left(a \cdot b\right) \cdot -27} \]

      2. *-commutative 76.4%

         \[\leadsto x \cdot 2 - \color{blue}{\left(b \cdot a\right)} \cdot -27 \]

      3. associate-*l* 76.4%

         \[\leadsto x \cdot 2 - \color{blue}{b \cdot \left(a \cdot -27\right)} \]

   6. Simplified 76.4%

      \[\leadsto x \cdot 2 - \color{blue}{b \cdot \left(a \cdot -27\right)} \]

   if 2.1999999999999999e-70 < z < 9.9999999999999996e-39

   1. Initial program 99.6%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

   2. Taylor expanded in y around inf 38.6%

      \[\leadsto \color{blue}{-9 \cdot \left(y \cdot \left(t \cdot z\right)\right)} \]

   if 9.9999999999999996e-39 < z < 3.70000000000000006e115

   1. Initial program 99.7%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l- 99.7%

         \[\leadsto \color{blue}{x \cdot 2 - \left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t - \left(a \cdot 27\right) \cdot b\right)} \]

      2. sub-neg 99.7%

         \[\leadsto \color{blue}{x \cdot 2 + \left(-\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t - \left(a \cdot 27\right) \cdot b\right)\right)} \]

      3. neg-mul-1 99.7%

         \[\leadsto x \cdot 2 + \color{blue}{-1 \cdot \left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t - \left(a \cdot 27\right) \cdot b\right)} \]

      4. metadata-eval 99.7%

         \[\leadsto x \cdot 2 + \color{blue}{\left(-1\right)} \cdot \left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t - \left(a \cdot 27\right) \cdot b\right) \]

      5. metadata-eval 99.7%

         \[\leadsto x \cdot 2 + \left(-\color{blue}{\left(--1\right)}\right) \cdot \left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t - \left(a \cdot 27\right) \cdot b\right) \]

      6. cancel-sign-sub-inv 99.7%

         \[\leadsto \color{blue}{x \cdot 2 - \left(--1\right) \cdot \left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t - \left(a \cdot 27\right) \cdot b\right)} \]

      7. metadata-eval 99.7%

         \[\leadsto x \cdot 2 - \color{blue}{1} \cdot \left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t - \left(a \cdot 27\right) \cdot b\right) \]

      8. *-lft-identity 99.7%

         \[\leadsto x \cdot 2 - \color{blue}{\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t - \left(a \cdot 27\right) \cdot b\right)} \]

      9. associate-*l* 91.9%

         \[\leadsto x \cdot 2 - \left(\color{blue}{\left(y \cdot 9\right) \cdot \left(z \cdot t\right)} - \left(a \cdot 27\right) \cdot b\right) \]

      10. associate-*l* 91.8%

          \[\leadsto x \cdot 2 - \left(\left(y \cdot 9\right) \cdot \left(z \cdot t\right) - \color{blue}{a \cdot \left(27 \cdot b\right)}\right) \]

   3. Simplified 91.8%

      \[\leadsto \color{blue}{x \cdot 2 - \left(\left(y \cdot 9\right) \cdot \left(z \cdot t\right) - a \cdot \left(27 \cdot b\right)\right)} \]

   4. Taylor expanded in y around 0 59.9%

      \[\leadsto x \cdot 2 - \color{blue}{-27 \cdot \left(a \cdot b\right)} \]
   5. Step-by-step derivation

      1. *-commutative 59.9%

         \[\leadsto x \cdot 2 - \color{blue}{\left(a \cdot b\right) \cdot -27} \]

      2. associate-*r* 59.8%

         \[\leadsto x \cdot 2 - \color{blue}{a \cdot \left(b \cdot -27\right)} \]

   6. Simplified 59.8%

      \[\leadsto x \cdot 2 - \color{blue}{a \cdot \left(b \cdot -27\right)} \]

   if 3.70000000000000006e115 < z

   1. Initial program 82.3%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

   2. Taylor expanded in y around 0 82.3%

      \[\leadsto \left(x \cdot 2 - \color{blue}{\left(9 \cdot \left(y \cdot z\right)\right)} \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

