Statistics.Distribution.Beta:$centropy from math-functions-0.1.5.2

Percentage Accurate: 95.1% → 98.6%

Time: 16.6s

Alternatives: 24

Speedup: 0.5×

• 36.3% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ \left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (+ (- (- x (* (- y 1.0) z)) (* (- t 1.0) a)) (* (- (+ y t) 2.0) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	return ((x - ((y - 1.0) * z)) - ((t - 1.0) * a)) + (((y + t) - 2.0) * 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 - ((y - 1.0d0) * z)) - ((t - 1.0d0) * a)) + (((y + t) - 2.0d0) * b)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return ((x - ((y - 1.0) * z)) - ((t - 1.0) * a)) + (((y + t) - 2.0) * b);
}

Python

def code(x, y, z, t, a, b):
	return ((x - ((y - 1.0) * z)) - ((t - 1.0) * a)) + (((y + t) - 2.0) * b)

Julia

function code(x, y, z, t, a, b)
	return Float64(Float64(Float64(x - Float64(Float64(y - 1.0) * z)) - Float64(Float64(t - 1.0) * a)) + Float64(Float64(Float64(y + t) - 2.0) * b))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = ((x - ((y - 1.0) * z)) - ((t - 1.0) * a)) + (((y + t) - 2.0) * b);
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(N[(x - N[(N[(y - 1.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] - N[(N[(t - 1.0), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]

Initial Program: 95.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (+ (- (- x (* (- y 1.0) z)) (* (- t 1.0) a)) (* (- (+ y t) 2.0) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	return ((x - ((y - 1.0) * z)) - ((t - 1.0) * a)) + (((y + t) - 2.0) * 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 - ((y - 1.0d0) * z)) - ((t - 1.0d0) * a)) + (((y + t) - 2.0d0) * b)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return ((x - ((y - 1.0) * z)) - ((t - 1.0) * a)) + (((y + t) - 2.0) * b);
}

Python

def code(x, y, z, t, a, b):
	return ((x - ((y - 1.0) * z)) - ((t - 1.0) * a)) + (((y + t) - 2.0) * b)

Julia

function code(x, y, z, t, a, b)
	return Float64(Float64(Float64(x - Float64(Float64(y - 1.0) * z)) - Float64(Float64(t - 1.0) * a)) + Float64(Float64(Float64(y + t) - 2.0) * b))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = ((x - ((y - 1.0) * z)) - ((t - 1.0) * a)) + (((y + t) - 2.0) * b);
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(N[(x - N[(N[(y - 1.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] - N[(N[(t - 1.0), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]

Alternative 1: 98.6% accurate, 0.2× speedup

Math

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

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1
         (+ (+ (- x (* z (- y 1.0))) (* a (- 1.0 t))) (* b (- (+ t y) 2.0)))))
   (if (<= t_1 INFINITY) t_1 (fma y (- b z) (* b (+ t -2.0))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((x - (z * (y - 1.0))) + (a * (1.0 - t))) + (b * ((t + y) - 2.0));
	double tmp;
	if (t_1 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = fma(y, (b - z), (b * (t + -2.0)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(x - Float64(z * Float64(y - 1.0))) + Float64(a * Float64(1.0 - t))) + Float64(b * Float64(Float64(t + y) - 2.0)))
	tmp = 0.0
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = fma(y, Float64(b - z), Float64(b * Float64(t + -2.0)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(x - N[(z * N[(y - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[(y * N[(b - z), $MachinePrecision] + N[(b * N[(t + -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 (-.f64 (-.f64 x (*.f64 (-.f64 y 1) z)) (*.f64 (-.f64 t 1) a)) (*.f64 (-.f64 (+.f64 y t) 2) b)) < +inf.0

   1. Initial program 100.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   if +inf.0 < (+.f64 (-.f64 (-.f64 x (*.f64 (-.f64 y 1) z)) (*.f64 (-.f64 t 1) a)) (*.f64 (-.f64 (+.f64 y t) 2) b))

   1. Initial program 0.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in y around inf 23.1%

      \[\leadsto \color{blue}{-1 \cdot \left(y \cdot z\right)} + \left(\left(y + t\right) - 2\right) \cdot b \]
   3. Step-by-step derivation

      1. mul-1-neg 23.1%

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

      2. distribute-rgt-neg-in 23.1%

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

   4. Simplified 23.1%

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

   5. Taylor expanded in y around 0 46.2%

      \[\leadsto \color{blue}{\left(-1 \cdot z + b\right) \cdot y + \left(t - 2\right) \cdot b} \]
   6. Step-by-step derivation

      1. *-commutative 46.2%

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

      2. sub-neg 46.2%

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

      3. metadata-eval 46.2%

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

      4. *-commutative 46.2%

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

      5. fma-def 61.5%

         \[\leadsto \color{blue}{\mathsf{fma}\left(y, -1 \cdot z + b, b \cdot \left(t + -2\right)\right)} \]

      6. +-commutative 61.5%

         \[\leadsto \mathsf{fma}\left(y, \color{blue}{b + -1 \cdot z}, b \cdot \left(t + -2\right)\right) \]

      7. mul-1-neg 61.5%

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

      8. unsub-neg 61.5%

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

   7. Simplified 61.5%

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

4. Final simplification 98.0%

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

Alternative 2: 97.5% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(t + \left(y - 2\right), b, x - \mathsf{fma}\left(y - 1, z, a \cdot \left(t + -1\right)\right)\right) \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (fma (+ t (- y 2.0)) b (- x (fma (- y 1.0) z (* a (+ t -1.0))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	return fma((t + (y - 2.0)), b, (x - fma((y - 1.0), z, (a * (t + -1.0)))));
}

Julia

function code(x, y, z, t, a, b)
	return fma(Float64(t + Float64(y - 2.0)), b, Float64(x - fma(Float64(y - 1.0), z, Float64(a * Float64(t + -1.0)))))
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(t + N[(y - 2.0), $MachinePrecision]), $MachinePrecision] * b + N[(x - N[(N[(y - 1.0), $MachinePrecision] * z + N[(a * N[(t + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 94.9%

   \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
2. Step-by-step derivation

   1. +-commutative 94.9%

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

   2. fma-def 97.2%

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

   3. +-commutative 97.2%

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

   4. associate--l+ 97.2%

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

   5. sub-neg 97.2%

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

   6. associate-+l- 97.2%

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

   7. fma-neg 97.6%

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

   8. sub-neg 97.6%

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

   9. metadata-eval 97.6%

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

   10. distribute-lft-neg-in 97.6%

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

   11. distribute-lft-neg-in 97.6%

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

   12. remove-double-neg 97.6%

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

   13. sub-neg 97.6%

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

   14. metadata-eval 97.6%

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

3. Simplified 97.6%

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

4. Final simplification 97.6%

   \[\leadsto \mathsf{fma}\left(t + \left(y - 2\right), b, x - \mathsf{fma}\left(y - 1, z, a \cdot \left(t + -1\right)\right)\right) \]

Alternative 3: 98.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(x - z \cdot \left(y - 1\right)\right) + a \cdot \left(1 - t\right)\right) + b \cdot \left(\left(t + y\right) - 2\right)\\ \mathbf{if}\;t_1 \leq \infty:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1
         (+ (+ (- x (* z (- y 1.0))) (* a (- 1.0 t))) (* b (- (+ t y) 2.0)))))
   (if (<= t_1 INFINITY) t_1 (* y (- b z)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((x - (z * (y - 1.0))) + (a * (1.0 - t))) + (b * ((t + y) - 2.0));
	double tmp;
	if (t_1 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = y * (b - z);
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((x - (z * (y - 1.0))) + (a * (1.0 - t))) + (b * ((t + y) - 2.0));
	double tmp;
	if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else {
		tmp = y * (b - z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((x - (z * (y - 1.0))) + (a * (1.0 - t))) + (b * ((t + y) - 2.0))
	tmp = 0
	if t_1 <= math.inf:
		tmp = t_1
	else:
		tmp = y * (b - z)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(x - Float64(z * Float64(y - 1.0))) + Float64(a * Float64(1.0 - t))) + Float64(b * Float64(Float64(t + y) - 2.0)))
	tmp = 0.0
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = Float64(y * Float64(b - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((x - (z * (y - 1.0))) + (a * (1.0 - t))) + (b * ((t + y) - 2.0));
	tmp = 0.0;
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = y * (b - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(x - N[(z * N[(y - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 (-.f64 (-.f64 x (*.f64 (-.f64 y 1) z)) (*.f64 (-.f64 t 1) a)) (*.f64 (-.f64 (+.f64 y t) 2) b)) < +inf.0

   1. Initial program 100.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   if +inf.0 < (+.f64 (-.f64 (-.f64 x (*.f64 (-.f64 y 1) z)) (*.f64 (-.f64 t 1) a)) (*.f64 (-.f64 (+.f64 y t) 2) b))

   1. Initial program 0.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in y around inf 54.3%

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

4. Final simplification 97.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left(x - z \cdot \left(y - 1\right)\right) + a \cdot \left(1 - t\right)\right) + b \cdot \left(\left(t + y\right) - 2\right) \leq \infty:\\ \;\;\;\;\left(\left(x - z \cdot \left(y - 1\right)\right) + a \cdot \left(1 - t\right)\right) + b \cdot \left(\left(t + y\right) - 2\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \end{array} \]

Alternative 4: 64.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(z - y \cdot z\right)\\ t_2 := x + b \cdot \left(\left(t + y\right) - 2\right)\\ t_3 := x + \left(a - t \cdot a\right)\\ \mathbf{if}\;b \leq -1.2 \cdot 10^{+32}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -9.2 \cdot 10^{-265}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 10^{-256}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq 9.5 \cdot 10^{-212}:\\ \;\;\;\;\left(z + a\right) - y \cdot z\\ \mathbf{elif}\;b \leq 6 \cdot 10^{-70}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq 1.56 \cdot 10^{+44}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (- z (* y z))))
        (t_2 (+ x (* b (- (+ t y) 2.0))))
        (t_3 (+ x (- a (* t a)))))
   (if (<= b -1.2e+32)
     t_2
     (if (<= b -9.2e-265)
       t_1
       (if (<= b 1e-256)
         t_3
         (if (<= b 9.5e-212)
           (- (+ z a) (* y z))
           (if (<= b 6e-70) t_3 (if (<= b 1.56e+44) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (z - (y * z));
	double t_2 = x + (b * ((t + y) - 2.0));
	double t_3 = x + (a - (t * a));
	double tmp;
	if (b <= -1.2e+32) {
		tmp = t_2;
	} else if (b <= -9.2e-265) {
		tmp = t_1;
	} else if (b <= 1e-256) {
		tmp = t_3;
	} else if (b <= 9.5e-212) {
		tmp = (z + a) - (y * z);
	} else if (b <= 6e-70) {
		tmp = t_3;
	} else if (b <= 1.56e+44) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	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) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = x + (z - (y * z))
    t_2 = x + (b * ((t + y) - 2.0d0))
    t_3 = x + (a - (t * a))
    if (b <= (-1.2d+32)) then
        tmp = t_2
    else if (b <= (-9.2d-265)) then
        tmp = t_1
    else if (b <= 1d-256) then
        tmp = t_3
    else if (b <= 9.5d-212) then
        tmp = (z + a) - (y * z)
    else if (b <= 6d-70) then
        tmp = t_3
    else if (b <= 1.56d+44) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (z - (y * z));
	double t_2 = x + (b * ((t + y) - 2.0));
	double t_3 = x + (a - (t * a));
	double tmp;
	if (b <= -1.2e+32) {
		tmp = t_2;
	} else if (b <= -9.2e-265) {
		tmp = t_1;
	} else if (b <= 1e-256) {
		tmp = t_3;
	} else if (b <= 9.5e-212) {
		tmp = (z + a) - (y * z);
	} else if (b <= 6e-70) {
		tmp = t_3;
	} else if (b <= 1.56e+44) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (z - (y * z))
	t_2 = x + (b * ((t + y) - 2.0))
	t_3 = x + (a - (t * a))
	tmp = 0
	if b <= -1.2e+32:
		tmp = t_2
	elif b <= -9.2e-265:
		tmp = t_1
	elif b <= 1e-256:
		tmp = t_3
	elif b <= 9.5e-212:
		tmp = (z + a) - (y * z)
	elif b <= 6e-70:
		tmp = t_3
	elif b <= 1.56e+44:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(z - Float64(y * z)))
	t_2 = Float64(x + Float64(b * Float64(Float64(t + y) - 2.0)))
	t_3 = Float64(x + Float64(a - Float64(t * a)))
	tmp = 0.0
	if (b <= -1.2e+32)
		tmp = t_2;
	elseif (b <= -9.2e-265)
		tmp = t_1;
	elseif (b <= 1e-256)
		tmp = t_3;
	elseif (b <= 9.5e-212)
		tmp = Float64(Float64(z + a) - Float64(y * z));
	elseif (b <= 6e-70)
		tmp = t_3;
	elseif (b <= 1.56e+44)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (z - (y * z));
	t_2 = x + (b * ((t + y) - 2.0));
	t_3 = x + (a - (t * a));
	tmp = 0.0;
	if (b <= -1.2e+32)
		tmp = t_2;
	elseif (b <= -9.2e-265)
		tmp = t_1;
	elseif (b <= 1e-256)
		tmp = t_3;
	elseif (b <= 9.5e-212)
		tmp = (z + a) - (y * z);
	elseif (b <= 6e-70)
		tmp = t_3;
	elseif (b <= 1.56e+44)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(z - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(b * N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x + N[(a - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.2e+32], t$95$2, If[LessEqual[b, -9.2e-265], t$95$1, If[LessEqual[b, 1e-256], t$95$3, If[LessEqual[b, 9.5e-212], N[(N[(z + a), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 6e-70], t$95$3, If[LessEqual[b, 1.56e+44], t$95$1, t$95$2]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -1.19999999999999996e32 or 1.56e44 < b

