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

Percentage Accurate: 94.9% → 97.9%

Time: 18.2s

Alternatives: 28

Speedup: 0.5×

• 35.8% 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: 94.9% 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: 97.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(1 - t\right)\\ t_2 := z \cdot \left(1 - y\right)\\ \mathbf{if}\;\left(\left(x + t_2\right) + t_1\right) + b \cdot \left(\left(t + y\right) - 2\right) \leq \infty:\\ \;\;\;\;\left(x + \left(t_1 - b \cdot \left(2 - \left(t + y\right)\right)\right)\right) + t_2\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (- 1.0 t))) (t_2 (* z (- 1.0 y))))
   (if (<= (+ (+ (+ x t_2) t_1) (* b (- (+ t y) 2.0))) INFINITY)
     (+ (+ x (- t_1 (* b (- 2.0 (+ t y))))) t_2)
     (* t (- b a)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double t_2 = z * (1.0 - y);
	double tmp;
	if ((((x + t_2) + t_1) + (b * ((t + y) - 2.0))) <= ((double) INFINITY)) {
		tmp = (x + (t_1 - (b * (2.0 - (t + y))))) + t_2;
	} else {
		tmp = t * (b - a);
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double t_2 = z * (1.0 - y);
	double tmp;
	if ((((x + t_2) + t_1) + (b * ((t + y) - 2.0))) <= Double.POSITIVE_INFINITY) {
		tmp = (x + (t_1 - (b * (2.0 - (t + y))))) + t_2;
	} else {
		tmp = t * (b - a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (1.0 - t)
	t_2 = z * (1.0 - y)
	tmp = 0
	if (((x + t_2) + t_1) + (b * ((t + y) - 2.0))) <= math.inf:
		tmp = (x + (t_1 - (b * (2.0 - (t + y))))) + t_2
	else:
		tmp = t * (b - a)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(1.0 - t))
	t_2 = Float64(z * Float64(1.0 - y))
	tmp = 0.0
	if (Float64(Float64(Float64(x + t_2) + t_1) + Float64(b * Float64(Float64(t + y) - 2.0))) <= Inf)
		tmp = Float64(Float64(x + Float64(t_1 - Float64(b * Float64(2.0 - Float64(t + y))))) + t_2);
	else
		tmp = Float64(t * Float64(b - a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (1.0 - t);
	t_2 = z * (1.0 - y);
	tmp = 0.0;
	if ((((x + t_2) + t_1) + (b * ((t + y) - 2.0))) <= Inf)
		tmp = (x + (t_1 - (b * (2.0 - (t + y))))) + t_2;
	else
		tmp = t * (b - a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(N[(N[(x + t$95$2), $MachinePrecision] + t$95$1), $MachinePrecision] + N[(b * N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], Infinity], N[(N[(x + N[(t$95$1 - N[(b * N[(2.0 - N[(t + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$2), $MachinePrecision], N[(t * N[(b - a), $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%

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

   2. Taylor expanded in a around 0 100.0%

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

   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 t around inf 86.7%

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

4. Final simplification 99.6%

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

Alternative 2: 97.3% 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 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. Step-by-step derivation

   1. +-commutative 97.2%

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

   2. fma-def 98.0%

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

   3. sub-neg 98.0%

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

   4. +-commutative 98.0%

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

   5. associate-+l+ 98.0%

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

   6. metadata-eval 98.0%

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

   7. associate--l- 98.0%

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

   8. fma-def 99.2%

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

   9. sub-neg 99.2%

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

   10. metadata-eval 99.2%

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

   11. sub-neg 99.2%

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

   12. metadata-eval 99.2%

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

3. Simplified 99.2%

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

4. Final simplification 99.2%

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

Alternative 3: 97.9% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(x + Float64(z * Float64(1.0 - y))) + 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(t * Float64(b - a));
	end
	return tmp
end

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(x + N[(z * N[(1.0 - y), $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[(t * N[(b - a), $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 t around inf 86.7%

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

4. Final simplification 99.6%

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

Alternative 4: 57.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(\left(t + y\right) - 2\right)\\ t_2 := x - a \cdot \left(t + -1\right)\\ \mathbf{if}\;b \leq -6.8 \cdot 10^{+91}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -104000:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;b \leq -4.5 \cdot 10^{-8}:\\ \;\;\;\;a - b \cdot \left(2 - y\right)\\ \mathbf{elif}\;b \leq -1.15 \cdot 10^{-169}:\\ \;\;\;\;x - y \cdot z\\ \mathbf{elif}\;b \leq -4.5 \cdot 10^{-238}:\\ \;\;\;\;x + \left(z + a\right)\\ \mathbf{elif}\;b \leq 2.3 \cdot 10^{-200}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 3.4 \cdot 10^{-154}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq 3.4 \cdot 10^{+89}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- (+ t y) 2.0))) (t_2 (- x (* a (+ t -1.0)))))
   (if (<= b -6.8e+91)
     t_1
     (if (<= b -104000.0)
       (* y (- b z))
       (if (<= b -4.5e-8)
         (- a (* b (- 2.0 y)))
         (if (<= b -1.15e-169)
           (- x (* y z))
           (if (<= b -4.5e-238)
             (+ x (+ z a))
             (if (<= b 2.3e-200)
               t_2
               (if (<= b 3.4e-154)
                 (* z (- 1.0 y))
                 (if (<= b 3.4e+89) t_2 t_1))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * ((t + y) - 2.0);
	double t_2 = x - (a * (t + -1.0));
	double tmp;
	if (b <= -6.8e+91) {
		tmp = t_1;
	} else if (b <= -104000.0) {
		tmp = y * (b - z);
	} else if (b <= -4.5e-8) {
		tmp = a - (b * (2.0 - y));
	} else if (b <= -1.15e-169) {
		tmp = x - (y * z);
	} else if (b <= -4.5e-238) {
		tmp = x + (z + a);
	} else if (b <= 2.3e-200) {
		tmp = t_2;
	} else if (b <= 3.4e-154) {
		tmp = z * (1.0 - y);
	} else if (b <= 3.4e+89) {
		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 = b * ((t + y) - 2.0d0)
    t_2 = x - (a * (t + (-1.0d0)))
    if (b <= (-6.8d+91)) then
        tmp = t_1
    else if (b <= (-104000.0d0)) then
        tmp = y * (b - z)
    else if (b <= (-4.5d-8)) then
        tmp = a - (b * (2.0d0 - y))
    else if (b <= (-1.15d-169)) then
        tmp = x - (y * z)
    else if (b <= (-4.5d-238)) then
        tmp = x + (z + a)
    else if (b <= 2.3d-200) then
        tmp = t_2
    else if (b <= 3.4d-154) then
        tmp = z * (1.0d0 - y)
    else if (b <= 3.4d+89) 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 = b * ((t + y) - 2.0);
	double t_2 = x - (a * (t + -1.0));
	double tmp;
	if (b <= -6.8e+91) {
		tmp = t_1;
	} else if (b <= -104000.0) {
		tmp = y * (b - z);
	} else if (b <= -4.5e-8) {
		tmp = a - (b * (2.0 - y));
	} else if (b <= -1.15e-169) {
		tmp = x - (y * z);
	} else if (b <= -4.5e-238) {
		tmp = x + (z + a);
	} else if (b <= 2.3e-200) {
		tmp = t_2;
	} else if (b <= 3.4e-154) {
		tmp = z * (1.0 - y);
	} else if (b <= 3.4e+89) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * ((t + y) - 2.0)
	t_2 = x - (a * (t + -1.0))
	tmp = 0
	if b <= -6.8e+91:
		tmp = t_1
	elif b <= -104000.0:
		tmp = y * (b - z)
	elif b <= -4.5e-8:
		tmp = a - (b * (2.0 - y))
	elif b <= -1.15e-169:
		tmp = x - (y * z)
	elif b <= -4.5e-238:
		tmp = x + (z + a)
	elif b <= 2.3e-200:
		tmp = t_2
	elif b <= 3.4e-154:
		tmp = z * (1.0 - y)
	elif b <= 3.4e+89:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(Float64(t + y) - 2.0))
	t_2 = Float64(x - Float64(a * Float64(t + -1.0)))
	tmp = 0.0
	if (b <= -6.8e+91)
		tmp = t_1;
	elseif (b <= -104000.0)
		tmp = Float64(y * Float64(b - z));
	elseif (b <= -4.5e-8)
		tmp = Float64(a - Float64(b * Float64(2.0 - y)));
	elseif (b <= -1.15e-169)
		tmp = Float64(x - Float64(y * z));
	elseif (b <= -4.5e-238)
		tmp = Float64(x + Float64(z + a));
	elseif (b <= 2.3e-200)
		tmp = t_2;
	elseif (b <= 3.4e-154)
		tmp = Float64(z * Float64(1.0 - y));
	elseif (b <= 3.4e+89)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * ((t + y) - 2.0);
	t_2 = x - (a * (t + -1.0));
	tmp = 0.0;
	if (b <= -6.8e+91)
		tmp = t_1;
	elseif (b <= -104000.0)
		tmp = y * (b - z);
	elseif (b <= -4.5e-8)
		tmp = a - (b * (2.0 - y));
	elseif (b <= -1.15e-169)
		tmp = x - (y * z);
	elseif (b <= -4.5e-238)
		tmp = x + (z + a);
	elseif (b <= 2.3e-200)
		tmp = t_2;
	elseif (b <= 3.4e-154)
		tmp = z * (1.0 - y);
	elseif (b <= 3.4e+89)
		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[(b * N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x - N[(a * N[(t + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -6.8e+91], t$95$1, If[LessEqual[b, -104000.0], N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -4.5e-8], N[(a - N[(b * N[(2.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -1.15e-169], N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -4.5e-238], N[(x + N[(z + a), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.3e-200], t$95$2, If[LessEqual[b, 3.4e-154], N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.4e+89], t$95$2, t$95$1]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if b < -6.8000000000000002e91 or 3.4000000000000002e89 < b

   1. Initial program 93.1%

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

   2. Taylor expanded in b around inf 88.8%

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

   if -6.8000000000000002e91 < b < -104000

   1. Initial program 95.7%

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

   2. Taylor expanded in y around inf 53.7%

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

   if -104000 < b < -4.49999999999999993e-8

   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 z around 0 100.0%

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

      1. sub-neg 100.0%

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

      2. mul-1-neg 100.0%

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

      3. +-commutative 100.0%

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

      4. mul-1-neg 100.0%

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

      5. *-commutative 100.0%

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

      6. sub-neg 100.0%

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

      7. metadata-eval 100.0%

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

      8. distribute-lft-neg-in 100.0%

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

      9. *-commutative 100.0%

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

      10. fma-def 100.0%

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

      11. distribute-neg-in 100.0%

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

      12. metadata-eval 100.0%

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

      13. +-commutative 100.0%

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

      14. sub-neg 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in x around 0 80.2%

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

   6. Taylor expanded in t around 0 81.3%

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

   if -4.49999999999999993e-8 < b < -1.15e-169

   1. Initial program 97.7%

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

   2. Taylor expanded in b around 0 87.1%

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

   3. Taylor expanded in y around inf 61.1%

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

   if -1.15e-169 < b < -4.49999999999999996e-238

   1. Initial program 99.9%

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

   2. Taylor expanded in b around 0 94.5%

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

   3. Taylor expanded in y around 0 75.7%

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

   4. Taylor expanded in t around 0 65.0%

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

      1. sub-neg 65.0%

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

      2. neg-sub0 65.0%

         \[\leadsto x + \color{blue}{\left(0 - \left(-1 \cdot a + -1 \cdot z\right)\right)} \]

      3. +-commutative 65.0%

         \[\leadsto x + \left(0 - \color{blue}{\left(-1 \cdot z + -1 \cdot a\right)}\right) \]

      4. mul-1-neg 65.0%

         \[\leadsto x + \left(0 - \left(-1 \cdot z + \color{blue}{\left(-a\right)}\right)\right) \]

      5. unsub-neg 65.0%

         \[\leadsto x + \left(0 - \color{blue}{\left(-1 \cdot z - a\right)}\right) \]

      6. associate-+l- 65.0%

         \[\leadsto x + \color{blue}{\left(\left(0 - -1 \cdot z\right) + a\right)} \]

      7. neg-sub0 65.0%

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

      8. mul-1-neg 65.0%

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

      9. remove-double-neg 65.0%

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

      10. +-commutative 65.0%

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

   6. Simplified 65.0%

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

   if -4.49999999999999996e-238 < b < 2.30000000000000007e-200 or 3.3999999999999998e-154 < b < 3.4000000000000002e89

   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 88.9%

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

   3. Taylor expanded in a around inf 63.5%

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

   if 2.30000000000000007e-200 < b < 3.3999999999999998e-154

   1. Initial program 99.8%

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

   2. Taylor expanded in z around inf 77.5%

      \[\leadsto \color{blue}{z \cdot \left(1 - y\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 70.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -6.8 \cdot 10^{+91}:\\ \;\;\;\;b \cdot \left(\left(t + y\right) - 2\right)\\ \mathbf{elif}\;b \leq -104000:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;b \leq -4.5 \cdot 10^{-8}:\\ \;\;\;\;a - b \cdot \left(2 - y\right)\\ \mathbf{elif}\;b \leq -1.15 \cdot 10^{-169}:\\ \;\;\;\;x - y \cdot z\\ \mathbf{elif}\;b \leq -4.5 \cdot 10^{-238}:\\ \;\;\;\;x + \left(z + a\right)\\ \mathbf{elif}\;b \leq 2.3 \cdot 10^{-200}:\\ \;\;\;\;x - a \cdot \left(t + -1\right)\\ \mathbf{elif}\;b \leq 3.4 \cdot 10^{-154}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq 3.4 \cdot 10^{+89}:\\ \;\;\;\;x - a \cdot \left(t + -1\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(t + y\right) - 2\right)\\ \end{array} \]

