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

Percentage Accurate: 95.2% → 98.2%

Time: 17.8s

Alternatives: 26

Speedup: 0.5×

• 35.9% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = ((x - ((y - 1.0d0) * z)) - ((t - 1.0d0) * a)) + (((y + t) - 2.0d0) * b)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 95.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = ((x - ((y - 1.0d0) * z)) - ((t - 1.0d0) * a)) + (((y + t) - 2.0d0) * b)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.2% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[N[(N[(N[(x + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision], Infinity], N[(N[(y + N[(t + -2.0), $MachinePrecision]), $MachinePrecision] * b + N[(x - N[(N[(y + -1.0), $MachinePrecision] * z + N[(N[(t + -1.0), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $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. Step-by-step derivation

      1. +-commutative 100.0%

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

      2. fma-def 100.0%

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

      3. associate--l+ 100.0%

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

      4. sub-neg 100.0%

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

      5. metadata-eval 100.0%

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

      6. sub-neg 100.0%

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

      7. associate-+l- 100.0%

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

      8. fma-neg 100.0%

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

      9. sub-neg 100.0%

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

      10. metadata-eval 100.0%

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

      11. remove-double-neg 100.0%

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

      12. sub-neg 100.0%

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

      13. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   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 83.6%

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

4. Final simplification 99.2%

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

Alternative 2: 98.2% accurate, 0.5× speedup

Math

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

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1
         (+ (+ (+ x (* z (- 1.0 y))) (* a (- 1.0 t))) (* (- (+ y t) 2.0) b))))
   (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))) + (((y + t) - 2.0) * b);
	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))) + (((y + t) - 2.0) * b);
	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))) + (((y + t) - 2.0) * b)
	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(Float64(Float64(y + t) - 2.0) * b))
	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))) + (((y + t) - 2.0) * b);
	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[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $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 83.6%

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

4. Final simplification 99.2%

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

Alternative 3: 55.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a + z \cdot \left(1 - y\right)\\ t_2 := \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{if}\;b \leq -7.3 \cdot 10^{+50}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -3.6 \cdot 10^{-152}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -6.8 \cdot 10^{-240}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;b \leq -9 \cdot 10^{-249}:\\ \;\;\;\;z - y \cdot z\\ \mathbf{elif}\;b \leq -2.9 \cdot 10^{-292}:\\ \;\;\;\;a - t \cdot a\\ \mathbf{elif}\;b \leq 1.05 \cdot 10^{-292}:\\ \;\;\;\;x - y \cdot z\\ \mathbf{elif}\;b \leq 2.3 \cdot 10^{-30}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 3.1 \cdot 10^{+24}:\\ \;\;\;\;x + b \cdot \left(y - 2\right)\\ \mathbf{elif}\;b \leq 1.35 \cdot 10^{+70}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ a (* z (- 1.0 y)))) (t_2 (* (- (+ y t) 2.0) b)))
   (if (<= b -7.3e+50)
     t_2
     (if (<= b -3.6e-152)
       t_1
       (if (<= b -6.8e-240)
         (+ x a)
         (if (<= b -9e-249)
           (- z (* y z))
           (if (<= b -2.9e-292)
             (- a (* t a))
             (if (<= b 1.05e-292)
               (- x (* y z))
               (if (<= b 2.3e-30)
                 t_1
                 (if (<= b 3.1e+24)
                   (+ x (* b (- y 2.0)))
                   (if (<= b 1.35e+70) (* t (- b a)) t_2)))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a + (z * (1.0 - y));
	double t_2 = ((y + t) - 2.0) * b;
	double tmp;
	if (b <= -7.3e+50) {
		tmp = t_2;
	} else if (b <= -3.6e-152) {
		tmp = t_1;
	} else if (b <= -6.8e-240) {
		tmp = x + a;
	} else if (b <= -9e-249) {
		tmp = z - (y * z);
	} else if (b <= -2.9e-292) {
		tmp = a - (t * a);
	} else if (b <= 1.05e-292) {
		tmp = x - (y * z);
	} else if (b <= 2.3e-30) {
		tmp = t_1;
	} else if (b <= 3.1e+24) {
		tmp = x + (b * (y - 2.0));
	} else if (b <= 1.35e+70) {
		tmp = t * (b - a);
	} 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 = a + (z * (1.0d0 - y))
    t_2 = ((y + t) - 2.0d0) * b
    if (b <= (-7.3d+50)) then
        tmp = t_2
    else if (b <= (-3.6d-152)) then
        tmp = t_1
    else if (b <= (-6.8d-240)) then
        tmp = x + a
    else if (b <= (-9d-249)) then
        tmp = z - (y * z)
    else if (b <= (-2.9d-292)) then
        tmp = a - (t * a)
    else if (b <= 1.05d-292) then
        tmp = x - (y * z)
    else if (b <= 2.3d-30) then
        tmp = t_1
    else if (b <= 3.1d+24) then
        tmp = x + (b * (y - 2.0d0))
    else if (b <= 1.35d+70) then
        tmp = t * (b - a)
    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 = a + (z * (1.0 - y));
	double t_2 = ((y + t) - 2.0) * b;
	double tmp;
	if (b <= -7.3e+50) {
		tmp = t_2;
	} else if (b <= -3.6e-152) {
		tmp = t_1;
	} else if (b <= -6.8e-240) {
		tmp = x + a;
	} else if (b <= -9e-249) {
		tmp = z - (y * z);
	} else if (b <= -2.9e-292) {
		tmp = a - (t * a);
	} else if (b <= 1.05e-292) {
		tmp = x - (y * z);
	} else if (b <= 2.3e-30) {
		tmp = t_1;
	} else if (b <= 3.1e+24) {
		tmp = x + (b * (y - 2.0));
	} else if (b <= 1.35e+70) {
		tmp = t * (b - a);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a + (z * (1.0 - y))
	t_2 = ((y + t) - 2.0) * b
	tmp = 0
	if b <= -7.3e+50:
		tmp = t_2
	elif b <= -3.6e-152:
		tmp = t_1
	elif b <= -6.8e-240:
		tmp = x + a
	elif b <= -9e-249:
		tmp = z - (y * z)
	elif b <= -2.9e-292:
		tmp = a - (t * a)
	elif b <= 1.05e-292:
		tmp = x - (y * z)
	elif b <= 2.3e-30:
		tmp = t_1
	elif b <= 3.1e+24:
		tmp = x + (b * (y - 2.0))
	elif b <= 1.35e+70:
		tmp = t * (b - a)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a + Float64(z * Float64(1.0 - y)))
	t_2 = Float64(Float64(Float64(y + t) - 2.0) * b)
	tmp = 0.0
	if (b <= -7.3e+50)
		tmp = t_2;
	elseif (b <= -3.6e-152)
		tmp = t_1;
	elseif (b <= -6.8e-240)
		tmp = Float64(x + a);
	elseif (b <= -9e-249)
		tmp = Float64(z - Float64(y * z));
	elseif (b <= -2.9e-292)
		tmp = Float64(a - Float64(t * a));
	elseif (b <= 1.05e-292)
		tmp = Float64(x - Float64(y * z));
	elseif (b <= 2.3e-30)
		tmp = t_1;
	elseif (b <= 3.1e+24)
		tmp = Float64(x + Float64(b * Float64(y - 2.0)));
	elseif (b <= 1.35e+70)
		tmp = Float64(t * Float64(b - a));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a + (z * (1.0 - y));
	t_2 = ((y + t) - 2.0) * b;
	tmp = 0.0;
	if (b <= -7.3e+50)
		tmp = t_2;
	elseif (b <= -3.6e-152)
		tmp = t_1;
	elseif (b <= -6.8e-240)
		tmp = x + a;
	elseif (b <= -9e-249)
		tmp = z - (y * z);
	elseif (b <= -2.9e-292)
		tmp = a - (t * a);
	elseif (b <= 1.05e-292)
		tmp = x - (y * z);
	elseif (b <= 2.3e-30)
		tmp = t_1;
	elseif (b <= 3.1e+24)
		tmp = x + (b * (y - 2.0));
	elseif (b <= 1.35e+70)
		tmp = t * (b - a);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[b, -7.3e+50], t$95$2, If[LessEqual[b, -3.6e-152], t$95$1, If[LessEqual[b, -6.8e-240], N[(x + a), $MachinePrecision], If[LessEqual[b, -9e-249], N[(z - N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -2.9e-292], N[(a - N[(t * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.05e-292], N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.3e-30], t$95$1, If[LessEqual[b, 3.1e+24], N[(x + N[(b * N[(y - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.35e+70], N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if b < -7.3000000000000003e50 or 1.35e70 < b

   1. Initial program 90.3%

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

   2. Taylor expanded in b around inf 80.4%

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

   if -7.3000000000000003e50 < b < -3.6e-152 or 1.04999999999999994e-292 < b < 2.29999999999999984e-30

   1. Initial program 98.8%

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

   2. Taylor expanded in b around 0 94.0%

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

   3. Taylor expanded in t around 0 78.1%

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

      1. neg-mul-1 78.1%

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

   5. Simplified 78.1%

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

   6. Taylor expanded in x around 0 61.2%

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

   if -3.6e-152 < b < -6.79999999999999979e-240

   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 88.0%

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

   3. Taylor expanded in b around 0 88.0%

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

   4. Taylor expanded in t around 0 75.5%

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

      1. cancel-sign-sub-inv 75.5%

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

      2. metadata-eval 75.5%

         \[\leadsto x + \color{blue}{1} \cdot a \]

      3. *-lft-identity 75.5%

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

   6. Simplified 75.5%

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

   if -6.79999999999999979e-240 < b < -8.99999999999999962e-249

   1. Initial program 99.5%

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

   2. Taylor expanded in z around inf 99.5%

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

   3. Taylor expanded in y around 0 100.0%

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

   if -8.99999999999999962e-249 < b < -2.89999999999999993e-292

   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 a around inf 63.4%

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

   3. Taylor expanded in t around 0 63.6%

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

   if -2.89999999999999993e-292 < b < 1.04999999999999994e-292

   1. Initial program 100.0%

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

   2. Taylor expanded in b around 0 100.0%

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

   3. Taylor expanded in y around inf 55.9%

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

   if 2.29999999999999984e-30 < b < 3.10000000000000011e24

   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 z around 0 88.0%

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

   3. Taylor expanded in t around inf 81.8%

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

      1. *-commutative 81.8%

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

   5. Simplified 81.8%

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

   6. Taylor expanded in t around 0 63.5%

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

   if 3.10000000000000011e24 < b < 1.35e70

   1. Initial program 87.5%

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

   2. Taylor expanded in t around inf 75.7%

      \[\leadsto \color{blue}{t \cdot \left(b - a\right)} \]
3. Recombined 8 regimes into one program.