   1. Initial program 89.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in a around 0 85.2%

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

   3. Taylor expanded in z around 0 83.0%

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

   if -1.19999999999999996e32 < b < -9.1999999999999996e-265 or 6.0000000000000003e-70 < b < 1.56e44

   1. Initial program 99.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in b around 0 89.9%

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

   3. Taylor expanded in a around 0 64.4%

      \[\leadsto x - \color{blue}{z \cdot \left(y - 1\right)} \]
   4. Step-by-step derivation

      1. sub-neg 64.4%

         \[\leadsto x - z \cdot \color{blue}{\left(y + \left(-1\right)\right)} \]

      2. metadata-eval 64.4%

         \[\leadsto x - z \cdot \left(y + \color{blue}{-1}\right) \]

      3. distribute-rgt-in 64.4%

         \[\leadsto x - \color{blue}{\left(y \cdot z + -1 \cdot z\right)} \]

      4. neg-mul-1 64.4%

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

      5. unsub-neg 64.4%

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

      6. *-commutative 64.4%

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

   5. Simplified 64.4%

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

   if -9.1999999999999996e-265 < b < 9.99999999999999977e-257 or 9.50000000000000029e-212 < b < 6.0000000000000003e-70

   1. Initial program 100.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in b around 0 87.3%

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

   3. Taylor expanded in a around inf 67.7%

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

      1. sub-neg 67.7%

         \[\leadsto x - \color{blue}{\left(t + \left(-1\right)\right)} \cdot a \]

      2. metadata-eval 67.7%

         \[\leadsto x - \left(t + \color{blue}{-1}\right) \cdot a \]

      3. *-commutative 67.7%

         \[\leadsto x - \color{blue}{a \cdot \left(t + -1\right)} \]

      4. distribute-rgt-in 67.7%

         \[\leadsto x - \color{blue}{\left(t \cdot a + -1 \cdot a\right)} \]

      5. neg-mul-1 67.7%

         \[\leadsto x - \left(t \cdot a + \color{blue}{\left(-a\right)}\right) \]

      6. unsub-neg 67.7%

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

      7. *-commutative 67.7%

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

   5. Simplified 67.7%

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

   if 9.99999999999999977e-257 < b < 9.50000000000000029e-212

   1. Initial program 100.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in b around 0 100.0%

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

   3. Taylor expanded in t around 0 83.9%

      \[\leadsto x - \color{blue}{\left(z \cdot \left(y - 1\right) + -1 \cdot a\right)} \]
   4. Step-by-step derivation

      1. fma-def 84.0%

         \[\leadsto x - \color{blue}{\mathsf{fma}\left(z, y - 1, -1 \cdot a\right)} \]

      2. sub-neg 84.0%

         \[\leadsto x - \mathsf{fma}\left(z, \color{blue}{y + \left(-1\right)}, -1 \cdot a\right) \]

      3. metadata-eval 84.0%

         \[\leadsto x - \mathsf{fma}\left(z, y + \color{blue}{-1}, -1 \cdot a\right) \]

      4. fma-def 83.9%

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

      5. neg-mul-1 83.9%

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

      6. unsub-neg 83.9%

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

      7. distribute-rgt-in 83.9%

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

      8. neg-mul-1 83.9%

         \[\leadsto x - \left(\left(y \cdot z + \color{blue}{\left(-z\right)}\right) - a\right) \]

      9. unsub-neg 83.9%

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

      10. *-commutative 83.9%

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

   5. Simplified 83.9%

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

   6. Taylor expanded in x around 0 75.4%

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

4. Final simplification 73.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.2 \cdot 10^{+32}:\\ \;\;\;\;x + b \cdot \left(\left(t + y\right) - 2\right)\\ \mathbf{elif}\;b \leq -9.2 \cdot 10^{-265}:\\ \;\;\;\;x + \left(z - y \cdot z\right)\\ \mathbf{elif}\;b \leq 10^{-256}:\\ \;\;\;\;x + \left(a - t \cdot a\right)\\ \mathbf{elif}\;b \leq 9.5 \cdot 10^{-212}:\\ \;\;\;\;\left(z + a\right) - y \cdot z\\ \mathbf{elif}\;b \leq 6 \cdot 10^{-70}:\\ \;\;\;\;x + \left(a - t \cdot a\right)\\ \mathbf{elif}\;b \leq 1.56 \cdot 10^{+44}:\\ \;\;\;\;x + \left(z - y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + b \cdot \left(\left(t + y\right) - 2\right)\\ \end{array} \]

Alternative 5: 61.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(z - y \cdot z\right)\\ t_2 := b \cdot \left(\left(t + y\right) - 2\right)\\ t_3 := x + \left(a - t \cdot a\right)\\ \mathbf{if}\;b \leq -1.05 \cdot 10^{+32}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -3.6 \cdot 10^{-264}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 2.35 \cdot 10^{-282}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq 2.1 \cdot 10^{-211}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 6 \cdot 10^{-70}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq 1.05 \cdot 10^{+110}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (- z (* y z))))
        (t_2 (* b (- (+ t y) 2.0)))
        (t_3 (+ x (- a (* t a)))))
   (if (<= b -1.05e+32)
     t_2
     (if (<= b -3.6e-264)
       t_1
       (if (<= b 2.35e-282)
         t_3
         (if (<= b 2.1e-211)
           t_1
           (if (<= b 6e-70) t_3 (if (<= b 1.05e+110) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (z - (y * z));
	double t_2 = b * ((t + y) - 2.0);
	double t_3 = x + (a - (t * a));
	double tmp;
	if (b <= -1.05e+32) {
		tmp = t_2;
	} else if (b <= -3.6e-264) {
		tmp = t_1;
	} else if (b <= 2.35e-282) {
		tmp = t_3;
	} else if (b <= 2.1e-211) {
		tmp = t_1;
	} else if (b <= 6e-70) {
		tmp = t_3;
	} else if (b <= 1.05e+110) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	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) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = x + (z - (y * z))
    t_2 = b * ((t + y) - 2.0d0)
    t_3 = x + (a - (t * a))
    if (b <= (-1.05d+32)) then
        tmp = t_2
    else if (b <= (-3.6d-264)) then
        tmp = t_1
    else if (b <= 2.35d-282) then
        tmp = t_3
    else if (b <= 2.1d-211) then
        tmp = t_1
    else if (b <= 6d-70) then
        tmp = t_3
    else if (b <= 1.05d+110) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (z - (y * z));
	double t_2 = b * ((t + y) - 2.0);
	double t_3 = x + (a - (t * a));
	double tmp;
	if (b <= -1.05e+32) {
		tmp = t_2;
	} else if (b <= -3.6e-264) {
		tmp = t_1;
	} else if (b <= 2.35e-282) {
		tmp = t_3;
	} else if (b <= 2.1e-211) {
		tmp = t_1;
	} else if (b <= 6e-70) {
		tmp = t_3;
	} else if (b <= 1.05e+110) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (z - (y * z))
	t_2 = b * ((t + y) - 2.0)
	t_3 = x + (a - (t * a))
	tmp = 0
	if b <= -1.05e+32:
		tmp = t_2
	elif b <= -3.6e-264:
		tmp = t_1
	elif b <= 2.35e-282:
		tmp = t_3
	elif b <= 2.1e-211:
		tmp = t_1
	elif b <= 6e-70:
		tmp = t_3
	elif b <= 1.05e+110:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(z - Float64(y * z)))
	t_2 = Float64(b * Float64(Float64(t + y) - 2.0))
	t_3 = Float64(x + Float64(a - Float64(t * a)))
	tmp = 0.0
	if (b <= -1.05e+32)
		tmp = t_2;
	elseif (b <= -3.6e-264)
		tmp = t_1;
	elseif (b <= 2.35e-282)
		tmp = t_3;
	elseif (b <= 2.1e-211)
		tmp = t_1;
	elseif (b <= 6e-70)
		tmp = t_3;
	elseif (b <= 1.05e+110)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (z - (y * z));
	t_2 = b * ((t + y) - 2.0);
	t_3 = x + (a - (t * a));
	tmp = 0.0;
	if (b <= -1.05e+32)
		tmp = t_2;
	elseif (b <= -3.6e-264)
		tmp = t_1;
	elseif (b <= 2.35e-282)
		tmp = t_3;
	elseif (b <= 2.1e-211)
		tmp = t_1;
	elseif (b <= 6e-70)
		tmp = t_3;
	elseif (b <= 1.05e+110)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(z - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x + N[(a - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.05e+32], t$95$2, If[LessEqual[b, -3.6e-264], t$95$1, If[LessEqual[b, 2.35e-282], t$95$3, If[LessEqual[b, 2.1e-211], t$95$1, If[LessEqual[b, 6e-70], t$95$3, If[LessEqual[b, 1.05e+110], t$95$1, t$95$2]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.05e32 or 1.05000000000000007e110 < b

   1. Initial program 89.9%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in b around inf 82.4%

      \[\leadsto \color{blue}{\left(\left(y + t\right) - 2\right) \cdot b} \]

   if -1.05e32 < b < -3.6000000000000002e-264 or 2.35e-282 < b < 2.10000000000000008e-211 or 6.0000000000000003e-70 < b < 1.05000000000000007e110

   1. Initial program 97.5%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in b around 0 88.2%

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

   3. Taylor expanded in a around 0 63.8%

      \[\leadsto x - \color{blue}{z \cdot \left(y - 1\right)} \]
   4. Step-by-step derivation

      1. sub-neg 63.8%

         \[\leadsto x - z \cdot \color{blue}{\left(y + \left(-1\right)\right)} \]

      2. metadata-eval 63.8%

         \[\leadsto x - z \cdot \left(y + \color{blue}{-1}\right) \]

      3. distribute-rgt-in 63.8%

         \[\leadsto x - \color{blue}{\left(y \cdot z + -1 \cdot z\right)} \]

      4. neg-mul-1 63.8%

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

      5. unsub-neg 63.8%

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

      6. *-commutative 63.8%

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

   5. Simplified 63.8%

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

   if -3.6000000000000002e-264 < b < 2.35e-282 or 2.10000000000000008e-211 < b < 6.0000000000000003e-70

   1. Initial program 100.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in b around 0 87.0%

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

   3. Taylor expanded in a around inf 66.8%

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

      1. sub-neg 66.8%

         \[\leadsto x - \color{blue}{\left(t + \left(-1\right)\right)} \cdot a \]

      2. metadata-eval 66.8%

         \[\leadsto x - \left(t + \color{blue}{-1}\right) \cdot a \]

      3. *-commutative 66.8%

         \[\leadsto x - \color{blue}{a \cdot \left(t + -1\right)} \]

      4. distribute-rgt-in 66.8%

         \[\leadsto x - \color{blue}{\left(t \cdot a + -1 \cdot a\right)} \]

      5. neg-mul-1 66.8%

         \[\leadsto x - \left(t \cdot a + \color{blue}{\left(-a\right)}\right) \]

      6. unsub-neg 66.8%

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

      7. *-commutative 66.8%

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

   5. Simplified 66.8%

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

4. Final simplification 71.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.05 \cdot 10^{+32}:\\ \;\;\;\;b \cdot \left(\left(t + y\right) - 2\right)\\ \mathbf{elif}\;b \leq -3.6 \cdot 10^{-264}:\\ \;\;\;\;x + \left(z - y \cdot z\right)\\ \mathbf{elif}\;b \leq 2.35 \cdot 10^{-282}:\\ \;\;\;\;x + \left(a - t \cdot a\right)\\ \mathbf{elif}\;b \leq 2.1 \cdot 10^{-211}:\\ \;\;\;\;x + \left(z - y \cdot z\right)\\ \mathbf{elif}\;b \leq 6 \cdot 10^{-70}:\\ \;\;\;\;x + \left(a - t \cdot a\right)\\ \mathbf{elif}\;b \leq 1.05 \cdot 10^{+110}:\\ \;\;\;\;x + \left(z - y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(t + y\right) - 2\right)\\ \end{array} \]