Alternative 5: 55.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(z + a\right)\\ t_2 := b \cdot \left(\left(t + y\right) - 2\right)\\ \mathbf{if}\;b \leq -2.8 \cdot 10^{+93}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -4600000:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;b \leq -4.5 \cdot 10^{-7}:\\ \;\;\;\;a - b \cdot \left(2 - y\right)\\ \mathbf{elif}\;b \leq -1.8 \cdot 10^{-169}:\\ \;\;\;\;x - y \cdot z\\ \mathbf{elif}\;b \leq -1 \cdot 10^{-264}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 9 \cdot 10^{-219}:\\ \;\;\;\;x - t \cdot a\\ \mathbf{elif}\;b \leq 8.8 \cdot 10^{+52}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (+ z a))) (t_2 (* b (- (+ t y) 2.0))))
   (if (<= b -2.8e+93)
     t_2
     (if (<= b -4600000.0)
       (* y (- b z))
       (if (<= b -4.5e-7)
         (- a (* b (- 2.0 y)))
         (if (<= b -1.8e-169)
           (- x (* y z))
           (if (<= b -1e-264)
             t_1
             (if (<= b 9e-219)
               (- x (* t a))
               (if (<= b 8.8e+52) t_1 t_2)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (z + a);
	double t_2 = b * ((t + y) - 2.0);
	double tmp;
	if (b <= -2.8e+93) {
		tmp = t_2;
	} else if (b <= -4600000.0) {
		tmp = y * (b - z);
	} else if (b <= -4.5e-7) {
		tmp = a - (b * (2.0 - y));
	} else if (b <= -1.8e-169) {
		tmp = x - (y * z);
	} else if (b <= -1e-264) {
		tmp = t_1;
	} else if (b <= 9e-219) {
		tmp = x - (t * a);
	} else if (b <= 8.8e+52) {
		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 + (z + a)
    t_2 = b * ((t + y) - 2.0d0)
    if (b <= (-2.8d+93)) then
        tmp = t_2
    else if (b <= (-4600000.0d0)) then
        tmp = y * (b - z)
    else if (b <= (-4.5d-7)) then
        tmp = a - (b * (2.0d0 - y))
    else if (b <= (-1.8d-169)) then
        tmp = x - (y * z)
    else if (b <= (-1d-264)) then
        tmp = t_1
    else if (b <= 9d-219) then
        tmp = x - (t * a)
    else if (b <= 8.8d+52) 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 + a);
	double t_2 = b * ((t + y) - 2.0);
	double tmp;
	if (b <= -2.8e+93) {
		tmp = t_2;
	} else if (b <= -4600000.0) {
		tmp = y * (b - z);
	} else if (b <= -4.5e-7) {
		tmp = a - (b * (2.0 - y));
	} else if (b <= -1.8e-169) {
		tmp = x - (y * z);
	} else if (b <= -1e-264) {
		tmp = t_1;
	} else if (b <= 9e-219) {
		tmp = x - (t * a);
	} else if (b <= 8.8e+52) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (z + a)
	t_2 = b * ((t + y) - 2.0)
	tmp = 0
	if b <= -2.8e+93:
		tmp = t_2
	elif b <= -4600000.0:
		tmp = y * (b - z)
	elif b <= -4.5e-7:
		tmp = a - (b * (2.0 - y))
	elif b <= -1.8e-169:
		tmp = x - (y * z)
	elif b <= -1e-264:
		tmp = t_1
	elif b <= 9e-219:
		tmp = x - (t * a)
	elif b <= 8.8e+52:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(z + a))
	t_2 = Float64(b * Float64(Float64(t + y) - 2.0))
	tmp = 0.0
	if (b <= -2.8e+93)
		tmp = t_2;
	elseif (b <= -4600000.0)
		tmp = Float64(y * Float64(b - z));
	elseif (b <= -4.5e-7)
		tmp = Float64(a - Float64(b * Float64(2.0 - y)));
	elseif (b <= -1.8e-169)
		tmp = Float64(x - Float64(y * z));
	elseif (b <= -1e-264)
		tmp = t_1;
	elseif (b <= 9e-219)
		tmp = Float64(x - Float64(t * a));
	elseif (b <= 8.8e+52)
		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 + a);
	t_2 = b * ((t + y) - 2.0);
	tmp = 0.0;
	if (b <= -2.8e+93)
		tmp = t_2;
	elseif (b <= -4600000.0)
		tmp = y * (b - z);
	elseif (b <= -4.5e-7)
		tmp = a - (b * (2.0 - y));
	elseif (b <= -1.8e-169)
		tmp = x - (y * z);
	elseif (b <= -1e-264)
		tmp = t_1;
	elseif (b <= 9e-219)
		tmp = x - (t * a);
	elseif (b <= 8.8e+52)
		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 + a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2.8e+93], t$95$2, If[LessEqual[b, -4600000.0], N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -4.5e-7], N[(a - N[(b * N[(2.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -1.8e-169], N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -1e-264], t$95$1, If[LessEqual[b, 9e-219], N[(x - N[(t * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 8.8e+52], t$95$1, t$95$2]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if b < -2.79999999999999989e93 or 8.7999999999999999e52 < b

   1. Initial program 93.5%

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

   2. Taylor expanded in b around inf 85.7%

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

   if -2.79999999999999989e93 < b < -4.6e6

   1. Initial program 95.7%

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

   2. Taylor expanded in y around inf 53.7%

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

   if -4.6e6 < b < -4.4999999999999998e-7

   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 z around 0 100.0%

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

      1. sub-neg 100.0%

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

      2. mul-1-neg 100.0%

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

      3. +-commutative 100.0%

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

      4. mul-1-neg 100.0%

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

      5. *-commutative 100.0%

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

      6. sub-neg 100.0%

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

      7. metadata-eval 100.0%

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

      8. distribute-lft-neg-in 100.0%

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

      9. *-commutative 100.0%

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

      10. fma-def 100.0%

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

      11. distribute-neg-in 100.0%

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

      12. metadata-eval 100.0%

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

      13. +-commutative 100.0%

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

      14. sub-neg 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in x around 0 80.2%

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

   6. Taylor expanded in t around 0 81.3%

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

   if -4.4999999999999998e-7 < b < -1.80000000000000001e-169

   1. Initial program 97.7%

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

   2. Taylor expanded in b around 0 87.1%

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

   3. Taylor expanded in y around inf 61.1%

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

   if -1.80000000000000001e-169 < b < -1e-264 or 9.00000000000000029e-219 < b < 8.7999999999999999e52

   1. Initial program 99.9%

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

   2. Taylor expanded in b around 0 89.1%

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

   3. Taylor expanded in y around 0 67.6%

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

   4. Taylor expanded in t around 0 54.2%

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

      1. sub-neg 54.2%

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

      2. neg-sub0 54.2%

         \[\leadsto x + \color{blue}{\left(0 - \left(-1 \cdot a + -1 \cdot z\right)\right)} \]

      3. +-commutative 54.2%

         \[\leadsto x + \left(0 - \color{blue}{\left(-1 \cdot z + -1 \cdot a\right)}\right) \]

      4. mul-1-neg 54.2%

         \[\leadsto x + \left(0 - \left(-1 \cdot z + \color{blue}{\left(-a\right)}\right)\right) \]

      5. unsub-neg 54.2%

         \[\leadsto x + \left(0 - \color{blue}{\left(-1 \cdot z - a\right)}\right) \]

      6. associate-+l- 54.2%

         \[\leadsto x + \color{blue}{\left(\left(0 - -1 \cdot z\right) + a\right)} \]

      7. neg-sub0 54.2%

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

      8. mul-1-neg 54.2%

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

      9. remove-double-neg 54.2%

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

      10. +-commutative 54.2%

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

   6. Simplified 54.2%

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

   if -1e-264 < b < 9.00000000000000029e-219

   1. Initial program 99.9%

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

   2. Taylor expanded in b around 0 99.9%

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

   3. Taylor expanded in t around inf 73.6%

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

4. Final simplification 67.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.8 \cdot 10^{+93}:\\ \;\;\;\;b \cdot \left(\left(t + y\right) - 2\right)\\ \mathbf{elif}\;b \leq -4600000:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;b \leq -4.5 \cdot 10^{-7}:\\ \;\;\;\;a - b \cdot \left(2 - y\right)\\ \mathbf{elif}\;b \leq -1.8 \cdot 10^{-169}:\\ \;\;\;\;x - y \cdot z\\ \mathbf{elif}\;b \leq -1 \cdot 10^{-264}:\\ \;\;\;\;x + \left(z + a\right)\\ \mathbf{elif}\;b \leq 9 \cdot 10^{-219}:\\ \;\;\;\;x - t \cdot a\\ \mathbf{elif}\;b \leq 8.8 \cdot 10^{+52}:\\ \;\;\;\;x + \left(z + a\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(t + y\right) - 2\right)\\ \end{array} \]

Alternative 6: 39.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(y - 2\right)\\ \mathbf{if}\;b \leq -5.2 \cdot 10^{+44}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -4.2 \cdot 10^{-247}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;b \leq 1.9 \cdot 10^{-218}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 1.4 \cdot 10^{-119}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;b \leq 1.02 \cdot 10^{+53}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;b \leq 2.8 \cdot 10^{+114}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;b \leq 1.35 \cdot 10^{+181}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t - 2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- y 2.0))))
   (if (<= b -5.2e+44)
     t_1
     (if (<= b -4.2e-247)
       (+ x z)
       (if (<= b 1.9e-218)
         (* a (- 1.0 t))
         (if (<= b 1.4e-119)
           (+ x z)
           (if (<= b 1.02e+53)
             (+ x a)
             (if (<= b 2.8e+114)
               (* t (- b a))
               (if (<= b 1.35e+181) t_1 (* b (- t 2.0)))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (y - 2.0);
	double tmp;
	if (b <= -5.2e+44) {
		tmp = t_1;
	} else if (b <= -4.2e-247) {
		tmp = x + z;
	} else if (b <= 1.9e-218) {
		tmp = a * (1.0 - t);
	} else if (b <= 1.4e-119) {
		tmp = x + z;
	} else if (b <= 1.02e+53) {
		tmp = x + a;
	} else if (b <= 2.8e+114) {
		tmp = t * (b - a);
	} else if (b <= 1.35e+181) {
		tmp = t_1;
	} else {
		tmp = b * (t - 2.0);
	}
	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) :: t_1
    real(8) :: tmp
    t_1 = b * (y - 2.0d0)
    if (b <= (-5.2d+44)) then
        tmp = t_1
    else if (b <= (-4.2d-247)) then
        tmp = x + z
    else if (b <= 1.9d-218) then
        tmp = a * (1.0d0 - t)
    else if (b <= 1.4d-119) then
        tmp = x + z
    else if (b <= 1.02d+53) then
        tmp = x + a
    else if (b <= 2.8d+114) then
        tmp = t * (b - a)
    else if (b <= 1.35d+181) then
        tmp = t_1
    else
        tmp = b * (t - 2.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (y - 2.0);
	double tmp;
	if (b <= -5.2e+44) {
		tmp = t_1;
	} else if (b <= -4.2e-247) {
		tmp = x + z;
	} else if (b <= 1.9e-218) {
		tmp = a * (1.0 - t);
	} else if (b <= 1.4e-119) {
		tmp = x + z;
	} else if (b <= 1.02e+53) {
		tmp = x + a;
	} else if (b <= 2.8e+114) {
		tmp = t * (b - a);
	} else if (b <= 1.35e+181) {
		tmp = t_1;
	} else {
		tmp = b * (t - 2.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * (y - 2.0)
	tmp = 0
	if b <= -5.2e+44:
		tmp = t_1
	elif b <= -4.2e-247:
		tmp = x + z
	elif b <= 1.9e-218:
		tmp = a * (1.0 - t)
	elif b <= 1.4e-119:
		tmp = x + z
	elif b <= 1.02e+53:
		tmp = x + a
	elif b <= 2.8e+114:
		tmp = t * (b - a)
	elif b <= 1.35e+181:
		tmp = t_1
	else:
		tmp = b * (t - 2.0)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(y - 2.0))
	tmp = 0.0
	if (b <= -5.2e+44)
		tmp = t_1;
	elseif (b <= -4.2e-247)
		tmp = Float64(x + z);
	elseif (b <= 1.9e-218)
		tmp = Float64(a * Float64(1.0 - t));
	elseif (b <= 1.4e-119)
		tmp = Float64(x + z);
	elseif (b <= 1.02e+53)
		tmp = Float64(x + a);
	elseif (b <= 2.8e+114)
		tmp = Float64(t * Float64(b - a));
	elseif (b <= 1.35e+181)
		tmp = t_1;
	else
		tmp = Float64(b * Float64(t - 2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * (y - 2.0);
	tmp = 0.0;
	if (b <= -5.2e+44)
		tmp = t_1;
	elseif (b <= -4.2e-247)
		tmp = x + z;
	elseif (b <= 1.9e-218)
		tmp = a * (1.0 - t);
	elseif (b <= 1.4e-119)
		tmp = x + z;
	elseif (b <= 1.02e+53)
		tmp = x + a;
	elseif (b <= 2.8e+114)
		tmp = t * (b - a);
	elseif (b <= 1.35e+181)
		tmp = t_1;
	else
		tmp = b * (t - 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(y - 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -5.2e+44], t$95$1, If[LessEqual[b, -4.2e-247], N[(x + z), $MachinePrecision], If[LessEqual[b, 1.9e-218], N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.4e-119], N[(x + z), $MachinePrecision], If[LessEqual[b, 1.02e+53], N[(x + a), $MachinePrecision], If[LessEqual[b, 2.8e+114], N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.35e+181], t$95$1, N[(b * N[(t - 2.0), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if b < -5.1999999999999998e44 or 2.8e114 < b < 1.35000000000000004e181

   1. Initial program 93.2%

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

   2. Taylor expanded in b around inf 77.8%

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

   3. Taylor expanded in t around 0 60.9%

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

   if -5.1999999999999998e44 < b < -4.20000000000000027e-247 or 1.8999999999999999e-218 < b < 1.4e-119

   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 89.7%

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

   3. Taylor expanded in y around 0 64.9%

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

   4. Taylor expanded in a around 0 41.9%

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

      1. sub-neg 41.9%

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

      2. mul-1-neg 41.9%

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

      3. remove-double-neg 41.9%

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

   6. Simplified 41.9%

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

   if -4.20000000000000027e-247 < b < 1.8999999999999999e-218

   1. Initial program 99.9%

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

   2. Taylor expanded in a around inf 60.5%

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

   if 1.4e-119 < b < 1.01999999999999999e53

   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 78.5%

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

   3. Taylor expanded in t around 0 67.1%

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

      1. +-commutative 67.1%

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

      2. sub-neg 67.1%

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

      3. metadata-eval 67.1%

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

      4. mul-1-neg 67.1%

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

      5. unsub-neg 67.1%

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

   5. Simplified 67.1%

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

   6. Taylor expanded in z around 0 39.4%

      \[\leadsto x - \color{blue}{-1 \cdot a} \]
   7. Step-by-step derivation

      1. mul-1-neg 39.4%

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

   8. Simplified 39.4%

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

   if 1.01999999999999999e53 < b < 2.8e114

   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 t around inf 71.5%

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

   if 1.35000000000000004e181 < b

   1. Initial program 90.9%

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

   2. Taylor expanded in b around inf 95.5%

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

   3. Taylor expanded in y around 0 69.8%

      \[\leadsto \color{blue}{b \cdot \left(t - 2\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 51.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5.2 \cdot 10^{+44}:\\ \;\;\;\;b \cdot \left(y - 2\right)\\ \mathbf{elif}\;b \leq -4.2 \cdot 10^{-247}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;b \leq 1.9 \cdot 10^{-218}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 1.4 \cdot 10^{-119}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;b \leq 1.02 \cdot 10^{+53}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;b \leq 2.8 \cdot 10^{+114}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;b \leq 1.35 \cdot 10^{+181}:\\ \;\;\;\;b \cdot \left(y - 2\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t - 2\right)\\ \end{array} \]