   3. Taylor expanded in y around inf 64.8%

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

      1. *-commutative 64.8%

         \[\leadsto -9 \cdot \left(y \cdot \color{blue}{\left(z \cdot t\right)}\right) \]

      2. associate-*r* 56.2%

         \[\leadsto -9 \cdot \color{blue}{\left(\left(y \cdot z\right) \cdot t\right)} \]

   5. Simplified 56.2%

      \[\leadsto \color{blue}{-9 \cdot \left(\left(y \cdot z\right) \cdot t\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 64.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.95 \cdot 10^{+77}:\\ \;\;\;\;y \cdot \left(z \cdot \left(t \cdot -9\right)\right)\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-70}:\\ \;\;\;\;x \cdot 2 - b \cdot \left(a \cdot -27\right)\\ \mathbf{elif}\;z \leq 10^{-38}:\\ \;\;\;\;-9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{+115}:\\ \;\;\;\;x \cdot 2 - a \cdot \left(b \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;-9 \cdot \left(t \cdot \left(z \cdot y\right)\right)\\ \end{array} \]

Alternative 11: 75.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;b \leq -5 \cdot 10^{-106} \lor \neg \left(b \leq 1.1 \cdot 10^{+160}\right):\\ \;\;\;\;t \cdot \left(y \cdot \left(z \cdot -9\right)\right) + 27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 - 9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -5e-106) (not (<= b 1.1e+160)))
   (+ (* t (* y (* z -9.0))) (* 27.0 (* a b)))
   (- (* x 2.0) (* 9.0 (* y (* z t))))))

C

assert(y < z && z < t);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -5e-106) || !(b <= 1.1e+160)) {
		tmp = (t * (y * (z * -9.0))) + (27.0 * (a * b));
	} else {
		tmp = (x * 2.0) - (9.0 * (y * (z * t)));
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    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) :: tmp
    if ((b <= (-5d-106)) .or. (.not. (b <= 1.1d+160))) then
        tmp = (t * (y * (z * (-9.0d0)))) + (27.0d0 * (a * b))
    else
        tmp = (x * 2.0d0) - (9.0d0 * (y * (z * t)))
    end if
    code = tmp
end function

Java

assert y < z && z < t;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -5e-106) || !(b <= 1.1e+160)) {
		tmp = (t * (y * (z * -9.0))) + (27.0 * (a * b));
	} else {
		tmp = (x * 2.0) - (9.0 * (y * (z * t)));
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -5e-106) or not (b <= 1.1e+160):
		tmp = (t * (y * (z * -9.0))) + (27.0 * (a * b))
	else:
		tmp = (x * 2.0) - (9.0 * (y * (z * t)))
	return tmp

Julia

y, z, t = sort([y, z, t])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -5e-106) || !(b <= 1.1e+160))
		tmp = Float64(Float64(t * Float64(y * Float64(z * -9.0))) + Float64(27.0 * Float64(a * b)));
	else
		tmp = Float64(Float64(x * 2.0) - Float64(9.0 * Float64(y * Float64(z * t))));
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -5e-106) || ~((b <= 1.1e+160)))
		tmp = (t * (y * (z * -9.0))) + (27.0 * (a * b));
	else
		tmp = (x * 2.0) - (9.0 * (y * (z * t)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -5e-106], N[Not[LessEqual[b, 1.1e+160]], $MachinePrecision]], N[(N[(t * N[(y * N[(z * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * 2.0), $MachinePrecision] - N[(9.0 * N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -4.99999999999999983e-106 or 1.09999999999999996e160 < b

   1. Initial program 97.0%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

   2. Taylor expanded in x around 0 75.2%

      \[\leadsto \color{blue}{27 \cdot \left(a \cdot b\right) - 9 \cdot \left(y \cdot \left(t \cdot z\right)\right)} \]
   3. Step-by-step derivation

      1. cancel-sign-sub-inv 75.2%

         \[\leadsto \color{blue}{27 \cdot \left(a \cdot b\right) + \left(-9\right) \cdot \left(y \cdot \left(t \cdot z\right)\right)} \]