4. Final simplification 70.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -7.3 \cdot 10^{+50}:\\ \;\;\;\;\left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{elif}\;b \leq -3.6 \cdot 10^{-152}:\\ \;\;\;\;a + z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq -6.8 \cdot 10^{-240}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;b \leq -9 \cdot 10^{-249}:\\ \;\;\;\;z - y \cdot z\\ \mathbf{elif}\;b \leq -2.9 \cdot 10^{-292}:\\ \;\;\;\;a - t \cdot a\\ \mathbf{elif}\;b \leq 1.05 \cdot 10^{-292}:\\ \;\;\;\;x - y \cdot z\\ \mathbf{elif}\;b \leq 2.3 \cdot 10^{-30}:\\ \;\;\;\;a + z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq 3.1 \cdot 10^{+24}:\\ \;\;\;\;x + b \cdot \left(y - 2\right)\\ \mathbf{elif}\;b \leq 1.35 \cdot 10^{+70}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(y + t\right) - 2\right) \cdot b\\ \end{array} \]

Alternative 4: 50.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(b - z\right)\\ t_2 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -4.9 \cdot 10^{+61}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -9.2 \cdot 10^{-171}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq -1.3 \cdot 10^{-261}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{-298}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq 5 \cdot 10^{-294}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{-273}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;t \leq 3.3 \cdot 10^{-261}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq 4.3 \cdot 10^{-119}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 9.4 \cdot 10^{+19}:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (- b z))) (t_2 (* t (- b a))))
   (if (<= t -4.9e+61)
     t_2
     (if (<= t -9.2e-171)
       (+ x a)
       (if (<= t -1.3e-261)
         t_1
         (if (<= t 1.15e-298)
           (+ x a)
           (if (<= t 5e-294)
             t_1
             (if (<= t 2.7e-273)
               (+ x z)
               (if (<= t 3.3e-261)
                 (+ x a)
                 (if (<= t 4.3e-119)
                   t_1
                   (if (<= t 9.4e+19) (+ x a) t_2)))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (b - z);
	double t_2 = t * (b - a);
	double tmp;
	if (t <= -4.9e+61) {
		tmp = t_2;
	} else if (t <= -9.2e-171) {
		tmp = x + a;
	} else if (t <= -1.3e-261) {
		tmp = t_1;
	} else if (t <= 1.15e-298) {
		tmp = x + a;
	} else if (t <= 5e-294) {
		tmp = t_1;
	} else if (t <= 2.7e-273) {
		tmp = x + z;
	} else if (t <= 3.3e-261) {
		tmp = x + a;
	} else if (t <= 4.3e-119) {
		tmp = t_1;
	} else if (t <= 9.4e+19) {
		tmp = x + a;
	} 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 = y * (b - z)
    t_2 = t * (b - a)
    if (t <= (-4.9d+61)) then
        tmp = t_2
    else if (t <= (-9.2d-171)) then
        tmp = x + a
    else if (t <= (-1.3d-261)) then
        tmp = t_1
    else if (t <= 1.15d-298) then
        tmp = x + a
    else if (t <= 5d-294) then
        tmp = t_1
    else if (t <= 2.7d-273) then
        tmp = x + z
    else if (t <= 3.3d-261) then
        tmp = x + a
    else if (t <= 4.3d-119) then
        tmp = t_1
    else if (t <= 9.4d+19) then
        tmp = x + a
    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 = y * (b - z);
	double t_2 = t * (b - a);
	double tmp;
	if (t <= -4.9e+61) {
		tmp = t_2;
	} else if (t <= -9.2e-171) {
		tmp = x + a;
	} else if (t <= -1.3e-261) {
		tmp = t_1;
	} else if (t <= 1.15e-298) {
		tmp = x + a;
	} else if (t <= 5e-294) {
		tmp = t_1;
	} else if (t <= 2.7e-273) {
		tmp = x + z;
	} else if (t <= 3.3e-261) {
		tmp = x + a;
	} else if (t <= 4.3e-119) {
		tmp = t_1;
	} else if (t <= 9.4e+19) {
		tmp = x + a;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y * (b - z)
	t_2 = t * (b - a)
	tmp = 0
	if t <= -4.9e+61:
		tmp = t_2
	elif t <= -9.2e-171:
		tmp = x + a
	elif t <= -1.3e-261:
		tmp = t_1
	elif t <= 1.15e-298:
		tmp = x + a
	elif t <= 5e-294:
		tmp = t_1
	elif t <= 2.7e-273:
		tmp = x + z
	elif t <= 3.3e-261:
		tmp = x + a
	elif t <= 4.3e-119:
		tmp = t_1
	elif t <= 9.4e+19:
		tmp = x + a
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y * Float64(b - z))
	t_2 = Float64(t * Float64(b - a))
	tmp = 0.0
	if (t <= -4.9e+61)
		tmp = t_2;
	elseif (t <= -9.2e-171)
		tmp = Float64(x + a);
	elseif (t <= -1.3e-261)
		tmp = t_1;
	elseif (t <= 1.15e-298)
		tmp = Float64(x + a);
	elseif (t <= 5e-294)
		tmp = t_1;
	elseif (t <= 2.7e-273)
		tmp = Float64(x + z);
	elseif (t <= 3.3e-261)
		tmp = Float64(x + a);
	elseif (t <= 4.3e-119)
		tmp = t_1;
	elseif (t <= 9.4e+19)
		tmp = Float64(x + a);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y * (b - z);
	t_2 = t * (b - a);
	tmp = 0.0;
	if (t <= -4.9e+61)
		tmp = t_2;
	elseif (t <= -9.2e-171)
		tmp = x + a;
	elseif (t <= -1.3e-261)
		tmp = t_1;
	elseif (t <= 1.15e-298)
		tmp = x + a;
	elseif (t <= 5e-294)
		tmp = t_1;
	elseif (t <= 2.7e-273)
		tmp = x + z;
	elseif (t <= 3.3e-261)
		tmp = x + a;
	elseif (t <= 4.3e-119)
		tmp = t_1;
	elseif (t <= 9.4e+19)
		tmp = x + a;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -4.9e+61], t$95$2, If[LessEqual[t, -9.2e-171], N[(x + a), $MachinePrecision], If[LessEqual[t, -1.3e-261], t$95$1, If[LessEqual[t, 1.15e-298], N[(x + a), $MachinePrecision], If[LessEqual[t, 5e-294], t$95$1, If[LessEqual[t, 2.7e-273], N[(x + z), $MachinePrecision], If[LessEqual[t, 3.3e-261], N[(x + a), $MachinePrecision], If[LessEqual[t, 4.3e-119], t$95$1, If[LessEqual[t, 9.4e+19], N[(x + a), $MachinePrecision], t$95$2]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -4.90000000000000025e61 or 9.4e19 < t

   1. Initial program 90.4%

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

   2. Taylor expanded in t around inf 71.7%

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

   if -4.90000000000000025e61 < t < -9.19999999999999911e-171 or -1.3000000000000001e-261 < t < 1.15e-298 or 2.69999999999999984e-273 < t < 3.2999999999999998e-261 or 4.3e-119 < t < 9.4e19

   1. Initial program 98.8%

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

   2. Taylor expanded in z around 0 77.2%

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

   3. Taylor expanded in b around 0 53.6%

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

   4. Taylor expanded in t around 0 51.1%

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

      1. cancel-sign-sub-inv 51.1%

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

      2. metadata-eval 51.1%

         \[\leadsto x + \color{blue}{1} \cdot a \]

      3. *-lft-identity 51.1%

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

   6. Simplified 51.1%

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

   if -9.19999999999999911e-171 < t < -1.3000000000000001e-261 or 1.15e-298 < t < 5.0000000000000003e-294 or 3.2999999999999998e-261 < t < 4.3e-119

   1. Initial program 98.2%

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

   2. Taylor expanded in y around inf 57.7%

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

   if 5.0000000000000003e-294 < t < 2.69999999999999984e-273

   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 86.5%

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

   3. Taylor expanded in b around 0 72.0%

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

   4. Taylor expanded in y around 0 72.0%

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

      1. cancel-sign-sub-inv 72.0%

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

      2. metadata-eval 72.0%

         \[\leadsto x + \color{blue}{1} \cdot z \]

      3. *-lft-identity 72.0%

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

   6. Simplified 72.0%

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

4. Final simplification 61.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.9 \cdot 10^{+61}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq -9.2 \cdot 10^{-171}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq -1.3 \cdot 10^{-261}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{-298}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq 5 \cdot 10^{-294}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{-273}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;t \leq 3.3 \cdot 10^{-261}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq 4.3 \cdot 10^{-119}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;t \leq 9.4 \cdot 10^{+19}:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \]

Alternative 5: 64.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(1 - y\right)\\ t_2 := x + \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{if}\;b \leq -5.8 \cdot 10^{+20}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -4 \cdot 10^{-59}:\\ \;\;\;\;a + t_1\\ \mathbf{elif}\;b \leq 1.45 \cdot 10^{-280}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 4.2 \cdot 10^{-22}:\\ \;\;\;\;x + t_1\\ \mathbf{elif}\;b \leq 6.2 \cdot 10^{+24}:\\ \;\;\;\;x + \left(a + b \cdot \left(y + -2\right)\right)\\ \mathbf{elif}\;b \leq 4.5 \cdot 10^{+70}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (- 1.0 y))) (t_2 (+ x (* (- (+ y t) 2.0) b))))
   (if (<= b -5.8e+20)
     t_2
     (if (<= b -4e-59)
       (+ a t_1)
       (if (<= b 1.45e-280)
         (+ x (* a (- 1.0 t)))
         (if (<= b 4.2e-22)
           (+ x t_1)
           (if (<= b 6.2e+24)
             (+ x (+ a (* b (+ y -2.0))))
             (if (<= b 4.5e+70) (* t (- b a)) t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (1.0 - y);
	double t_2 = x + (((y + t) - 2.0) * b);
	double tmp;
	if (b <= -5.8e+20) {
		tmp = t_2;
	} else if (b <= -4e-59) {
		tmp = a + t_1;
	} else if (b <= 1.45e-280) {
		tmp = x + (a * (1.0 - t));
	} else if (b <= 4.2e-22) {
		tmp = x + t_1;
	} else if (b <= 6.2e+24) {
		tmp = x + (a + (b * (y + -2.0)));
	} else if (b <= 4.5e+70) {
		tmp = t * (b - a);
	} 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 = z * (1.0d0 - y)
    t_2 = x + (((y + t) - 2.0d0) * b)
    if (b <= (-5.8d+20)) then
        tmp = t_2
    else if (b <= (-4d-59)) then
        tmp = a + t_1
    else if (b <= 1.45d-280) then
        tmp = x + (a * (1.0d0 - t))
    else if (b <= 4.2d-22) then
        tmp = x + t_1
    else if (b <= 6.2d+24) then
        tmp = x + (a + (b * (y + (-2.0d0))))
    else if (b <= 4.5d+70) then
        tmp = t * (b - a)
    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 = z * (1.0 - y);
	double t_2 = x + (((y + t) - 2.0) * b);
	double tmp;
	if (b <= -5.8e+20) {
		tmp = t_2;
	} else if (b <= -4e-59) {
		tmp = a + t_1;
	} else if (b <= 1.45e-280) {
		tmp = x + (a * (1.0 - t));
	} else if (b <= 4.2e-22) {
		tmp = x + t_1;
	} else if (b <= 6.2e+24) {
		tmp = x + (a + (b * (y + -2.0)));
	} else if (b <= 4.5e+70) {
		tmp = t * (b - a);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * (1.0 - y)
	t_2 = x + (((y + t) - 2.0) * b)
	tmp = 0
	if b <= -5.8e+20:
		tmp = t_2
	elif b <= -4e-59:
		tmp = a + t_1
	elif b <= 1.45e-280:
		tmp = x + (a * (1.0 - t))
	elif b <= 4.2e-22:
		tmp = x + t_1
	elif b <= 6.2e+24:
		tmp = x + (a + (b * (y + -2.0)))
	elif b <= 4.5e+70:
		tmp = t * (b - a)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(1.0 - y))
	t_2 = Float64(x + Float64(Float64(Float64(y + t) - 2.0) * b))
	tmp = 0.0
	if (b <= -5.8e+20)
		tmp = t_2;
	elseif (b <= -4e-59)
		tmp = Float64(a + t_1);
	elseif (b <= 1.45e-280)
		tmp = Float64(x + Float64(a * Float64(1.0 - t)));
	elseif (b <= 4.2e-22)
		tmp = Float64(x + t_1);
	elseif (b <= 6.2e+24)
		tmp = Float64(x + Float64(a + Float64(b * Float64(y + -2.0))));
	elseif (b <= 4.5e+70)
		tmp = Float64(t * Float64(b - a));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * (1.0 - y);
	t_2 = x + (((y + t) - 2.0) * b);
	tmp = 0.0;
	if (b <= -5.8e+20)
		tmp = t_2;
	elseif (b <= -4e-59)
		tmp = a + t_1;
	elseif (b <= 1.45e-280)
		tmp = x + (a * (1.0 - t));
	elseif (b <= 4.2e-22)
		tmp = x + t_1;
	elseif (b <= 6.2e+24)
		tmp = x + (a + (b * (y + -2.0)));
	elseif (b <= 4.5e+70)
		tmp = t * (b - a);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -5.8e+20], t$95$2, If[LessEqual[b, -4e-59], N[(a + t$95$1), $MachinePrecision], If[LessEqual[b, 1.45e-280], N[(x + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 4.2e-22], N[(x + t$95$1), $MachinePrecision], If[LessEqual[b, 6.2e+24], N[(x + N[(a + N[(b * N[(y + -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 4.5e+70], N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if b < -5.8e20 or 4.4999999999999999e70 < b