Alternative 7: 64.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + z \cdot \left(1 - y\right)\\ t_2 := b \cdot \left(\left(t + y\right) - 2\right)\\ t_3 := x - a \cdot \left(t + -1\right)\\ \mathbf{if}\;b \leq -3.2 \cdot 10^{+79}:\\ \;\;\;\;a + t_2\\ \mathbf{elif}\;b \leq -3.7 \cdot 10^{-275}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 7.4 \cdot 10^{-218}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq 2.4 \cdot 10^{-43}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 2.55 \cdot 10^{+22}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;x + t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* z (- 1.0 y))))
        (t_2 (* b (- (+ t y) 2.0)))
        (t_3 (- x (* a (+ t -1.0)))))
   (if (<= b -3.2e+79)
     (+ a t_2)
     (if (<= b -3.7e-275)
       t_1
       (if (<= b 7.4e-218)
         t_3
         (if (<= b 2.4e-43) t_1 (if (<= b 2.55e+22) t_3 (+ x t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (z * (1.0 - y));
	double t_2 = b * ((t + y) - 2.0);
	double t_3 = x - (a * (t + -1.0));
	double tmp;
	if (b <= -3.2e+79) {
		tmp = a + t_2;
	} else if (b <= -3.7e-275) {
		tmp = t_1;
	} else if (b <= 7.4e-218) {
		tmp = t_3;
	} else if (b <= 2.4e-43) {
		tmp = t_1;
	} else if (b <= 2.55e+22) {
		tmp = t_3;
	} else {
		tmp = x + 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 * (1.0d0 - y))
    t_2 = b * ((t + y) - 2.0d0)
    t_3 = x - (a * (t + (-1.0d0)))
    if (b <= (-3.2d+79)) then
        tmp = a + t_2
    else if (b <= (-3.7d-275)) then
        tmp = t_1
    else if (b <= 7.4d-218) then
        tmp = t_3
    else if (b <= 2.4d-43) then
        tmp = t_1
    else if (b <= 2.55d+22) then
        tmp = t_3
    else
        tmp = x + 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 * (1.0 - y));
	double t_2 = b * ((t + y) - 2.0);
	double t_3 = x - (a * (t + -1.0));
	double tmp;
	if (b <= -3.2e+79) {
		tmp = a + t_2;
	} else if (b <= -3.7e-275) {
		tmp = t_1;
	} else if (b <= 7.4e-218) {
		tmp = t_3;
	} else if (b <= 2.4e-43) {
		tmp = t_1;
	} else if (b <= 2.55e+22) {
		tmp = t_3;
	} else {
		tmp = x + t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (z * (1.0 - y))
	t_2 = b * ((t + y) - 2.0)
	t_3 = x - (a * (t + -1.0))
	tmp = 0
	if b <= -3.2e+79:
		tmp = a + t_2
	elif b <= -3.7e-275:
		tmp = t_1
	elif b <= 7.4e-218:
		tmp = t_3
	elif b <= 2.4e-43:
		tmp = t_1
	elif b <= 2.55e+22:
		tmp = t_3
	else:
		tmp = x + t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(z * Float64(1.0 - y)))
	t_2 = Float64(b * Float64(Float64(t + y) - 2.0))
	t_3 = Float64(x - Float64(a * Float64(t + -1.0)))
	tmp = 0.0
	if (b <= -3.2e+79)
		tmp = Float64(a + t_2);
	elseif (b <= -3.7e-275)
		tmp = t_1;
	elseif (b <= 7.4e-218)
		tmp = t_3;
	elseif (b <= 2.4e-43)
		tmp = t_1;
	elseif (b <= 2.55e+22)
		tmp = t_3;
	else
		tmp = Float64(x + t_2);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (z * (1.0 - y));
	t_2 = b * ((t + y) - 2.0);
	t_3 = x - (a * (t + -1.0));
	tmp = 0.0;
	if (b <= -3.2e+79)
		tmp = a + t_2;
	elseif (b <= -3.7e-275)
		tmp = t_1;
	elseif (b <= 7.4e-218)
		tmp = t_3;
	elseif (b <= 2.4e-43)
		tmp = t_1;
	elseif (b <= 2.55e+22)
		tmp = t_3;
	else
		tmp = x + t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(z * N[(1.0 - y), $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 + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -3.2e+79], N[(a + t$95$2), $MachinePrecision], If[LessEqual[b, -3.7e-275], t$95$1, If[LessEqual[b, 7.4e-218], t$95$3, If[LessEqual[b, 2.4e-43], t$95$1, If[LessEqual[b, 2.55e+22], t$95$3, N[(x + t$95$2), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -3.20000000000000003e79

   1. Initial program 92.9%

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

   2. Taylor expanded in z around 0 92.9%

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

      1. sub-neg 92.9%

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

      2. mul-1-neg 92.9%

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

      3. +-commutative 92.9%

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

      4. mul-1-neg 92.9%

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

      5. *-commutative 92.9%

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

      6. sub-neg 92.9%

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

      7. metadata-eval 92.9%

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

      8. distribute-lft-neg-in 92.9%

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

      9. *-commutative 92.9%

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

      10. fma-def 92.9%

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

      11. distribute-neg-in 92.9%

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

      12. metadata-eval 92.9%

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

      13. +-commutative 92.9%

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

      14. sub-neg 92.9%

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

   4. Simplified 92.9%

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

   5. Taylor expanded in x around 0 86.1%

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

   6. Taylor expanded in t around 0 83.8%

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

   if -3.20000000000000003e79 < b < -3.69999999999999971e-275 or 7.4000000000000005e-218 < b < 2.4000000000000002e-43

   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 88.0%

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

   3. Taylor expanded in a around 0 65.6%

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

   if -3.69999999999999971e-275 < b < 7.4000000000000005e-218 or 2.4000000000000002e-43 < b < 2.5500000000000001e22

   1. Initial program 99.9%

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

   2. Taylor expanded in b around 0 94.5%

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

   3. Taylor expanded in a around inf 80.6%

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

   if 2.5500000000000001e22 < b

   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 z around 0 90.1%

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

      1. sub-neg 90.1%

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

      2. mul-1-neg 90.1%

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

      3. +-commutative 90.1%

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

      4. mul-1-neg 90.1%

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

      5. *-commutative 90.1%

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

      6. sub-neg 90.1%

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

      7. metadata-eval 90.1%

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

      8. distribute-lft-neg-in 90.1%

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

      9. *-commutative 90.1%

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

      10. fma-def 90.1%

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

      11. distribute-neg-in 90.1%

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

      12. metadata-eval 90.1%

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

      13. +-commutative 90.1%

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

      14. sub-neg 90.1%

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

   4. Simplified 90.1%

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

   5. Taylor expanded in a around 0 86.3%

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

4. Final simplification 74.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.2 \cdot 10^{+79}:\\ \;\;\;\;a + b \cdot \left(\left(t + y\right) - 2\right)\\ \mathbf{elif}\;b \leq -3.7 \cdot 10^{-275}:\\ \;\;\;\;x + z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq 7.4 \cdot 10^{-218}:\\ \;\;\;\;x - a \cdot \left(t + -1\right)\\ \mathbf{elif}\;b \leq 2.4 \cdot 10^{-43}:\\ \;\;\;\;x + z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq 2.55 \cdot 10^{+22}:\\ \;\;\;\;x - a \cdot \left(t + -1\right)\\ \mathbf{else}:\\ \;\;\;\;x + b \cdot \left(\left(t + y\right) - 2\right)\\ \end{array} \]

Alternative 8: 85.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -5.6 \cdot 10^{+79} \lor \neg \left(b \leq 2.55 \cdot 10^{-67}\right):\\ \;\;\;\;\left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) + a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x - a \cdot \left(t + -1\right)\right) + z \cdot \left(1 - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -5.6e+79) (not (<= b 2.55e-67)))
   (+ (+ x (* b (- (+ t y) 2.0))) (* a (- 1.0 t)))
   (+ (- x (* a (+ t -1.0))) (* z (- 1.0 y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -5.6e+79) || !(b <= 2.55e-67)) {
		tmp = (x + (b * ((t + y) - 2.0))) + (a * (1.0 - t));
	} else {
		tmp = (x - (a * (t + -1.0))) + (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 ((b <= (-5.6d+79)) .or. (.not. (b <= 2.55d-67))) then
        tmp = (x + (b * ((t + y) - 2.0d0))) + (a * (1.0d0 - t))
    else
        tmp = (x - (a * (t + (-1.0d0)))) + (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 ((b <= -5.6e+79) || !(b <= 2.55e-67)) {
		tmp = (x + (b * ((t + y) - 2.0))) + (a * (1.0 - t));
	} else {
		tmp = (x - (a * (t + -1.0))) + (z * (1.0 - y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -5.6e+79) or not (b <= 2.55e-67):
		tmp = (x + (b * ((t + y) - 2.0))) + (a * (1.0 - t))
	else:
		tmp = (x - (a * (t + -1.0))) + (z * (1.0 - y))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -5.6e+79) || !(b <= 2.55e-67))
		tmp = Float64(Float64(x + Float64(b * Float64(Float64(t + y) - 2.0))) + Float64(a * Float64(1.0 - t)));
	else
		tmp = Float64(Float64(x - Float64(a * Float64(t + -1.0))) + 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 ((b <= -5.6e+79) || ~((b <= 2.55e-67)))
		tmp = (x + (b * ((t + y) - 2.0))) + (a * (1.0 - t));
	else
		tmp = (x - (a * (t + -1.0))) + (z * (1.0 - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -5.6e+79], N[Not[LessEqual[b, 2.55e-67]], $MachinePrecision]], N[(N[(x + N[(b * N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x - N[(a * N[(t + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -5.6000000000000002e79 or 2.54999999999999991e-67 < b

   1. Initial program 94.5%

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

   2. Taylor expanded in z around 0 89.6%

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

   if -5.6000000000000002e79 < b < 2.54999999999999991e-67

   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 a around 0 99.3%

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

   3. Taylor expanded in b around 0 91.4%

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

4. Final simplification 90.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5.6 \cdot 10^{+79} \lor \neg \left(b \leq 2.55 \cdot 10^{-67}\right):\\ \;\;\;\;\left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) + a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x - a \cdot \left(t + -1\right)\right) + z \cdot \left(1 - y\right)\\ \end{array} \]

Alternative 9: 37.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t - 2\right)\\ \mathbf{if}\;b \leq -1.75 \cdot 10^{+251}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -1.08 \cdot 10^{+46}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;b \leq -5.2 \cdot 10^{-244}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;b \leq 8.3 \cdot 10^{-218}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 1.55 \cdot 10^{-119}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;b \leq 2.8 \cdot 10^{+54}:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- t 2.0))))
   (if (<= b -1.75e+251)
     t_1
     (if (<= b -1.08e+46)
       (* y b)
       (if (<= b -5.2e-244)
         (+ x z)
         (if (<= b 8.3e-218)
           (* a (- 1.0 t))
           (if (<= b 1.55e-119) (+ x z) (if (<= b 2.8e+54) (+ x a) t_1))))))))

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 <= -1.75e+251) {
		tmp = t_1;
	} else if (b <= -1.08e+46) {
		tmp = y * b;
	} else if (b <= -5.2e-244) {
		tmp = x + z;
	} else if (b <= 8.3e-218) {
		tmp = a * (1.0 - t);
	} else if (b <= 1.55e-119) {
		tmp = x + z;
	} else if (b <= 2.8e+54) {
		tmp = x + a;
	} 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) :: tmp
    t_1 = b * (t - 2.0d0)
    if (b <= (-1.75d+251)) then
        tmp = t_1
    else if (b <= (-1.08d+46)) then
        tmp = y * b
    else if (b <= (-5.2d-244)) then
        tmp = x + z
    else if (b <= 8.3d-218) then
        tmp = a * (1.0d0 - t)
    else if (b <= 1.55d-119) then
        tmp = x + z
    else if (b <= 2.8d+54) then
        tmp = x + a
    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 = b * (t - 2.0);
	double tmp;
	if (b <= -1.75e+251) {
		tmp = t_1;
	} else if (b <= -1.08e+46) {
		tmp = y * b;
	} else if (b <= -5.2e-244) {
		tmp = x + z;
	} else if (b <= 8.3e-218) {
		tmp = a * (1.0 - t);
	} else if (b <= 1.55e-119) {
		tmp = x + z;
	} else if (b <= 2.8e+54) {
		tmp = x + a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * (t - 2.0)
	tmp = 0
	if b <= -1.75e+251:
		tmp = t_1
	elif b <= -1.08e+46:
		tmp = y * b
	elif b <= -5.2e-244:
		tmp = x + z
	elif b <= 8.3e-218:
		tmp = a * (1.0 - t)
	elif b <= 1.55e-119:
		tmp = x + z
	elif b <= 2.8e+54:
		tmp = x + a
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(t - 2.0))
	tmp = 0.0
	if (b <= -1.75e+251)
		tmp = t_1;
	elseif (b <= -1.08e+46)
		tmp = Float64(y * b);
	elseif (b <= -5.2e-244)
		tmp = Float64(x + z);
	elseif (b <= 8.3e-218)
		tmp = Float64(a * Float64(1.0 - t));
	elseif (b <= 1.55e-119)
		tmp = Float64(x + z);
	elseif (b <= 2.8e+54)
		tmp = Float64(x + a);
	else
		tmp = t_1;
	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 <= -1.75e+251)
		tmp = t_1;
	elseif (b <= -1.08e+46)
		tmp = y * b;
	elseif (b <= -5.2e-244)
		tmp = x + z;
	elseif (b <= 8.3e-218)
		tmp = a * (1.0 - t);
	elseif (b <= 1.55e-119)
		tmp = x + z;
	elseif (b <= 2.8e+54)
		tmp = x + a;
	else
		tmp = t_1;
	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, -1.75e+251], t$95$1, If[LessEqual[b, -1.08e+46], N[(y * b), $MachinePrecision], If[LessEqual[b, -5.2e-244], N[(x + z), $MachinePrecision], If[LessEqual[b, 8.3e-218], N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.55e-119], N[(x + z), $MachinePrecision], If[LessEqual[b, 2.8e+54], N[(x + a), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -1.75000000000000002e251 or 2.80000000000000015e54 < b

   1. Initial program 94.1%

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

   2. Taylor expanded in b around inf 88.7%

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

   3. Taylor expanded in y around 0 64.4%

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

   if -1.75000000000000002e251 < b < -1.07999999999999994e46

   1. Initial program 91.9%

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

   2. Taylor expanded in z around 0 86.5%

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

      1. sub-neg 86.5%

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

      2. mul-1-neg 86.5%

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

      3. +-commutative 86.5%

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

      4. mul-1-neg 86.5%

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

      5. *-commutative 86.5%

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

      6. sub-neg 86.5%

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

      7. metadata-eval 86.5%

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

      8. distribute-lft-neg-in 86.5%

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

      9. *-commutative 86.5%

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

      10. fma-def 86.5%

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

      11. distribute-neg-in 86.5%

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

      12. metadata-eval 86.5%

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

      13. +-commutative 86.5%

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

      14. sub-neg 86.5%

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

   4. Simplified 86.5%

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

   5. Taylor expanded in y around inf 47.1%

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

   if -1.07999999999999994e46 < b < -5.2000000000000003e-244 or 8.3000000000000001e-218 < b < 1.54999999999999989e-119