Alternative 6: 61.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(z - y \cdot z\right)\\ t_2 := b \cdot \left(\left(t + y\right) - 2\right)\\ t_3 := x + \left(a - t \cdot a\right)\\ \mathbf{if}\;b \leq -1.3 \cdot 10^{+32}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -1.1 \cdot 10^{-264}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 1.8 \cdot 10^{-266}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq 1.25 \cdot 10^{-211}:\\ \;\;\;\;\left(z + a\right) - y \cdot z\\ \mathbf{elif}\;b \leq 2.6 \cdot 10^{-67}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq 9.6 \cdot 10^{+109}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (- z (* y z))))
        (t_2 (* b (- (+ t y) 2.0)))
        (t_3 (+ x (- a (* t a)))))
   (if (<= b -1.3e+32)
     t_2
     (if (<= b -1.1e-264)
       t_1
       (if (<= b 1.8e-266)
         t_3
         (if (<= b 1.25e-211)
           (- (+ z a) (* y z))
           (if (<= b 2.6e-67) t_3 (if (<= b 9.6e+109) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (z - (y * z));
	double t_2 = b * ((t + y) - 2.0);
	double t_3 = x + (a - (t * a));
	double tmp;
	if (b <= -1.3e+32) {
		tmp = t_2;
	} else if (b <= -1.1e-264) {
		tmp = t_1;
	} else if (b <= 1.8e-266) {
		tmp = t_3;
	} else if (b <= 1.25e-211) {
		tmp = (z + a) - (y * z);
	} else if (b <= 2.6e-67) {
		tmp = t_3;
	} else if (b <= 9.6e+109) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	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) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = x + (z - (y * z))
    t_2 = b * ((t + y) - 2.0d0)
    t_3 = x + (a - (t * a))
    if (b <= (-1.3d+32)) then
        tmp = t_2
    else if (b <= (-1.1d-264)) then
        tmp = t_1
    else if (b <= 1.8d-266) then
        tmp = t_3
    else if (b <= 1.25d-211) then
        tmp = (z + a) - (y * z)
    else if (b <= 2.6d-67) then
        tmp = t_3
    else if (b <= 9.6d+109) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (z - (y * z));
	double t_2 = b * ((t + y) - 2.0);
	double t_3 = x + (a - (t * a));
	double tmp;
	if (b <= -1.3e+32) {
		tmp = t_2;
	} else if (b <= -1.1e-264) {
		tmp = t_1;
	} else if (b <= 1.8e-266) {
		tmp = t_3;
	} else if (b <= 1.25e-211) {
		tmp = (z + a) - (y * z);
	} else if (b <= 2.6e-67) {
		tmp = t_3;
	} else if (b <= 9.6e+109) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (z - (y * z))
	t_2 = b * ((t + y) - 2.0)
	t_3 = x + (a - (t * a))
	tmp = 0
	if b <= -1.3e+32:
		tmp = t_2
	elif b <= -1.1e-264:
		tmp = t_1
	elif b <= 1.8e-266:
		tmp = t_3
	elif b <= 1.25e-211:
		tmp = (z + a) - (y * z)
	elif b <= 2.6e-67:
		tmp = t_3
	elif b <= 9.6e+109:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(z - Float64(y * z)))
	t_2 = Float64(b * Float64(Float64(t + y) - 2.0))
	t_3 = Float64(x + Float64(a - Float64(t * a)))
	tmp = 0.0
	if (b <= -1.3e+32)
		tmp = t_2;
	elseif (b <= -1.1e-264)
		tmp = t_1;
	elseif (b <= 1.8e-266)
		tmp = t_3;
	elseif (b <= 1.25e-211)
		tmp = Float64(Float64(z + a) - Float64(y * z));
	elseif (b <= 2.6e-67)
		tmp = t_3;
	elseif (b <= 9.6e+109)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (z - (y * z));
	t_2 = b * ((t + y) - 2.0);
	t_3 = x + (a - (t * a));
	tmp = 0.0;
	if (b <= -1.3e+32)
		tmp = t_2;
	elseif (b <= -1.1e-264)
		tmp = t_1;
	elseif (b <= 1.8e-266)
		tmp = t_3;
	elseif (b <= 1.25e-211)
		tmp = (z + a) - (y * z);
	elseif (b <= 2.6e-67)
		tmp = t_3;
	elseif (b <= 9.6e+109)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(z - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x + N[(a - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.3e+32], t$95$2, If[LessEqual[b, -1.1e-264], t$95$1, If[LessEqual[b, 1.8e-266], t$95$3, If[LessEqual[b, 1.25e-211], N[(N[(z + a), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.6e-67], t$95$3, If[LessEqual[b, 9.6e+109], t$95$1, t$95$2]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -1.3000000000000001e32 or 9.59999999999999949e109 < b

   1. Initial program 89.9%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in b around inf 82.4%

      \[\leadsto \color{blue}{\left(\left(y + t\right) - 2\right) \cdot b} \]

   if -1.3000000000000001e32 < b < -1.09999999999999997e-264 or 2.5999999999999999e-67 < b < 9.59999999999999949e109

   1. Initial program 97.2%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in b around 0 86.7%

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

   3. Taylor expanded in a around 0 62.7%

      \[\leadsto x - \color{blue}{z \cdot \left(y - 1\right)} \]
   4. Step-by-step derivation

      1. sub-neg 62.7%

         \[\leadsto x - z \cdot \color{blue}{\left(y + \left(-1\right)\right)} \]

      2. metadata-eval 62.7%

         \[\leadsto x - z \cdot \left(y + \color{blue}{-1}\right) \]

      3. distribute-rgt-in 62.7%

         \[\leadsto x - \color{blue}{\left(y \cdot z + -1 \cdot z\right)} \]

      4. neg-mul-1 62.7%

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

      5. unsub-neg 62.7%

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

      6. *-commutative 62.7%

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

   5. Simplified 62.7%

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

   if -1.09999999999999997e-264 < b < 1.8e-266 or 1.2500000000000001e-211 < b < 2.5999999999999999e-67

   1. Initial program 100.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in b around 0 87.3%

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

   3. Taylor expanded in a around inf 67.7%

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

      1. sub-neg 67.7%

         \[\leadsto x - \color{blue}{\left(t + \left(-1\right)\right)} \cdot a \]

      2. metadata-eval 67.7%

         \[\leadsto x - \left(t + \color{blue}{-1}\right) \cdot a \]

      3. *-commutative 67.7%

         \[\leadsto x - \color{blue}{a \cdot \left(t + -1\right)} \]

      4. distribute-rgt-in 67.7%

         \[\leadsto x - \color{blue}{\left(t \cdot a + -1 \cdot a\right)} \]

      5. neg-mul-1 67.7%

         \[\leadsto x - \left(t \cdot a + \color{blue}{\left(-a\right)}\right) \]

      6. unsub-neg 67.7%

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

      7. *-commutative 67.7%

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

   5. Simplified 67.7%

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

   if 1.8e-266 < b < 1.2500000000000001e-211

   1. Initial program 100.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in b around 0 100.0%

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

   3. Taylor expanded in t around 0 83.9%

      \[\leadsto x - \color{blue}{\left(z \cdot \left(y - 1\right) + -1 \cdot a\right)} \]
   4. Step-by-step derivation

      1. fma-def 84.0%

         \[\leadsto x - \color{blue}{\mathsf{fma}\left(z, y - 1, -1 \cdot a\right)} \]

      2. sub-neg 84.0%

         \[\leadsto x - \mathsf{fma}\left(z, \color{blue}{y + \left(-1\right)}, -1 \cdot a\right) \]

      3. metadata-eval 84.0%

         \[\leadsto x - \mathsf{fma}\left(z, y + \color{blue}{-1}, -1 \cdot a\right) \]

      4. fma-def 83.9%

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

      5. neg-mul-1 83.9%

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

      6. unsub-neg 83.9%

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

      7. distribute-rgt-in 83.9%

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

      8. neg-mul-1 83.9%

         \[\leadsto x - \left(\left(y \cdot z + \color{blue}{\left(-z\right)}\right) - a\right) \]

      9. unsub-neg 83.9%

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

      10. *-commutative 83.9%

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

   5. Simplified 83.9%

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

   6. Taylor expanded in x around 0 75.4%

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

4. Final simplification 71.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.3 \cdot 10^{+32}:\\ \;\;\;\;b \cdot \left(\left(t + y\right) - 2\right)\\ \mathbf{elif}\;b \leq -1.1 \cdot 10^{-264}:\\ \;\;\;\;x + \left(z - y \cdot z\right)\\ \mathbf{elif}\;b \leq 1.8 \cdot 10^{-266}:\\ \;\;\;\;x + \left(a - t \cdot a\right)\\ \mathbf{elif}\;b \leq 1.25 \cdot 10^{-211}:\\ \;\;\;\;\left(z + a\right) - y \cdot z\\ \mathbf{elif}\;b \leq 2.6 \cdot 10^{-67}:\\ \;\;\;\;x + \left(a - t \cdot a\right)\\ \mathbf{elif}\;b \leq 9.6 \cdot 10^{+109}:\\ \;\;\;\;x + \left(z - y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(t + y\right) - 2\right)\\ \end{array} \]

Alternative 7: 84.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -7 \cdot 10^{+165} \lor \neg \left(a \leq 1.15 \cdot 10^{+99}\right):\\ \;\;\;\;x + \left(a \cdot \left(1 - t\right) - z \cdot \left(y - 1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) + z \cdot \left(1 - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -7e+165) (not (<= a 1.15e+99)))
   (+ x (- (* a (- 1.0 t)) (* z (- y 1.0))))
   (+ (+ x (* b (- (+ t y) 2.0))) (* z (- 1.0 y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -7e+165) || !(a <= 1.15e+99)) {
		tmp = x + ((a * (1.0 - t)) - (z * (y - 1.0)));
	} else {
		tmp = (x + (b * ((t + y) - 2.0))) + (z * (1.0 - y));
	}
	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 ((a <= (-7d+165)) .or. (.not. (a <= 1.15d+99))) then
        tmp = x + ((a * (1.0d0 - t)) - (z * (y - 1.0d0)))
    else
        tmp = (x + (b * ((t + y) - 2.0d0))) + (z * (1.0d0 - y))
    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 ((a <= -7e+165) || !(a <= 1.15e+99)) {
		tmp = x + ((a * (1.0 - t)) - (z * (y - 1.0)));
	} else {
		tmp = (x + (b * ((t + y) - 2.0))) + (z * (1.0 - y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (a <= -7e+165) or not (a <= 1.15e+99):
		tmp = x + ((a * (1.0 - t)) - (z * (y - 1.0)))
	else:
		tmp = (x + (b * ((t + y) - 2.0))) + (z * (1.0 - y))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((a <= -7e+165) || !(a <= 1.15e+99))
		tmp = Float64(x + Float64(Float64(a * Float64(1.0 - t)) - Float64(z * Float64(y - 1.0))));
	else
		tmp = Float64(Float64(x + Float64(b * Float64(Float64(t + y) - 2.0))) + Float64(z * Float64(1.0 - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((a <= -7e+165) || ~((a <= 1.15e+99)))
		tmp = x + ((a * (1.0 - t)) - (z * (y - 1.0)));
	else
		tmp = (x + (b * ((t + y) - 2.0))) + (z * (1.0 - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[a, -7e+165], N[Not[LessEqual[a, 1.15e+99]], $MachinePrecision]], N[(x + N[(N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision] - N[(z * N[(y - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(b * N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -6.99999999999999991e165 or 1.1500000000000001e99 < a

   1. Initial program 89.7%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in b around 0 88.0%

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

   if -6.99999999999999991e165 < a < 1.1500000000000001e99

   1. Initial program 97.2%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in a around 0 89.1%

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

4. Final simplification 88.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7 \cdot 10^{+165} \lor \neg \left(a \leq 1.15 \cdot 10^{+99}\right):\\ \;\;\;\;x + \left(a \cdot \left(1 - t\right) - z \cdot \left(y - 1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) + z \cdot \left(1 - y\right)\\ \end{array} \]

Alternative 8: 50.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(b - z\right)\\ t_2 := b \cdot \left(t - 2\right)\\ \mathbf{if}\;y \leq -7.5 \cdot 10^{+36}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -6 \cdot 10^{-126}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;y \leq -4.2 \cdot 10^{-207}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;y \leq -1.15 \cdot 10^{-267}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{-141}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;y \leq 3.5:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (- b z))) (t_2 (* b (- t 2.0))))
   (if (<= y -7.5e+36)
     t_1
     (if (<= y -6e-126)
       (* t (- b a))
       (if (<= y -4.2e-207)
         (+ x z)
         (if (<= y -1.15e-267)
           t_2
           (if (<= y 4.6e-141) (+ x z) (if (<= y 3.5) t_2 t_1))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (b - z);
	double t_2 = b * (t - 2.0);
	double tmp;
	if (y <= -7.5e+36) {
		tmp = t_1;
	} else if (y <= -6e-126) {
		tmp = t * (b - a);
	} else if (y <= -4.2e-207) {
		tmp = x + z;
	} else if (y <= -1.15e-267) {
		tmp = t_2;
	} else if (y <= 4.6e-141) {
		tmp = x + z;
	} else if (y <= 3.5) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y * (b - z)
    t_2 = b * (t - 2.0d0)
    if (y <= (-7.5d+36)) then
        tmp = t_1
    else if (y <= (-6d-126)) then
        tmp = t * (b - a)
    else if (y <= (-4.2d-207)) then
        tmp = x + z
    else if (y <= (-1.15d-267)) then
        tmp = t_2
    else if (y <= 4.6d-141) then
        tmp = x + z
    else if (y <= 3.5d0) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (b - z);
	double t_2 = b * (t - 2.0);
	double tmp;
	if (y <= -7.5e+36) {
		tmp = t_1;
	} else if (y <= -6e-126) {
		tmp = t * (b - a);
	} else if (y <= -4.2e-207) {
		tmp = x + z;
	} else if (y <= -1.15e-267) {
		tmp = t_2;
	} else if (y <= 4.6e-141) {
		tmp = x + z;
	} else if (y <= 3.5) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y * (b - z)
	t_2 = b * (t - 2.0)
	tmp = 0
	if y <= -7.5e+36:
		tmp = t_1
	elif y <= -6e-126:
		tmp = t * (b - a)
	elif y <= -4.2e-207:
		tmp = x + z
	elif y <= -1.15e-267:
		tmp = t_2
	elif y <= 4.6e-141:
		tmp = x + z
	elif y <= 3.5:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y * Float64(b - z))
	t_2 = Float64(b * Float64(t - 2.0))
	tmp = 0.0
	if (y <= -7.5e+36)
		tmp = t_1;
	elseif (y <= -6e-126)
		tmp = Float64(t * Float64(b - a));
	elseif (y <= -4.2e-207)
		tmp = Float64(x + z);
	elseif (y <= -1.15e-267)
		tmp = t_2;
	elseif (y <= 4.6e-141)
		tmp = Float64(x + z);
	elseif (y <= 3.5)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y * (b - z);
	t_2 = b * (t - 2.0);
	tmp = 0.0;
	if (y <= -7.5e+36)
		tmp = t_1;
	elseif (y <= -6e-126)
		tmp = t * (b - a);
	elseif (y <= -4.2e-207)
		tmp = x + z;
	elseif (y <= -1.15e-267)
		tmp = t_2;
	elseif (y <= 4.6e-141)
		tmp = x + z;
	elseif (y <= 3.5)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(t - 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -7.5e+36], t$95$1, If[LessEqual[y, -6e-126], N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -4.2e-207], N[(x + z), $MachinePrecision], If[LessEqual[y, -1.15e-267], t$95$2, If[LessEqual[y, 4.6e-141], N[(x + z), $MachinePrecision], If[LessEqual[y, 3.5], t$95$2, t$95$1]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -7.50000000000000054e36 or 3.5 < y