   1. Initial program 89.8%

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

   2. Taylor expanded in z around 0 84.0%

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

   3. Taylor expanded in a around 0 80.8%

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

   if -5.8e20 < b < -4.0000000000000001e-59

   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 87.6%

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

   3. Taylor expanded in t around 0 87.3%

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

      1. neg-mul-1 87.3%

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

   5. Simplified 87.3%

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

   6. Taylor expanded in x around 0 81.4%

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

   if -4.0000000000000001e-59 < b < 1.45e-280

   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 z around 0 75.2%

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

   3. Taylor expanded in b around 0 71.5%

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

   if 1.45e-280 < b < 4.20000000000000016e-22

   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 68.9%

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

   3. Taylor expanded in b around 0 66.8%

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

   if 4.20000000000000016e-22 < b < 6.20000000000000022e24

   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 z around 0 92.3%

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

   3. Taylor expanded in t around 0 75.7%

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

      1. associate--l+ 75.7%

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

      2. sub-neg 75.7%

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

      3. metadata-eval 75.7%

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

      4. neg-mul-1 75.7%

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

   5. Simplified 75.7%

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

   if 6.20000000000000022e24 < b < 4.4999999999999999e70

   1. Initial program 88.9%

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

   2. Taylor expanded in t around inf 78.4%

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

4. Final simplification 75.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5.8 \cdot 10^{+20}:\\ \;\;\;\;x + \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{elif}\;b \leq -4 \cdot 10^{-59}:\\ \;\;\;\;a + z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq 1.45 \cdot 10^{-280}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 4.2 \cdot 10^{-22}:\\ \;\;\;\;x + z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq 6.2 \cdot 10^{+24}:\\ \;\;\;\;x + \left(a + b \cdot \left(y + -2\right)\right)\\ \mathbf{elif}\;b \leq 4.5 \cdot 10^{+70}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(\left(y + t\right) - 2\right) \cdot b\\ \end{array} \]

Alternative 6: 74.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(1 - y\right)\\ t_2 := x + \left(a + t_1\right)\\ t_3 := x + \left(\left(y + t\right) - 2\right) \cdot b\\ t_4 := x + \left(t_1 - t \cdot a\right)\\ \mathbf{if}\;b \leq -5.7 \cdot 10^{+51}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq -2.15 \cdot 10^{-74}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 1.4 \cdot 10^{-289}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;b \leq 4.1 \cdot 10^{-122}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 1.9 \cdot 10^{+70}:\\ \;\;\;\;t_4\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (- 1.0 y)))
        (t_2 (+ x (+ a t_1)))
        (t_3 (+ x (* (- (+ y t) 2.0) b)))
        (t_4 (+ x (- t_1 (* t a)))))
   (if (<= b -5.7e+51)
     t_3
     (if (<= b -2.15e-74)
       t_2
       (if (<= b 1.4e-289)
         t_4
         (if (<= b 4.1e-122) t_2 (if (<= b 1.9e+70) t_4 t_3)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (1.0 - y);
	double t_2 = x + (a + t_1);
	double t_3 = x + (((y + t) - 2.0) * b);
	double t_4 = x + (t_1 - (t * a));
	double tmp;
	if (b <= -5.7e+51) {
		tmp = t_3;
	} else if (b <= -2.15e-74) {
		tmp = t_2;
	} else if (b <= 1.4e-289) {
		tmp = t_4;
	} else if (b <= 4.1e-122) {
		tmp = t_2;
	} else if (b <= 1.9e+70) {
		tmp = t_4;
	} else {
		tmp = t_3;
	}
	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) :: t_4
    real(8) :: tmp
    t_1 = z * (1.0d0 - y)
    t_2 = x + (a + t_1)
    t_3 = x + (((y + t) - 2.0d0) * b)
    t_4 = x + (t_1 - (t * a))
    if (b <= (-5.7d+51)) then
        tmp = t_3
    else if (b <= (-2.15d-74)) then
        tmp = t_2
    else if (b <= 1.4d-289) then
        tmp = t_4
    else if (b <= 4.1d-122) then
        tmp = t_2
    else if (b <= 1.9d+70) then
        tmp = t_4
    else
        tmp = t_3
    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 = z * (1.0 - y);
	double t_2 = x + (a + t_1);
	double t_3 = x + (((y + t) - 2.0) * b);
	double t_4 = x + (t_1 - (t * a));
	double tmp;
	if (b <= -5.7e+51) {
		tmp = t_3;
	} else if (b <= -2.15e-74) {
		tmp = t_2;
	} else if (b <= 1.4e-289) {
		tmp = t_4;
	} else if (b <= 4.1e-122) {
		tmp = t_2;
	} else if (b <= 1.9e+70) {
		tmp = t_4;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * (1.0 - y)
	t_2 = x + (a + t_1)
	t_3 = x + (((y + t) - 2.0) * b)
	t_4 = x + (t_1 - (t * a))
	tmp = 0
	if b <= -5.7e+51:
		tmp = t_3
	elif b <= -2.15e-74:
		tmp = t_2
	elif b <= 1.4e-289:
		tmp = t_4
	elif b <= 4.1e-122:
		tmp = t_2
	elif b <= 1.9e+70:
		tmp = t_4
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(1.0 - y))
	t_2 = Float64(x + Float64(a + t_1))
	t_3 = Float64(x + Float64(Float64(Float64(y + t) - 2.0) * b))
	t_4 = Float64(x + Float64(t_1 - Float64(t * a)))
	tmp = 0.0
	if (b <= -5.7e+51)
		tmp = t_3;
	elseif (b <= -2.15e-74)
		tmp = t_2;
	elseif (b <= 1.4e-289)
		tmp = t_4;
	elseif (b <= 4.1e-122)
		tmp = t_2;
	elseif (b <= 1.9e+70)
		tmp = t_4;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * (1.0 - y);
	t_2 = x + (a + t_1);
	t_3 = x + (((y + t) - 2.0) * b);
	t_4 = x + (t_1 - (t * a));
	tmp = 0.0;
	if (b <= -5.7e+51)
		tmp = t_3;
	elseif (b <= -2.15e-74)
		tmp = t_2;
	elseif (b <= 1.4e-289)
		tmp = t_4;
	elseif (b <= 4.1e-122)
		tmp = t_2;
	elseif (b <= 1.9e+70)
		tmp = t_4;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(a + t$95$1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x + N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(x + N[(t$95$1 - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -5.7e+51], t$95$3, If[LessEqual[b, -2.15e-74], t$95$2, If[LessEqual[b, 1.4e-289], t$95$4, If[LessEqual[b, 4.1e-122], t$95$2, If[LessEqual[b, 1.9e+70], t$95$4, t$95$3]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -5.7000000000000002e51 or 1.8999999999999999e70 < b

   1. Initial program 90.3%

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

   2. Taylor expanded in z around 0 85.1%

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

   3. Taylor expanded in a around 0 82.7%

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

   if -5.7000000000000002e51 < b < -2.14999999999999986e-74 or 1.39999999999999993e-289 < b < 4.1e-122

   1. Initial program 98.2%

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

   2. Taylor expanded in b around 0 94.8%

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

   3. Taylor expanded in t around 0 84.6%

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

      1. neg-mul-1 84.6%

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

   5. Simplified 84.6%

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

   if -2.14999999999999986e-74 < b < 1.39999999999999993e-289 or 4.1e-122 < b < 1.8999999999999999e70

   1. Initial program 98.9%

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

   2. Taylor expanded in b around 0 90.4%

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

   3. Taylor expanded in t around inf 78.7%

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

      1. *-commutative 62.8%

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

   5. Simplified 78.7%

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

4. Final simplification 81.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5.7 \cdot 10^{+51}:\\ \;\;\;\;x + \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{elif}\;b \leq -2.15 \cdot 10^{-74}:\\ \;\;\;\;x + \left(a + z \cdot \left(1 - y\right)\right)\\ \mathbf{elif}\;b \leq 1.4 \cdot 10^{-289}:\\ \;\;\;\;x + \left(z \cdot \left(1 - y\right) - t \cdot a\right)\\ \mathbf{elif}\;b \leq 4.1 \cdot 10^{-122}:\\ \;\;\;\;x + \left(a + z \cdot \left(1 - y\right)\right)\\ \mathbf{elif}\;b \leq 1.9 \cdot 10^{+70}:\\ \;\;\;\;x + \left(z \cdot \left(1 - y\right) - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(\left(y + t\right) - 2\right) \cdot b\\ \end{array} \]

Alternative 7: 86.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(1 - y\right)\\ t_2 := x + \left(\left(y + t\right) - 2\right) \cdot b\\ t_3 := t_2 + t_1\\ t_4 := a \cdot \left(1 - t\right)\\ \mathbf{if}\;b \leq -4.7 \cdot 10^{+49}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq 4.5 \cdot 10^{-22}:\\ \;\;\;\;x + \left(t_1 + t_4\right)\\ \mathbf{elif}\;b \leq 2.1 \cdot 10^{+150}:\\ \;\;\;\;t_2 + t_4\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (- 1.0 y)))
        (t_2 (+ x (* (- (+ y t) 2.0) b)))
        (t_3 (+ t_2 t_1))
        (t_4 (* a (- 1.0 t))))
   (if (<= b -4.7e+49)
     t_3
     (if (<= b 4.5e-22)
       (+ x (+ t_1 t_4))
       (if (<= b 2.1e+150) (+ t_2 t_4) t_3)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (1.0 - y);
	double t_2 = x + (((y + t) - 2.0) * b);
	double t_3 = t_2 + t_1;
	double t_4 = a * (1.0 - t);
	double tmp;
	if (b <= -4.7e+49) {
		tmp = t_3;
	} else if (b <= 4.5e-22) {
		tmp = x + (t_1 + t_4);
	} else if (b <= 2.1e+150) {
		tmp = t_2 + t_4;
	} else {
		tmp = t_3;
	}
	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) :: t_4
    real(8) :: tmp
    t_1 = z * (1.0d0 - y)
    t_2 = x + (((y + t) - 2.0d0) * b)
    t_3 = t_2 + t_1
    t_4 = a * (1.0d0 - t)
    if (b <= (-4.7d+49)) then
        tmp = t_3
    else if (b <= 4.5d-22) then
        tmp = x + (t_1 + t_4)
    else if (b <= 2.1d+150) then
        tmp = t_2 + t_4
    else
        tmp = t_3
    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 = z * (1.0 - y);
	double t_2 = x + (((y + t) - 2.0) * b);
	double t_3 = t_2 + t_1;
	double t_4 = a * (1.0 - t);
	double tmp;
	if (b <= -4.7e+49) {
		tmp = t_3;
	} else if (b <= 4.5e-22) {
		tmp = x + (t_1 + t_4);
	} else if (b <= 2.1e+150) {
		tmp = t_2 + t_4;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * (1.0 - y)
	t_2 = x + (((y + t) - 2.0) * b)
	t_3 = t_2 + t_1
	t_4 = a * (1.0 - t)
	tmp = 0
	if b <= -4.7e+49:
		tmp = t_3
	elif b <= 4.5e-22:
		tmp = x + (t_1 + t_4)
	elif b <= 2.1e+150:
		tmp = t_2 + t_4
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(1.0 - y))
	t_2 = Float64(x + Float64(Float64(Float64(y + t) - 2.0) * b))
	t_3 = Float64(t_2 + t_1)
	t_4 = Float64(a * Float64(1.0 - t))
	tmp = 0.0
	if (b <= -4.7e+49)
		tmp = t_3;
	elseif (b <= 4.5e-22)
		tmp = Float64(x + Float64(t_1 + t_4));
	elseif (b <= 2.1e+150)
		tmp = Float64(t_2 + t_4);
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * (1.0 - y);
	t_2 = x + (((y + t) - 2.0) * b);
	t_3 = t_2 + t_1;
	t_4 = a * (1.0 - t);
	tmp = 0.0;
	if (b <= -4.7e+49)
		tmp = t_3;
	elseif (b <= 4.5e-22)
		tmp = x + (t_1 + t_4);
	elseif (b <= 2.1e+150)
		tmp = t_2 + t_4;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 + t$95$1), $MachinePrecision]}, Block[{t$95$4 = N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -4.7e+49], t$95$3, If[LessEqual[b, 4.5e-22], N[(x + N[(t$95$1 + t$95$4), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.1e+150], N[(t$95$2 + t$95$4), $MachinePrecision], t$95$3]]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -4.6999999999999997e49 or 2.09999999999999998e150 < b