   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 89.7%

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

   3. Taylor expanded in y around 0 64.9%

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

   4. Taylor expanded in a around 0 41.9%

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

      1. sub-neg 41.9%

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

      2. mul-1-neg 41.9%

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

      3. remove-double-neg 41.9%

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

   6. Simplified 41.9%

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

   if -5.2000000000000003e-244 < b < 8.3000000000000001e-218

   1. Initial program 99.9%

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

   2. Taylor expanded in a around inf 60.5%

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

   if 1.54999999999999989e-119 < b < 2.80000000000000015e54

   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 78.5%

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

   3. Taylor expanded in t around 0 67.1%

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

      1. +-commutative 67.1%

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

      2. sub-neg 67.1%

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

      3. metadata-eval 67.1%

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

      4. mul-1-neg 67.1%

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

      5. unsub-neg 67.1%

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

   5. Simplified 67.1%

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

   6. Taylor expanded in z around 0 39.4%

      \[\leadsto x - \color{blue}{-1 \cdot a} \]
   7. Step-by-step derivation

      1. mul-1-neg 39.4%

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

   8. Simplified 39.4%

      \[\leadsto x - \color{blue}{\left(-a\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 49.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.75 \cdot 10^{+251}:\\ \;\;\;\;b \cdot \left(t - 2\right)\\ \mathbf{elif}\;b \leq -1.08 \cdot 10^{+46}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;b \leq -5.2 \cdot 10^{-244}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;b \leq 8.3 \cdot 10^{-218}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 1.55 \cdot 10^{-119}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;b \leq 2.8 \cdot 10^{+54}:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t - 2\right)\\ \end{array} \]

Alternative 10: 61.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + z \cdot \left(1 - y\right)\\ t_2 := b \cdot \left(\left(t + y\right) - 2\right)\\ t_3 := x - a \cdot \left(t + -1\right)\\ \mathbf{if}\;b \leq -4 \cdot 10^{+80}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -2.2 \cdot 10^{-270}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 4.6 \cdot 10^{-218}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq 6.4 \cdot 10^{-46}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 3.1 \cdot 10^{+82}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* z (- 1.0 y))))
        (t_2 (* b (- (+ t y) 2.0)))
        (t_3 (- x (* a (+ t -1.0)))))
   (if (<= b -4e+80)
     t_2
     (if (<= b -2.2e-270)
       t_1
       (if (<= b 4.6e-218)
         t_3
         (if (<= b 6.4e-46) t_1 (if (<= b 3.1e+82) t_3 t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (z * (1.0 - y));
	double t_2 = b * ((t + y) - 2.0);
	double t_3 = x - (a * (t + -1.0));
	double tmp;
	if (b <= -4e+80) {
		tmp = t_2;
	} else if (b <= -2.2e-270) {
		tmp = t_1;
	} else if (b <= 4.6e-218) {
		tmp = t_3;
	} else if (b <= 6.4e-46) {
		tmp = t_1;
	} else if (b <= 3.1e+82) {
		tmp = t_3;
	} 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 * (1.0d0 - y))
    t_2 = b * ((t + y) - 2.0d0)
    t_3 = x - (a * (t + (-1.0d0)))
    if (b <= (-4d+80)) then
        tmp = t_2
    else if (b <= (-2.2d-270)) then
        tmp = t_1
    else if (b <= 4.6d-218) then
        tmp = t_3
    else if (b <= 6.4d-46) then
        tmp = t_1
    else if (b <= 3.1d+82) then
        tmp = t_3
    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 * (1.0 - y));
	double t_2 = b * ((t + y) - 2.0);
	double t_3 = x - (a * (t + -1.0));
	double tmp;
	if (b <= -4e+80) {
		tmp = t_2;
	} else if (b <= -2.2e-270) {
		tmp = t_1;
	} else if (b <= 4.6e-218) {
		tmp = t_3;
	} else if (b <= 6.4e-46) {
		tmp = t_1;
	} else if (b <= 3.1e+82) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (z * (1.0 - y))
	t_2 = b * ((t + y) - 2.0)
	t_3 = x - (a * (t + -1.0))
	tmp = 0
	if b <= -4e+80:
		tmp = t_2
	elif b <= -2.2e-270:
		tmp = t_1
	elif b <= 4.6e-218:
		tmp = t_3
	elif b <= 6.4e-46:
		tmp = t_1
	elif b <= 3.1e+82:
		tmp = t_3
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(z * Float64(1.0 - y)))
	t_2 = Float64(b * Float64(Float64(t + y) - 2.0))
	t_3 = Float64(x - Float64(a * Float64(t + -1.0)))
	tmp = 0.0
	if (b <= -4e+80)
		tmp = t_2;
	elseif (b <= -2.2e-270)
		tmp = t_1;
	elseif (b <= 4.6e-218)
		tmp = t_3;
	elseif (b <= 6.4e-46)
		tmp = t_1;
	elseif (b <= 3.1e+82)
		tmp = t_3;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (z * (1.0 - y));
	t_2 = b * ((t + y) - 2.0);
	t_3 = x - (a * (t + -1.0));
	tmp = 0.0;
	if (b <= -4e+80)
		tmp = t_2;
	elseif (b <= -2.2e-270)
		tmp = t_1;
	elseif (b <= 4.6e-218)
		tmp = t_3;
	elseif (b <= 6.4e-46)
		tmp = t_1;
	elseif (b <= 3.1e+82)
		tmp = t_3;
	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[(1.0 - y), $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 + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -4e+80], t$95$2, If[LessEqual[b, -2.2e-270], t$95$1, If[LessEqual[b, 4.6e-218], t$95$3, If[LessEqual[b, 6.4e-46], t$95$1, If[LessEqual[b, 3.1e+82], t$95$3, t$95$2]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -4e80 or 3.10000000000000032e82 < b

   1. Initial program 92.3%

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

   2. Taylor expanded in b around inf 85.8%

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

   if -4e80 < b < -2.1999999999999998e-270 or 4.59999999999999989e-218 < b < 6.3999999999999998e-46

   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 88.0%

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

   3. Taylor expanded in a around 0 65.6%

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

   if -2.1999999999999998e-270 < b < 4.59999999999999989e-218 or 6.3999999999999998e-46 < b < 3.10000000000000032e82

   1. Initial program 99.9%

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

   2. Taylor expanded in b around 0 86.4%

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

   3. Taylor expanded in a around inf 70.4%

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

4. Final simplification 72.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4 \cdot 10^{+80}:\\ \;\;\;\;b \cdot \left(\left(t + y\right) - 2\right)\\ \mathbf{elif}\;b \leq -2.2 \cdot 10^{-270}:\\ \;\;\;\;x + z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq 4.6 \cdot 10^{-218}:\\ \;\;\;\;x - a \cdot \left(t + -1\right)\\ \mathbf{elif}\;b \leq 6.4 \cdot 10^{-46}:\\ \;\;\;\;x + z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq 3.1 \cdot 10^{+82}:\\ \;\;\;\;x - a \cdot \left(t + -1\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(t + y\right) - 2\right)\\ \end{array} \]

Alternative 11: 63.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + z \cdot \left(1 - y\right)\\ t_2 := a + b \cdot \left(\left(t + y\right) - 2\right)\\ \mathbf{if}\;b \leq -3.2 \cdot 10^{+79}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -1.15 \cdot 10^{-274}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 1.05 \cdot 10^{-218}:\\ \;\;\;\;x - a \cdot \left(t + -1\right)\\ \mathbf{elif}\;b \leq 10^{-44}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* z (- 1.0 y)))) (t_2 (+ a (* b (- (+ t y) 2.0)))))
   (if (<= b -3.2e+79)
     t_2
     (if (<= b -1.15e-274)
       t_1
       (if (<= b 1.05e-218)
         (- x (* a (+ t -1.0)))
         (if (<= b 1e-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 * (1.0 - y));
	double t_2 = a + (b * ((t + y) - 2.0));
	double tmp;
	if (b <= -3.2e+79) {
		tmp = t_2;
	} else if (b <= -1.15e-274) {
		tmp = t_1;
	} else if (b <= 1.05e-218) {
		tmp = x - (a * (t + -1.0));
	} else if (b <= 1e-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) :: tmp
    t_1 = x + (z * (1.0d0 - y))
    t_2 = a + (b * ((t + y) - 2.0d0))
    if (b <= (-3.2d+79)) then
        tmp = t_2
    else if (b <= (-1.15d-274)) then
        tmp = t_1
    else if (b <= 1.05d-218) then
        tmp = x - (a * (t + (-1.0d0)))
    else if (b <= 1d-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 * (1.0 - y));
	double t_2 = a + (b * ((t + y) - 2.0));
	double tmp;
	if (b <= -3.2e+79) {
		tmp = t_2;
	} else if (b <= -1.15e-274) {
		tmp = t_1;
	} else if (b <= 1.05e-218) {
		tmp = x - (a * (t + -1.0));
	} else if (b <= 1e-44) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (z * (1.0 - y))
	t_2 = a + (b * ((t + y) - 2.0))
	tmp = 0
	if b <= -3.2e+79:
		tmp = t_2
	elif b <= -1.15e-274:
		tmp = t_1
	elif b <= 1.05e-218:
		tmp = x - (a * (t + -1.0))
	elif b <= 1e-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(1.0 - y)))
	t_2 = Float64(a + Float64(b * Float64(Float64(t + y) - 2.0)))
	tmp = 0.0
	if (b <= -3.2e+79)
		tmp = t_2;
	elseif (b <= -1.15e-274)
		tmp = t_1;
	elseif (b <= 1.05e-218)
		tmp = Float64(x - Float64(a * Float64(t + -1.0)));
	elseif (b <= 1e-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 * (1.0 - y));
	t_2 = a + (b * ((t + y) - 2.0));
	tmp = 0.0;
	if (b <= -3.2e+79)
		tmp = t_2;
	elseif (b <= -1.15e-274)
		tmp = t_1;
	elseif (b <= 1.05e-218)
		tmp = x - (a * (t + -1.0));
	elseif (b <= 1e-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[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a + N[(b * N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -3.2e+79], t$95$2, If[LessEqual[b, -1.15e-274], t$95$1, If[LessEqual[b, 1.05e-218], N[(x - N[(a * N[(t + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1e-44], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -3.20000000000000003e79 or 9.99999999999999953e-45 < b

   1. Initial program 94.1%

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

   2. Taylor expanded in z around 0 91.2%

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

      1. sub-neg 91.2%

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

      2. mul-1-neg 91.2%

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

      3. +-commutative 91.2%

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

      4. mul-1-neg 91.2%

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

      5. *-commutative 91.2%

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

      6. sub-neg 91.2%

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

      7. metadata-eval 91.2%

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

      8. distribute-lft-neg-in 91.2%

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

      9. *-commutative 91.2%

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

      10. fma-def 91.2%

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

      11. distribute-neg-in 91.2%

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

      12. metadata-eval 91.2%

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

      13. +-commutative 91.2%

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

      14. sub-neg 91.2%

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

   4. Simplified 91.2%

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

   5. Taylor expanded in x around 0 83.6%

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

   6. Taylor expanded in t around 0 80.7%

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

   if -3.20000000000000003e79 < b < -1.14999999999999998e-274 or 1.04999999999999997e-218 < b < 9.99999999999999953e-45

   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 88.0%

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

   3. Taylor expanded in a around 0 65.6%

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

   if -1.14999999999999998e-274 < b < 1.04999999999999997e-218

   1. Initial program 99.9%

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

   2. Taylor expanded in b around 0 99.9%

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

   3. Taylor expanded in a around inf 84.4%

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

4. Final simplification 73.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.2 \cdot 10^{+79}:\\ \;\;\;\;a + b \cdot \left(\left(t + y\right) - 2\right)\\ \mathbf{elif}\;b \leq -1.15 \cdot 10^{-274}:\\ \;\;\;\;x + z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq 1.05 \cdot 10^{-218}:\\ \;\;\;\;x - a \cdot \left(t + -1\right)\\ \mathbf{elif}\;b \leq 10^{-44}:\\ \;\;\;\;x + z \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;a + b \cdot \left(\left(t + y\right) - 2\right)\\ \end{array} \]

Alternative 12: 69.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(a + z \cdot \left(1 - y\right)\right)\\ t_2 := b \cdot \left(\left(t + y\right) - 2\right)\\ \mathbf{if}\;b \leq -2.3 \cdot 10^{+80}:\\ \;\;\;\;a + t_2\\ \mathbf{elif}\;b \leq -5.2 \cdot 10^{-272}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 1.25 \cdot 10^{-218}:\\ \;\;\;\;x - a \cdot \left(t + -1\right)\\ \mathbf{elif}\;b \leq 1.7 \cdot 10^{+54}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (+ a (* z (- 1.0 y))))) (t_2 (* b (- (+ t y) 2.0))))
   (if (<= b -2.3e+80)
     (+ a t_2)
     (if (<= b -5.2e-272)
       t_1
       (if (<= b 1.25e-218)
         (- x (* a (+ t -1.0)))
         (if (<= b 1.7e+54) t_1 (+ x t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (a + (z * (1.0 - y)));
	double t_2 = b * ((t + y) - 2.0);
	double tmp;
	if (b <= -2.3e+80) {
		tmp = a + t_2;
	} else if (b <= -5.2e-272) {
		tmp = t_1;
	} else if (b <= 1.25e-218) {
		tmp = x - (a * (t + -1.0));
	} else if (b <= 1.7e+54) {
		tmp = t_1;
	} else {
		tmp = x + 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 + (a + (z * (1.0d0 - y)))
    t_2 = b * ((t + y) - 2.0d0)
    if (b <= (-2.3d+80)) then
        tmp = a + t_2
    else if (b <= (-5.2d-272)) then
        tmp = t_1
    else if (b <= 1.25d-218) then
        tmp = x - (a * (t + (-1.0d0)))
    else if (b <= 1.7d+54) then
        tmp = t_1
    else
        tmp = x + 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 + (a + (z * (1.0 - y)));
	double t_2 = b * ((t + y) - 2.0);
	double tmp;
	if (b <= -2.3e+80) {
		tmp = a + t_2;
	} else if (b <= -5.2e-272) {
		tmp = t_1;
	} else if (b <= 1.25e-218) {
		tmp = x - (a * (t + -1.0));
	} else if (b <= 1.7e+54) {
		tmp = t_1;
	} else {
		tmp = x + t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (a + (z * (1.0 - y)))
	t_2 = b * ((t + y) - 2.0)
	tmp = 0
	if b <= -2.3e+80:
		tmp = a + t_2
	elif b <= -5.2e-272:
		tmp = t_1
	elif b <= 1.25e-218:
		tmp = x - (a * (t + -1.0))
	elif b <= 1.7e+54:
		tmp = t_1
	else:
		tmp = x + t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(a + Float64(z * Float64(1.0 - y))))
	t_2 = Float64(b * Float64(Float64(t + y) - 2.0))
	tmp = 0.0
	if (b <= -2.3e+80)
		tmp = Float64(a + t_2);
	elseif (b <= -5.2e-272)
		tmp = t_1;
	elseif (b <= 1.25e-218)
		tmp = Float64(x - Float64(a * Float64(t + -1.0)));
	elseif (b <= 1.7e+54)
		tmp = t_1;
	else
		tmp = Float64(x + t_2);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (a + (z * (1.0 - y)));
	t_2 = b * ((t + y) - 2.0);
	tmp = 0.0;
	if (b <= -2.3e+80)
		tmp = a + t_2;
	elseif (b <= -5.2e-272)
		tmp = t_1;
	elseif (b <= 1.25e-218)
		tmp = x - (a * (t + -1.0));
	elseif (b <= 1.7e+54)
		tmp = t_1;
	else
		tmp = x + t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(a + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2.3e+80], N[(a + t$95$2), $MachinePrecision], If[LessEqual[b, -5.2e-272], t$95$1, If[LessEqual[b, 1.25e-218], N[(x - N[(a * N[(t + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.7e+54], t$95$1, N[(x + t$95$2), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -2.30000000000000004e80