   1. Initial program 92.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in y around inf 70.9%

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

   if -7.50000000000000054e36 < y < -6.0000000000000003e-126

   1. Initial program 97.2%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in t around inf 51.1%

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

   if -6.0000000000000003e-126 < y < -4.20000000000000007e-207 or -1.15000000000000003e-267 < y < 4.5999999999999999e-141

   1. Initial program 98.1%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in b around 0 71.6%

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

   3. Taylor expanded in a around 0 51.2%

      \[\leadsto x - \color{blue}{z \cdot \left(y - 1\right)} \]
   4. Step-by-step derivation

      1. sub-neg 51.2%

         \[\leadsto x - z \cdot \color{blue}{\left(y + \left(-1\right)\right)} \]

      2. metadata-eval 51.2%

         \[\leadsto x - z \cdot \left(y + \color{blue}{-1}\right) \]

      3. distribute-rgt-in 51.2%

         \[\leadsto x - \color{blue}{\left(y \cdot z + -1 \cdot z\right)} \]

      4. neg-mul-1 51.2%

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

      5. unsub-neg 51.2%

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

      6. *-commutative 51.2%

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

   5. Simplified 51.2%

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

   6. Taylor expanded in y around 0 51.2%

      \[\leadsto \color{blue}{z + x} \]

   if -4.20000000000000007e-207 < y < -1.15000000000000003e-267 or 4.5999999999999999e-141 < y < 3.5

   1. Initial program 97.6%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in b around inf 51.5%

      \[\leadsto \color{blue}{\left(\left(y + t\right) - 2\right) \cdot b} \]

   3. Taylor expanded in y around 0 51.5%

      \[\leadsto \color{blue}{b \cdot \left(t - 2\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 60.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{+36}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;y \leq -6 \cdot 10^{-126}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;y \leq -4.2 \cdot 10^{-207}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;y \leq -1.15 \cdot 10^{-267}:\\ \;\;\;\;b \cdot \left(t - 2\right)\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{-141}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;y \leq 3.5:\\ \;\;\;\;b \cdot \left(t - 2\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \end{array} \]

Alternative 9: 71.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + b \cdot \left(\left(t + y\right) - 2\right)\\ \mathbf{if}\;b \leq -3 \cdot 10^{+31}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 1.4 \cdot 10^{-98}:\\ \;\;\;\;a \cdot \left(1 - t\right) - z \cdot \left(y - 1\right)\\ \mathbf{elif}\;b \leq 7.5 \cdot 10^{-82} \lor \neg \left(b \leq 1.06 \cdot 10^{+55}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + \left(a + \left(z - y \cdot z\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* b (- (+ t y) 2.0)))))
   (if (<= b -3e+31)
     t_1
     (if (<= b 1.4e-98)
       (- (* a (- 1.0 t)) (* z (- y 1.0)))
       (if (or (<= b 7.5e-82) (not (<= b 1.06e+55)))
         t_1
         (+ x (+ a (- z (* y z)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (b * ((t + y) - 2.0));
	double tmp;
	if (b <= -3e+31) {
		tmp = t_1;
	} else if (b <= 1.4e-98) {
		tmp = (a * (1.0 - t)) - (z * (y - 1.0));
	} else if ((b <= 7.5e-82) || !(b <= 1.06e+55)) {
		tmp = t_1;
	} else {
		tmp = x + (a + (z - (y * z)));
	}
	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) :: t_1
    real(8) :: tmp
    t_1 = x + (b * ((t + y) - 2.0d0))
    if (b <= (-3d+31)) then
        tmp = t_1
    else if (b <= 1.4d-98) then
        tmp = (a * (1.0d0 - t)) - (z * (y - 1.0d0))
    else if ((b <= 7.5d-82) .or. (.not. (b <= 1.06d+55))) then
        tmp = t_1
    else
        tmp = x + (a + (z - (y * z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (b * ((t + y) - 2.0));
	double tmp;
	if (b <= -3e+31) {
		tmp = t_1;
	} else if (b <= 1.4e-98) {
		tmp = (a * (1.0 - t)) - (z * (y - 1.0));
	} else if ((b <= 7.5e-82) || !(b <= 1.06e+55)) {
		tmp = t_1;
	} else {
		tmp = x + (a + (z - (y * z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (b * ((t + y) - 2.0))
	tmp = 0
	if b <= -3e+31:
		tmp = t_1
	elif b <= 1.4e-98:
		tmp = (a * (1.0 - t)) - (z * (y - 1.0))
	elif (b <= 7.5e-82) or not (b <= 1.06e+55):
		tmp = t_1
	else:
		tmp = x + (a + (z - (y * z)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(b * Float64(Float64(t + y) - 2.0)))
	tmp = 0.0
	if (b <= -3e+31)
		tmp = t_1;
	elseif (b <= 1.4e-98)
		tmp = Float64(Float64(a * Float64(1.0 - t)) - Float64(z * Float64(y - 1.0)));
	elseif ((b <= 7.5e-82) || !(b <= 1.06e+55))
		tmp = t_1;
	else
		tmp = Float64(x + Float64(a + Float64(z - Float64(y * z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (b * ((t + y) - 2.0));
	tmp = 0.0;
	if (b <= -3e+31)
		tmp = t_1;
	elseif (b <= 1.4e-98)
		tmp = (a * (1.0 - t)) - (z * (y - 1.0));
	elseif ((b <= 7.5e-82) || ~((b <= 1.06e+55)))
		tmp = t_1;
	else
		tmp = x + (a + (z - (y * z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(b * N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -3e+31], t$95$1, If[LessEqual[b, 1.4e-98], N[(N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision] - N[(z * N[(y - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[b, 7.5e-82], N[Not[LessEqual[b, 1.06e+55]], $MachinePrecision]], t$95$1, N[(x + N[(a + N[(z - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -2.99999999999999989e31 or 1.3999999999999999e-98 < b < 7.4999999999999997e-82 or 1.06000000000000004e55 < b

   1. Initial program 89.4%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in a around 0 86.6%

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

   3. Taylor expanded in z around 0 84.4%

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

   if -2.99999999999999989e31 < b < 1.3999999999999999e-98

   1. Initial program 99.1%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. sub-neg 99.1%

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

      2. +-commutative 99.1%

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

      3. associate-+l+ 99.1%

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

      4. *-commutative 99.1%

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

      5. distribute-rgt-neg-in 99.1%

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

      6. +-commutative 99.1%

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

      7. fma-def 100.0%

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

      8. neg-sub0 100.0%

         \[\leadsto \mathsf{fma}\left(a, \color{blue}{0 - \left(t - 1\right)}, \left(\left(y + t\right) - 2\right) \cdot b + \left(x - \left(y - 1\right) \cdot z\right)\right) \]

      9. associate--r- 100.0%

         \[\leadsto \mathsf{fma}\left(a, \color{blue}{\left(0 - t\right) + 1}, \left(\left(y + t\right) - 2\right) \cdot b + \left(x - \left(y - 1\right) \cdot z\right)\right) \]

      10. neg-sub0 100.0%

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

      11. +-commutative 100.0%

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

      12. sub-neg 100.0%

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

      13. fma-def 100.0%

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

      14. sub-neg 100.0%

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

      15. associate-+l+ 100.0%

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

      16. metadata-eval 100.0%

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

      17. sub-neg 100.0%

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

      18. +-commutative 100.0%

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

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(y + \left(t + -2\right), b, \mathsf{fma}\left(z, 1 - y, x\right)\right)\right)} \]

   4. Taylor expanded in x around 0 82.3%

      \[\leadsto \mathsf{fma}\left(a, 1 - t, \color{blue}{\left(\left(y + t\right) - 2\right) \cdot b + z \cdot \left(1 - y\right)}\right) \]
   5. Step-by-step derivation

      1. +-commutative 82.3%

         \[\leadsto \mathsf{fma}\left(a, 1 - t, \color{blue}{z \cdot \left(1 - y\right) + \left(\left(y + t\right) - 2\right) \cdot b}\right) \]

      2. fma-def 82.3%

         \[\leadsto \mathsf{fma}\left(a, 1 - t, \color{blue}{\mathsf{fma}\left(z, 1 - y, \left(\left(y + t\right) - 2\right) \cdot b\right)}\right) \]

      3. sub-neg 82.3%

         \[\leadsto \mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(z, 1 - y, \color{blue}{\left(\left(y + t\right) + \left(-2\right)\right)} \cdot b\right)\right) \]

      4. metadata-eval 82.3%

         \[\leadsto \mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(z, 1 - y, \left(\left(y + t\right) + \color{blue}{-2}\right) \cdot b\right)\right) \]

      5. associate-+r+ 82.3%

         \[\leadsto \mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(z, 1 - y, \color{blue}{\left(y + \left(t + -2\right)\right)} \cdot b\right)\right) \]

      6. *-commutative 82.3%

         \[\leadsto \mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(z, 1 - y, \color{blue}{b \cdot \left(y + \left(t + -2\right)\right)}\right)\right) \]

   6. Simplified 82.3%

      \[\leadsto \mathsf{fma}\left(a, 1 - t, \color{blue}{\mathsf{fma}\left(z, 1 - y, b \cdot \left(y + \left(t + -2\right)\right)\right)}\right) \]

   7. Taylor expanded in b around 0 75.3%

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

   if 7.4999999999999997e-82 < b < 1.06000000000000004e55

   1. Initial program 100.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in b around 0 87.7%

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

   3. Taylor expanded in t around 0 75.0%

      \[\leadsto x - \color{blue}{\left(z \cdot \left(y - 1\right) + -1 \cdot a\right)} \]
   4. Step-by-step derivation

      1. fma-def 75.0%

         \[\leadsto x - \color{blue}{\mathsf{fma}\left(z, y - 1, -1 \cdot a\right)} \]

      2. sub-neg 75.0%

         \[\leadsto x - \mathsf{fma}\left(z, \color{blue}{y + \left(-1\right)}, -1 \cdot a\right) \]

      3. metadata-eval 75.0%

         \[\leadsto x - \mathsf{fma}\left(z, y + \color{blue}{-1}, -1 \cdot a\right) \]

      4. fma-def 75.0%

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

      5. neg-mul-1 75.0%

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

      6. unsub-neg 75.0%

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

      7. distribute-rgt-in 75.0%

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

      8. neg-mul-1 75.0%

         \[\leadsto x - \left(\left(y \cdot z + \color{blue}{\left(-z\right)}\right) - a\right) \]

      9. unsub-neg 75.0%

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

      10. *-commutative 75.0%

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

   5. Simplified 75.0%

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

4. Final simplification 79.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3 \cdot 10^{+31}:\\ \;\;\;\;x + b \cdot \left(\left(t + y\right) - 2\right)\\ \mathbf{elif}\;b \leq 1.4 \cdot 10^{-98}:\\ \;\;\;\;a \cdot \left(1 - t\right) - z \cdot \left(y - 1\right)\\ \mathbf{elif}\;b \leq 7.5 \cdot 10^{-82} \lor \neg \left(b \leq 1.06 \cdot 10^{+55}\right):\\ \;\;\;\;x + b \cdot \left(\left(t + y\right) - 2\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(a + \left(z - y \cdot z\right)\right)\\ \end{array} \]

Alternative 10: 83.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.3 \cdot 10^{+32} \lor \neg \left(b \leq 5.8 \cdot 10^{+52}\right):\\ \;\;\;\;x + b \cdot \left(\left(t + y\right) - 2\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(a \cdot \left(1 - t\right) - z \cdot \left(y - 1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -1.3e+32) (not (<= b 5.8e+52)))
   (+ x (* b (- (+ t y) 2.0)))
   (+ x (- (* a (- 1.0 t)) (* z (- y 1.0))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -1.3e+32) || !(b <= 5.8e+52)) {
		tmp = x + (b * ((t + y) - 2.0));
	} else {
		tmp = x + ((a * (1.0 - t)) - (z * (y - 1.0)));
	}
	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 ((b <= (-1.3d+32)) .or. (.not. (b <= 5.8d+52))) then
        tmp = x + (b * ((t + y) - 2.0d0))
    else
        tmp = x + ((a * (1.0d0 - t)) - (z * (y - 1.0d0)))
    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 ((b <= -1.3e+32) || !(b <= 5.8e+52)) {
		tmp = x + (b * ((t + y) - 2.0));
	} else {
		tmp = x + ((a * (1.0 - t)) - (z * (y - 1.0)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -1.3e+32) or not (b <= 5.8e+52):
		tmp = x + (b * ((t + y) - 2.0))
	else:
		tmp = x + ((a * (1.0 - t)) - (z * (y - 1.0)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -1.3e+32) || !(b <= 5.8e+52))
		tmp = Float64(x + Float64(b * Float64(Float64(t + y) - 2.0)));
	else
		tmp = Float64(x + Float64(Float64(a * Float64(1.0 - t)) - Float64(z * Float64(y - 1.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -1.3e+32) || ~((b <= 5.8e+52)))
		tmp = x + (b * ((t + y) - 2.0));
	else
		tmp = x + ((a * (1.0 - t)) - (z * (y - 1.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -1.3e+32], N[Not[LessEqual[b, 5.8e+52]], $MachinePrecision]], N[(x + N[(b * N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision] - N[(z * N[(y - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.3000000000000001e32 or 5.8e52 < b