   1. Initial program 91.6%

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

   2. Taylor expanded in a around 0 91.8%

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

   if -4.6999999999999997e49 < b < 4.49999999999999987e-22

   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 95.9%

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

   if 4.49999999999999987e-22 < b < 2.09999999999999998e150

   1. Initial program 89.7%

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

   2. Taylor expanded in z around 0 87.5%

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

4. Final simplification 93.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.7 \cdot 10^{+49}:\\ \;\;\;\;\left(x + \left(\left(y + t\right) - 2\right) \cdot b\right) + z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq 4.5 \cdot 10^{-22}:\\ \;\;\;\;x + \left(z \cdot \left(1 - y\right) + a \cdot \left(1 - t\right)\right)\\ \mathbf{elif}\;b \leq 2.1 \cdot 10^{+150}:\\ \;\;\;\;\left(x + \left(\left(y + t\right) - 2\right) \cdot b\right) + a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + \left(\left(y + t\right) - 2\right) \cdot b\right) + z \cdot \left(1 - y\right)\\ \end{array} \]

Alternative 8: 38.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(1 - t\right)\\ \mathbf{if}\;a \leq -1.06 \cdot 10^{+91}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -1.7 \cdot 10^{-28}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;a \leq -7.2 \cdot 10^{-45}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;a \leq -1.5 \cdot 10^{-116}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;a \leq 4.1 \cdot 10^{-141}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;a \leq 1.44 \cdot 10^{-39}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;a \leq 1.05 \cdot 10^{+78}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (- 1.0 t))))
   (if (<= a -1.06e+91)
     t_1
     (if (<= a -1.7e-28)
       (* y (- z))
       (if (<= a -7.2e-45)
         (+ x z)
         (if (<= a -1.5e-116)
           (* t b)
           (if (<= a 4.1e-141)
             (+ x z)
             (if (<= a 1.44e-39)
               (* y b)
               (if (<= a 1.05e+78) (+ x z) t_1)))))))))

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 (a <= -1.06e+91) {
		tmp = t_1;
	} else if (a <= -1.7e-28) {
		tmp = y * -z;
	} else if (a <= -7.2e-45) {
		tmp = x + z;
	} else if (a <= -1.5e-116) {
		tmp = t * b;
	} else if (a <= 4.1e-141) {
		tmp = x + z;
	} else if (a <= 1.44e-39) {
		tmp = y * b;
	} else if (a <= 1.05e+78) {
		tmp = x + z;
	} 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 = a * (1.0d0 - t)
    if (a <= (-1.06d+91)) then
        tmp = t_1
    else if (a <= (-1.7d-28)) then
        tmp = y * -z
    else if (a <= (-7.2d-45)) then
        tmp = x + z
    else if (a <= (-1.5d-116)) then
        tmp = t * b
    else if (a <= 4.1d-141) then
        tmp = x + z
    else if (a <= 1.44d-39) then
        tmp = y * b
    else if (a <= 1.05d+78) then
        tmp = x + z
    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 = a * (1.0 - t);
	double tmp;
	if (a <= -1.06e+91) {
		tmp = t_1;
	} else if (a <= -1.7e-28) {
		tmp = y * -z;
	} else if (a <= -7.2e-45) {
		tmp = x + z;
	} else if (a <= -1.5e-116) {
		tmp = t * b;
	} else if (a <= 4.1e-141) {
		tmp = x + z;
	} else if (a <= 1.44e-39) {
		tmp = y * b;
	} else if (a <= 1.05e+78) {
		tmp = x + z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (1.0 - t)
	tmp = 0
	if a <= -1.06e+91:
		tmp = t_1
	elif a <= -1.7e-28:
		tmp = y * -z
	elif a <= -7.2e-45:
		tmp = x + z
	elif a <= -1.5e-116:
		tmp = t * b
	elif a <= 4.1e-141:
		tmp = x + z
	elif a <= 1.44e-39:
		tmp = y * b
	elif a <= 1.05e+78:
		tmp = x + z
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(1.0 - t))
	tmp = 0.0
	if (a <= -1.06e+91)
		tmp = t_1;
	elseif (a <= -1.7e-28)
		tmp = Float64(y * Float64(-z));
	elseif (a <= -7.2e-45)
		tmp = Float64(x + z);
	elseif (a <= -1.5e-116)
		tmp = Float64(t * b);
	elseif (a <= 4.1e-141)
		tmp = Float64(x + z);
	elseif (a <= 1.44e-39)
		tmp = Float64(y * b);
	elseif (a <= 1.05e+78)
		tmp = Float64(x + z);
	else
		tmp = t_1;
	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 (a <= -1.06e+91)
		tmp = t_1;
	elseif (a <= -1.7e-28)
		tmp = y * -z;
	elseif (a <= -7.2e-45)
		tmp = x + z;
	elseif (a <= -1.5e-116)
		tmp = t * b;
	elseif (a <= 4.1e-141)
		tmp = x + z;
	elseif (a <= 1.44e-39)
		tmp = y * b;
	elseif (a <= 1.05e+78)
		tmp = x + z;
	else
		tmp = t_1;
	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[a, -1.06e+91], t$95$1, If[LessEqual[a, -1.7e-28], N[(y * (-z)), $MachinePrecision], If[LessEqual[a, -7.2e-45], N[(x + z), $MachinePrecision], If[LessEqual[a, -1.5e-116], N[(t * b), $MachinePrecision], If[LessEqual[a, 4.1e-141], N[(x + z), $MachinePrecision], If[LessEqual[a, 1.44e-39], N[(y * b), $MachinePrecision], If[LessEqual[a, 1.05e+78], N[(x + z), $MachinePrecision], t$95$1]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -1.05999999999999996e91 or 1.05e78 < a

   1. Initial program 92.4%

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

   2. Taylor expanded in a around inf 65.6%

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

   if -1.05999999999999996e91 < a < -1.7e-28

   1. Initial program 88.4%

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

   2. Taylor expanded in z around inf 43.6%

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

   3. Taylor expanded in y around inf 32.0%

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

      1. associate-*r* 32.0%

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

      2. neg-mul-1 32.0%

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

      3. *-commutative 32.0%

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

   5. Simplified 32.0%

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

   if -1.7e-28 < a < -7.20000000000000001e-45 or -1.50000000000000013e-116 < a < 4.10000000000000002e-141 or 1.44e-39 < a < 1.05e78

   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 a around 0 93.1%

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

   3. Taylor expanded in b around 0 58.4%

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

   4. Taylor expanded in y around 0 44.0%

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

      1. cancel-sign-sub-inv 44.0%

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

      2. metadata-eval 44.0%

         \[\leadsto x + \color{blue}{1} \cdot z \]

      3. *-lft-identity 44.0%

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

   6. Simplified 44.0%

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

   if -7.20000000000000001e-45 < a < -1.50000000000000013e-116

   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 0 93.7%

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

   3. Taylor expanded in t around inf 54.8%

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

   if 4.10000000000000002e-141 < a < 1.44e-39

   1. Initial program 95.4%

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

   2. Taylor expanded in z around 0 78.3%

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

   3. Taylor expanded in t around inf 78.3%

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

      1. *-commutative 78.3%

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

   5. Simplified 78.3%

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

   6. Taylor expanded in y around inf 41.3%

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

4. Final simplification 50.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.06 \cdot 10^{+91}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;a \leq -1.7 \cdot 10^{-28}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;a \leq -7.2 \cdot 10^{-45}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;a \leq -1.5 \cdot 10^{-116}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;a \leq 4.1 \cdot 10^{-141}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;a \leq 1.44 \cdot 10^{-39}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;a \leq 1.05 \cdot 10^{+78}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \end{array} \]

Alternative 9: 54.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{if}\;b \leq -2.1 \cdot 10^{+49}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -2.45 \cdot 10^{-14}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;b \leq -2.1 \cdot 10^{-36}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;b \leq -7.5 \cdot 10^{-52}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;b \leq -2.1 \cdot 10^{-107}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 29000000:\\ \;\;\;\;x - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- (+ y t) 2.0) b)))
   (if (<= b -2.1e+49)
     t_1
     (if (<= b -2.45e-14)
       (+ x a)
       (if (<= b -2.1e-36)
         (* y (- b z))
         (if (<= b -7.5e-52)
           (+ x z)
           (if (<= b -2.1e-107)
             (* a (- 1.0 t))
             (if (<= b 29000000.0) (- x (* y z)) t_1))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((y + t) - 2.0) * b;
	double tmp;
	if (b <= -2.1e+49) {
		tmp = t_1;
	} else if (b <= -2.45e-14) {
		tmp = x + a;
	} else if (b <= -2.1e-36) {
		tmp = y * (b - z);
	} else if (b <= -7.5e-52) {
		tmp = x + z;
	} else if (b <= -2.1e-107) {
		tmp = a * (1.0 - t);
	} else if (b <= 29000000.0) {
		tmp = x - (y * z);
	} 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 + t) - 2.0d0) * b
    if (b <= (-2.1d+49)) then
        tmp = t_1
    else if (b <= (-2.45d-14)) then
        tmp = x + a
    else if (b <= (-2.1d-36)) then
        tmp = y * (b - z)
    else if (b <= (-7.5d-52)) then
        tmp = x + z
    else if (b <= (-2.1d-107)) then
        tmp = a * (1.0d0 - t)
    else if (b <= 29000000.0d0) then
        tmp = x - (y * z)
    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 + t) - 2.0) * b;
	double tmp;
	if (b <= -2.1e+49) {
		tmp = t_1;
	} else if (b <= -2.45e-14) {
		tmp = x + a;
	} else if (b <= -2.1e-36) {
		tmp = y * (b - z);
	} else if (b <= -7.5e-52) {
		tmp = x + z;
	} else if (b <= -2.1e-107) {
		tmp = a * (1.0 - t);
	} else if (b <= 29000000.0) {
		tmp = x - (y * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((y + t) - 2.0) * b
	tmp = 0
	if b <= -2.1e+49:
		tmp = t_1
	elif b <= -2.45e-14:
		tmp = x + a
	elif b <= -2.1e-36:
		tmp = y * (b - z)
	elif b <= -7.5e-52:
		tmp = x + z
	elif b <= -2.1e-107:
		tmp = a * (1.0 - t)
	elif b <= 29000000.0:
		tmp = x - (y * z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(y + t) - 2.0) * b)
	tmp = 0.0
	if (b <= -2.1e+49)
		tmp = t_1;
	elseif (b <= -2.45e-14)
		tmp = Float64(x + a);
	elseif (b <= -2.1e-36)
		tmp = Float64(y * Float64(b - z));
	elseif (b <= -7.5e-52)
		tmp = Float64(x + z);
	elseif (b <= -2.1e-107)
		tmp = Float64(a * Float64(1.0 - t));
	elseif (b <= 29000000.0)
		tmp = Float64(x - Float64(y * z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((y + t) - 2.0) * b;
	tmp = 0.0;
	if (b <= -2.1e+49)
		tmp = t_1;
	elseif (b <= -2.45e-14)
		tmp = x + a;
	elseif (b <= -2.1e-36)
		tmp = y * (b - z);
	elseif (b <= -7.5e-52)
		tmp = x + z;
	elseif (b <= -2.1e-107)
		tmp = a * (1.0 - t);
	elseif (b <= 29000000.0)
		tmp = x - (y * z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[b, -2.1e+49], t$95$1, If[LessEqual[b, -2.45e-14], N[(x + a), $MachinePrecision], If[LessEqual[b, -2.1e-36], N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -7.5e-52], N[(x + z), $MachinePrecision], If[LessEqual[b, -2.1e-107], N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 29000000.0], N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 6 regimes

2. if b < -2.10000000000000011e49 or 2.9e7 < b

   1. Initial program 90.3%

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

   2. Taylor expanded in b around inf 75.5%

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

   if -2.10000000000000011e49 < b < -2.44999999999999997e-14

   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 z around 0 72.9%

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

   3. Taylor expanded in b around 0 73.3%

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

   4. Taylor expanded in t around 0 56.5%

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

      1. cancel-sign-sub-inv 56.5%

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

      2. metadata-eval 56.5%

         \[\leadsto x + \color{blue}{1} \cdot a \]

      3. *-lft-identity 56.5%

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

   6. Simplified 56.5%

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

   if -2.44999999999999997e-14 < b < -2.09999999999999991e-36

   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 y around inf 76.2%

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

   if -2.09999999999999991e-36 < b < -7.50000000000000006e-52

   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%

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

   3. Taylor expanded in b around 0 100.0%

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

   4. Taylor expanded in y around 0 100.0%

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

      1. cancel-sign-sub-inv 100.0%

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

      2. metadata-eval 100.0%

         \[\leadsto x + \color{blue}{1} \cdot z \]