   1. Initial program 92.9%

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

   2. Taylor expanded in z around 0 92.9%

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

      1. sub-neg 92.9%

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

      2. mul-1-neg 92.9%

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

      3. +-commutative 92.9%

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

      4. mul-1-neg 92.9%

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

      5. *-commutative 92.9%

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

      6. sub-neg 92.9%

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

      7. metadata-eval 92.9%

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

      8. distribute-lft-neg-in 92.9%

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

      9. *-commutative 92.9%

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

      10. fma-def 92.9%

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

      11. distribute-neg-in 92.9%

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

      12. metadata-eval 92.9%

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

      13. +-commutative 92.9%

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

      14. sub-neg 92.9%

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

   4. Simplified 92.9%

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

   5. Taylor expanded in x around 0 86.1%

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

   6. Taylor expanded in t around 0 83.8%

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

   if -2.30000000000000004e80 < b < -5.19999999999999983e-272 or 1.2500000000000001e-218 < b < 1.7e54

   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 86.3%

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

   3. Taylor expanded in t around 0 76.5%

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

      1. +-commutative 76.5%

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

      2. sub-neg 76.5%

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

      3. metadata-eval 76.5%

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

      4. mul-1-neg 76.5%

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

      5. unsub-neg 76.5%

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

   5. Simplified 76.5%

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

   if -5.19999999999999983e-272 < b < 1.2500000000000001e-218

   1. Initial program 99.9%

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

   2. Taylor expanded in b around 0 99.9%

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

   3. Taylor expanded in a around inf 84.4%

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

   if 1.7e54 < b

   1. Initial program 92.7%

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

   2. Taylor expanded in z around 0 95.1%

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

      1. sub-neg 95.1%

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

      2. mul-1-neg 95.1%

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

      3. +-commutative 95.1%

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

      4. mul-1-neg 95.1%

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

      5. *-commutative 95.1%

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

      6. sub-neg 95.1%

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

      7. metadata-eval 95.1%

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

      8. distribute-lft-neg-in 95.1%

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

      9. *-commutative 95.1%

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

      10. fma-def 95.1%

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

      11. distribute-neg-in 95.1%

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

      12. metadata-eval 95.1%

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

      13. +-commutative 95.1%

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

      14. sub-neg 95.1%

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

   4. Simplified 95.1%

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

   5. Taylor expanded in a around 0 95.3%

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

4. Final simplification 81.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.3 \cdot 10^{+80}:\\ \;\;\;\;a + b \cdot \left(\left(t + y\right) - 2\right)\\ \mathbf{elif}\;b \leq -5.2 \cdot 10^{-272}:\\ \;\;\;\;x + \left(a + z \cdot \left(1 - y\right)\right)\\ \mathbf{elif}\;b \leq 1.25 \cdot 10^{-218}:\\ \;\;\;\;x - a \cdot \left(t + -1\right)\\ \mathbf{elif}\;b \leq 1.7 \cdot 10^{+54}:\\ \;\;\;\;x + \left(a + z \cdot \left(1 - y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + b \cdot \left(\left(t + y\right) - 2\right)\\ \end{array} \]

Alternative 13: 70.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(a + z \cdot \left(1 - y\right)\right)\\ t_2 := b \cdot \left(\left(t + y\right) - 2\right)\\ \mathbf{if}\;b \leq -3.2 \cdot 10^{+79}:\\ \;\;\;\;a + t_2\\ \mathbf{elif}\;b \leq -1 \cdot 10^{-270}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 1.9 \cdot 10^{-218}:\\ \;\;\;\;\left(x + z\right) - a \cdot \left(t + -1\right)\\ \mathbf{elif}\;b \leq 8.6 \cdot 10^{+52}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (+ a (* z (- 1.0 y))))) (t_2 (* b (- (+ t y) 2.0))))
   (if (<= b -3.2e+79)
     (+ a t_2)
     (if (<= b -1e-270)
       t_1
       (if (<= b 1.9e-218)
         (- (+ x z) (* a (+ t -1.0)))
         (if (<= b 8.6e+52) t_1 (+ x t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (a + (z * (1.0 - y)));
	double t_2 = b * ((t + y) - 2.0);
	double tmp;
	if (b <= -3.2e+79) {
		tmp = a + t_2;
	} else if (b <= -1e-270) {
		tmp = t_1;
	} else if (b <= 1.9e-218) {
		tmp = (x + z) - (a * (t + -1.0));
	} else if (b <= 8.6e+52) {
		tmp = t_1;
	} else {
		tmp = x + 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 + (a + (z * (1.0d0 - y)))
    t_2 = b * ((t + y) - 2.0d0)
    if (b <= (-3.2d+79)) then
        tmp = a + t_2
    else if (b <= (-1d-270)) then
        tmp = t_1
    else if (b <= 1.9d-218) then
        tmp = (x + z) - (a * (t + (-1.0d0)))
    else if (b <= 8.6d+52) then
        tmp = t_1
    else
        tmp = x + 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 + (a + (z * (1.0 - y)));
	double t_2 = b * ((t + y) - 2.0);
	double tmp;
	if (b <= -3.2e+79) {
		tmp = a + t_2;
	} else if (b <= -1e-270) {
		tmp = t_1;
	} else if (b <= 1.9e-218) {
		tmp = (x + z) - (a * (t + -1.0));
	} else if (b <= 8.6e+52) {
		tmp = t_1;
	} else {
		tmp = x + t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (a + (z * (1.0 - y)))
	t_2 = b * ((t + y) - 2.0)
	tmp = 0
	if b <= -3.2e+79:
		tmp = a + t_2
	elif b <= -1e-270:
		tmp = t_1
	elif b <= 1.9e-218:
		tmp = (x + z) - (a * (t + -1.0))
	elif b <= 8.6e+52:
		tmp = t_1
	else:
		tmp = x + t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(a + Float64(z * Float64(1.0 - y))))
	t_2 = Float64(b * Float64(Float64(t + y) - 2.0))
	tmp = 0.0
	if (b <= -3.2e+79)
		tmp = Float64(a + t_2);
	elseif (b <= -1e-270)
		tmp = t_1;
	elseif (b <= 1.9e-218)
		tmp = Float64(Float64(x + z) - Float64(a * Float64(t + -1.0)));
	elseif (b <= 8.6e+52)
		tmp = t_1;
	else
		tmp = Float64(x + t_2);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (a + (z * (1.0 - y)));
	t_2 = b * ((t + y) - 2.0);
	tmp = 0.0;
	if (b <= -3.2e+79)
		tmp = a + t_2;
	elseif (b <= -1e-270)
		tmp = t_1;
	elseif (b <= 1.9e-218)
		tmp = (x + z) - (a * (t + -1.0));
	elseif (b <= 8.6e+52)
		tmp = t_1;
	else
		tmp = x + t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(a + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -3.2e+79], N[(a + t$95$2), $MachinePrecision], If[LessEqual[b, -1e-270], t$95$1, If[LessEqual[b, 1.9e-218], N[(N[(x + z), $MachinePrecision] - N[(a * N[(t + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 8.6e+52], t$95$1, N[(x + t$95$2), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -3.20000000000000003e79

   1. Initial program 92.9%

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

   2. Taylor expanded in z around 0 92.9%

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

      1. sub-neg 92.9%

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

      2. mul-1-neg 92.9%

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

      3. +-commutative 92.9%

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

      4. mul-1-neg 92.9%

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

      5. *-commutative 92.9%

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

      6. sub-neg 92.9%

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

      7. metadata-eval 92.9%

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

      8. distribute-lft-neg-in 92.9%

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

      9. *-commutative 92.9%

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

      10. fma-def 92.9%

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

      11. distribute-neg-in 92.9%

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

      12. metadata-eval 92.9%

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

      13. +-commutative 92.9%

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

      14. sub-neg 92.9%

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

   4. Simplified 92.9%

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

   5. Taylor expanded in x around 0 86.1%

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

   6. Taylor expanded in t around 0 83.8%

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

   if -3.20000000000000003e79 < b < -1e-270 or 1.8999999999999999e-218 < b < 8.5999999999999999e52

   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 86.3%

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

   3. Taylor expanded in t around 0 76.5%

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

      1. +-commutative 76.5%

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

      2. sub-neg 76.5%

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

      3. metadata-eval 76.5%

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

      4. mul-1-neg 76.5%

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

      5. unsub-neg 76.5%

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

   5. Simplified 76.5%

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

   if -1e-270 < b < 1.8999999999999999e-218

   1. Initial program 99.9%

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

   2. Taylor expanded in b around 0 99.9%

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

   3. Taylor expanded in y around 0 92.0%

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

   4. Taylor expanded in z around 0 92.0%

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

   if 8.5999999999999999e52 < b

   1. Initial program 92.7%

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

   2. Taylor expanded in z around 0 95.1%

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

      1. sub-neg 95.1%

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

      2. mul-1-neg 95.1%

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

      3. +-commutative 95.1%

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

      4. mul-1-neg 95.1%

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

      5. *-commutative 95.1%

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

      6. sub-neg 95.1%

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

      7. metadata-eval 95.1%

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

      8. distribute-lft-neg-in 95.1%

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

      9. *-commutative 95.1%

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

      10. fma-def 95.1%

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

      11. distribute-neg-in 95.1%

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

      12. metadata-eval 95.1%

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

      13. +-commutative 95.1%

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

      14. sub-neg 95.1%

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

   4. Simplified 95.1%

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

   5. Taylor expanded in a around 0 95.3%

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

4. Final simplification 82.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.2 \cdot 10^{+79}:\\ \;\;\;\;a + b \cdot \left(\left(t + y\right) - 2\right)\\ \mathbf{elif}\;b \leq -1 \cdot 10^{-270}:\\ \;\;\;\;x + \left(a + z \cdot \left(1 - y\right)\right)\\ \mathbf{elif}\;b \leq 1.9 \cdot 10^{-218}:\\ \;\;\;\;\left(x + z\right) - a \cdot \left(t + -1\right)\\ \mathbf{elif}\;b \leq 8.6 \cdot 10^{+52}:\\ \;\;\;\;x + \left(a + z \cdot \left(1 - y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + b \cdot \left(\left(t + y\right) - 2\right)\\ \end{array} \]

Alternative 14: 70.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(a + z \cdot \left(1 - y\right)\right)\\ \mathbf{if}\;b \leq -4.2 \cdot 10^{+61}:\\ \;\;\;\;a \cdot \left(1 - t\right) - b \cdot \left(2 - \left(t + y\right)\right)\\ \mathbf{elif}\;b \leq -1.5 \cdot 10^{-274}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 1.1 \cdot 10^{-217}:\\ \;\;\;\;\left(x + z\right) - a \cdot \left(t + -1\right)\\ \mathbf{elif}\;b \leq 4.5 \cdot 10^{+54}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + b \cdot \left(\left(t + y\right) - 2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (+ a (* z (- 1.0 y))))))
   (if (<= b -4.2e+61)
     (- (* a (- 1.0 t)) (* b (- 2.0 (+ t y))))
     (if (<= b -1.5e-274)
       t_1
       (if (<= b 1.1e-217)
         (- (+ x z) (* a (+ t -1.0)))
         (if (<= b 4.5e+54) t_1 (+ x (* b (- (+ t y) 2.0)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (a + (z * (1.0 - y)));
	double tmp;
	if (b <= -4.2e+61) {
		tmp = (a * (1.0 - t)) - (b * (2.0 - (t + y)));
	} else if (b <= -1.5e-274) {
		tmp = t_1;
	} else if (b <= 1.1e-217) {
		tmp = (x + z) - (a * (t + -1.0));
	} else if (b <= 4.5e+54) {
		tmp = t_1;
	} else {
		tmp = x + (b * ((t + y) - 2.0));
	}
	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) :: t_1
    real(8) :: tmp
    t_1 = x + (a + (z * (1.0d0 - y)))
    if (b <= (-4.2d+61)) then
        tmp = (a * (1.0d0 - t)) - (b * (2.0d0 - (t + y)))
    else if (b <= (-1.5d-274)) then
        tmp = t_1
    else if (b <= 1.1d-217) then
        tmp = (x + z) - (a * (t + (-1.0d0)))
    else if (b <= 4.5d+54) then
        tmp = t_1
    else
        tmp = x + (b * ((t + y) - 2.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (a + (z * (1.0 - y)));
	double tmp;
	if (b <= -4.2e+61) {
		tmp = (a * (1.0 - t)) - (b * (2.0 - (t + y)));
	} else if (b <= -1.5e-274) {
		tmp = t_1;
	} else if (b <= 1.1e-217) {
		tmp = (x + z) - (a * (t + -1.0));
	} else if (b <= 4.5e+54) {
		tmp = t_1;
	} else {
		tmp = x + (b * ((t + y) - 2.0));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (a + (z * (1.0 - y)))
	tmp = 0
	if b <= -4.2e+61:
		tmp = (a * (1.0 - t)) - (b * (2.0 - (t + y)))
	elif b <= -1.5e-274:
		tmp = t_1
	elif b <= 1.1e-217:
		tmp = (x + z) - (a * (t + -1.0))
	elif b <= 4.5e+54:
		tmp = t_1
	else:
		tmp = x + (b * ((t + y) - 2.0))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(a + Float64(z * Float64(1.0 - y))))
	tmp = 0.0
	if (b <= -4.2e+61)
		tmp = Float64(Float64(a * Float64(1.0 - t)) - Float64(b * Float64(2.0 - Float64(t + y))));
	elseif (b <= -1.5e-274)
		tmp = t_1;
	elseif (b <= 1.1e-217)
		tmp = Float64(Float64(x + z) - Float64(a * Float64(t + -1.0)));
	elseif (b <= 4.5e+54)
		tmp = t_1;
	else
		tmp = Float64(x + Float64(b * Float64(Float64(t + y) - 2.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (a + (z * (1.0 - y)));
	tmp = 0.0;
	if (b <= -4.2e+61)
		tmp = (a * (1.0 - t)) - (b * (2.0 - (t + y)));
	elseif (b <= -1.5e-274)
		tmp = t_1;
	elseif (b <= 1.1e-217)
		tmp = (x + z) - (a * (t + -1.0));
	elseif (b <= 4.5e+54)
		tmp = t_1;
	else
		tmp = x + (b * ((t + y) - 2.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(a + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -4.2e+61], N[(N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision] - N[(b * N[(2.0 - N[(t + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -1.5e-274], t$95$1, If[LessEqual[b, 1.1e-217], N[(N[(x + z), $MachinePrecision] - N[(a * N[(t + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 4.5e+54], t$95$1, N[(x + N[(b * N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -4.2000000000000002e61