   1. Initial program 88.9%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in a around 0 85.9%

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

   3. Taylor expanded in z around 0 83.7%

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

   if -1.3000000000000001e32 < b < 5.8e52

   1. Initial program 99.3%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in b around 0 90.1%

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

4. Final simplification 87.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.3 \cdot 10^{+32} \lor \neg \left(b \leq 5.8 \cdot 10^{+52}\right):\\ \;\;\;\;x + b \cdot \left(\left(t + y\right) - 2\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(a \cdot \left(1 - t\right) - z \cdot \left(y - 1\right)\right)\\ \end{array} \]

Alternative 11: 35.6% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t - 2\right)\\ \mathbf{if}\;b \leq -1.26 \cdot 10^{+32}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -2.15 \cdot 10^{-147}:\\ \;\;\;\;z \cdot \left(-y\right)\\ \mathbf{elif}\;b \leq -3.4 \cdot 10^{-264}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;b \leq 8.5 \cdot 10^{+65}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;b \leq 2.15 \cdot 10^{+170}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- t 2.0))))
   (if (<= b -1.26e+32)
     t_1
     (if (<= b -2.15e-147)
       (* z (- y))
       (if (<= b -3.4e-264)
         (+ x z)
         (if (<= b 8.5e+65) (+ x a) (if (<= b 2.15e+170) t_1 (* y b))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (t - 2.0);
	double tmp;
	if (b <= -1.26e+32) {
		tmp = t_1;
	} else if (b <= -2.15e-147) {
		tmp = z * -y;
	} else if (b <= -3.4e-264) {
		tmp = x + z;
	} else if (b <= 8.5e+65) {
		tmp = x + a;
	} else if (b <= 2.15e+170) {
		tmp = t_1;
	} else {
		tmp = y * 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) :: t_1
    real(8) :: tmp
    t_1 = b * (t - 2.0d0)
    if (b <= (-1.26d+32)) then
        tmp = t_1
    else if (b <= (-2.15d-147)) then
        tmp = z * -y
    else if (b <= (-3.4d-264)) then
        tmp = x + z
    else if (b <= 8.5d+65) then
        tmp = x + a
    else if (b <= 2.15d+170) then
        tmp = t_1
    else
        tmp = y * 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 t_1 = b * (t - 2.0);
	double tmp;
	if (b <= -1.26e+32) {
		tmp = t_1;
	} else if (b <= -2.15e-147) {
		tmp = z * -y;
	} else if (b <= -3.4e-264) {
		tmp = x + z;
	} else if (b <= 8.5e+65) {
		tmp = x + a;
	} else if (b <= 2.15e+170) {
		tmp = t_1;
	} else {
		tmp = y * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * (t - 2.0)
	tmp = 0
	if b <= -1.26e+32:
		tmp = t_1
	elif b <= -2.15e-147:
		tmp = z * -y
	elif b <= -3.4e-264:
		tmp = x + z
	elif b <= 8.5e+65:
		tmp = x + a
	elif b <= 2.15e+170:
		tmp = t_1
	else:
		tmp = y * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(t - 2.0))
	tmp = 0.0
	if (b <= -1.26e+32)
		tmp = t_1;
	elseif (b <= -2.15e-147)
		tmp = Float64(z * Float64(-y));
	elseif (b <= -3.4e-264)
		tmp = Float64(x + z);
	elseif (b <= 8.5e+65)
		tmp = Float64(x + a);
	elseif (b <= 2.15e+170)
		tmp = t_1;
	else
		tmp = Float64(y * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * (t - 2.0);
	tmp = 0.0;
	if (b <= -1.26e+32)
		tmp = t_1;
	elseif (b <= -2.15e-147)
		tmp = z * -y;
	elseif (b <= -3.4e-264)
		tmp = x + z;
	elseif (b <= 8.5e+65)
		tmp = x + a;
	elseif (b <= 2.15e+170)
		tmp = t_1;
	else
		tmp = y * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(t - 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.26e+32], t$95$1, If[LessEqual[b, -2.15e-147], N[(z * (-y)), $MachinePrecision], If[LessEqual[b, -3.4e-264], N[(x + z), $MachinePrecision], If[LessEqual[b, 8.5e+65], N[(x + a), $MachinePrecision], If[LessEqual[b, 2.15e+170], t$95$1, N[(y * b), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -1.26e32 or 8.50000000000000075e65 < b < 2.1499999999999999e170

   1. Initial program 88.4%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in b around inf 73.6%

      \[\leadsto \color{blue}{\left(\left(y + t\right) - 2\right) \cdot b} \]

   3. Taylor expanded in y around 0 56.3%

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

   if -1.26e32 < b < -2.1500000000000001e-147

   1. Initial program 97.3%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in y around inf 39.4%

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

   3. Taylor expanded in b around 0 39.4%

      \[\leadsto \color{blue}{-1 \cdot \left(y \cdot z\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg 39.4%

         \[\leadsto \color{blue}{-y \cdot z} \]

      2. *-commutative 39.4%

         \[\leadsto -\color{blue}{z \cdot y} \]

      3. distribute-rgt-neg-in 39.4%

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

   5. Simplified 39.4%

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

   if -2.1500000000000001e-147 < b < -3.3999999999999999e-264

   1. Initial program 100.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in b around 0 93.6%

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

   3. Taylor expanded in a around 0 67.3%

      \[\leadsto x - \color{blue}{z \cdot \left(y - 1\right)} \]
   4. Step-by-step derivation

      1. sub-neg 67.3%

         \[\leadsto x - z \cdot \color{blue}{\left(y + \left(-1\right)\right)} \]

      2. metadata-eval 67.3%

         \[\leadsto x - z \cdot \left(y + \color{blue}{-1}\right) \]

      3. distribute-rgt-in 67.3%

         \[\leadsto x - \color{blue}{\left(y \cdot z + -1 \cdot z\right)} \]

      4. neg-mul-1 67.3%

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

      5. unsub-neg 67.3%

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

      6. *-commutative 67.3%

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

   5. Simplified 67.3%

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

   6. Taylor expanded in y around 0 44.9%

      \[\leadsto \color{blue}{z + x} \]

   if -3.3999999999999999e-264 < b < 8.50000000000000075e65

   1. Initial program 100.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in b around 0 89.2%

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

   3. Taylor expanded in t around 0 72.1%

      \[\leadsto x - \color{blue}{\left(z \cdot \left(y - 1\right) + -1 \cdot a\right)} \]
   4. Step-by-step derivation

      1. fma-def 72.2%

         \[\leadsto x - \color{blue}{\mathsf{fma}\left(z, y - 1, -1 \cdot a\right)} \]

      2. sub-neg 72.2%

         \[\leadsto x - \mathsf{fma}\left(z, \color{blue}{y + \left(-1\right)}, -1 \cdot a\right) \]

      3. metadata-eval 72.2%

         \[\leadsto x - \mathsf{fma}\left(z, y + \color{blue}{-1}, -1 \cdot a\right) \]

      4. fma-def 72.1%

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

      5. neg-mul-1 72.1%

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

      6. unsub-neg 72.1%

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

      7. distribute-rgt-in 72.1%

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

      8. neg-mul-1 72.1%

         \[\leadsto x - \left(\left(y \cdot z + \color{blue}{\left(-z\right)}\right) - a\right) \]

      9. unsub-neg 72.1%

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

      10. *-commutative 72.1%

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

   5. Simplified 72.1%

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

   6. Taylor expanded in z around 0 36.8%

      \[\leadsto \color{blue}{a + x} \]
   7. Step-by-step derivation

      1. +-commutative 36.8%

         \[\leadsto \color{blue}{x + a} \]

   8. Simplified 36.8%

      \[\leadsto \color{blue}{x + a} \]

   if 2.1499999999999999e170 < b

   1. Initial program 89.9%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in b around inf 93.9%

      \[\leadsto \color{blue}{\left(\left(y + t\right) - 2\right) \cdot b} \]

   3. Taylor expanded in y around inf 64.9%

      \[\leadsto \color{blue}{y \cdot b} \]
3. Recombined 5 regimes into one program.

4. Final simplification 47.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.26 \cdot 10^{+32}:\\ \;\;\;\;b \cdot \left(t - 2\right)\\ \mathbf{elif}\;b \leq -2.15 \cdot 10^{-147}:\\ \;\;\;\;z \cdot \left(-y\right)\\ \mathbf{elif}\;b \leq -3.4 \cdot 10^{-264}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;b \leq 8.5 \cdot 10^{+65}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;b \leq 2.15 \cdot 10^{+170}:\\ \;\;\;\;b \cdot \left(t - 2\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \]

Alternative 12: 49.7% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t - 2\right)\\ t_2 := y \cdot \left(b - z\right)\\ \mathbf{if}\;y \leq -1.3 \cdot 10^{+37}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -1.55 \cdot 10^{-71}:\\ \;\;\;\;a - t \cdot a\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{-293}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{-144}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;y \leq 175000:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- t 2.0))) (t_2 (* y (- b z))))
   (if (<= y -1.3e+37)
     t_2
     (if (<= y -1.55e-71)
       (- a (* t a))
       (if (<= y 2.1e-293)
         t_1
         (if (<= y 7.2e-144) (+ x z) (if (<= y 175000.0) t_1 t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (t - 2.0);
	double t_2 = y * (b - z);
	double tmp;
	if (y <= -1.3e+37) {
		tmp = t_2;
	} else if (y <= -1.55e-71) {
		tmp = a - (t * a);
	} else if (y <= 2.1e-293) {
		tmp = t_1;
	} else if (y <= 7.2e-144) {
		tmp = x + z;
	} else if (y <= 175000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = b * (t - 2.0d0)
    t_2 = y * (b - z)
    if (y <= (-1.3d+37)) then
        tmp = t_2
    else if (y <= (-1.55d-71)) then
        tmp = a - (t * a)
    else if (y <= 2.1d-293) then
        tmp = t_1
    else if (y <= 7.2d-144) then
        tmp = x + z
    else if (y <= 175000.0d0) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (t - 2.0);
	double t_2 = y * (b - z);
	double tmp;
	if (y <= -1.3e+37) {
		tmp = t_2;
	} else if (y <= -1.55e-71) {
		tmp = a - (t * a);
	} else if (y <= 2.1e-293) {
		tmp = t_1;
	} else if (y <= 7.2e-144) {
		tmp = x + z;
	} else if (y <= 175000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * (t - 2.0)
	t_2 = y * (b - z)
	tmp = 0
	if y <= -1.3e+37:
		tmp = t_2
	elif y <= -1.55e-71:
		tmp = a - (t * a)
	elif y <= 2.1e-293:
		tmp = t_1
	elif y <= 7.2e-144:
		tmp = x + z
	elif y <= 175000.0:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(t - 2.0))
	t_2 = Float64(y * Float64(b - z))
	tmp = 0.0
	if (y <= -1.3e+37)
		tmp = t_2;
	elseif (y <= -1.55e-71)
		tmp = Float64(a - Float64(t * a));
	elseif (y <= 2.1e-293)
		tmp = t_1;
	elseif (y <= 7.2e-144)
		tmp = Float64(x + z);
	elseif (y <= 175000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * (t - 2.0);
	t_2 = y * (b - z);
	tmp = 0.0;
	if (y <= -1.3e+37)
		tmp = t_2;
	elseif (y <= -1.55e-71)
		tmp = a - (t * a);
	elseif (y <= 2.1e-293)
		tmp = t_1;
	elseif (y <= 7.2e-144)
		tmp = x + z;
	elseif (y <= 175000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(t - 2.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.3e+37], t$95$2, If[LessEqual[y, -1.55e-71], N[(a - N[(t * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.1e-293], t$95$1, If[LessEqual[y, 7.2e-144], N[(x + z), $MachinePrecision], If[LessEqual[y, 175000.0], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.3e37 or 175000 < y

   1. Initial program 92.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in y around inf 70.9%

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

   if -1.3e37 < y < -1.55000000000000001e-71

   1. Initial program 95.8%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in a around inf 63.8%

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

      1. sub-neg 63.8%

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

      2. distribute-lft-in 63.8%

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

      3. *-rgt-identity 63.8%

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

      4. distribute-rgt-neg-in 63.8%

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

      5. sub-neg 63.8%

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

      6. *-commutative 63.8%

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

   4. Simplified 63.8%

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

   if -1.55000000000000001e-71 < y < 2.10000000000000005e-293 or 7.2000000000000001e-144 < y < 175000

   1. Initial program 98.7%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in b around inf 46.5%

      \[\leadsto \color{blue}{\left(\left(y + t\right) - 2\right) \cdot b} \]

   3. Taylor expanded in y around 0 46.5%

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

   if 2.10000000000000005e-293 < y < 7.2000000000000001e-144

   1. Initial program 96.4%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in b around 0 75.7%

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

   3. Taylor expanded in a around 0 51.6%

      \[\leadsto x - \color{blue}{z \cdot \left(y - 1\right)} \]
   4. Step-by-step derivation

      1. sub-neg 51.6%

         \[\leadsto x - z \cdot \color{blue}{\left(y + \left(-1\right)\right)} \]

      2. metadata-eval 51.6%

         \[\leadsto x - z \cdot \left(y + \color{blue}{-1}\right) \]

      3. distribute-rgt-in 51.6%

         \[\leadsto x - \color{blue}{\left(y \cdot z + -1 \cdot z\right)} \]

      4. neg-mul-1 51.6%

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

      5. unsub-neg 51.6%

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

      6. *-commutative 51.6%

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

   5. Simplified 51.6%

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

   6. Taylor expanded in y around 0 51.6%

      \[\leadsto \color{blue}{z + x} \]
3. Recombined 4 regimes into one program.