      3. *-lft-identity 100.0%

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

   6. Simplified 100.0%

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

   if -7.50000000000000006e-52 < b < -2.0999999999999999e-107

   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 a around inf 47.6%

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

   if -2.0999999999999999e-107 < b < 2.9e7

   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 94.9%

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

   3. Taylor expanded in y around inf 49.3%

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

4. Final simplification 62.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.1 \cdot 10^{+49}:\\ \;\;\;\;\left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{elif}\;b \leq -2.45 \cdot 10^{-14}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;b \leq -2.1 \cdot 10^{-36}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;b \leq -7.5 \cdot 10^{-52}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;b \leq -2.1 \cdot 10^{-107}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 29000000:\\ \;\;\;\;x - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;\left(\left(y + t\right) - 2\right) \cdot b\\ \end{array} \]

Alternative 10: 55.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + b \cdot \left(y - 2\right)\\ t_2 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -6 \cdot 10^{+61}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -6.8 \cdot 10^{-176}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -3.95 \cdot 10^{-264}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{elif}\;t \leq 9.2 \cdot 10^{-122}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 6.6 \cdot 10^{-34}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq 2.95 \cdot 10^{+57}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* b (- y 2.0)))) (t_2 (* t (- b a))))
   (if (<= t -6e+61)
     t_2
     (if (<= t -6.8e-176)
       t_1
       (if (<= t -3.95e-264)
         (* z (- 1.0 y))
         (if (<= t 9.2e-122)
           t_1
           (if (<= t 6.6e-34) (+ x a) (if (<= t 2.95e+57) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (b * (y - 2.0));
	double t_2 = t * (b - a);
	double tmp;
	if (t <= -6e+61) {
		tmp = t_2;
	} else if (t <= -6.8e-176) {
		tmp = t_1;
	} else if (t <= -3.95e-264) {
		tmp = z * (1.0 - y);
	} else if (t <= 9.2e-122) {
		tmp = t_1;
	} else if (t <= 6.6e-34) {
		tmp = x + a;
	} else if (t <= 2.95e+57) {
		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 + (b * (y - 2.0d0))
    t_2 = t * (b - a)
    if (t <= (-6d+61)) then
        tmp = t_2
    else if (t <= (-6.8d-176)) then
        tmp = t_1
    else if (t <= (-3.95d-264)) then
        tmp = z * (1.0d0 - y)
    else if (t <= 9.2d-122) then
        tmp = t_1
    else if (t <= 6.6d-34) then
        tmp = x + a
    else if (t <= 2.95d+57) 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 + (b * (y - 2.0));
	double t_2 = t * (b - a);
	double tmp;
	if (t <= -6e+61) {
		tmp = t_2;
	} else if (t <= -6.8e-176) {
		tmp = t_1;
	} else if (t <= -3.95e-264) {
		tmp = z * (1.0 - y);
	} else if (t <= 9.2e-122) {
		tmp = t_1;
	} else if (t <= 6.6e-34) {
		tmp = x + a;
	} else if (t <= 2.95e+57) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (b * (y - 2.0))
	t_2 = t * (b - a)
	tmp = 0
	if t <= -6e+61:
		tmp = t_2
	elif t <= -6.8e-176:
		tmp = t_1
	elif t <= -3.95e-264:
		tmp = z * (1.0 - y)
	elif t <= 9.2e-122:
		tmp = t_1
	elif t <= 6.6e-34:
		tmp = x + a
	elif t <= 2.95e+57:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(b * Float64(y - 2.0)))
	t_2 = Float64(t * Float64(b - a))
	tmp = 0.0
	if (t <= -6e+61)
		tmp = t_2;
	elseif (t <= -6.8e-176)
		tmp = t_1;
	elseif (t <= -3.95e-264)
		tmp = Float64(z * Float64(1.0 - y));
	elseif (t <= 9.2e-122)
		tmp = t_1;
	elseif (t <= 6.6e-34)
		tmp = Float64(x + a);
	elseif (t <= 2.95e+57)
		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 + (b * (y - 2.0));
	t_2 = t * (b - a);
	tmp = 0.0;
	if (t <= -6e+61)
		tmp = t_2;
	elseif (t <= -6.8e-176)
		tmp = t_1;
	elseif (t <= -3.95e-264)
		tmp = z * (1.0 - y);
	elseif (t <= 9.2e-122)
		tmp = t_1;
	elseif (t <= 6.6e-34)
		tmp = x + a;
	elseif (t <= 2.95e+57)
		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[(b * N[(y - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -6e+61], t$95$2, If[LessEqual[t, -6.8e-176], t$95$1, If[LessEqual[t, -3.95e-264], N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 9.2e-122], t$95$1, If[LessEqual[t, 6.6e-34], N[(x + a), $MachinePrecision], If[LessEqual[t, 2.95e+57], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -6e61 or 2.95000000000000006e57 < t

   1. Initial program 90.0%

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

   2. Taylor expanded in t around inf 73.5%

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

   if -6e61 < t < -6.7999999999999994e-176 or -3.94999999999999996e-264 < t < 9.20000000000000028e-122 or 6.59999999999999965e-34 < t < 2.95000000000000006e57

   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 z around 0 76.7%

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

   3. Taylor expanded in t around inf 55.7%

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

      1. *-commutative 55.7%

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

   5. Simplified 55.7%

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

   6. Taylor expanded in t around 0 53.7%

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

   if -6.7999999999999994e-176 < t < -3.94999999999999996e-264

   1. Initial program 94.8%

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

   2. Taylor expanded in z around inf 69.5%

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

   if 9.20000000000000028e-122 < t < 6.59999999999999965e-34

   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 z around 0 68.2%

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

   3. Taylor expanded in b around 0 63.7%

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

   4. Taylor expanded in t around 0 63.7%

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

      1. cancel-sign-sub-inv 63.7%

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

      2. metadata-eval 63.7%

         \[\leadsto x + \color{blue}{1} \cdot a \]

      3. *-lft-identity 63.7%

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

   6. Simplified 63.7%

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

4. Final simplification 63.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6 \cdot 10^{+61}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq -6.8 \cdot 10^{-176}:\\ \;\;\;\;x + b \cdot \left(y - 2\right)\\ \mathbf{elif}\;t \leq -3.95 \cdot 10^{-264}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{elif}\;t \leq 9.2 \cdot 10^{-122}:\\ \;\;\;\;x + b \cdot \left(y - 2\right)\\ \mathbf{elif}\;t \leq 6.6 \cdot 10^{-34}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq 2.95 \cdot 10^{+57}:\\ \;\;\;\;x + b \cdot \left(y - 2\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \]

Alternative 11: 55.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + b \cdot \left(y - 2\right)\\ t_2 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -4.9 \cdot 10^{+61}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -6.8 \cdot 10^{-176}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.14 \cdot 10^{-265}:\\ \;\;\;\;z - y \cdot z\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{-122}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 4 \cdot 10^{-33}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq 8 \cdot 10^{+59}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* b (- y 2.0)))) (t_2 (* t (- b a))))
   (if (<= t -4.9e+61)
     t_2
     (if (<= t -6.8e-176)
       t_1
       (if (<= t -1.14e-265)
         (- z (* y z))
         (if (<= t 2.5e-122)
           t_1
           (if (<= t 4e-33) (+ x a) (if (<= t 8e+59) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (b * (y - 2.0));
	double t_2 = t * (b - a);
	double tmp;
	if (t <= -4.9e+61) {
		tmp = t_2;
	} else if (t <= -6.8e-176) {
		tmp = t_1;
	} else if (t <= -1.14e-265) {
		tmp = z - (y * z);
	} else if (t <= 2.5e-122) {
		tmp = t_1;
	} else if (t <= 4e-33) {
		tmp = x + a;
	} else if (t <= 8e+59) {
		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 + (b * (y - 2.0d0))
    t_2 = t * (b - a)
    if (t <= (-4.9d+61)) then
        tmp = t_2
    else if (t <= (-6.8d-176)) then
        tmp = t_1
    else if (t <= (-1.14d-265)) then
        tmp = z - (y * z)
    else if (t <= 2.5d-122) then
        tmp = t_1
    else if (t <= 4d-33) then
        tmp = x + a
    else if (t <= 8d+59) 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 + (b * (y - 2.0));
	double t_2 = t * (b - a);
	double tmp;
	if (t <= -4.9e+61) {
		tmp = t_2;
	} else if (t <= -6.8e-176) {
		tmp = t_1;
	} else if (t <= -1.14e-265) {
		tmp = z - (y * z);
	} else if (t <= 2.5e-122) {
		tmp = t_1;
	} else if (t <= 4e-33) {
		tmp = x + a;
	} else if (t <= 8e+59) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (b * (y - 2.0))
	t_2 = t * (b - a)
	tmp = 0
	if t <= -4.9e+61:
		tmp = t_2
	elif t <= -6.8e-176:
		tmp = t_1
	elif t <= -1.14e-265:
		tmp = z - (y * z)
	elif t <= 2.5e-122:
		tmp = t_1
	elif t <= 4e-33:
		tmp = x + a
	elif t <= 8e+59:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(b * Float64(y - 2.0)))
	t_2 = Float64(t * Float64(b - a))
	tmp = 0.0
	if (t <= -4.9e+61)
		tmp = t_2;
	elseif (t <= -6.8e-176)
		tmp = t_1;
	elseif (t <= -1.14e-265)
		tmp = Float64(z - Float64(y * z));
	elseif (t <= 2.5e-122)
		tmp = t_1;
	elseif (t <= 4e-33)
		tmp = Float64(x + a);
	elseif (t <= 8e+59)
		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 + (b * (y - 2.0));
	t_2 = t * (b - a);
	tmp = 0.0;
	if (t <= -4.9e+61)
		tmp = t_2;
	elseif (t <= -6.8e-176)
		tmp = t_1;
	elseif (t <= -1.14e-265)
		tmp = z - (y * z);
	elseif (t <= 2.5e-122)
		tmp = t_1;
	elseif (t <= 4e-33)
		tmp = x + a;
	elseif (t <= 8e+59)
		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[(b * N[(y - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -4.9e+61], t$95$2, If[LessEqual[t, -6.8e-176], t$95$1, If[LessEqual[t, -1.14e-265], N[(z - N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.5e-122], t$95$1, If[LessEqual[t, 4e-33], N[(x + a), $MachinePrecision], If[LessEqual[t, 8e+59], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -4.90000000000000025e61 or 7.99999999999999977e59 < t

   1. Initial program 90.0%

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

   2. Taylor expanded in t around inf 73.5%

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

   if -4.90000000000000025e61 < t < -6.7999999999999994e-176 or -1.1400000000000001e-265 < t < 2.4999999999999999e-122 or 4.0000000000000002e-33 < t < 7.99999999999999977e59

   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 z around 0 76.7%

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

   3. Taylor expanded in t around inf 55.7%

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

      1. *-commutative 55.7%

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

   5. Simplified 55.7%

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

   6. Taylor expanded in t around 0 53.7%

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

   if -6.7999999999999994e-176 < t < -1.1400000000000001e-265

   1. Initial program 94.8%

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

   2. Taylor expanded in z around inf 69.5%

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

   3. Taylor expanded in y around 0 69.6%

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

   if 2.4999999999999999e-122 < t < 4.0000000000000002e-33

   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 z around 0 68.2%

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

   3. Taylor expanded in b around 0 63.7%

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

   4. Taylor expanded in t around 0 63.7%

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

      1. cancel-sign-sub-inv 63.7%

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

      2. metadata-eval 63.7%

         \[\leadsto x + \color{blue}{1} \cdot a \]

      3. *-lft-identity 63.7%

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

   6. Simplified 63.7%

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

4. Final simplification 63.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.9 \cdot 10^{+61}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq -6.8 \cdot 10^{-176}:\\ \;\;\;\;x + b \cdot \left(y - 2\right)\\ \mathbf{elif}\;t \leq -1.14 \cdot 10^{-265}:\\ \;\;\;\;z - y \cdot z\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{-122}:\\ \;\;\;\;x + b \cdot \left(y - 2\right)\\ \mathbf{elif}\;t \leq 4 \cdot 10^{-33}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq 8 \cdot 10^{+59}:\\ \;\;\;\;x + b \cdot \left(y - 2\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \]