   1. Initial program 93.3%

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

   2. Taylor expanded in z around 0 91.1%

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

      1. sub-neg 91.1%

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

      2. mul-1-neg 91.1%

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

      3. +-commutative 91.1%

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

      4. mul-1-neg 91.1%

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

      5. *-commutative 91.1%

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

      6. sub-neg 91.1%

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

      7. metadata-eval 91.1%

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

      8. distribute-lft-neg-in 91.1%

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

      9. *-commutative 91.1%

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

      10. fma-def 91.1%

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

      11. distribute-neg-in 91.1%

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

      12. metadata-eval 91.1%

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

      13. +-commutative 91.1%

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

      14. sub-neg 91.1%

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

   4. Simplified 91.1%

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

   5. Taylor expanded in x around 0 84.8%

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

   if -4.2000000000000002e61 < b < -1.49999999999999989e-274 or 1.09999999999999991e-217 < b < 4.49999999999999984e54

   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 86.6%

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

   3. Taylor expanded in t around 0 77.4%

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

      1. +-commutative 77.4%

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

      2. sub-neg 77.4%

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

      3. metadata-eval 77.4%

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

      4. mul-1-neg 77.4%

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

      5. unsub-neg 77.4%

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

   5. Simplified 77.4%

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

   if -1.49999999999999989e-274 < b < 1.09999999999999991e-217

   1. Initial program 99.9%

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

   2. Taylor expanded in b around 0 99.9%

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

   3. Taylor expanded in y around 0 92.0%

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

   4. Taylor expanded in z around 0 92.0%

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

   if 4.49999999999999984e54 < b

   1. Initial program 92.7%

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

   2. Taylor expanded in z around 0 95.1%

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

      1. sub-neg 95.1%

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

      2. mul-1-neg 95.1%

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

      3. +-commutative 95.1%

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

      4. mul-1-neg 95.1%

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

      5. *-commutative 95.1%

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

      6. sub-neg 95.1%

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

      7. metadata-eval 95.1%

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

      8. distribute-lft-neg-in 95.1%

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

      9. *-commutative 95.1%

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

      10. fma-def 95.1%

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

      11. distribute-neg-in 95.1%

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

      12. metadata-eval 95.1%

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

      13. +-commutative 95.1%

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

      14. sub-neg 95.1%

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

   4. Simplified 95.1%

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

   5. Taylor expanded in a around 0 95.3%

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

4. Final simplification 83.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.2 \cdot 10^{+61}:\\ \;\;\;\;a \cdot \left(1 - t\right) - b \cdot \left(2 - \left(t + y\right)\right)\\ \mathbf{elif}\;b \leq -1.5 \cdot 10^{-274}:\\ \;\;\;\;x + \left(a + z \cdot \left(1 - y\right)\right)\\ \mathbf{elif}\;b \leq 1.1 \cdot 10^{-217}:\\ \;\;\;\;\left(x + z\right) - a \cdot \left(t + -1\right)\\ \mathbf{elif}\;b \leq 4.5 \cdot 10^{+54}:\\ \;\;\;\;x + \left(a + z \cdot \left(1 - y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + b \cdot \left(\left(t + y\right) - 2\right)\\ \end{array} \]

Alternative 15: 83.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(1 - t\right)\\ \mathbf{if}\;b \leq -1.08 \cdot 10^{+80}:\\ \;\;\;\;t_1 - b \cdot \left(2 - \left(t + y\right)\right)\\ \mathbf{elif}\;b \leq 2.95 \cdot 10^{+69}:\\ \;\;\;\;x + \left(z \cdot \left(1 - y\right) + t_1\right)\\ \mathbf{else}:\\ \;\;\;\;x + b \cdot \left(\left(t + y\right) - 2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (- 1.0 t))))
   (if (<= b -1.08e+80)
     (- t_1 (* b (- 2.0 (+ t y))))
     (if (<= b 2.95e+69)
       (+ x (+ (* z (- 1.0 y)) t_1))
       (+ x (* b (- (+ t y) 2.0)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double tmp;
	if (b <= -1.08e+80) {
		tmp = t_1 - (b * (2.0 - (t + y)));
	} else if (b <= 2.95e+69) {
		tmp = x + ((z * (1.0 - y)) + t_1);
	} else {
		tmp = x + (b * ((t + y) - 2.0));
	}
	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) :: t_1
    real(8) :: tmp
    t_1 = a * (1.0d0 - t)
    if (b <= (-1.08d+80)) then
        tmp = t_1 - (b * (2.0d0 - (t + y)))
    else if (b <= 2.95d+69) then
        tmp = x + ((z * (1.0d0 - y)) + t_1)
    else
        tmp = x + (b * ((t + y) - 2.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double tmp;
	if (b <= -1.08e+80) {
		tmp = t_1 - (b * (2.0 - (t + y)));
	} else if (b <= 2.95e+69) {
		tmp = x + ((z * (1.0 - y)) + t_1);
	} else {
		tmp = x + (b * ((t + y) - 2.0));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (1.0 - t)
	tmp = 0
	if b <= -1.08e+80:
		tmp = t_1 - (b * (2.0 - (t + y)))
	elif b <= 2.95e+69:
		tmp = x + ((z * (1.0 - y)) + t_1)
	else:
		tmp = x + (b * ((t + y) - 2.0))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(1.0 - t))
	tmp = 0.0
	if (b <= -1.08e+80)
		tmp = Float64(t_1 - Float64(b * Float64(2.0 - Float64(t + y))));
	elseif (b <= 2.95e+69)
		tmp = Float64(x + Float64(Float64(z * Float64(1.0 - y)) + t_1));
	else
		tmp = Float64(x + Float64(b * Float64(Float64(t + y) - 2.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (1.0 - t);
	tmp = 0.0;
	if (b <= -1.08e+80)
		tmp = t_1 - (b * (2.0 - (t + y)));
	elseif (b <= 2.95e+69)
		tmp = x + ((z * (1.0 - y)) + t_1);
	else
		tmp = x + (b * ((t + y) - 2.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.08e+80], N[(t$95$1 - N[(b * N[(2.0 - N[(t + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.95e+69], N[(x + N[(N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision], N[(x + N[(b * N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.08e80

   1. Initial program 92.9%

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

   2. Taylor expanded in z around 0 92.9%

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

      1. sub-neg 92.9%

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

      2. mul-1-neg 92.9%

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

      3. +-commutative 92.9%

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

      4. mul-1-neg 92.9%

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

      5. *-commutative 92.9%

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

      6. sub-neg 92.9%

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

      7. metadata-eval 92.9%

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

      8. distribute-lft-neg-in 92.9%

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

      9. *-commutative 92.9%

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

      10. fma-def 92.9%

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

      11. distribute-neg-in 92.9%

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

      12. metadata-eval 92.9%

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

      13. +-commutative 92.9%

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

      14. sub-neg 92.9%

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

   4. Simplified 92.9%

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

   5. Taylor expanded in x around 0 86.1%

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

   if -1.08e80 < b < 2.95000000000000002e69

   1. Initial program 99.4%

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

   2. Taylor expanded in b around 0 88.0%

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

   if 2.95000000000000002e69 < 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 z around 0 94.7%

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

      1. sub-neg 94.7%

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

      2. mul-1-neg 94.7%

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

      3. +-commutative 94.7%

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

      4. mul-1-neg 94.7%

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

      5. *-commutative 94.7%

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

      6. sub-neg 94.7%

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

      7. metadata-eval 94.7%

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

      8. distribute-lft-neg-in 94.7%

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

      9. *-commutative 94.7%

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

      10. fma-def 94.7%

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

      11. distribute-neg-in 94.7%

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

      12. metadata-eval 94.7%

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

      13. +-commutative 94.7%

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

      14. sub-neg 94.7%

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

   4. Simplified 94.7%

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

   5. Taylor expanded in a around 0 97.4%

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

4. Final simplification 89.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.08 \cdot 10^{+80}:\\ \;\;\;\;a \cdot \left(1 - t\right) - b \cdot \left(2 - \left(t + y\right)\right)\\ \mathbf{elif}\;b \leq 2.95 \cdot 10^{+69}:\\ \;\;\;\;x + \left(z \cdot \left(1 - y\right) + a \cdot \left(1 - t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + b \cdot \left(\left(t + y\right) - 2\right)\\ \end{array} \]

Alternative 16: 83.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -5.1 \cdot 10^{+79}:\\ \;\;\;\;a \cdot \left(1 - t\right) - b \cdot \left(2 - \left(t + y\right)\right)\\ \mathbf{elif}\;b \leq 10^{+70}:\\ \;\;\;\;\left(x - a \cdot \left(t + -1\right)\right) + z \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;x + b \cdot \left(\left(t + y\right) - 2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -5.1e+79)
   (- (* a (- 1.0 t)) (* b (- 2.0 (+ t y))))
   (if (<= b 1e+70)
     (+ (- x (* a (+ t -1.0))) (* z (- 1.0 y)))
     (+ x (* b (- (+ t y) 2.0))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -5.1e+79) {
		tmp = (a * (1.0 - t)) - (b * (2.0 - (t + y)));
	} else if (b <= 1e+70) {
		tmp = (x - (a * (t + -1.0))) + (z * (1.0 - y));
	} else {
		tmp = x + (b * ((t + y) - 2.0));
	}
	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 <= (-5.1d+79)) then
        tmp = (a * (1.0d0 - t)) - (b * (2.0d0 - (t + y)))
    else if (b <= 1d+70) then
        tmp = (x - (a * (t + (-1.0d0)))) + (z * (1.0d0 - y))
    else
        tmp = x + (b * ((t + y) - 2.0d0))
    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 <= -5.1e+79) {
		tmp = (a * (1.0 - t)) - (b * (2.0 - (t + y)));
	} else if (b <= 1e+70) {
		tmp = (x - (a * (t + -1.0))) + (z * (1.0 - y));
	} else {
		tmp = x + (b * ((t + y) - 2.0));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -5.1e+79:
		tmp = (a * (1.0 - t)) - (b * (2.0 - (t + y)))
	elif b <= 1e+70:
		tmp = (x - (a * (t + -1.0))) + (z * (1.0 - y))
	else:
		tmp = x + (b * ((t + y) - 2.0))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -5.1e+79)
		tmp = Float64(Float64(a * Float64(1.0 - t)) - Float64(b * Float64(2.0 - Float64(t + y))));
	elseif (b <= 1e+70)
		tmp = Float64(Float64(x - Float64(a * Float64(t + -1.0))) + Float64(z * Float64(1.0 - y)));
	else
		tmp = Float64(x + Float64(b * Float64(Float64(t + y) - 2.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -5.1e+79)
		tmp = (a * (1.0 - t)) - (b * (2.0 - (t + y)));
	elseif (b <= 1e+70)
		tmp = (x - (a * (t + -1.0))) + (z * (1.0 - y));
	else
		tmp = x + (b * ((t + y) - 2.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -5.1e+79], N[(N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision] - N[(b * N[(2.0 - N[(t + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1e+70], N[(N[(x - N[(a * N[(t + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(b * N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -5.1000000000000001e79

   1. Initial program 92.9%

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

   2. Taylor expanded in z around 0 92.9%

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

      1. sub-neg 92.9%

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

      2. mul-1-neg 92.9%

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

      3. +-commutative 92.9%

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

      4. mul-1-neg 92.9%

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

      5. *-commutative 92.9%

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

      6. sub-neg 92.9%

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

      7. metadata-eval 92.9%

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

      8. distribute-lft-neg-in 92.9%

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

      9. *-commutative 92.9%

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

      10. fma-def 92.9%

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

      11. distribute-neg-in 92.9%

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

      12. metadata-eval 92.9%

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

      13. +-commutative 92.9%

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

      14. sub-neg 92.9%

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

   4. Simplified 92.9%

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

   5. Taylor expanded in x around 0 86.1%

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

   if -5.1000000000000001e79 < b < 1.00000000000000007e70

   1. Initial program 99.4%

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

   2. Taylor expanded in a around 0 99.4%

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

   3. Taylor expanded in b around 0 88.0%

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

   if 1.00000000000000007e70 < 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 z around 0 94.7%

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

      1. sub-neg 94.7%

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

      2. mul-1-neg 94.7%

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

      3. +-commutative 94.7%

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

      4. mul-1-neg 94.7%

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

      5. *-commutative 94.7%

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

      6. sub-neg 94.7%

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

      7. metadata-eval 94.7%

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

      8. distribute-lft-neg-in 94.7%

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

      9. *-commutative 94.7%

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

      10. fma-def 94.7%

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

      11. distribute-neg-in 94.7%

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

      12. metadata-eval 94.7%

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

      13. +-commutative 94.7%

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

      14. sub-neg 94.7%

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

   4. Simplified 94.7%

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

   5. Taylor expanded in a around 0 97.4%

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

4. Final simplification 89.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5.1 \cdot 10^{+79}:\\ \;\;\;\;a \cdot \left(1 - t\right) - b \cdot \left(2 - \left(t + y\right)\right)\\ \mathbf{elif}\;b \leq 10^{+70}:\\ \;\;\;\;\left(x - a \cdot \left(t + -1\right)\right) + z \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;x + b \cdot \left(\left(t + y\right) - 2\right)\\ \end{array} \]

Alternative 17: 39.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -6.5 \cdot 10^{+41}:\\ \;\;\;\;b \cdot \left(y - 2\right)\\ \mathbf{elif}\;b \leq -3.5 \cdot 10^{-242}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;b \leq 6.6 \cdot 10^{-218}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 1.8 \cdot 10^{-116}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;b \leq 2.75 \cdot 10^{+54}:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t - 2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -6.5e+41)
   (* b (- y 2.0))
   (if (<= b -3.5e-242)
     (+ x z)
     (if (<= b 6.6e-218)
       (* a (- 1.0 t))
       (if (<= b 1.8e-116)
         (+ x z)
         (if (<= b 2.75e+54) (+ x a) (* b (- t 2.0))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -6.5e+41) {
		tmp = b * (y - 2.0);
	} else if (b <= -3.5e-242) {
		tmp = x + z;
	} else if (b <= 6.6e-218) {
		tmp = a * (1.0 - t);
	} else if (b <= 1.8e-116) {
		tmp = x + z;
	} else if (b <= 2.75e+54) {
		tmp = x + a;
	} else {
		tmp = b * (t - 2.0);
	}
	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 <= (-6.5d+41)) then
        tmp = b * (y - 2.0d0)
    else if (b <= (-3.5d-242)) then
        tmp = x + z
    else if (b <= 6.6d-218) then
        tmp = a * (1.0d0 - t)
    else if (b <= 1.8d-116) then
        tmp = x + z
    else if (b <= 2.75d+54) then
        tmp = x + a
    else
        tmp = b * (t - 2.0d0)
    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 <= -6.5e+41) {
		tmp = b * (y - 2.0);
	} else if (b <= -3.5e-242) {
		tmp = x + z;
	} else if (b <= 6.6e-218) {
		tmp = a * (1.0 - t);
	} else if (b <= 1.8e-116) {
		tmp = x + z;
	} else if (b <= 2.75e+54) {
		tmp = x + a;
	} else {
		tmp = b * (t - 2.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -6.5e+41:
		tmp = b * (y - 2.0)
	elif b <= -3.5e-242:
		tmp = x + z
	elif b <= 6.6e-218:
		tmp = a * (1.0 - t)
	elif b <= 1.8e-116:
		tmp = x + z
	elif b <= 2.75e+54:
		tmp = x + a
	else:
		tmp = b * (t - 2.0)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -6.5e+41)
		tmp = Float64(b * Float64(y - 2.0));
	elseif (b <= -3.5e-242)
		tmp = Float64(x + z);
	elseif (b <= 6.6e-218)
		tmp = Float64(a * Float64(1.0 - t));
	elseif (b <= 1.8e-116)
		tmp = Float64(x + z);
	elseif (b <= 2.75e+54)
		tmp = Float64(x + a);
	else
		tmp = Float64(b * Float64(t - 2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -6.5e+41)
		tmp = b * (y - 2.0);
	elseif (b <= -3.5e-242)
		tmp = x + z;
	elseif (b <= 6.6e-218)
		tmp = a * (1.0 - t);
	elseif (b <= 1.8e-116)
		tmp = x + z;
	elseif (b <= 2.75e+54)
		tmp = x + a;
	else
		tmp = b * (t - 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -6.5e+41], N[(b * N[(y - 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -3.5e-242], N[(x + z), $MachinePrecision], If[LessEqual[b, 6.6e-218], N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.8e-116], N[(x + z), $MachinePrecision], If[LessEqual[b, 2.75e+54], N[(x + a), $MachinePrecision], N[(b * N[(t - 2.0), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -6.49999999999999975e41