4. Final simplification 60.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{+37}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;y \leq -1.55 \cdot 10^{-71}:\\ \;\;\;\;a - t \cdot a\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{-293}:\\ \;\;\;\;b \cdot \left(t - 2\right)\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{-144}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;y \leq 175000:\\ \;\;\;\;b \cdot \left(t - 2\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \end{array} \]

Alternative 13: 55.0% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - y \cdot z\\ t_2 := b \cdot \left(\left(t + y\right) - 2\right)\\ \mathbf{if}\;b \leq -5.5 \cdot 10^{+31}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -2.8 \cdot 10^{-241}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -6.2 \cdot 10^{-307}:\\ \;\;\;\;a - t \cdot a\\ \mathbf{elif}\;b \leq 7.6 \cdot 10^{+21}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- x (* y z))) (t_2 (* b (- (+ t y) 2.0))))
   (if (<= b -5.5e+31)
     t_2
     (if (<= b -2.8e-241)
       t_1
       (if (<= b -6.2e-307) (- a (* t a)) (if (<= b 7.6e+21) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x - (y * z);
	double t_2 = b * ((t + y) - 2.0);
	double tmp;
	if (b <= -5.5e+31) {
		tmp = t_2;
	} else if (b <= -2.8e-241) {
		tmp = t_1;
	} else if (b <= -6.2e-307) {
		tmp = a - (t * a);
	} else if (b <= 7.6e+21) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x - (y * z)
    t_2 = b * ((t + y) - 2.0d0)
    if (b <= (-5.5d+31)) then
        tmp = t_2
    else if (b <= (-2.8d-241)) then
        tmp = t_1
    else if (b <= (-6.2d-307)) then
        tmp = a - (t * a)
    else if (b <= 7.6d+21) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x - (y * z);
	double t_2 = b * ((t + y) - 2.0);
	double tmp;
	if (b <= -5.5e+31) {
		tmp = t_2;
	} else if (b <= -2.8e-241) {
		tmp = t_1;
	} else if (b <= -6.2e-307) {
		tmp = a - (t * a);
	} else if (b <= 7.6e+21) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x - (y * z)
	t_2 = b * ((t + y) - 2.0)
	tmp = 0
	if b <= -5.5e+31:
		tmp = t_2
	elif b <= -2.8e-241:
		tmp = t_1
	elif b <= -6.2e-307:
		tmp = a - (t * a)
	elif b <= 7.6e+21:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x - Float64(y * z))
	t_2 = Float64(b * Float64(Float64(t + y) - 2.0))
	tmp = 0.0
	if (b <= -5.5e+31)
		tmp = t_2;
	elseif (b <= -2.8e-241)
		tmp = t_1;
	elseif (b <= -6.2e-307)
		tmp = Float64(a - Float64(t * a));
	elseif (b <= 7.6e+21)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x - (y * z);
	t_2 = b * ((t + y) - 2.0);
	tmp = 0.0;
	if (b <= -5.5e+31)
		tmp = t_2;
	elseif (b <= -2.8e-241)
		tmp = t_1;
	elseif (b <= -6.2e-307)
		tmp = a - (t * a);
	elseif (b <= 7.6e+21)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -5.5e+31], t$95$2, If[LessEqual[b, -2.8e-241], t$95$1, If[LessEqual[b, -6.2e-307], N[(a - N[(t * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 7.6e+21], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -5.50000000000000002e31 or 7.6e21 < b

   1. Initial program 89.3%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in b around inf 77.4%

      \[\leadsto \color{blue}{\left(\left(y + t\right) - 2\right) \cdot b} \]

   if -5.50000000000000002e31 < b < -2.7999999999999999e-241 or -6.1999999999999996e-307 < b < 7.6e21

   1. Initial program 99.2%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in b around 0 90.3%

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

   3. Taylor expanded in y around inf 51.8%

      \[\leadsto x - \color{blue}{y \cdot z} \]
   4. Step-by-step derivation

      1. *-commutative 51.8%

         \[\leadsto x - \color{blue}{z \cdot y} \]

   5. Simplified 51.8%

      \[\leadsto x - \color{blue}{z \cdot y} \]

   if -2.7999999999999999e-241 < b < -6.1999999999999996e-307

   1. Initial program 100.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in a around inf 55.7%

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

      1. sub-neg 55.7%

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

      2. distribute-lft-in 55.7%

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

      3. *-rgt-identity 55.7%

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

      4. distribute-rgt-neg-in 55.7%

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

      5. sub-neg 55.7%

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

      6. *-commutative 55.7%

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

   4. Simplified 55.7%

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

4. Final simplification 63.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5.5 \cdot 10^{+31}:\\ \;\;\;\;b \cdot \left(\left(t + y\right) - 2\right)\\ \mathbf{elif}\;b \leq -2.8 \cdot 10^{-241}:\\ \;\;\;\;x - y \cdot z\\ \mathbf{elif}\;b \leq -6.2 \cdot 10^{-307}:\\ \;\;\;\;a - t \cdot a\\ \mathbf{elif}\;b \leq 7.6 \cdot 10^{+21}:\\ \;\;\;\;x - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(t + y\right) - 2\right)\\ \end{array} \]

Alternative 14: 31.6% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -4.4 \cdot 10^{+86}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;b \leq -29000000:\\ \;\;\;\;x + a\\ \mathbf{elif}\;b \leq -2.3 \cdot 10^{-149}:\\ \;\;\;\;z \cdot \left(-y\right)\\ \mathbf{elif}\;b \leq -1.05 \cdot 10^{-264}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;b \leq 4.9 \cdot 10^{+128}:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -4.4e+86)
   (* t b)
   (if (<= b -29000000.0)
     (+ x a)
     (if (<= b -2.3e-149)
       (* z (- y))
       (if (<= b -1.05e-264) (+ x z) (if (<= b 4.9e+128) (+ x a) (* y b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -4.4e+86) {
		tmp = t * b;
	} else if (b <= -29000000.0) {
		tmp = x + a;
	} else if (b <= -2.3e-149) {
		tmp = z * -y;
	} else if (b <= -1.05e-264) {
		tmp = x + z;
	} else if (b <= 4.9e+128) {
		tmp = x + a;
	} else {
		tmp = y * 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 (b <= (-4.4d+86)) then
        tmp = t * b
    else if (b <= (-29000000.0d0)) then
        tmp = x + a
    else if (b <= (-2.3d-149)) then
        tmp = z * -y
    else if (b <= (-1.05d-264)) then
        tmp = x + z
    else if (b <= 4.9d+128) then
        tmp = x + a
    else
        tmp = y * 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 (b <= -4.4e+86) {
		tmp = t * b;
	} else if (b <= -29000000.0) {
		tmp = x + a;
	} else if (b <= -2.3e-149) {
		tmp = z * -y;
	} else if (b <= -1.05e-264) {
		tmp = x + z;
	} else if (b <= 4.9e+128) {
		tmp = x + a;
	} else {
		tmp = y * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -4.4e+86:
		tmp = t * b
	elif b <= -29000000.0:
		tmp = x + a
	elif b <= -2.3e-149:
		tmp = z * -y
	elif b <= -1.05e-264:
		tmp = x + z
	elif b <= 4.9e+128:
		tmp = x + a
	else:
		tmp = y * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -4.4e+86)
		tmp = Float64(t * b);
	elseif (b <= -29000000.0)
		tmp = Float64(x + a);
	elseif (b <= -2.3e-149)
		tmp = Float64(z * Float64(-y));
	elseif (b <= -1.05e-264)
		tmp = Float64(x + z);
	elseif (b <= 4.9e+128)
		tmp = Float64(x + a);
	else
		tmp = Float64(y * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -4.4e+86)
		tmp = t * b;
	elseif (b <= -29000000.0)
		tmp = x + a;
	elseif (b <= -2.3e-149)
		tmp = z * -y;
	elseif (b <= -1.05e-264)
		tmp = x + z;
	elseif (b <= 4.9e+128)
		tmp = x + a;
	else
		tmp = y * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -4.4e+86], N[(t * b), $MachinePrecision], If[LessEqual[b, -29000000.0], N[(x + a), $MachinePrecision], If[LessEqual[b, -2.3e-149], N[(z * (-y)), $MachinePrecision], If[LessEqual[b, -1.05e-264], N[(x + z), $MachinePrecision], If[LessEqual[b, 4.9e+128], N[(x + a), $MachinePrecision], N[(y * b), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -4.40000000000000006e86

   1. Initial program 88.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in b around inf 83.0%

      \[\leadsto \color{blue}{\left(\left(y + t\right) - 2\right) \cdot b} \]

   3. Taylor expanded in t around inf 43.9%

      \[\leadsto \color{blue}{t \cdot b} \]

   if -4.40000000000000006e86 < b < -2.9e7 or -1.0500000000000001e-264 < b < 4.90000000000000018e128

   1. Initial program 97.2%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in b around 0 80.5%

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

   3. Taylor expanded in t around 0 66.3%

      \[\leadsto x - \color{blue}{\left(z \cdot \left(y - 1\right) + -1 \cdot a\right)} \]
   4. Step-by-step derivation

      1. fma-def 66.3%

         \[\leadsto x - \color{blue}{\mathsf{fma}\left(z, y - 1, -1 \cdot a\right)} \]

      2. sub-neg 66.3%

         \[\leadsto x - \mathsf{fma}\left(z, \color{blue}{y + \left(-1\right)}, -1 \cdot a\right) \]

      3. metadata-eval 66.3%

         \[\leadsto x - \mathsf{fma}\left(z, y + \color{blue}{-1}, -1 \cdot a\right) \]

      4. fma-def 66.3%

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

      5. neg-mul-1 66.3%

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

      6. unsub-neg 66.3%

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

      7. distribute-rgt-in 66.3%

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

      8. neg-mul-1 66.3%

         \[\leadsto x - \left(\left(y \cdot z + \color{blue}{\left(-z\right)}\right) - a\right) \]

      9. unsub-neg 66.3%

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

      10. *-commutative 66.3%

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

   5. Simplified 66.3%

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

   6. Taylor expanded in z around 0 36.3%

      \[\leadsto \color{blue}{a + x} \]
   7. Step-by-step derivation

      1. +-commutative 36.3%

         \[\leadsto \color{blue}{x + a} \]

   8. Simplified 36.3%

      \[\leadsto \color{blue}{x + a} \]

   if -2.9e7 < b < -2.3e-149

   1. Initial program 97.1%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in y around inf 42.8%

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

   3. Taylor expanded in b around 0 42.7%

      \[\leadsto \color{blue}{-1 \cdot \left(y \cdot z\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg 42.7%

         \[\leadsto \color{blue}{-y \cdot z} \]

      2. *-commutative 42.7%

         \[\leadsto -\color{blue}{z \cdot y} \]

      3. distribute-rgt-neg-in 42.7%

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

   5. Simplified 42.7%

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

   if -2.3e-149 < b < -1.0500000000000001e-264

   1. Initial program 100.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in b around 0 93.6%

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

   3. Taylor expanded in a around 0 67.3%

      \[\leadsto x - \color{blue}{z \cdot \left(y - 1\right)} \]
   4. Step-by-step derivation

      1. sub-neg 67.3%

         \[\leadsto x - z \cdot \color{blue}{\left(y + \left(-1\right)\right)} \]

      2. metadata-eval 67.3%

         \[\leadsto x - z \cdot \left(y + \color{blue}{-1}\right) \]

      3. distribute-rgt-in 67.3%

         \[\leadsto x - \color{blue}{\left(y \cdot z + -1 \cdot z\right)} \]

      4. neg-mul-1 67.3%

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

      5. unsub-neg 67.3%

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

      6. *-commutative 67.3%

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

   5. Simplified 67.3%

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

   6. Taylor expanded in y around 0 44.9%

      \[\leadsto \color{blue}{z + x} \]

   if 4.90000000000000018e128 < b

   1. Initial program 91.4%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in b around inf 94.3%

      \[\leadsto \color{blue}{\left(\left(y + t\right) - 2\right) \cdot b} \]

   3. Taylor expanded in y around inf 61.1%

      \[\leadsto \color{blue}{y \cdot b} \]
3. Recombined 5 regimes into one program.