Alternative 12: 86.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(1 - t\right)\\ \mathbf{if}\;b \leq -2.26 \cdot 10^{+49} \lor \neg \left(b \leq 2.7 \cdot 10^{-21}\right):\\ \;\;\;\;\left(x + \left(\left(y + t\right) - 2\right) \cdot b\right) + t_1\\ \mathbf{else}:\\ \;\;\;\;x + \left(z \cdot \left(1 - y\right) + t_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (- 1.0 t))))
   (if (or (<= b -2.26e+49) (not (<= b 2.7e-21)))
     (+ (+ x (* (- (+ y t) 2.0) b)) t_1)
     (+ x (+ (* z (- 1.0 y)) t_1)))))

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 <= -2.26e+49) || !(b <= 2.7e-21)) {
		tmp = (x + (((y + t) - 2.0) * b)) + t_1;
	} else {
		tmp = x + ((z * (1.0 - y)) + 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 = a * (1.0d0 - t)
    if ((b <= (-2.26d+49)) .or. (.not. (b <= 2.7d-21))) then
        tmp = (x + (((y + t) - 2.0d0) * b)) + t_1
    else
        tmp = x + ((z * (1.0d0 - y)) + 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 = a * (1.0 - t);
	double tmp;
	if ((b <= -2.26e+49) || !(b <= 2.7e-21)) {
		tmp = (x + (((y + t) - 2.0) * b)) + t_1;
	} else {
		tmp = x + ((z * (1.0 - y)) + t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (1.0 - t)
	tmp = 0
	if (b <= -2.26e+49) or not (b <= 2.7e-21):
		tmp = (x + (((y + t) - 2.0) * b)) + t_1
	else:
		tmp = x + ((z * (1.0 - y)) + t_1)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(1.0 - t))
	tmp = 0.0
	if ((b <= -2.26e+49) || !(b <= 2.7e-21))
		tmp = Float64(Float64(x + Float64(Float64(Float64(y + t) - 2.0) * b)) + t_1);
	else
		tmp = Float64(x + Float64(Float64(z * Float64(1.0 - y)) + t_1));
	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 <= -2.26e+49) || ~((b <= 2.7e-21)))
		tmp = (x + (((y + t) - 2.0) * b)) + t_1;
	else
		tmp = x + ((z * (1.0 - y)) + t_1);
	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[Or[LessEqual[b, -2.26e+49], N[Not[LessEqual[b, 2.7e-21]], $MachinePrecision]], N[(N[(x + N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], N[(x + N[(N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if b < -2.26e49 or 2.7000000000000001e-21 < b

   1. Initial program 91.0%

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

   2. Taylor expanded in z around 0 85.2%

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

   if -2.26e49 < b < 2.7000000000000001e-21

   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 95.9%

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

4. Final simplification 90.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.26 \cdot 10^{+49} \lor \neg \left(b \leq 2.7 \cdot 10^{-21}\right):\\ \;\;\;\;\left(x + \left(\left(y + t\right) - 2\right) \cdot b\right) + a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(z \cdot \left(1 - y\right) + a \cdot \left(1 - t\right)\right)\\ \end{array} \]

Alternative 13: 34.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(-a\right)\\ \mathbf{if}\;t \leq -3.4 \cdot 10^{+213}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.85 \cdot 10^{+62}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;t \leq -7 \cdot 10^{-176}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq -4.7 \cdot 10^{-261}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{-259}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{-200}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;t \leq 10^{+56}:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (- a))))
   (if (<= t -3.4e+213)
     t_1
     (if (<= t -1.85e+62)
       (* t b)
       (if (<= t -7e-176)
         (+ x a)
         (if (<= t -4.7e-261)
           (* y (- z))
           (if (<= t 1.05e-259)
             (+ x a)
             (if (<= t 6.5e-200) (* y b) (if (<= t 1e+56) (+ x a) t_1)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * -a;
	double tmp;
	if (t <= -3.4e+213) {
		tmp = t_1;
	} else if (t <= -1.85e+62) {
		tmp = t * b;
	} else if (t <= -7e-176) {
		tmp = x + a;
	} else if (t <= -4.7e-261) {
		tmp = y * -z;
	} else if (t <= 1.05e-259) {
		tmp = x + a;
	} else if (t <= 6.5e-200) {
		tmp = y * b;
	} else if (t <= 1e+56) {
		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 = t * -a
    if (t <= (-3.4d+213)) then
        tmp = t_1
    else if (t <= (-1.85d+62)) then
        tmp = t * b
    else if (t <= (-7d-176)) then
        tmp = x + a
    else if (t <= (-4.7d-261)) then
        tmp = y * -z
    else if (t <= 1.05d-259) then
        tmp = x + a
    else if (t <= 6.5d-200) then
        tmp = y * b
    else if (t <= 1d+56) 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 = t * -a;
	double tmp;
	if (t <= -3.4e+213) {
		tmp = t_1;
	} else if (t <= -1.85e+62) {
		tmp = t * b;
	} else if (t <= -7e-176) {
		tmp = x + a;
	} else if (t <= -4.7e-261) {
		tmp = y * -z;
	} else if (t <= 1.05e-259) {
		tmp = x + a;
	} else if (t <= 6.5e-200) {
		tmp = y * b;
	} else if (t <= 1e+56) {
		tmp = x + a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t * -a
	tmp = 0
	if t <= -3.4e+213:
		tmp = t_1
	elif t <= -1.85e+62:
		tmp = t * b
	elif t <= -7e-176:
		tmp = x + a
	elif t <= -4.7e-261:
		tmp = y * -z
	elif t <= 1.05e-259:
		tmp = x + a
	elif t <= 6.5e-200:
		tmp = y * b
	elif t <= 1e+56:
		tmp = x + a
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t * Float64(-a))
	tmp = 0.0
	if (t <= -3.4e+213)
		tmp = t_1;
	elseif (t <= -1.85e+62)
		tmp = Float64(t * b);
	elseif (t <= -7e-176)
		tmp = Float64(x + a);
	elseif (t <= -4.7e-261)
		tmp = Float64(y * Float64(-z));
	elseif (t <= 1.05e-259)
		tmp = Float64(x + a);
	elseif (t <= 6.5e-200)
		tmp = Float64(y * b);
	elseif (t <= 1e+56)
		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 = t * -a;
	tmp = 0.0;
	if (t <= -3.4e+213)
		tmp = t_1;
	elseif (t <= -1.85e+62)
		tmp = t * b;
	elseif (t <= -7e-176)
		tmp = x + a;
	elseif (t <= -4.7e-261)
		tmp = y * -z;
	elseif (t <= 1.05e-259)
		tmp = x + a;
	elseif (t <= 6.5e-200)
		tmp = y * b;
	elseif (t <= 1e+56)
		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[(t * (-a)), $MachinePrecision]}, If[LessEqual[t, -3.4e+213], t$95$1, If[LessEqual[t, -1.85e+62], N[(t * b), $MachinePrecision], If[LessEqual[t, -7e-176], N[(x + a), $MachinePrecision], If[LessEqual[t, -4.7e-261], N[(y * (-z)), $MachinePrecision], If[LessEqual[t, 1.05e-259], N[(x + a), $MachinePrecision], If[LessEqual[t, 6.5e-200], N[(y * b), $MachinePrecision], If[LessEqual[t, 1e+56], N[(x + a), $MachinePrecision], t$95$1]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -3.39999999999999992e213 or 1.00000000000000009e56 < t

   1. Initial program 87.1%

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

   2. Taylor expanded in z around 0 81.9%

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

   3. Taylor expanded in b around 0 56.3%

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

   4. Taylor expanded in t around inf 47.2%

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

      1. associate-*r* 47.2%

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

      2. neg-mul-1 47.2%

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

   6. Simplified 47.2%

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

   if -3.39999999999999992e213 < t < -1.85000000000000007e62

   1. Initial program 96.7%

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

   2. Taylor expanded in a around 0 90.4%

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

   3. Taylor expanded in t around inf 52.9%

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

   if -1.85000000000000007e62 < t < -7e-176 or -4.6999999999999996e-261 < t < 1.04999999999999999e-259 or 6.5000000000000002e-200 < t < 1.00000000000000009e56

   1. Initial program 99.1%

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

   2. Taylor expanded in z around 0 75.4%

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

   3. Taylor expanded in b around 0 46.2%

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

   4. Taylor expanded in t around 0 44.6%

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

      1. cancel-sign-sub-inv 44.6%

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

      2. metadata-eval 44.6%

         \[\leadsto x + \color{blue}{1} \cdot a \]

      3. *-lft-identity 44.6%

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

   6. Simplified 44.6%

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

   if -7e-176 < t < -4.6999999999999996e-261

   1. Initial program 94.3%

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

   2. Taylor expanded in z around inf 66.1%

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

   3. Taylor expanded in y around inf 41.1%

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

      1. associate-*r* 41.1%

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

      2. neg-mul-1 41.1%

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

      3. *-commutative 41.1%

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

   5. Simplified 41.1%

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

   if 1.04999999999999999e-259 < t < 6.5000000000000002e-200

   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 65.2%

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

   3. Taylor expanded in t around inf 58.2%

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

      1. *-commutative 58.2%

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

   5. Simplified 58.2%

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

   6. Taylor expanded in y around inf 51.1%

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

4. Final simplification 46.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.4 \cdot 10^{+213}:\\ \;\;\;\;t \cdot \left(-a\right)\\ \mathbf{elif}\;t \leq -1.85 \cdot 10^{+62}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;t \leq -7 \cdot 10^{-176}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq -4.7 \cdot 10^{-261}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{-259}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{-200}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;t \leq 10^{+56}:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-a\right)\\ \end{array} \]

Alternative 14: 48.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -1.75 \cdot 10^{+62}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -7.2 \cdot 10^{-176}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq -4.9 \cdot 10^{-261}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{-259}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{-200}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{+17}:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (- b a))))
   (if (<= t -1.75e+62)
     t_1
     (if (<= t -7.2e-176)
       (+ x a)
       (if (<= t -4.9e-261)
         (* y (- z))
         (if (<= t 2.3e-259)
           (+ x a)
           (if (<= t 5.2e-200) (* y b) (if (<= t 3.4e+17) (+ x a) t_1))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (b - a);
	double tmp;
	if (t <= -1.75e+62) {
		tmp = t_1;
	} else if (t <= -7.2e-176) {
		tmp = x + a;
	} else if (t <= -4.9e-261) {
		tmp = y * -z;
	} else if (t <= 2.3e-259) {
		tmp = x + a;
	} else if (t <= 5.2e-200) {
		tmp = y * b;
	} else if (t <= 3.4e+17) {
		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 = t * (b - a)
    if (t <= (-1.75d+62)) then
        tmp = t_1
    else if (t <= (-7.2d-176)) then
        tmp = x + a
    else if (t <= (-4.9d-261)) then
        tmp = y * -z
    else if (t <= 2.3d-259) then
        tmp = x + a
    else if (t <= 5.2d-200) then
        tmp = y * b
    else if (t <= 3.4d+17) 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 = t * (b - a);
	double tmp;
	if (t <= -1.75e+62) {
		tmp = t_1;
	} else if (t <= -7.2e-176) {
		tmp = x + a;
	} else if (t <= -4.9e-261) {
		tmp = y * -z;
	} else if (t <= 2.3e-259) {
		tmp = x + a;
	} else if (t <= 5.2e-200) {
		tmp = y * b;
	} else if (t <= 3.4e+17) {
		tmp = x + a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t * (b - a)
	tmp = 0
	if t <= -1.75e+62:
		tmp = t_1
	elif t <= -7.2e-176:
		tmp = x + a
	elif t <= -4.9e-261:
		tmp = y * -z
	elif t <= 2.3e-259:
		tmp = x + a
	elif t <= 5.2e-200:
		tmp = y * b
	elif t <= 3.4e+17:
		tmp = x + a
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t * Float64(b - a))
	tmp = 0.0
	if (t <= -1.75e+62)
		tmp = t_1;
	elseif (t <= -7.2e-176)
		tmp = Float64(x + a);
	elseif (t <= -4.9e-261)
		tmp = Float64(y * Float64(-z));
	elseif (t <= 2.3e-259)
		tmp = Float64(x + a);
	elseif (t <= 5.2e-200)
		tmp = Float64(y * b);
	elseif (t <= 3.4e+17)
		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 = t * (b - a);
	tmp = 0.0;
	if (t <= -1.75e+62)
		tmp = t_1;
	elseif (t <= -7.2e-176)
		tmp = x + a;
	elseif (t <= -4.9e-261)
		tmp = y * -z;
	elseif (t <= 2.3e-259)
		tmp = x + a;
	elseif (t <= 5.2e-200)
		tmp = y * b;
	elseif (t <= 3.4e+17)
		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[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.75e+62], t$95$1, If[LessEqual[t, -7.2e-176], N[(x + a), $MachinePrecision], If[LessEqual[t, -4.9e-261], N[(y * (-z)), $MachinePrecision], If[LessEqual[t, 2.3e-259], N[(x + a), $MachinePrecision], If[LessEqual[t, 5.2e-200], N[(y * b), $MachinePrecision], If[LessEqual[t, 3.4e+17], N[(x + a), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.74999999999999992e62 or 3.4e17 < t