   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 b around inf 72.2%

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

   3. Taylor expanded in t around 0 55.2%

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

   if -6.49999999999999975e41 < b < -3.4999999999999999e-242 or 6.60000000000000046e-218 < b < 1.79999999999999988e-116

   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 89.7%

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

   3. Taylor expanded in y around 0 64.9%

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

   4. Taylor expanded in a around 0 41.9%

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

      1. sub-neg 41.9%

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

      2. mul-1-neg 41.9%

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

      3. remove-double-neg 41.9%

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

   6. Simplified 41.9%

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

   if -3.4999999999999999e-242 < b < 6.60000000000000046e-218

   1. Initial program 99.9%

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

   2. Taylor expanded in a around inf 60.5%

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

   if 1.79999999999999988e-116 < b < 2.75000000000000013e54

   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 78.5%

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

   3. Taylor expanded in t around 0 67.1%

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

      1. +-commutative 67.1%

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

      2. sub-neg 67.1%

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

      3. metadata-eval 67.1%

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

      4. mul-1-neg 67.1%

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

      5. unsub-neg 67.1%

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

   5. Simplified 67.1%

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

   6. Taylor expanded in z around 0 39.4%

      \[\leadsto x - \color{blue}{-1 \cdot a} \]
   7. Step-by-step derivation

      1. mul-1-neg 39.4%

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

   8. Simplified 39.4%

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

   if 2.75000000000000013e54 < b

   1. Initial program 92.7%

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

   2. Taylor expanded in b around inf 90.5%

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

   3. Taylor expanded in y around 0 62.5%

      \[\leadsto \color{blue}{b \cdot \left(t - 2\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 49.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -6.5 \cdot 10^{+41}:\\ \;\;\;\;b \cdot \left(y - 2\right)\\ \mathbf{elif}\;b \leq -3.5 \cdot 10^{-242}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;b \leq 6.6 \cdot 10^{-218}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 1.8 \cdot 10^{-116}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;b \leq 2.75 \cdot 10^{+54}:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t - 2\right)\\ \end{array} \]

Alternative 18: 50.4% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(b - z\right)\\ \mathbf{if}\;y \leq -1300000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.75 \cdot 10^{-230}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;y \leq 3 \cdot 10^{-305}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{-201}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{+44}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (- b z))))
   (if (<= y -1300000.0)
     t_1
     (if (<= y -1.75e-230)
       (+ x z)
       (if (<= y 3e-305)
         (* a (- 1.0 t))
         (if (<= y 7.5e-201)
           (+ x z)
           (if (<= y 2.4e+44) (* t (- b a)) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (b - z);
	double tmp;
	if (y <= -1300000.0) {
		tmp = t_1;
	} else if (y <= -1.75e-230) {
		tmp = x + z;
	} else if (y <= 3e-305) {
		tmp = a * (1.0 - t);
	} else if (y <= 7.5e-201) {
		tmp = x + z;
	} else if (y <= 2.4e+44) {
		tmp = t * (b - a);
	} 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) :: tmp
    t_1 = y * (b - z)
    if (y <= (-1300000.0d0)) then
        tmp = t_1
    else if (y <= (-1.75d-230)) then
        tmp = x + z
    else if (y <= 3d-305) then
        tmp = a * (1.0d0 - t)
    else if (y <= 7.5d-201) then
        tmp = x + z
    else if (y <= 2.4d+44) then
        tmp = t * (b - a)
    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 tmp;
	if (y <= -1300000.0) {
		tmp = t_1;
	} else if (y <= -1.75e-230) {
		tmp = x + z;
	} else if (y <= 3e-305) {
		tmp = a * (1.0 - t);
	} else if (y <= 7.5e-201) {
		tmp = x + z;
	} else if (y <= 2.4e+44) {
		tmp = t * (b - a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y * (b - z)
	tmp = 0
	if y <= -1300000.0:
		tmp = t_1
	elif y <= -1.75e-230:
		tmp = x + z
	elif y <= 3e-305:
		tmp = a * (1.0 - t)
	elif y <= 7.5e-201:
		tmp = x + z
	elif y <= 2.4e+44:
		tmp = t * (b - a)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y * Float64(b - z))
	tmp = 0.0
	if (y <= -1300000.0)
		tmp = t_1;
	elseif (y <= -1.75e-230)
		tmp = Float64(x + z);
	elseif (y <= 3e-305)
		tmp = Float64(a * Float64(1.0 - t));
	elseif (y <= 7.5e-201)
		tmp = Float64(x + z);
	elseif (y <= 2.4e+44)
		tmp = Float64(t * Float64(b - a));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y * (b - z);
	tmp = 0.0;
	if (y <= -1300000.0)
		tmp = t_1;
	elseif (y <= -1.75e-230)
		tmp = x + z;
	elseif (y <= 3e-305)
		tmp = a * (1.0 - t);
	elseif (y <= 7.5e-201)
		tmp = x + z;
	elseif (y <= 2.4e+44)
		tmp = t * (b - a);
	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]}, If[LessEqual[y, -1300000.0], t$95$1, If[LessEqual[y, -1.75e-230], N[(x + z), $MachinePrecision], If[LessEqual[y, 3e-305], N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7.5e-201], N[(x + z), $MachinePrecision], If[LessEqual[y, 2.4e+44], N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.3e6 or 2.40000000000000013e44 < y

   1. Initial program 95.0%

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

   2. Taylor expanded in y around inf 67.0%

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

   if -1.3e6 < y < -1.74999999999999994e-230 or 3.0000000000000001e-305 < y < 7.49999999999999987e-201

   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 71.2%

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

   3. Taylor expanded in y around 0 71.2%

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

   4. Taylor expanded in a around 0 54.5%

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

      1. sub-neg 54.5%

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

      2. mul-1-neg 54.5%

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

      3. remove-double-neg 54.5%

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

   6. Simplified 54.5%

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

   if -1.74999999999999994e-230 < y < 3.0000000000000001e-305

   1. Initial program 99.9%

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

   2. Taylor expanded in a around inf 46.8%

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

   if 7.49999999999999987e-201 < y < 2.40000000000000013e44

   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 t around inf 54.7%

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

4. Final simplification 59.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1300000:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;y \leq -1.75 \cdot 10^{-230}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;y \leq 3 \cdot 10^{-305}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{-201}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{+44}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \end{array} \]

Alternative 19: 32.9% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -5.8 \cdot 10^{+48}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;b \leq -2.5 \cdot 10^{-269}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;b \leq 8.8 \cdot 10^{-219}:\\ \;\;\;\;-t \cdot a\\ \mathbf{elif}\;b \leq 5.1 \cdot 10^{+92}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -5.8e+48)
   (* y b)
   (if (<= b -2.5e-269)
     (+ x z)
     (if (<= b 8.8e-219) (- (* t a)) (if (<= b 5.1e+92) (+ x z) (* t b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -5.8e+48) {
		tmp = y * b;
	} else if (b <= -2.5e-269) {
		tmp = x + z;
	} else if (b <= 8.8e-219) {
		tmp = -(t * a);
	} else if (b <= 5.1e+92) {
		tmp = x + z;
	} 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 <= (-5.8d+48)) then
        tmp = y * b
    else if (b <= (-2.5d-269)) then
        tmp = x + z
    else if (b <= 8.8d-219) then
        tmp = -(t * a)
    else if (b <= 5.1d+92) then
        tmp = x + z
    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 <= -5.8e+48) {
		tmp = y * b;
	} else if (b <= -2.5e-269) {
		tmp = x + z;
	} else if (b <= 8.8e-219) {
		tmp = -(t * a);
	} else if (b <= 5.1e+92) {
		tmp = x + z;
	} else {
		tmp = t * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -5.8e+48:
		tmp = y * b
	elif b <= -2.5e-269:
		tmp = x + z
	elif b <= 8.8e-219:
		tmp = -(t * a)
	elif b <= 5.1e+92:
		tmp = x + z
	else:
		tmp = t * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -5.8e+48)
		tmp = Float64(y * b);
	elseif (b <= -2.5e-269)
		tmp = Float64(x + z);
	elseif (b <= 8.8e-219)
		tmp = Float64(-Float64(t * a));
	elseif (b <= 5.1e+92)
		tmp = Float64(x + z);
	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 <= -5.8e+48)
		tmp = y * b;
	elseif (b <= -2.5e-269)
		tmp = x + z;
	elseif (b <= 8.8e-219)
		tmp = -(t * a);
	elseif (b <= 5.1e+92)
		tmp = x + z;
	else
		tmp = t * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -5.8e+48], N[(y * b), $MachinePrecision], If[LessEqual[b, -2.5e-269], N[(x + z), $MachinePrecision], If[LessEqual[b, 8.8e-219], (-N[(t * a), $MachinePrecision]), If[LessEqual[b, 5.1e+92], N[(x + z), $MachinePrecision], N[(t * b), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -5.7999999999999998e48

   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 z around 0 89.4%

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

      1. sub-neg 89.4%

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

      2. mul-1-neg 89.4%

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

      3. +-commutative 89.4%

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

      4. mul-1-neg 89.4%

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

      5. *-commutative 89.4%

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

      6. sub-neg 89.4%

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

      7. metadata-eval 89.4%

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

      8. distribute-lft-neg-in 89.4%

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

      9. *-commutative 89.4%

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

      10. fma-def 89.4%

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

      11. distribute-neg-in 89.4%

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

      12. metadata-eval 89.4%

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

      13. +-commutative 89.4%

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

      14. sub-neg 89.4%

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

   4. Simplified 89.4%

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

   5. Taylor expanded in y around inf 39.9%

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

   if -5.7999999999999998e48 < b < -2.49999999999999989e-269 or 8.7999999999999998e-219 < b < 5.1000000000000003e92

   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 86.2%

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

   3. Taylor expanded in y around 0 63.3%

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

   4. Taylor expanded in a around 0 37.3%

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

      1. sub-neg 37.3%

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

      2. mul-1-neg 37.3%

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

      3. remove-double-neg 37.3%

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

   6. Simplified 37.3%

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

   if -2.49999999999999989e-269 < b < 8.7999999999999998e-219

   1. Initial program 99.9%

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

   2. Taylor expanded in a around inf 61.9%

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

   3. Taylor expanded in t around inf 54.3%

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

      1. mul-1-neg 54.3%

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

      2. distribute-rgt-neg-out 54.3%

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

   5. Simplified 54.3%

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

   if 5.1000000000000003e92 < b

   1. Initial program 91.7%

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

   2. Taylor expanded in b around inf 97.2%

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

   3. Taylor expanded in t around inf 42.3%

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

      1. *-commutative 42.3%

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

   5. Simplified 42.3%

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

4. Final simplification 40.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5.8 \cdot 10^{+48}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;b \leq -2.5 \cdot 10^{-269}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;b \leq 8.8 \cdot 10^{-219}:\\ \;\;\;\;-t \cdot a\\ \mathbf{elif}\;b \leq 5.1 \cdot 10^{+92}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \]

Alternative 20: 55.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(b - z\right)\\ \mathbf{if}\;y \leq -4000000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{-146}:\\ \;\;\;\;x + \left(z + a\right)\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{+45}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (- b z))))
   (if (<= y -4000000000.0)
     t_1
     (if (<= y 1.45e-146)
       (+ x (+ z a))
       (if (<= y 1.05e+45) (* t (- b a)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (b - z);
	double tmp;
	if (y <= -4000000000.0) {
		tmp = t_1;
	} else if (y <= 1.45e-146) {
		tmp = x + (z + a);
	} else if (y <= 1.05e+45) {
		tmp = t * (b - a);
	} 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) :: tmp
    t_1 = y * (b - z)
    if (y <= (-4000000000.0d0)) then
        tmp = t_1
    else if (y <= 1.45d-146) then
        tmp = x + (z + a)
    else if (y <= 1.05d+45) then
        tmp = t * (b - a)
    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 tmp;
	if (y <= -4000000000.0) {
		tmp = t_1;
	} else if (y <= 1.45e-146) {
		tmp = x + (z + a);
	} else if (y <= 1.05e+45) {
		tmp = t * (b - a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y * (b - z)
	tmp = 0
	if y <= -4000000000.0:
		tmp = t_1
	elif y <= 1.45e-146:
		tmp = x + (z + a)
	elif y <= 1.05e+45:
		tmp = t * (b - a)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y * Float64(b - z))
	tmp = 0.0
	if (y <= -4000000000.0)
		tmp = t_1;
	elseif (y <= 1.45e-146)
		tmp = Float64(x + Float64(z + a));
	elseif (y <= 1.05e+45)
		tmp = Float64(t * Float64(b - a));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y * (b - z);
	tmp = 0.0;
	if (y <= -4000000000.0)
		tmp = t_1;
	elseif (y <= 1.45e-146)
		tmp = x + (z + a);
	elseif (y <= 1.05e+45)
		tmp = t * (b - a);
	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]}, If[LessEqual[y, -4000000000.0], t$95$1, If[LessEqual[y, 1.45e-146], N[(x + N[(z + a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.05e+45], N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4e9 or 1.04999999999999997e45 < y

   1. Initial program 95.0%

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

   2. Taylor expanded in y around inf 67.5%

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

   if -4e9 < y < 1.45000000000000005e-146

   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 71.0%

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

   3. Taylor expanded in y around 0 71.0%

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

   4. Taylor expanded in t around 0 60.3%

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

      1. sub-neg 60.3%

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

      2. neg-sub0 60.3%

         \[\leadsto x + \color{blue}{\left(0 - \left(-1 \cdot a + -1 \cdot z\right)\right)} \]

      3. +-commutative 60.3%

         \[\leadsto x + \left(0 - \color{blue}{\left(-1 \cdot z + -1 \cdot a\right)}\right) \]

      4. mul-1-neg 60.3%

         \[\leadsto x + \left(0 - \left(-1 \cdot z + \color{blue}{\left(-a\right)}\right)\right) \]

      5. unsub-neg 60.3%

         \[\leadsto x + \left(0 - \color{blue}{\left(-1 \cdot z - a\right)}\right) \]