      2. metadata-eval 75.2%

         \[\leadsto 27 \cdot \left(a \cdot b\right) + \color{blue}{-9} \cdot \left(y \cdot \left(t \cdot z\right)\right) \]

      3. +-commutative 75.2%

         \[\leadsto \color{blue}{-9 \cdot \left(y \cdot \left(t \cdot z\right)\right) + 27 \cdot \left(a \cdot b\right)} \]

      4. *-commutative 75.2%

         \[\leadsto \color{blue}{\left(y \cdot \left(t \cdot z\right)\right) \cdot -9} + 27 \cdot \left(a \cdot b\right) \]

      5. associate-*r* 74.0%

         \[\leadsto \color{blue}{\left(\left(y \cdot t\right) \cdot z\right)} \cdot -9 + 27 \cdot \left(a \cdot b\right) \]

      6. associate-*l* 74.0%

         \[\leadsto \color{blue}{\left(y \cdot t\right) \cdot \left(z \cdot -9\right)} + 27 \cdot \left(a \cdot b\right) \]

      7. associate-*r* 74.0%

         \[\leadsto \left(y \cdot t\right) \cdot \left(z \cdot -9\right) + \color{blue}{\left(27 \cdot a\right) \cdot b} \]

      8. *-commutative 74.0%

         \[\leadsto \left(y \cdot t\right) \cdot \left(z \cdot -9\right) + \color{blue}{\left(a \cdot 27\right)} \cdot b \]

      9. associate-*r* 74.0%

         \[\leadsto \left(y \cdot t\right) \cdot \left(z \cdot -9\right) + \color{blue}{a \cdot \left(27 \cdot b\right)} \]

      10. fma-udef 74.7%

          \[\leadsto \color{blue}{\mathsf{fma}\left(y \cdot t, z \cdot -9, a \cdot \left(27 \cdot b\right)\right)} \]

      11. *-commutative 74.7%

          \[\leadsto \mathsf{fma}\left(\color{blue}{t \cdot y}, z \cdot -9, a \cdot \left(27 \cdot b\right)\right) \]

      12. fma-def 74.0%

          \[\leadsto \color{blue}{\left(t \cdot y\right) \cdot \left(z \cdot -9\right) + a \cdot \left(27 \cdot b\right)} \]

      13. associate-*r* 76.6%

          \[\leadsto \color{blue}{t \cdot \left(y \cdot \left(z \cdot -9\right)\right)} + a \cdot \left(27 \cdot b\right) \]

      14. fma-def 77.4%

          \[\leadsto \color{blue}{\mathsf{fma}\left(t, y \cdot \left(z \cdot -9\right), a \cdot \left(27 \cdot b\right)\right)} \]

      15. associate-*r* 77.4%

          \[\leadsto \mathsf{fma}\left(t, y \cdot \left(z \cdot -9\right), \color{blue}{\left(a \cdot 27\right) \cdot b}\right) \]

      16. *-commutative 77.4%

          \[\leadsto \mathsf{fma}\left(t, y \cdot \left(z \cdot -9\right), \color{blue}{\left(27 \cdot a\right)} \cdot b\right) \]

      17. associate-*r* 77.4%

          \[\leadsto \mathsf{fma}\left(t, y \cdot \left(z \cdot -9\right), \color{blue}{27 \cdot \left(a \cdot b\right)}\right) \]

   4. Simplified 77.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, y \cdot \left(z \cdot -9\right), 27 \cdot \left(a \cdot b\right)\right)} \]
   5. Step-by-step derivation

      1. fma-udef 76.6%

         \[\leadsto \color{blue}{t \cdot \left(y \cdot \left(z \cdot -9\right)\right) + 27 \cdot \left(a \cdot b\right)} \]

   6. Applied egg-rr 76.6%

      \[\leadsto \color{blue}{t \cdot \left(y \cdot \left(z \cdot -9\right)\right) + 27 \cdot \left(a \cdot b\right)} \]

   if -4.99999999999999983e-106 < b < 1.09999999999999996e160

   1. Initial program 93.0%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

   2. Taylor expanded in a around 0 81.8%

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

4. Final simplification 79.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5 \cdot 10^{-106} \lor \neg \left(b \leq 1.1 \cdot 10^{+160}\right):\\ \;\;\;\;t \cdot \left(y \cdot \left(z \cdot -9\right)\right) + 27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 - 9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \end{array} \]