   1. Initial program 90.4%

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

   2. Taylor expanded in t around inf 71.7%

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

   if -1.74999999999999992e62 < t < -7.2000000000000005e-176 or -4.90000000000000005e-261 < t < 2.2999999999999999e-259 or 5.19999999999999979e-200 < t < 3.4e17

   1. Initial program 99.1%

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

   2. Taylor expanded in z around 0 74.6%

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

   3. Taylor expanded in b around 0 47.7%

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

   4. Taylor expanded in t around 0 45.9%

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

      1. cancel-sign-sub-inv 45.9%

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

      2. metadata-eval 45.9%

         \[\leadsto x + \color{blue}{1} \cdot a \]

      3. *-lft-identity 45.9%

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

   6. Simplified 45.9%

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

   if -7.2000000000000005e-176 < t < -4.90000000000000005e-261

   1. Initial program 94.3%

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

   2. Taylor expanded in z around inf 66.1%

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

   3. Taylor expanded in y around inf 41.1%

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

      1. associate-*r* 41.1%

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

      2. neg-mul-1 41.1%

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

      3. *-commutative 41.1%

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

   5. Simplified 41.1%

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

   if 2.2999999999999999e-259 < t < 5.19999999999999979e-200

   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 65.2%

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

   3. Taylor expanded in t around inf 58.2%

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

      1. *-commutative 58.2%

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

   5. Simplified 58.2%

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

   6. Taylor expanded in y around inf 51.1%

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

4. Final simplification 56.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.75 \cdot 10^{+62}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq -7.2 \cdot 10^{-176}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq -4.9 \cdot 10^{-261}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{-259}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{-200}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{+17}:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \]

Alternative 15: 50.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -4.9 \cdot 10^{+61}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -7.2 \cdot 10^{-176}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq -2.05 \cdot 10^{-264}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{-261}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{-120}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;t \leq 3.75 \cdot 10^{+22}:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (- b a))))
   (if (<= t -4.9e+61)
     t_1
     (if (<= t -7.2e-176)
       (+ x a)
       (if (<= t -2.05e-264)
         (* z (- 1.0 y))
         (if (<= t 6.2e-261)
           (+ x a)
           (if (<= t 1.7e-120)
             (* y (- b z))
             (if (<= t 3.75e+22) (+ x a) t_1))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (b - a);
	double tmp;
	if (t <= -4.9e+61) {
		tmp = t_1;
	} else if (t <= -7.2e-176) {
		tmp = x + a;
	} else if (t <= -2.05e-264) {
		tmp = z * (1.0 - y);
	} else if (t <= 6.2e-261) {
		tmp = x + a;
	} else if (t <= 1.7e-120) {
		tmp = y * (b - z);
	} else if (t <= 3.75e+22) {
		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 = t * (b - a)
    if (t <= (-4.9d+61)) then
        tmp = t_1
    else if (t <= (-7.2d-176)) then
        tmp = x + a
    else if (t <= (-2.05d-264)) then
        tmp = z * (1.0d0 - y)
    else if (t <= 6.2d-261) then
        tmp = x + a
    else if (t <= 1.7d-120) then
        tmp = y * (b - z)
    else if (t <= 3.75d+22) 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 = t * (b - a);
	double tmp;
	if (t <= -4.9e+61) {
		tmp = t_1;
	} else if (t <= -7.2e-176) {
		tmp = x + a;
	} else if (t <= -2.05e-264) {
		tmp = z * (1.0 - y);
	} else if (t <= 6.2e-261) {
		tmp = x + a;
	} else if (t <= 1.7e-120) {
		tmp = y * (b - z);
	} else if (t <= 3.75e+22) {
		tmp = x + a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t * (b - a)
	tmp = 0
	if t <= -4.9e+61:
		tmp = t_1
	elif t <= -7.2e-176:
		tmp = x + a
	elif t <= -2.05e-264:
		tmp = z * (1.0 - y)
	elif t <= 6.2e-261:
		tmp = x + a
	elif t <= 1.7e-120:
		tmp = y * (b - z)
	elif t <= 3.75e+22:
		tmp = x + a
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t * Float64(b - a))
	tmp = 0.0
	if (t <= -4.9e+61)
		tmp = t_1;
	elseif (t <= -7.2e-176)
		tmp = Float64(x + a);
	elseif (t <= -2.05e-264)
		tmp = Float64(z * Float64(1.0 - y));
	elseif (t <= 6.2e-261)
		tmp = Float64(x + a);
	elseif (t <= 1.7e-120)
		tmp = Float64(y * Float64(b - z));
	elseif (t <= 3.75e+22)
		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 = t * (b - a);
	tmp = 0.0;
	if (t <= -4.9e+61)
		tmp = t_1;
	elseif (t <= -7.2e-176)
		tmp = x + a;
	elseif (t <= -2.05e-264)
		tmp = z * (1.0 - y);
	elseif (t <= 6.2e-261)
		tmp = x + a;
	elseif (t <= 1.7e-120)
		tmp = y * (b - z);
	elseif (t <= 3.75e+22)
		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[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -4.9e+61], t$95$1, If[LessEqual[t, -7.2e-176], N[(x + a), $MachinePrecision], If[LessEqual[t, -2.05e-264], N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6.2e-261], N[(x + a), $MachinePrecision], If[LessEqual[t, 1.7e-120], N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.75e+22], N[(x + a), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -4.90000000000000025e61 or 3.7500000000000001e22 < t

   1. Initial program 90.4%

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

   2. Taylor expanded in t around inf 71.7%

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

   if -4.90000000000000025e61 < t < -7.2000000000000005e-176 or -2.05000000000000011e-264 < t < 6.1999999999999997e-261 or 1.70000000000000005e-120 < t < 3.7500000000000001e22

   1. Initial program 98.9%

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

   2. Taylor expanded in z around 0 76.4%

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

   3. Taylor expanded in b around 0 52.0%

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

   4. Taylor expanded in t around 0 49.7%

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

      1. cancel-sign-sub-inv 49.7%

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

      2. metadata-eval 49.7%

         \[\leadsto x + \color{blue}{1} \cdot a \]

      3. *-lft-identity 49.7%

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

   6. Simplified 49.7%

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

   if -7.2000000000000005e-176 < t < -2.05000000000000011e-264

   1. Initial program 94.8%

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

   2. Taylor expanded in z around inf 69.5%

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

   if 6.1999999999999997e-261 < t < 1.70000000000000005e-120

   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 y around inf 52.7%

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

4. Final simplification 60.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.9 \cdot 10^{+61}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq -7.2 \cdot 10^{-176}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq -2.05 \cdot 10^{-264}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{-261}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{-120}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;t \leq 3.75 \cdot 10^{+22}:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \]

Alternative 16: 60.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a + z \cdot \left(1 - y\right)\\ t_2 := \left(\left(y + t\right) - 2\right) \cdot b\\ t_3 := x + a \cdot \left(1 - t\right)\\ \mathbf{if}\;b \leq -2.65 \cdot 10^{+50}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -4.2 \cdot 10^{-59}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 2.2 \cdot 10^{-272}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq 1.2 \cdot 10^{-85}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 1.3 \cdot 10^{+70}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ a (* z (- 1.0 y))))
        (t_2 (* (- (+ y t) 2.0) b))
        (t_3 (+ x (* a (- 1.0 t)))))
   (if (<= b -2.65e+50)
     t_2
     (if (<= b -4.2e-59)
       t_1
       (if (<= b 2.2e-272)
         t_3
         (if (<= b 1.2e-85) t_1 (if (<= b 1.3e+70) t_3 t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a + (z * (1.0 - y));
	double t_2 = ((y + t) - 2.0) * b;
	double t_3 = x + (a * (1.0 - t));
	double tmp;
	if (b <= -2.65e+50) {
		tmp = t_2;
	} else if (b <= -4.2e-59) {
		tmp = t_1;
	} else if (b <= 2.2e-272) {
		tmp = t_3;
	} else if (b <= 1.2e-85) {
		tmp = t_1;
	} else if (b <= 1.3e+70) {
		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 = a + (z * (1.0d0 - y))
    t_2 = ((y + t) - 2.0d0) * b
    t_3 = x + (a * (1.0d0 - t))
    if (b <= (-2.65d+50)) then
        tmp = t_2
    else if (b <= (-4.2d-59)) then
        tmp = t_1
    else if (b <= 2.2d-272) then
        tmp = t_3
    else if (b <= 1.2d-85) then
        tmp = t_1
    else if (b <= 1.3d+70) 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 = a + (z * (1.0 - y));
	double t_2 = ((y + t) - 2.0) * b;
	double t_3 = x + (a * (1.0 - t));
	double tmp;
	if (b <= -2.65e+50) {
		tmp = t_2;
	} else if (b <= -4.2e-59) {
		tmp = t_1;
	} else if (b <= 2.2e-272) {
		tmp = t_3;
	} else if (b <= 1.2e-85) {
		tmp = t_1;
	} else if (b <= 1.3e+70) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a + (z * (1.0 - y))
	t_2 = ((y + t) - 2.0) * b
	t_3 = x + (a * (1.0 - t))
	tmp = 0
	if b <= -2.65e+50:
		tmp = t_2
	elif b <= -4.2e-59:
		tmp = t_1
	elif b <= 2.2e-272:
		tmp = t_3
	elif b <= 1.2e-85:
		tmp = t_1
	elif b <= 1.3e+70:
		tmp = t_3
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a + Float64(z * Float64(1.0 - y)))
	t_2 = Float64(Float64(Float64(y + t) - 2.0) * b)
	t_3 = Float64(x + Float64(a * Float64(1.0 - t)))
	tmp = 0.0
	if (b <= -2.65e+50)
		tmp = t_2;
	elseif (b <= -4.2e-59)
		tmp = t_1;
	elseif (b <= 2.2e-272)
		tmp = t_3;
	elseif (b <= 1.2e-85)
		tmp = t_1;
	elseif (b <= 1.3e+70)
		tmp = t_3;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a + (z * (1.0 - y));
	t_2 = ((y + t) - 2.0) * b;
	t_3 = x + (a * (1.0 - t));
	tmp = 0.0;
	if (b <= -2.65e+50)
		tmp = t_2;
	elseif (b <= -4.2e-59)
		tmp = t_1;
	elseif (b <= 2.2e-272)
		tmp = t_3;
	elseif (b <= 1.2e-85)
		tmp = t_1;
	elseif (b <= 1.3e+70)
		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[(a + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]}, Block[{t$95$3 = N[(x + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2.65e+50], t$95$2, If[LessEqual[b, -4.2e-59], t$95$1, If[LessEqual[b, 2.2e-272], t$95$3, If[LessEqual[b, 1.2e-85], t$95$1, If[LessEqual[b, 1.3e+70], t$95$3, t$95$2]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -2.6500000000000001e50 or 1.3e70 < b

   1. Initial program 90.3%

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

   2. Taylor expanded in b around inf 80.4%

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

   if -2.6500000000000001e50 < b < -4.19999999999999993e-59 or 2.19999999999999988e-272 < b < 1.2e-85

   1. Initial program 98.1%

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

   2. Taylor expanded in b around 0 96.3%

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

   3. Taylor expanded in t around 0 84.0%

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

      1. neg-mul-1 84.0%

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

   5. Simplified 84.0%

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

   6. Taylor expanded in x around 0 68.3%

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

   if -4.19999999999999993e-59 < b < 2.19999999999999988e-272 or 1.2e-85 < b < 1.3e70

   1. Initial program 98.9%

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

   2. Taylor expanded in z around 0 76.4%

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

   3. Taylor expanded in b around 0 67.1%

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

4. Final simplification 72.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.65 \cdot 10^{+50}:\\ \;\;\;\;\left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{elif}\;b \leq -4.2 \cdot 10^{-59}:\\ \;\;\;\;a + z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq 2.2 \cdot 10^{-272}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 1.2 \cdot 10^{-85}:\\ \;\;\;\;a + z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq 1.3 \cdot 10^{+70}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(y + t\right) - 2\right) \cdot b\\ \end{array} \]