      6. associate-+l- 60.3%

         \[\leadsto x + \color{blue}{\left(\left(0 - -1 \cdot z\right) + a\right)} \]

      7. neg-sub0 60.3%

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

      8. mul-1-neg 60.3%

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

      9. remove-double-neg 60.3%

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

      10. +-commutative 60.3%

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

   6. Simplified 60.3%

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

   if 1.45000000000000005e-146 < y < 1.04999999999999997e45

   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 t around inf 59.3%

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

4. Final simplification 63.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4000000000:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{-146}:\\ \;\;\;\;x + \left(z + a\right)\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{+45}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \end{array} \]

Alternative 21: 41.5% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -4.8 \cdot 10^{+19} \lor \neg \left(a \leq 16000000000\right):\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -4.8e+19) (not (<= a 16000000000.0))) (* a (- 1.0 t)) (+ x z)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -4.8e+19) || !(a <= 16000000000.0)) {
		tmp = a * (1.0 - t);
	} else {
		tmp = x + 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 ((a <= (-4.8d+19)) .or. (.not. (a <= 16000000000.0d0))) then
        tmp = a * (1.0d0 - t)
    else
        tmp = x + 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 ((a <= -4.8e+19) || !(a <= 16000000000.0)) {
		tmp = a * (1.0 - t);
	} else {
		tmp = x + z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (a <= -4.8e+19) or not (a <= 16000000000.0):
		tmp = a * (1.0 - t)
	else:
		tmp = x + z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((a <= -4.8e+19) || !(a <= 16000000000.0))
		tmp = Float64(a * Float64(1.0 - t));
	else
		tmp = Float64(x + z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((a <= -4.8e+19) || ~((a <= 16000000000.0)))
		tmp = a * (1.0 - t);
	else
		tmp = x + z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[a, -4.8e+19], N[Not[LessEqual[a, 16000000000.0]], $MachinePrecision]], N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision], N[(x + z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -4.8e19 or 1.6e10 < a

   1. Initial program 94.4%

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

   2. Taylor expanded in a around inf 44.4%

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

   if -4.8e19 < a < 1.6e10

   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 64.5%

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

   3. Taylor expanded in y around 0 44.3%

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

   4. Taylor expanded in a around 0 39.3%

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

      1. sub-neg 39.3%

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

      2. mul-1-neg 39.3%

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

      3. remove-double-neg 39.3%

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

   6. Simplified 39.3%

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

4. Final simplification 41.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.8 \cdot 10^{+19} \lor \neg \left(a \leq 16000000000\right):\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + z\\ \end{array} \]

Alternative 22: 32.1% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.6 \cdot 10^{+59}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;a \leq 0.003:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;-t \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -3.6e+59) (+ x a) (if (<= a 0.003) (+ x z) (- (* t a)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -3.6e+59) {
		tmp = x + a;
	} else if (a <= 0.003) {
		tmp = x + z;
	} else {
		tmp = -(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 (a <= (-3.6d+59)) then
        tmp = x + a
    else if (a <= 0.003d0) then
        tmp = x + z
    else
        tmp = -(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 (a <= -3.6e+59) {
		tmp = x + a;
	} else if (a <= 0.003) {
		tmp = x + z;
	} else {
		tmp = -(t * a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -3.6e+59:
		tmp = x + a
	elif a <= 0.003:
		tmp = x + z
	else:
		tmp = -(t * a)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -3.6e+59)
		tmp = Float64(x + a);
	elseif (a <= 0.003)
		tmp = Float64(x + z);
	else
		tmp = Float64(-Float64(t * a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= -3.6e+59)
		tmp = x + a;
	elseif (a <= 0.003)
		tmp = x + z;
	else
		tmp = -(t * a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -3.6e+59], N[(x + a), $MachinePrecision], If[LessEqual[a, 0.003], N[(x + z), $MachinePrecision], (-N[(t * a), $MachinePrecision])]]

Derivation

1. Split input into 3 regimes

2. if a < -3.5999999999999999e59

   1. Initial program 97.7%

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

   2. Taylor expanded in b around 0 76.7%

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

   3. Taylor expanded in t around 0 64.3%

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

      1. +-commutative 64.3%

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

      2. sub-neg 64.3%

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

      3. metadata-eval 64.3%

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

      4. mul-1-neg 64.3%

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

      5. unsub-neg 64.3%

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

   5. Simplified 64.3%

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

   6. Taylor expanded in z around 0 45.0%

      \[\leadsto x - \color{blue}{-1 \cdot a} \]
   7. Step-by-step derivation

      1. mul-1-neg 45.0%

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

   8. Simplified 45.0%

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

   if -3.5999999999999999e59 < a < 0.0030000000000000001

   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 61.2%

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

   3. Taylor expanded in y around 0 41.2%

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

   4. Taylor expanded in a around 0 37.0%

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

      1. sub-neg 37.0%

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

      2. mul-1-neg 37.0%

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

      3. remove-double-neg 37.0%

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

   6. Simplified 37.0%

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

   if 0.0030000000000000001 < a

   1. Initial program 92.2%

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

   2. Taylor expanded in a around inf 45.4%

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

   3. Taylor expanded in t around inf 35.3%

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

      1. mul-1-neg 35.3%

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

      2. distribute-rgt-neg-out 35.3%

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

   5. Simplified 35.3%

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

4. Final simplification 37.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.6 \cdot 10^{+59}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;a \leq 0.003:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;-t \cdot a\\ \end{array} \]

Alternative 23: 26.7% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -650 \lor \neg \left(b \leq 4.2 \cdot 10^{+79}\right):\\ \;\;\;\;y \cdot b\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -650.0) (not (<= b 4.2e+79))) (* y b) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -650.0) || !(b <= 4.2e+79)) {
		tmp = y * b;
	} 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 ((b <= (-650.0d0)) .or. (.not. (b <= 4.2d+79))) then
        tmp = y * b
    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 ((b <= -650.0) || !(b <= 4.2e+79)) {
		tmp = y * b;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -650.0) or not (b <= 4.2e+79):
		tmp = y * b
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -650.0) || !(b <= 4.2e+79))
		tmp = Float64(y * b);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -650.0) || ~((b <= 4.2e+79)))
		tmp = y * b;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -650.0], N[Not[LessEqual[b, 4.2e+79]], $MachinePrecision]], N[(y * b), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if b < -650 or 4.20000000000000016e79 < b

   1. Initial program 93.8%

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

   2. Taylor expanded in z around 0 86.0%

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

      1. sub-neg 86.0%

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

      2. mul-1-neg 86.0%

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

      3. +-commutative 86.0%

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

      4. mul-1-neg 86.0%

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

      5. *-commutative 86.0%

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

      6. sub-neg 86.0%

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

      7. metadata-eval 86.0%

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

      8. distribute-lft-neg-in 86.0%

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

      9. *-commutative 86.0%

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

      10. fma-def 86.0%

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

      11. distribute-neg-in 86.0%

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

      12. metadata-eval 86.0%

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

      13. +-commutative 86.0%

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

      14. sub-neg 86.0%

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

   4. Simplified 86.0%

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

   5. Taylor expanded in y around inf 36.7%

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

   if -650 < b < 4.20000000000000016e79

   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 23.6%

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

4. Final simplification 28.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -650 \lor \neg \left(b \leq 4.2 \cdot 10^{+79}\right):\\ \;\;\;\;y \cdot b\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 24: 27.0% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -72:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;b \leq 3.8 \cdot 10^{+23}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -72.0) (* y b) (if (<= b 3.8e+23) x (* t b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -72.0) {
		tmp = y * b;
	} else if (b <= 3.8e+23) {
		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 <= (-72.0d0)) then
        tmp = y * b
    else if (b <= 3.8d+23) 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 <= -72.0) {
		tmp = y * b;
	} else if (b <= 3.8e+23) {
		tmp = x;
	} else {
		tmp = t * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -72.0:
		tmp = y * b
	elif b <= 3.8e+23:
		tmp = x
	else:
		tmp = t * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -72.0)
		tmp = Float64(y * b);
	elseif (b <= 3.8e+23)
		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 <= -72.0)
		tmp = y * b;
	elseif (b <= 3.8e+23)
		tmp = x;
	else
		tmp = t * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -72.0], N[(y * b), $MachinePrecision], If[LessEqual[b, 3.8e+23], x, N[(t * b), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -72

   1. Initial program 95.1%

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

   2. Taylor expanded in z around 0 81.0%

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

      1. sub-neg 81.0%

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

      2. mul-1-neg 81.0%

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

      3. +-commutative 81.0%

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

      4. mul-1-neg 81.0%

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

      5. *-commutative 81.0%

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

      6. sub-neg 81.0%

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

      7. metadata-eval 81.0%

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

      8. distribute-lft-neg-in 81.0%

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

      9. *-commutative 81.0%

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

      10. fma-def 81.0%

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

      11. distribute-neg-in 81.0%

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

      12. metadata-eval 81.0%

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

      13. +-commutative 81.0%

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

      14. sub-neg 81.0%

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

   4. Simplified 81.0%

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

   5. Taylor expanded in y around inf 36.2%

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

   if -72 < b < 3.79999999999999975e23

   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 24.1%

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

   if 3.79999999999999975e23 < b

   1. Initial program 93.8%

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

   2. Taylor expanded in b around inf 81.8%

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

   3. Taylor expanded in t around inf 36.3%

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

      1. *-commutative 36.3%

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

   5. Simplified 36.3%

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

4. Final simplification 29.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -72:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;b \leq 3.8 \cdot 10^{+23}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \]

Alternative 25: 33.7% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -6 \cdot 10^{+41}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;b \leq 5.8 \cdot 10^{+81}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -6e+41) (* y b) (if (<= b 5.8e+81) (+ x z) (* t b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -6e+41) {
		tmp = y * b;
	} else if (b <= 5.8e+81) {
		tmp = x + z;
	} 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 <= (-6d+41)) then
        tmp = y * b
    else if (b <= 5.8d+81) then
        tmp = x + z
    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 <= -6e+41) {
		tmp = y * b;
	} else if (b <= 5.8e+81) {
		tmp = x + z;
	} else {
		tmp = t * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -6e+41:
		tmp = y * b
	elif b <= 5.8e+81:
		tmp = x + z
	else:
		tmp = t * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -6e+41)
		tmp = Float64(y * b);
	elseif (b <= 5.8e+81)
		tmp = Float64(x + z);
	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 <= -6e+41)
		tmp = y * b;
	elseif (b <= 5.8e+81)
		tmp = x + z;
	else
		tmp = t * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -6e+41], N[(y * b), $MachinePrecision], If[LessEqual[b, 5.8e+81], N[(x + z), $MachinePrecision], N[(t * b), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -5.9999999999999997e41

   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 z around 0 89.4%

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

      1. sub-neg 89.4%

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

      2. mul-1-neg 89.4%

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

      3. +-commutative 89.4%

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

      4. mul-1-neg 89.4%

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

      5. *-commutative 89.4%

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

      6. sub-neg 89.4%

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

      7. metadata-eval 89.4%

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

      8. distribute-lft-neg-in 89.4%

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

      9. *-commutative 89.4%

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

      10. fma-def 89.4%

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

      11. distribute-neg-in 89.4%

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

      12. metadata-eval 89.4%

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

      13. +-commutative 89.4%

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

      14. sub-neg 89.4%

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

   4. Simplified 89.4%

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

   5. Taylor expanded in y around inf 39.9%

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

   if -5.9999999999999997e41 < b < 5.7999999999999999e81

   1. Initial program 99.4%

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

   2. Taylor expanded in b around 0 88.3%

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

   3. Taylor expanded in y around 0 67.0%

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

   4. Taylor expanded in a around 0 36.1%

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

      1. sub-neg 36.1%

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

      2. mul-1-neg 36.1%

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

      3. remove-double-neg 36.1%

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

   6. Simplified 36.1%

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

   if 5.7999999999999999e81 < b

   1. Initial program 91.7%

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

   2. Taylor expanded in b around inf 97.2%

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

   3. Taylor expanded in t around inf 42.3%

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

      1. *-commutative 42.3%

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

   5. Simplified 42.3%

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

4. Final simplification 37.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -6 \cdot 10^{+41}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;b \leq 5.8 \cdot 10^{+81}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \]

Alternative 26: 20.8% accurate, 4.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.75 \cdot 10^{+146}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 4.8 \cdot 10^{+42}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -1.75e+146) x (if (<= x 4.8e+42) a x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -1.75e+146) {
		tmp = x;
	} else if (x <= 4.8e+42) {
		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 <= (-1.75d+146)) then
        tmp = x
    else if (x <= 4.8d+42) 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 <= -1.75e+146) {
		tmp = x;
	} else if (x <= 4.8e+42) {
		tmp = a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -1.75e+146:
		tmp = x
	elif x <= 4.8e+42:
		tmp = a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -1.75e+146)
		tmp = x;
	elseif (x <= 4.8e+42)
		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 <= -1.75e+146)
		tmp = x;
	elseif (x <= 4.8e+42)
		tmp = a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -1.75e+146], x, If[LessEqual[x, 4.8e+42], a, x]]

Derivation

1. Split input into 2 regimes

2. if x < -1.7500000000000001e146 or 4.7999999999999997e42 < x

   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 x around inf 40.4%

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

   if -1.7500000000000001e146 < x < 4.7999999999999997e42

   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 a around inf 30.5%

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

   3. Taylor expanded in t around 0 15.5%

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

4. Final simplification 23.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.75 \cdot 10^{+146}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 4.8 \cdot 10^{+42}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 27: 21.5% accurate, 4.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7.5 \cdot 10^{+53}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 8.8 \cdot 10^{+45}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -7.5e+53) x (if (<= x 8.8e+45) z x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -7.5e+53) {
		tmp = x;
	} else if (x <= 8.8e+45) {
		tmp = z;
	} 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 <= (-7.5d+53)) then
        tmp = x
    else if (x <= 8.8d+45) then
        tmp = z
    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 <= -7.5e+53) {
		tmp = x;
	} else if (x <= 8.8e+45) {
		tmp = z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -7.5e+53:
		tmp = x
	elif x <= 8.8e+45:
		tmp = z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -7.5e+53)
		tmp = x;
	elseif (x <= 8.8e+45)
		tmp = z;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -7.5e+53)
		tmp = x;
	elseif (x <= 8.8e+45)
		tmp = z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -7.5e+53], x, If[LessEqual[x, 8.8e+45], z, x]]

Derivation

1. Split input into 2 regimes

2. if x < -7.4999999999999997e53 or 8.8000000000000001e45 < x

   1. Initial program 97.0%

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

   2. Taylor expanded in x around inf 37.7%

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

   if -7.4999999999999997e53 < x < 8.8000000000000001e45

   1. Initial program 97.4%

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

   2. Taylor expanded in b around 0 65.5%

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

   3. Taylor expanded in y around 0 44.6%

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

   4. Taylor expanded in z around inf 16.3%

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

4. Final simplification 24.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.5 \cdot 10^{+53}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 8.8 \cdot 10^{+45}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 28: 10.7% 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 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 inf 25.5%

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

3. Taylor expanded in t around 0 11.9%

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

4. Final simplification 11.9%

   \[\leadsto a \]

Reproduce

herbie shell --seed 2023301 
(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)))