Alternative 12: 93.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ \\ b \cdot \left(a \cdot 27\right) + \left(x \cdot 2 - \left(z \cdot 9\right) \cdot \left(y \cdot t\right)\right) \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (+ (* b (* a 27.0)) (- (* x 2.0) (* (* z 9.0) (* y t)))))

C

assert(y < z && z < t);
double code(double x, double y, double z, double t, double a, double b) {
	return (b * (a * 27.0)) + ((x * 2.0) - ((z * 9.0) * (y * t)));
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    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
    code = (b * (a * 27.0d0)) + ((x * 2.0d0) - ((z * 9.0d0) * (y * t)))
end function

Java

assert y < z && z < t;
public static double code(double x, double y, double z, double t, double a, double b) {
	return (b * (a * 27.0)) + ((x * 2.0) - ((z * 9.0) * (y * t)));
}

Python

[y, z, t] = sort([y, z, t])
def code(x, y, z, t, a, b):
	return (b * (a * 27.0)) + ((x * 2.0) - ((z * 9.0) * (y * t)))

Julia

y, z, t = sort([y, z, t])
function code(x, y, z, t, a, b)
	return Float64(Float64(b * Float64(a * 27.0)) + Float64(Float64(x * 2.0) - Float64(Float64(z * 9.0) * Float64(y * t))))
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
function tmp = code(x, y, z, t, a, b)
	tmp = (b * (a * 27.0)) + ((x * 2.0) - ((z * 9.0) * (y * t)));
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := N[(N[(b * N[(a * 27.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x * 2.0), $MachinePrecision] - N[(N[(z * 9.0), $MachinePrecision] * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 95.1%

   \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

2. Taylor expanded in y around 0 95.0%

   \[\leadsto \left(x \cdot 2 - \color{blue}{9 \cdot \left(y \cdot \left(t \cdot z\right)\right)}\right) + \left(a \cdot 27\right) \cdot b \]
3. Step-by-step derivation

   1. *-commutative 95.0%

      \[\leadsto \left(x \cdot 2 - 9 \cdot \color{blue}{\left(\left(t \cdot z\right) \cdot y\right)}\right) + \left(a \cdot 27\right) \cdot b \]

   2. *-commutative 95.0%

      \[\leadsto \left(x \cdot 2 - 9 \cdot \left(\color{blue}{\left(z \cdot t\right)} \cdot y\right)\right) + \left(a \cdot 27\right) \cdot b \]

   3. associate-*l* 95.0%

      \[\leadsto \left(x \cdot 2 - \color{blue}{\left(9 \cdot \left(z \cdot t\right)\right) \cdot y}\right) + \left(a \cdot 27\right) \cdot b \]

   4. associate-*r* 95.0%

      \[\leadsto \left(x \cdot 2 - \color{blue}{\left(\left(9 \cdot z\right) \cdot t\right)} \cdot y\right) + \left(a \cdot 27\right) \cdot b \]

   5. associate-*l* 94.6%

      \[\leadsto \left(x \cdot 2 - \color{blue}{\left(9 \cdot z\right) \cdot \left(t \cdot y\right)}\right) + \left(a \cdot 27\right) \cdot b \]

   6. *-commutative 94.6%

      \[\leadsto \left(x \cdot 2 - \left(9 \cdot z\right) \cdot \color{blue}{\left(y \cdot t\right)}\right) + \left(a \cdot 27\right) \cdot b \]

4. Simplified 94.6%

   \[\leadsto \left(x \cdot 2 - \color{blue}{\left(9 \cdot z\right) \cdot \left(y \cdot t\right)}\right) + \left(a \cdot 27\right) \cdot b \]

5. Final simplification 94.6%

   \[\leadsto b \cdot \left(a \cdot 27\right) + \left(x \cdot 2 - \left(z \cdot 9\right) \cdot \left(y \cdot t\right)\right) \]