4. Final simplification 43.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.4 \cdot 10^{+86}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;b \leq -29000000:\\ \;\;\;\;x + a\\ \mathbf{elif}\;b \leq -2.3 \cdot 10^{-149}:\\ \;\;\;\;z \cdot \left(-y\right)\\ \mathbf{elif}\;b \leq -1.05 \cdot 10^{-264}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;b \leq 4.9 \cdot 10^{+128}:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \]

Alternative 15: 72.3% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.25 \cdot 10^{+32} \lor \neg \left(b \leq 2.9 \cdot 10^{+59}\right):\\ \;\;\;\;x + b \cdot \left(\left(t + y\right) - 2\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(a + \left(z - y \cdot z\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -1.25e+32) (not (<= b 2.9e+59)))
   (+ x (* b (- (+ t y) 2.0)))
   (+ x (+ a (- z (* y z))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -1.25e+32) || !(b <= 2.9e+59)) {
		tmp = x + (b * ((t + y) - 2.0));
	} else {
		tmp = x + (a + (z - (y * z)));
	}
	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 ((b <= (-1.25d+32)) .or. (.not. (b <= 2.9d+59))) then
        tmp = x + (b * ((t + y) - 2.0d0))
    else
        tmp = x + (a + (z - (y * z)))
    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 ((b <= -1.25e+32) || !(b <= 2.9e+59)) {
		tmp = x + (b * ((t + y) - 2.0));
	} else {
		tmp = x + (a + (z - (y * z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -1.25e+32) or not (b <= 2.9e+59):
		tmp = x + (b * ((t + y) - 2.0))
	else:
		tmp = x + (a + (z - (y * z)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -1.25e+32) || !(b <= 2.9e+59))
		tmp = Float64(x + Float64(b * Float64(Float64(t + y) - 2.0)));
	else
		tmp = Float64(x + Float64(a + Float64(z - Float64(y * z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -1.25e+32) || ~((b <= 2.9e+59)))
		tmp = x + (b * ((t + y) - 2.0));
	else
		tmp = x + (a + (z - (y * z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -1.25e+32], N[Not[LessEqual[b, 2.9e+59]], $MachinePrecision]], N[(x + N[(b * N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(a + N[(z - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.2499999999999999e32 or 2.89999999999999991e59 < b

   1. Initial program 88.9%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in a around 0 85.9%

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

   3. Taylor expanded in z around 0 83.7%

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

   if -1.2499999999999999e32 < b < 2.89999999999999991e59

   1. Initial program 99.3%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in b around 0 90.1%

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

   3. Taylor expanded in t around 0 72.2%

      \[\leadsto x - \color{blue}{\left(z \cdot \left(y - 1\right) + -1 \cdot a\right)} \]
   4. Step-by-step derivation

      1. fma-def 72.2%

         \[\leadsto x - \color{blue}{\mathsf{fma}\left(z, y - 1, -1 \cdot a\right)} \]

      2. sub-neg 72.2%

         \[\leadsto x - \mathsf{fma}\left(z, \color{blue}{y + \left(-1\right)}, -1 \cdot a\right) \]

      3. metadata-eval 72.2%

         \[\leadsto x - \mathsf{fma}\left(z, y + \color{blue}{-1}, -1 \cdot a\right) \]

      4. fma-def 72.2%

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

      5. neg-mul-1 72.2%

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

      6. unsub-neg 72.2%

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

      7. distribute-rgt-in 72.2%

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

      8. neg-mul-1 72.2%

         \[\leadsto x - \left(\left(y \cdot z + \color{blue}{\left(-z\right)}\right) - a\right) \]

      9. unsub-neg 72.2%

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

      10. *-commutative 72.2%

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

   5. Simplified 72.2%

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

4. Final simplification 77.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.25 \cdot 10^{+32} \lor \neg \left(b \leq 2.9 \cdot 10^{+59}\right):\\ \;\;\;\;x + b \cdot \left(\left(t + y\right) - 2\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(a + \left(z - y \cdot z\right)\right)\\ \end{array} \]

Alternative 16: 33.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -6.8 \cdot 10^{+88}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;b \leq -7.2 \cdot 10^{-42}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;b \leq -2.3 \cdot 10^{-264}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;b \leq 6.9 \cdot 10^{+133}:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -6.8e+88)
   (* t b)
   (if (<= b -7.2e-42)
     (+ x a)
     (if (<= b -2.3e-264) (+ x z) (if (<= b 6.9e+133) (+ x a) (* y b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -6.8e+88) {
		tmp = t * b;
	} else if (b <= -7.2e-42) {
		tmp = x + a;
	} else if (b <= -2.3e-264) {
		tmp = x + z;
	} else if (b <= 6.9e+133) {
		tmp = x + a;
	} else {
		tmp = y * 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 (b <= (-6.8d+88)) then
        tmp = t * b
    else if (b <= (-7.2d-42)) then
        tmp = x + a
    else if (b <= (-2.3d-264)) then
        tmp = x + z
    else if (b <= 6.9d+133) then
        tmp = x + a
    else
        tmp = y * 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 (b <= -6.8e+88) {
		tmp = t * b;
	} else if (b <= -7.2e-42) {
		tmp = x + a;
	} else if (b <= -2.3e-264) {
		tmp = x + z;
	} else if (b <= 6.9e+133) {
		tmp = x + a;
	} else {
		tmp = y * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -6.8e+88:
		tmp = t * b
	elif b <= -7.2e-42:
		tmp = x + a
	elif b <= -2.3e-264:
		tmp = x + z
	elif b <= 6.9e+133:
		tmp = x + a
	else:
		tmp = y * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -6.8e+88)
		tmp = Float64(t * b);
	elseif (b <= -7.2e-42)
		tmp = Float64(x + a);
	elseif (b <= -2.3e-264)
		tmp = Float64(x + z);
	elseif (b <= 6.9e+133)
		tmp = Float64(x + a);
	else
		tmp = Float64(y * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -6.8e+88)
		tmp = t * b;
	elseif (b <= -7.2e-42)
		tmp = x + a;
	elseif (b <= -2.3e-264)
		tmp = x + z;
	elseif (b <= 6.9e+133)
		tmp = x + a;
	else
		tmp = y * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -6.8e+88], N[(t * b), $MachinePrecision], If[LessEqual[b, -7.2e-42], N[(x + a), $MachinePrecision], If[LessEqual[b, -2.3e-264], N[(x + z), $MachinePrecision], If[LessEqual[b, 6.9e+133], N[(x + a), $MachinePrecision], N[(y * b), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -6.80000000000000008e88

   1. Initial program 88.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in b around inf 83.0%

      \[\leadsto \color{blue}{\left(\left(y + t\right) - 2\right) \cdot b} \]

   3. Taylor expanded in t around inf 43.9%

      \[\leadsto \color{blue}{t \cdot b} \]

   if -6.80000000000000008e88 < b < -7.2000000000000004e-42 or -2.30000000000000012e-264 < b < 6.9000000000000002e133

   1. Initial program 96.5%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in b around 0 81.3%

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

   3. Taylor expanded in t around 0 67.6%

      \[\leadsto x - \color{blue}{\left(z \cdot \left(y - 1\right) + -1 \cdot a\right)} \]
   4. Step-by-step derivation

      1. fma-def 67.6%

         \[\leadsto x - \color{blue}{\mathsf{fma}\left(z, y - 1, -1 \cdot a\right)} \]

      2. sub-neg 67.6%

         \[\leadsto x - \mathsf{fma}\left(z, \color{blue}{y + \left(-1\right)}, -1 \cdot a\right) \]

      3. metadata-eval 67.6%

         \[\leadsto x - \mathsf{fma}\left(z, y + \color{blue}{-1}, -1 \cdot a\right) \]

      4. fma-def 67.6%

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

      5. neg-mul-1 67.6%

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

      6. unsub-neg 67.6%

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

      7. distribute-rgt-in 67.6%

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

      8. neg-mul-1 67.6%

         \[\leadsto x - \left(\left(y \cdot z + \color{blue}{\left(-z\right)}\right) - a\right) \]

      9. unsub-neg 67.6%

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

      10. *-commutative 67.6%

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

   5. Simplified 67.6%

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

   6. Taylor expanded in z around 0 35.2%

      \[\leadsto \color{blue}{a + x} \]
   7. Step-by-step derivation

      1. +-commutative 35.2%

         \[\leadsto \color{blue}{x + a} \]

   8. Simplified 35.2%

      \[\leadsto \color{blue}{x + a} \]

   if -7.2000000000000004e-42 < b < -2.30000000000000012e-264

   1. Initial program 100.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in b around 0 91.1%

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

   3. Taylor expanded in a around 0 65.6%

      \[\leadsto x - \color{blue}{z \cdot \left(y - 1\right)} \]
   4. Step-by-step derivation

      1. sub-neg 65.6%

         \[\leadsto x - z \cdot \color{blue}{\left(y + \left(-1\right)\right)} \]

      2. metadata-eval 65.6%

         \[\leadsto x - z \cdot \left(y + \color{blue}{-1}\right) \]

      3. distribute-rgt-in 65.6%

         \[\leadsto x - \color{blue}{\left(y \cdot z + -1 \cdot z\right)} \]

      4. neg-mul-1 65.6%

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

      5. unsub-neg 65.6%

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

      6. *-commutative 65.6%

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

   5. Simplified 65.6%

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

   6. Taylor expanded in y around 0 38.6%

      \[\leadsto \color{blue}{z + x} \]

   if 6.9000000000000002e133 < b

   1. Initial program 91.4%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in b around inf 94.3%

      \[\leadsto \color{blue}{\left(\left(y + t\right) - 2\right) \cdot b} \]

   3. Taylor expanded in y around inf 61.1%

      \[\leadsto \color{blue}{y \cdot b} \]
3. Recombined 4 regimes into one program.

4. Final simplification 41.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -6.8 \cdot 10^{+88}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;b \leq -7.2 \cdot 10^{-42}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;b \leq -2.3 \cdot 10^{-264}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;b \leq 6.9 \cdot 10^{+133}:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \]

Alternative 17: 61.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.25 \cdot 10^{+90} \lor \neg \left(b \leq 3.5 \cdot 10^{+63}\right):\\ \;\;\;\;b \cdot \left(\left(t + y\right) - 2\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(a - t \cdot a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -1.25e+90) (not (<= b 3.5e+63)))
   (* b (- (+ t y) 2.0))
   (+ x (- a (* t a)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -1.25e+90) || !(b <= 3.5e+63)) {
		tmp = b * ((t + y) - 2.0);
	} else {
		tmp = x + (a - (t * a));
	}
	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 ((b <= (-1.25d+90)) .or. (.not. (b <= 3.5d+63))) then
        tmp = b * ((t + y) - 2.0d0)
    else
        tmp = x + (a - (t * a))
    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 ((b <= -1.25e+90) || !(b <= 3.5e+63)) {
		tmp = b * ((t + y) - 2.0);
	} else {
		tmp = x + (a - (t * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -1.25e+90) or not (b <= 3.5e+63):
		tmp = b * ((t + y) - 2.0)
	else:
		tmp = x + (a - (t * a))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -1.25e+90) || !(b <= 3.5e+63))
		tmp = Float64(b * Float64(Float64(t + y) - 2.0));
	else
		tmp = Float64(x + Float64(a - Float64(t * a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -1.25e+90) || ~((b <= 3.5e+63)))
		tmp = b * ((t + y) - 2.0);
	else
		tmp = x + (a - (t * a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -1.25e+90], N[Not[LessEqual[b, 3.5e+63]], $MachinePrecision]], N[(b * N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision], N[(x + N[(a - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.2500000000000001e90 or 3.50000000000000029e63 < b

   1. Initial program 88.6%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in b around inf 83.0%

      \[\leadsto \color{blue}{\left(\left(y + t\right) - 2\right) \cdot b} \]

   if -1.2500000000000001e90 < b < 3.50000000000000029e63

   1. Initial program 98.7%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in b around 0 87.2%

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

   3. Taylor expanded in a around inf 53.2%

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

      1. sub-neg 53.2%

         \[\leadsto x - \color{blue}{\left(t + \left(-1\right)\right)} \cdot a \]

      2. metadata-eval 53.2%

         \[\leadsto x - \left(t + \color{blue}{-1}\right) \cdot a \]

      3. *-commutative 53.2%

         \[\leadsto x - \color{blue}{a \cdot \left(t + -1\right)} \]

      4. distribute-rgt-in 53.2%

         \[\leadsto x - \color{blue}{\left(t \cdot a + -1 \cdot a\right)} \]

      5. neg-mul-1 53.2%

         \[\leadsto x - \left(t \cdot a + \color{blue}{\left(-a\right)}\right) \]

      6. unsub-neg 53.2%

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

      7. *-commutative 53.2%

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

   5. Simplified 53.2%

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

4. Final simplification 64.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.25 \cdot 10^{+90} \lor \neg \left(b \leq 3.5 \cdot 10^{+63}\right):\\ \;\;\;\;b \cdot \left(\left(t + y\right) - 2\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(a - t \cdot a\right)\\ \end{array} \]

Alternative 18: 50.1% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.6 \cdot 10^{+14} \lor \neg \left(t \leq 20000\right):\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{else}:\\ \;\;\;\;x + a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -3.6e+14) (not (<= t 20000.0))) (* t (- b a)) (+ x a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -3.6e+14) || !(t <= 20000.0)) {
		tmp = t * (b - a);
	} else {
		tmp = x + a;
	}
	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 ((t <= (-3.6d+14)) .or. (.not. (t <= 20000.0d0))) then
        tmp = t * (b - a)
    else
        tmp = x + a
    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 ((t <= -3.6e+14) || !(t <= 20000.0)) {
		tmp = t * (b - a);
	} else {
		tmp = x + a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -3.6e+14) or not (t <= 20000.0):
		tmp = t * (b - a)
	else:
		tmp = x + a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -3.6e+14) || !(t <= 20000.0))
		tmp = Float64(t * Float64(b - a));
	else
		tmp = Float64(x + a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -3.6e+14) || ~((t <= 20000.0)))
		tmp = t * (b - a);
	else
		tmp = x + a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -3.6e+14], N[Not[LessEqual[t, 20000.0]], $MachinePrecision]], N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision], N[(x + a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.6e14 or 2e4 < t

   1. Initial program 90.7%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in t around inf 65.8%

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

   if -3.6e14 < t < 2e4

   1. Initial program 98.5%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in b around 0 65.7%

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

   3. Taylor expanded in t around 0 65.1%

      \[\leadsto x - \color{blue}{\left(z \cdot \left(y - 1\right) + -1 \cdot a\right)} \]
   4. Step-by-step derivation

      1. fma-def 65.1%

         \[\leadsto x - \color{blue}{\mathsf{fma}\left(z, y - 1, -1 \cdot a\right)} \]

      2. sub-neg 65.1%

         \[\leadsto x - \mathsf{fma}\left(z, \color{blue}{y + \left(-1\right)}, -1 \cdot a\right) \]

      3. metadata-eval 65.1%

         \[\leadsto x - \mathsf{fma}\left(z, y + \color{blue}{-1}, -1 \cdot a\right) \]

      4. fma-def 65.1%

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

      5. neg-mul-1 65.1%

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

      6. unsub-neg 65.1%

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

      7. distribute-rgt-in 65.1%

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

      8. neg-mul-1 65.1%

         \[\leadsto x - \left(\left(y \cdot z + \color{blue}{\left(-z\right)}\right) - a\right) \]

      9. unsub-neg 65.1%

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

      10. *-commutative 65.1%

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

   5. Simplified 65.1%

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

   6. Taylor expanded in z around 0 35.4%

      \[\leadsto \color{blue}{a + x} \]
   7. Step-by-step derivation

      1. +-commutative 35.4%

         \[\leadsto \color{blue}{x + a} \]