Alternative 13: 74.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;b \leq -1.8 \cdot 10^{+45}:\\ \;\;\;\;x \cdot 2 - a \cdot \left(b \cdot -27\right)\\ \mathbf{elif}\;b \leq 1.02 \cdot 10^{+195}:\\ \;\;\;\;x \cdot 2 - 9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 - b \cdot \left(a \cdot -27\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1.8e+45)
   (- (* x 2.0) (* a (* b -27.0)))
   (if (<= b 1.02e+195)
     (- (* x 2.0) (* 9.0 (* y (* z t))))
     (- (* x 2.0) (* b (* a -27.0))))))

C

assert(y < z && z < t);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.8e+45) {
		tmp = (x * 2.0) - (a * (b * -27.0));
	} else if (b <= 1.02e+195) {
		tmp = (x * 2.0) - (9.0 * (y * (z * t)));
	} else {
		tmp = (x * 2.0) - (b * (a * -27.0));
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    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) :: tmp
    if (b <= (-1.8d+45)) then
        tmp = (x * 2.0d0) - (a * (b * (-27.0d0)))
    else if (b <= 1.02d+195) then
        tmp = (x * 2.0d0) - (9.0d0 * (y * (z * t)))
    else
        tmp = (x * 2.0d0) - (b * (a * (-27.0d0)))
    end if
    code = tmp
end function

Java

assert y < z && z < t;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.8e+45) {
		tmp = (x * 2.0) - (a * (b * -27.0));
	} else if (b <= 1.02e+195) {
		tmp = (x * 2.0) - (9.0 * (y * (z * t)));
	} else {
		tmp = (x * 2.0) - (b * (a * -27.0));
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -1.8e+45:
		tmp = (x * 2.0) - (a * (b * -27.0))
	elif b <= 1.02e+195:
		tmp = (x * 2.0) - (9.0 * (y * (z * t)))
	else:
		tmp = (x * 2.0) - (b * (a * -27.0))
	return tmp

Julia

y, z, t = sort([y, z, t])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1.8e+45)
		tmp = Float64(Float64(x * 2.0) - Float64(a * Float64(b * -27.0)));
	elseif (b <= 1.02e+195)
		tmp = Float64(Float64(x * 2.0) - Float64(9.0 * Float64(y * Float64(z * t))));
	else
		tmp = Float64(Float64(x * 2.0) - Float64(b * Float64(a * -27.0)));
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -1.8e+45)
		tmp = (x * 2.0) - (a * (b * -27.0));
	elseif (b <= 1.02e+195)
		tmp = (x * 2.0) - (9.0 * (y * (z * t)));
	else
		tmp = (x * 2.0) - (b * (a * -27.0));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1.8e+45], N[(N[(x * 2.0), $MachinePrecision] - N[(a * N[(b * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.02e+195], N[(N[(x * 2.0), $MachinePrecision] - N[(9.0 * N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * 2.0), $MachinePrecision] - N[(b * N[(a * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.8e45

   1. Initial program 94.9%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l- 94.9%

         \[\leadsto \color{blue}{x \cdot 2 - \left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t - \left(a \cdot 27\right) \cdot b\right)} \]

      2. sub-neg 94.9%

         \[\leadsto \color{blue}{x \cdot 2 + \left(-\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t - \left(a \cdot 27\right) \cdot b\right)\right)} \]

      3. neg-mul-1 94.9%

         \[\leadsto x \cdot 2 + \color{blue}{-1 \cdot \left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t - \left(a \cdot 27\right) \cdot b\right)} \]

      4. metadata-eval 94.9%

         \[\leadsto x \cdot 2 + \color{blue}{\left(-1\right)} \cdot \left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t - \left(a \cdot 27\right) \cdot b\right) \]

      5. metadata-eval 94.9%

         \[\leadsto x \cdot 2 + \left(-\color{blue}{\left(--1\right)}\right) \cdot \left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t - \left(a \cdot 27\right) \cdot b\right) \]

      6. cancel-sign-sub-inv 94.9%

         \[\leadsto \color{blue}{x \cdot 2 - \left(--1\right) \cdot \left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t - \left(a \cdot 27\right) \cdot b\right)} \]

      7. metadata-eval 94.9%

         \[\leadsto x \cdot 2 - \color{blue}{1} \cdot \left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t - \left(a \cdot 27\right) \cdot b\right) \]

      8. *-lft-identity 94.9%

         \[\leadsto x \cdot 2 - \color{blue}{\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t - \left(a \cdot 27\right) \cdot b\right)} \]

      9. associate-*l* 93.0%

         \[\leadsto x \cdot 2 - \left(\color{blue}{\left(y \cdot 9\right) \cdot \left(z \cdot t\right)} - \left(a \cdot 27\right) \cdot b\right) \]

      10. associate-*l* 93.0%

          \[\leadsto x \cdot 2 - \left(\left(y \cdot 9\right) \cdot \left(z \cdot t\right) - \color{blue}{a \cdot \left(27 \cdot b\right)}\right) \]

   3. Simplified 93.0%

      \[\leadsto \color{blue}{x \cdot 2 - \left(\left(y \cdot 9\right) \cdot \left(z \cdot t\right) - a \cdot \left(27 \cdot b\right)\right)} \]

   4. Taylor expanded in y around 0 74.2%

      \[\leadsto x \cdot 2 - \color{blue}{-27 \cdot \left(a \cdot b\right)} \]
   5. Step-by-step derivation

      1. *-commutative 74.2%

         \[\leadsto x \cdot 2 - \color{blue}{\left(a \cdot b\right) \cdot -27} \]

      2. associate-*r* 74.2%

         \[\leadsto x \cdot 2 - \color{blue}{a \cdot \left(b \cdot -27\right)} \]

   6. Simplified 74.2%

      \[\leadsto x \cdot 2 - \color{blue}{a \cdot \left(b \cdot -27\right)} \]

   if -1.8e45 < b < 1.02e195

   1. Initial program 94.4%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

   2. Taylor expanded in a around 0 77.5%

      \[\leadsto \color{blue}{2 \cdot x - 9 \cdot \left(y \cdot \left(t \cdot z\right)\right)} \]

   if 1.02e195 < b

   1. Initial program 99.9%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l- 99.9%

         \[\leadsto \color{blue}{x \cdot 2 - \left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t - \left(a \cdot 27\right) \cdot b\right)} \]

      2. sub-neg 99.9%

         \[\leadsto \color{blue}{x \cdot 2 + \left(-\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t - \left(a \cdot 27\right) \cdot b\right)\right)} \]

      3. neg-mul-1 99.9%

         \[\leadsto x \cdot 2 + \color{blue}{-1 \cdot \left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t - \left(a \cdot 27\right) \cdot b\right)} \]

      4. metadata-eval 99.9%

         \[\leadsto x \cdot 2 + \color{blue}{\left(-1\right)} \cdot \left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t - \left(a \cdot 27\right) \cdot b\right) \]

      5. metadata-eval 99.9%

         \[\leadsto x \cdot 2 + \left(-\color{blue}{\left(--1\right)}\right) \cdot \left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t - \left(a \cdot 27\right) \cdot b\right) \]

      6. cancel-sign-sub-inv 99.9%

         \[\leadsto \color{blue}{x \cdot 2 - \left(--1\right) \cdot \left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t - \left(a \cdot 27\right) \cdot b\right)} \]

      7. metadata-eval 99.9%

         \[\leadsto x \cdot 2 - \color{blue}{1} \cdot \left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t - \left(a \cdot 27\right) \cdot b\right) \]

      8. *-lft-identity 99.9%

         \[\leadsto x \cdot 2 - \color{blue}{\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t - \left(a \cdot 27\right) \cdot b\right)} \]

      9. associate-*l* 92.5%

         \[\leadsto x \cdot 2 - \left(\color{blue}{\left(y \cdot 9\right) \cdot \left(z \cdot t\right)} - \left(a \cdot 27\right) \cdot b\right) \]

      10. associate-*l* 92.5%

          \[\leadsto x \cdot 2 - \left(\left(y \cdot 9\right) \cdot \left(z \cdot t\right) - \color{blue}{a \cdot \left(27 \cdot b\right)}\right) \]