   8. Simplified 35.4%

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

4. Final simplification 49.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.6 \cdot 10^{+14} \lor \neg \left(t \leq 20000\right):\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{else}:\\ \;\;\;\;x + a\\ \end{array} \]

Alternative 19: 19.4% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.2 \cdot 10^{+86}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 5.8 \cdot 10^{-116}:\\ \;\;\;\;b \cdot -2\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{+76}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -4.2e+86)
   x
   (if (<= x 5.8e-116) (* b -2.0) (if (<= x 7.5e+76) a x))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -4.2e+86) {
		tmp = x;
	} else if (x <= 5.8e-116) {
		tmp = b * -2.0;
	} else if (x <= 7.5e+76) {
		tmp = a;
	} else {
		tmp = x;
	}
	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 (x <= (-4.2d+86)) then
        tmp = x
    else if (x <= 5.8d-116) then
        tmp = b * (-2.0d0)
    else if (x <= 7.5d+76) then
        tmp = a
    else
        tmp = x
    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 (x <= -4.2e+86) {
		tmp = x;
	} else if (x <= 5.8e-116) {
		tmp = b * -2.0;
	} else if (x <= 7.5e+76) {
		tmp = a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -4.2e+86:
		tmp = x
	elif x <= 5.8e-116:
		tmp = b * -2.0
	elif x <= 7.5e+76:
		tmp = a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -4.2e+86)
		tmp = x;
	elseif (x <= 5.8e-116)
		tmp = Float64(b * -2.0);
	elseif (x <= 7.5e+76)
		tmp = a;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -4.2e+86)
		tmp = x;
	elseif (x <= 5.8e-116)
		tmp = b * -2.0;
	elseif (x <= 7.5e+76)
		tmp = a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -4.2e+86], x, If[LessEqual[x, 5.8e-116], N[(b * -2.0), $MachinePrecision], If[LessEqual[x, 7.5e+76], a, x]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.1999999999999998e86 or 7.4999999999999995e76 < x

   1. Initial program 94.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in x around inf 35.5%

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

   if -4.1999999999999998e86 < x < 5.7999999999999996e-116

   1. Initial program 93.6%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in y around inf 62.2%

      \[\leadsto \color{blue}{-1 \cdot \left(y \cdot z\right)} + \left(\left(y + t\right) - 2\right) \cdot b \]
   3. Step-by-step derivation

      1. mul-1-neg 62.2%

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

      2. distribute-rgt-neg-in 62.2%

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

   4. Simplified 62.2%

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

   5. Taylor expanded in y around 0 31.5%

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

   6. Taylor expanded in t around 0 14.0%

      \[\leadsto \color{blue}{-2 \cdot b} \]
   7. Step-by-step derivation

      1. *-commutative 14.0%

         \[\leadsto \color{blue}{b \cdot -2} \]

   8. Simplified 14.0%

      \[\leadsto \color{blue}{b \cdot -2} \]

   if 5.7999999999999996e-116 < x < 7.4999999999999995e76

   1. Initial program 100.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in a around inf 33.0%

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

      1. sub-neg 33.0%

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

      2. distribute-lft-in 33.0%

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

      3. *-rgt-identity 33.0%

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

      4. distribute-rgt-neg-in 33.0%

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

      5. sub-neg 33.0%

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

      6. *-commutative 33.0%

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

   4. Simplified 33.0%

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

   5. Taylor expanded in t around 0 23.7%

      \[\leadsto \color{blue}{a} \]
3. Recombined 3 regimes into one program.

4. Final simplification 22.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.2 \cdot 10^{+86}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 5.8 \cdot 10^{-116}:\\ \;\;\;\;b \cdot -2\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{+76}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 20: 26.2% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.7 \cdot 10^{+19}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;b \leq 5.5 \cdot 10^{+16}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1.7e+19) (* t b) (if (<= b 5.5e+16) x (* t b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.7e+19) {
		tmp = t * b;
	} else if (b <= 5.5e+16) {
		tmp = x;
	} else {
		tmp = t * 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 (b <= (-1.7d+19)) then
        tmp = t * b
    else if (b <= 5.5d+16) then
        tmp = x
    else
        tmp = t * 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 (b <= -1.7e+19) {
		tmp = t * b;
	} else if (b <= 5.5e+16) {
		tmp = x;
	} else {
		tmp = t * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -1.7e+19:
		tmp = t * b
	elif b <= 5.5e+16:
		tmp = x
	else:
		tmp = t * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1.7e+19)
		tmp = Float64(t * b);
	elseif (b <= 5.5e+16)
		tmp = x;
	else
		tmp = Float64(t * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -1.7e+19)
		tmp = t * b;
	elseif (b <= 5.5e+16)
		tmp = x;
	else
		tmp = t * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1.7e+19], N[(t * b), $MachinePrecision], If[LessEqual[b, 5.5e+16], x, N[(t * b), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if b < -1.7e19 or 5.5e16 < b

   1. Initial program 89.6%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in b around inf 74.8%

      \[\leadsto \color{blue}{\left(\left(y + t\right) - 2\right) \cdot b} \]

   3. Taylor expanded in t around inf 30.5%

      \[\leadsto \color{blue}{t \cdot b} \]

   if -1.7e19 < b < 5.5e16

   1. Initial program 99.3%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in x around inf 20.5%

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

4. Final simplification 25.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.7 \cdot 10^{+19}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;b \leq 5.5 \cdot 10^{+16}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \]

Alternative 21: 25.8% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.8 \cdot 10^{+14}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;b \leq 2.6 \cdot 10^{+108}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1.8e+14) (* t b) (if (<= b 2.6e+108) x (* y b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.8e+14) {
		tmp = t * b;
	} else if (b <= 2.6e+108) {
		tmp = x;
	} else {
		tmp = y * 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 (b <= (-1.8d+14)) then
        tmp = t * b
    else if (b <= 2.6d+108) then
        tmp = x
    else
        tmp = y * 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 (b <= -1.8e+14) {
		tmp = t * b;
	} else if (b <= 2.6e+108) {
		tmp = x;
	} else {
		tmp = y * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -1.8e+14:
		tmp = t * b
	elif b <= 2.6e+108:
		tmp = x
	else:
		tmp = y * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1.8e+14)
		tmp = Float64(t * b);
	elseif (b <= 2.6e+108)
		tmp = x;
	else
		tmp = Float64(y * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -1.8e+14)
		tmp = t * b;
	elseif (b <= 2.6e+108)
		tmp = x;
	else
		tmp = y * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1.8e+14], N[(t * b), $MachinePrecision], If[LessEqual[b, 2.6e+108], x, N[(y * b), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.8e14

   1. Initial program 88.9%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in b around inf 73.9%

      \[\leadsto \color{blue}{\left(\left(y + t\right) - 2\right) \cdot b} \]

   3. Taylor expanded in t around inf 38.4%

      \[\leadsto \color{blue}{t \cdot b} \]

   if -1.8e14 < b < 2.6000000000000002e108

   1. Initial program 98.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in x around inf 19.3%

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

   if 2.6000000000000002e108 < b

   1. Initial program 92.1%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in b around inf 92.1%

      \[\leadsto \color{blue}{\left(\left(y + t\right) - 2\right) \cdot b} \]

   3. Taylor expanded in y around inf 59.0%

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

4. Final simplification 29.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.8 \cdot 10^{+14}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;b \leq 2.6 \cdot 10^{+108}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \]

Alternative 22: 33.2% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -7.5 \cdot 10^{+89}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;b \leq 1.6 \cdot 10^{+128}:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -7.5e+89) (* t b) (if (<= b 1.6e+128) (+ x a) (* y b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -7.5e+89) {
		tmp = t * b;
	} else if (b <= 1.6e+128) {
		tmp = x + a;
	} else {
		tmp = y * 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 (b <= (-7.5d+89)) then
        tmp = t * b
    else if (b <= 1.6d+128) then
        tmp = x + a
    else
        tmp = y * 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 (b <= -7.5e+89) {
		tmp = t * b;
	} else if (b <= 1.6e+128) {
		tmp = x + a;
	} else {
		tmp = y * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -7.5e+89:
		tmp = t * b
	elif b <= 1.6e+128:
		tmp = x + a
	else:
		tmp = y * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -7.5e+89)
		tmp = Float64(t * b);
	elseif (b <= 1.6e+128)
		tmp = Float64(x + a);
	else
		tmp = Float64(y * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -7.5e+89)
		tmp = t * b;
	elseif (b <= 1.6e+128)
		tmp = x + a;
	else
		tmp = y * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -7.5e+89], N[(t * b), $MachinePrecision], If[LessEqual[b, 1.6e+128], N[(x + a), $MachinePrecision], N[(y * b), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -7.49999999999999947e89

   1. Initial program 88.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in b around inf 83.0%

      \[\leadsto \color{blue}{\left(\left(y + t\right) - 2\right) \cdot b} \]

   3. Taylor expanded in t around inf 43.9%

      \[\leadsto \color{blue}{t \cdot b} \]

   if -7.49999999999999947e89 < b < 1.59999999999999993e128

   1. Initial program 97.6%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in b around 0 84.4%

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

   3. Taylor expanded in t around 0 68.0%

      \[\leadsto x - \color{blue}{\left(z \cdot \left(y - 1\right) + -1 \cdot a\right)} \]
   4. Step-by-step derivation

      1. fma-def 68.0%

         \[\leadsto x - \color{blue}{\mathsf{fma}\left(z, y - 1, -1 \cdot a\right)} \]

      2. sub-neg 68.0%

         \[\leadsto x - \mathsf{fma}\left(z, \color{blue}{y + \left(-1\right)}, -1 \cdot a\right) \]

      3. metadata-eval 68.0%

         \[\leadsto x - \mathsf{fma}\left(z, y + \color{blue}{-1}, -1 \cdot a\right) \]

      4. fma-def 68.0%

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

      5. neg-mul-1 68.0%

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

      6. unsub-neg 68.0%

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

      7. distribute-rgt-in 68.0%

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

      8. neg-mul-1 68.0%

         \[\leadsto x - \left(\left(y \cdot z + \color{blue}{\left(-z\right)}\right) - a\right) \]

      9. unsub-neg 68.0%

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

      10. *-commutative 68.0%

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

   5. Simplified 68.0%

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

   6. Taylor expanded in z around 0 31.9%

      \[\leadsto \color{blue}{a + x} \]
   7. Step-by-step derivation

      1. +-commutative 31.9%

         \[\leadsto \color{blue}{x + a} \]

   8. Simplified 31.9%

      \[\leadsto \color{blue}{x + a} \]

   if 1.59999999999999993e128 < b

   1. Initial program 91.4%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in b around inf 94.3%

      \[\leadsto \color{blue}{\left(\left(y + t\right) - 2\right) \cdot b} \]

   3. Taylor expanded in y around inf 61.1%

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

4. Final simplification 38.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -7.5 \cdot 10^{+89}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;b \leq 1.6 \cdot 10^{+128}:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \]

Alternative 23: 21.4% accurate, 4.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.85 \cdot 10^{+86}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{+75}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -1.85e+86) x (if (<= x 2.6e+75) a x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -1.85e+86) {
		tmp = x;
	} else if (x <= 2.6e+75) {
		tmp = a;
	} else {
		tmp = x;
	}
	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 (x <= (-1.85d+86)) then
        tmp = x
    else if (x <= 2.6d+75) then
        tmp = a
    else
        tmp = x
    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 (x <= -1.85e+86) {
		tmp = x;
	} else if (x <= 2.6e+75) {
		tmp = a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -1.85e+86:
		tmp = x
	elif x <= 2.6e+75:
		tmp = a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -1.85e+86)
		tmp = x;
	elseif (x <= 2.6e+75)
		tmp = a;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -1.85e+86)
		tmp = x;
	elseif (x <= 2.6e+75)
		tmp = a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -1.85e+86], x, If[LessEqual[x, 2.6e+75], a, x]]

Derivation

1. Split input into 2 regimes

2. if x < -1.84999999999999996e86 or 2.59999999999999985e75 < x

   1. Initial program 94.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in x around inf 35.5%

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

   if -1.84999999999999996e86 < x < 2.59999999999999985e75

   1. Initial program 95.3%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in a around inf 33.1%

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

      1. sub-neg 33.1%

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

      2. distribute-lft-in 33.1%

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

      3. *-rgt-identity 33.1%

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

      4. distribute-rgt-neg-in 33.1%

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

      5. sub-neg 33.1%

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

      6. *-commutative 33.1%

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

   4. Simplified 33.1%

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

   5. Taylor expanded in t around 0 14.2%

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

4. Final simplification 21.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.85 \cdot 10^{+86}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{+75}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 24: 11.4% accurate, 21.0× speedup

Math

\[\begin{array}{l} \\ a \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 a)

C

double code(double x, double y, double z, double t, double a, double b) {
	return a;
}

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 = a
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return a;
}

Python

def code(x, y, z, t, a, b):
	return a

Julia

function code(x, y, z, t, a, b)
	return a
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = a;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := a

Derivation

1. Initial program 94.9%

   \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

2. Taylor expanded in a around inf 27.9%

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

   1. sub-neg 27.9%

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

   2. distribute-lft-in 27.9%

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

   3. *-rgt-identity 27.9%

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

   4. distribute-rgt-neg-in 27.9%

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

   5. sub-neg 27.9%

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

   6. *-commutative 27.9%

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

4. Simplified 27.9%

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

5. Taylor expanded in t around 0 11.4%

   \[\leadsto \color{blue}{a} \]

6. Final simplification 11.4%

   \[\leadsto a \]

Reproduce

herbie shell --seed 2023192 
(FPCore (x y z t a b)
  :name "Statistics.Distribution.Beta:$centropy from math-functions-0.1.5.2"
  :precision binary64
  (+ (- (- x (* (- y 1.0) z)) (* (- t 1.0) a)) (* (- (+ y t) 2.0) b)))