   3. Simplified 92.5%

      \[\leadsto \color{blue}{x \cdot 2 - \left(\left(y \cdot 9\right) \cdot \left(z \cdot t\right) - a \cdot \left(27 \cdot b\right)\right)} \]

   4. Taylor expanded in y around 0 85.2%

      \[\leadsto x \cdot 2 - \color{blue}{-27 \cdot \left(a \cdot b\right)} \]
   5. Step-by-step derivation

      1. *-commutative 85.2%

         \[\leadsto x \cdot 2 - \color{blue}{\left(a \cdot b\right) \cdot -27} \]

      2. *-commutative 85.2%

         \[\leadsto x \cdot 2 - \color{blue}{\left(b \cdot a\right)} \cdot -27 \]

      3. associate-*l* 85.2%

         \[\leadsto x \cdot 2 - \color{blue}{b \cdot \left(a \cdot -27\right)} \]

   6. Simplified 85.2%

      \[\leadsto x \cdot 2 - \color{blue}{b \cdot \left(a \cdot -27\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 77.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.8 \cdot 10^{+45}:\\ \;\;\;\;x \cdot 2 - a \cdot \left(b \cdot -27\right)\\ \mathbf{elif}\;b \leq 1.02 \cdot 10^{+195}:\\ \;\;\;\;x \cdot 2 - 9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 - b \cdot \left(a \cdot -27\right)\\ \end{array} \]

Alternative 14: 44.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;b \leq -5.5 \cdot 10^{-106} \lor \neg \left(b \leq 7.8 \cdot 10^{+159}\right):\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2\\ \end{array} \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -5.5e-106) (not (<= b 7.8e+159))) (* 27.0 (* a b)) (* x 2.0)))

C

assert(y < z && z < t);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -5.5e-106) || !(b <= 7.8e+159)) {
		tmp = 27.0 * (a * b);
	} else {
		tmp = x * 2.0;
	}
	return tmp;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    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) :: tmp
    if ((b <= (-5.5d-106)) .or. (.not. (b <= 7.8d+159))) then
        tmp = 27.0d0 * (a * b)
    else
        tmp = x * 2.0d0
    end if
    code = tmp
end function

Java

assert y < z && z < t;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -5.5e-106) || !(b <= 7.8e+159)) {
		tmp = 27.0 * (a * b);
	} else {
		tmp = x * 2.0;
	}
	return tmp;
}

Python

[y, z, t] = sort([y, z, t])
def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -5.5e-106) or not (b <= 7.8e+159):
		tmp = 27.0 * (a * b)
	else:
		tmp = x * 2.0
	return tmp

Julia

y, z, t = sort([y, z, t])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -5.5e-106) || !(b <= 7.8e+159))
		tmp = Float64(27.0 * Float64(a * b));
	else
		tmp = Float64(x * 2.0);
	end
	return tmp
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -5.5e-106) || ~((b <= 7.8e+159)))
		tmp = 27.0 * (a * b);
	else
		tmp = x * 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -5.5e-106], N[Not[LessEqual[b, 7.8e+159]], $MachinePrecision]], N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision], N[(x * 2.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -5.5000000000000001e-106 or 7.8000000000000001e159 < b

   1. Initial program 97.0%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

   2. Taylor expanded in a around inf 47.0%

      \[\leadsto \color{blue}{27 \cdot \left(a \cdot b\right)} \]

   if -5.5000000000000001e-106 < b < 7.8000000000000001e159

   1. Initial program 93.0%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

   2. Taylor expanded in x around inf 46.0%

      \[\leadsto \color{blue}{2 \cdot x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 46.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5.5 \cdot 10^{-106} \lor \neg \left(b \leq 7.8 \cdot 10^{+159}\right):\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2\\ \end{array} \]

Alternative 15: 30.6% accurate, 5.7× speedup

Math

\[\begin{array}{l} [y, z, t] = \mathsf{sort}([y, z, t])\\ \\ x \cdot 2 \end{array} \]

FPCore

NOTE: y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a b) :precision binary64 (* x 2.0))

C

assert(y < z && z < t);
double code(double x, double y, double z, double t, double a, double b) {
	return x * 2.0;
}

Fortran

NOTE: y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    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
    code = x * 2.0d0
end function

Java

assert y < z && z < t;
public static double code(double x, double y, double z, double t, double a, double b) {
	return x * 2.0;
}

Python

[y, z, t] = sort([y, z, t])
def code(x, y, z, t, a, b):
	return x * 2.0

Julia

y, z, t = sort([y, z, t])
function code(x, y, z, t, a, b)
	return Float64(x * 2.0)
end

MATLAB

y, z, t = num2cell(sort([y, z, t])){:}
function tmp = code(x, y, z, t, a, b)
	tmp = x * 2.0;
end

Wolfram

NOTE: y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := N[(x * 2.0), $MachinePrecision]

Derivation

1. Initial program 95.1%

   \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

2. Taylor expanded in x around inf 33.4%

   \[\leadsto \color{blue}{2 \cdot x} \]

3. Final simplification 33.4%

   \[\leadsto x \cdot 2 \]

Developer target: 94.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y < 7.590524218811189 \cdot 10^{-161}:\\ \;\;\;\;\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + a \cdot \left(27 \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot 2 - 9 \cdot \left(y \cdot \left(t \cdot z\right)\right)\right) + \left(a \cdot 27\right) \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (< y 7.590524218811189e-161)
   (+ (- (* x 2.0) (* (* (* y 9.0) z) t)) (* a (* 27.0 b)))
   (+ (- (* x 2.0) (* 9.0 (* y (* t z)))) (* (* a 27.0) b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y < 7.590524218811189e-161) {
		tmp = ((x * 2.0) - (((y * 9.0) * z) * t)) + (a * (27.0 * b));
	} else {
		tmp = ((x * 2.0) - (9.0 * (y * (t * z)))) + ((a * 27.0) * b);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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) :: tmp
    if (y < 7.590524218811189d-161) then
        tmp = ((x * 2.0d0) - (((y * 9.0d0) * z) * t)) + (a * (27.0d0 * b))
    else
        tmp = ((x * 2.0d0) - (9.0d0 * (y * (t * z)))) + ((a * 27.0d0) * b)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y < 7.590524218811189e-161) {
		tmp = ((x * 2.0) - (((y * 9.0) * z) * t)) + (a * (27.0 * b));
	} else {
		tmp = ((x * 2.0) - (9.0 * (y * (t * z)))) + ((a * 27.0) * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y < 7.590524218811189e-161:
		tmp = ((x * 2.0) - (((y * 9.0) * z) * t)) + (a * (27.0 * b))
	else:
		tmp = ((x * 2.0) - (9.0 * (y * (t * z)))) + ((a * 27.0) * b)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y < 7.590524218811189e-161)
		tmp = Float64(Float64(Float64(x * 2.0) - Float64(Float64(Float64(y * 9.0) * z) * t)) + Float64(a * Float64(27.0 * b)));
	else
		tmp = Float64(Float64(Float64(x * 2.0) - Float64(9.0 * Float64(y * Float64(t * z)))) + Float64(Float64(a * 27.0) * b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y < 7.590524218811189e-161)
		tmp = ((x * 2.0) - (((y * 9.0) * z) * t)) + (a * (27.0 * b));
	else
		tmp = ((x * 2.0) - (9.0 * (y * (t * z)))) + ((a * 27.0) * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Less[y, 7.590524218811189e-161], N[(N[(N[(x * 2.0), $MachinePrecision] - N[(N[(N[(y * 9.0), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision] + N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x * 2.0), $MachinePrecision] - N[(9.0 * N[(y * N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(a * 27.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]]

Reproduce

herbie shell --seed 2023176 
(FPCore (x y z t a b)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, A"
  :precision binary64

  :herbie-target
  (if (< y 7.590524218811189e-161) (+ (- (* x 2.0) (* (* (* y 9.0) z) t)) (* a (* 27.0 b))) (+ (- (* x 2.0) (* 9.0 (* y (* t z)))) (* (* a 27.0) b)))

  (+ (- (* x 2.0) (* (* (* y 9.0) z) t)) (* (* a 27.0) b)))