Alternative 17: 62.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(1 - y\right)\\ t_2 := \left(\left(y + t\right) - 2\right) \cdot b\\ t_3 := x + a \cdot \left(1 - t\right)\\ \mathbf{if}\;b \leq -9.2 \cdot 10^{+50}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -4.2 \cdot 10^{-59}:\\ \;\;\;\;a + t_1\\ \mathbf{elif}\;b \leq 9.5 \cdot 10^{-283}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq 4 \cdot 10^{-86}:\\ \;\;\;\;x + t_1\\ \mathbf{elif}\;b \leq 5 \cdot 10^{+69}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (- 1.0 y)))
        (t_2 (* (- (+ y t) 2.0) b))
        (t_3 (+ x (* a (- 1.0 t)))))
   (if (<= b -9.2e+50)
     t_2
     (if (<= b -4.2e-59)
       (+ a t_1)
       (if (<= b 9.5e-283)
         t_3
         (if (<= b 4e-86) (+ x t_1) (if (<= b 5e+69) t_3 t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (1.0 - y);
	double t_2 = ((y + t) - 2.0) * b;
	double t_3 = x + (a * (1.0 - t));
	double tmp;
	if (b <= -9.2e+50) {
		tmp = t_2;
	} else if (b <= -4.2e-59) {
		tmp = a + t_1;
	} else if (b <= 9.5e-283) {
		tmp = t_3;
	} else if (b <= 4e-86) {
		tmp = x + t_1;
	} else if (b <= 5e+69) {
		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 = z * (1.0d0 - y)
    t_2 = ((y + t) - 2.0d0) * b
    t_3 = x + (a * (1.0d0 - t))
    if (b <= (-9.2d+50)) then
        tmp = t_2
    else if (b <= (-4.2d-59)) then
        tmp = a + t_1
    else if (b <= 9.5d-283) then
        tmp = t_3
    else if (b <= 4d-86) then
        tmp = x + t_1
    else if (b <= 5d+69) 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 = z * (1.0 - y);
	double t_2 = ((y + t) - 2.0) * b;
	double t_3 = x + (a * (1.0 - t));
	double tmp;
	if (b <= -9.2e+50) {
		tmp = t_2;
	} else if (b <= -4.2e-59) {
		tmp = a + t_1;
	} else if (b <= 9.5e-283) {
		tmp = t_3;
	} else if (b <= 4e-86) {
		tmp = x + t_1;
	} else if (b <= 5e+69) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * (1.0 - y)
	t_2 = ((y + t) - 2.0) * b
	t_3 = x + (a * (1.0 - t))
	tmp = 0
	if b <= -9.2e+50:
		tmp = t_2
	elif b <= -4.2e-59:
		tmp = a + t_1
	elif b <= 9.5e-283:
		tmp = t_3
	elif b <= 4e-86:
		tmp = x + t_1
	elif b <= 5e+69:
		tmp = t_3
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(1.0 - y))
	t_2 = Float64(Float64(Float64(y + t) - 2.0) * b)
	t_3 = Float64(x + Float64(a * Float64(1.0 - t)))
	tmp = 0.0
	if (b <= -9.2e+50)
		tmp = t_2;
	elseif (b <= -4.2e-59)
		tmp = Float64(a + t_1);
	elseif (b <= 9.5e-283)
		tmp = t_3;
	elseif (b <= 4e-86)
		tmp = Float64(x + t_1);
	elseif (b <= 5e+69)
		tmp = t_3;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * (1.0 - y);
	t_2 = ((y + t) - 2.0) * b;
	t_3 = x + (a * (1.0 - t));
	tmp = 0.0;
	if (b <= -9.2e+50)
		tmp = t_2;
	elseif (b <= -4.2e-59)
		tmp = a + t_1;
	elseif (b <= 9.5e-283)
		tmp = t_3;
	elseif (b <= 4e-86)
		tmp = x + t_1;
	elseif (b <= 5e+69)
		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[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]}, Block[{t$95$3 = N[(x + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -9.2e+50], t$95$2, If[LessEqual[b, -4.2e-59], N[(a + t$95$1), $MachinePrecision], If[LessEqual[b, 9.5e-283], t$95$3, If[LessEqual[b, 4e-86], N[(x + t$95$1), $MachinePrecision], If[LessEqual[b, 5e+69], t$95$3, t$95$2]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -9.19999999999999987e50 or 5.00000000000000036e69 < b

   1. Initial program 90.3%

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

   2. Taylor expanded in b around inf 80.4%

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

   if -9.19999999999999987e50 < b < -4.19999999999999993e-59

   1. Initial program 95.4%

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

   2. Taylor expanded in b around 0 91.0%

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

   3. Taylor expanded in t around 0 82.3%

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

      1. neg-mul-1 82.3%

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

   5. Simplified 82.3%

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

   6. Taylor expanded in x around 0 68.8%

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

   if -4.19999999999999993e-59 < b < 9.49999999999999979e-283 or 4.00000000000000034e-86 < b < 5.00000000000000036e69

   1. Initial program 98.9%

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

   2. Taylor expanded in z around 0 76.8%

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

   3. Taylor expanded in b around 0 67.4%

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

   if 9.49999999999999979e-283 < b < 4.00000000000000034e-86

   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 68.4%

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

   3. Taylor expanded in b around 0 68.5%

      \[\leadsto \color{blue}{x - z \cdot \left(y - 1\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 72.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -9.2 \cdot 10^{+50}:\\ \;\;\;\;\left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{elif}\;b \leq -4.2 \cdot 10^{-59}:\\ \;\;\;\;a + z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq 9.5 \cdot 10^{-283}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 4 \cdot 10^{-86}:\\ \;\;\;\;x + z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq 5 \cdot 10^{+69}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(y + t\right) - 2\right) \cdot b\\ \end{array} \]

Alternative 18: 65.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(1 - y\right)\\ t_2 := x + \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{if}\;b \leq -1.28 \cdot 10^{+20}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -2.65 \cdot 10^{-59}:\\ \;\;\;\;a + t_1\\ \mathbf{elif}\;b \leq 1.2 \cdot 10^{-282}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 1.75 \cdot 10^{-21}:\\ \;\;\;\;x + t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (- 1.0 y))) (t_2 (+ x (* (- (+ y t) 2.0) b))))
   (if (<= b -1.28e+20)
     t_2
     (if (<= b -2.65e-59)
       (+ a t_1)
       (if (<= b 1.2e-282)
         (+ x (* a (- 1.0 t)))
         (if (<= b 1.75e-21) (+ x t_1) t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (1.0 - y);
	double t_2 = x + (((y + t) - 2.0) * b);
	double tmp;
	if (b <= -1.28e+20) {
		tmp = t_2;
	} else if (b <= -2.65e-59) {
		tmp = a + t_1;
	} else if (b <= 1.2e-282) {
		tmp = x + (a * (1.0 - t));
	} else if (b <= 1.75e-21) {
		tmp = x + 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 = z * (1.0d0 - y)
    t_2 = x + (((y + t) - 2.0d0) * b)
    if (b <= (-1.28d+20)) then
        tmp = t_2
    else if (b <= (-2.65d-59)) then
        tmp = a + t_1
    else if (b <= 1.2d-282) then
        tmp = x + (a * (1.0d0 - t))
    else if (b <= 1.75d-21) then
        tmp = x + 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 = z * (1.0 - y);
	double t_2 = x + (((y + t) - 2.0) * b);
	double tmp;
	if (b <= -1.28e+20) {
		tmp = t_2;
	} else if (b <= -2.65e-59) {
		tmp = a + t_1;
	} else if (b <= 1.2e-282) {
		tmp = x + (a * (1.0 - t));
	} else if (b <= 1.75e-21) {
		tmp = x + t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * (1.0 - y)
	t_2 = x + (((y + t) - 2.0) * b)
	tmp = 0
	if b <= -1.28e+20:
		tmp = t_2
	elif b <= -2.65e-59:
		tmp = a + t_1
	elif b <= 1.2e-282:
		tmp = x + (a * (1.0 - t))
	elif b <= 1.75e-21:
		tmp = x + t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(1.0 - y))
	t_2 = Float64(x + Float64(Float64(Float64(y + t) - 2.0) * b))
	tmp = 0.0
	if (b <= -1.28e+20)
		tmp = t_2;
	elseif (b <= -2.65e-59)
		tmp = Float64(a + t_1);
	elseif (b <= 1.2e-282)
		tmp = Float64(x + Float64(a * Float64(1.0 - t)));
	elseif (b <= 1.75e-21)
		tmp = Float64(x + t_1);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * (1.0 - y);
	t_2 = x + (((y + t) - 2.0) * b);
	tmp = 0.0;
	if (b <= -1.28e+20)
		tmp = t_2;
	elseif (b <= -2.65e-59)
		tmp = a + t_1;
	elseif (b <= 1.2e-282)
		tmp = x + (a * (1.0 - t));
	elseif (b <= 1.75e-21)
		tmp = x + t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.28e+20], t$95$2, If[LessEqual[b, -2.65e-59], N[(a + t$95$1), $MachinePrecision], If[LessEqual[b, 1.2e-282], N[(x + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.75e-21], N[(x + t$95$1), $MachinePrecision], t$95$2]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -1.28e20 or 1.7500000000000002e-21 < b

   1. Initial program 90.7%

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

   2. Taylor expanded in z around 0 84.3%

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

   3. Taylor expanded in a around 0 76.3%

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

   if -1.28e20 < b < -2.6500000000000002e-59

   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 87.6%

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

   3. Taylor expanded in t around 0 87.3%

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

      1. neg-mul-1 87.3%

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

   5. Simplified 87.3%

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

   6. Taylor expanded in x around 0 81.4%

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

   if -2.6500000000000002e-59 < b < 1.19999999999999998e-282

   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 z around 0 75.2%

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

   3. Taylor expanded in b around 0 71.5%

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

   if 1.19999999999999998e-282 < b < 1.7500000000000002e-21

   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 68.9%

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

   3. Taylor expanded in b around 0 66.8%

      \[\leadsto \color{blue}{x - z \cdot \left(y - 1\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 73.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.28 \cdot 10^{+20}:\\ \;\;\;\;x + \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{elif}\;b \leq -2.65 \cdot 10^{-59}:\\ \;\;\;\;a + z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq 1.2 \cdot 10^{-282}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 1.75 \cdot 10^{-21}:\\ \;\;\;\;x + z \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(\left(y + t\right) - 2\right) \cdot b\\ \end{array} \]

Alternative 19: 83.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.6 \cdot 10^{+52} \lor \neg \left(b \leq 2.45 \cdot 10^{+70}\right):\\ \;\;\;\;x + \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;x + \left(z \cdot \left(1 - y\right) + a \cdot \left(1 - t\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -1.6e+52) (not (<= b 2.45e+70)))
   (+ x (* (- (+ y t) 2.0) b))
   (+ x (+ (* z (- 1.0 y)) (* a (- 1.0 t))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -1.6e+52) || !(b <= 2.45e+70)) {
		tmp = x + (((y + t) - 2.0) * b);
	} else {
		tmp = x + ((z * (1.0 - y)) + (a * (1.0 - t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-1.6d+52)) .or. (.not. (b <= 2.45d+70))) then
        tmp = x + (((y + t) - 2.0d0) * b)
    else
        tmp = x + ((z * (1.0d0 - y)) + (a * (1.0d0 - t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -1.6e+52) || !(b <= 2.45e+70)) {
		tmp = x + (((y + t) - 2.0) * b);
	} else {
		tmp = x + ((z * (1.0 - y)) + (a * (1.0 - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -1.6e+52) or not (b <= 2.45e+70):
		tmp = x + (((y + t) - 2.0) * b)
	else:
		tmp = x + ((z * (1.0 - y)) + (a * (1.0 - t)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -1.6e+52) || !(b <= 2.45e+70))
		tmp = Float64(x + Float64(Float64(Float64(y + t) - 2.0) * b));
	else
		tmp = Float64(x + Float64(Float64(z * Float64(1.0 - y)) + Float64(a * Float64(1.0 - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -1.6e+52) || ~((b <= 2.45e+70)))
		tmp = x + (((y + t) - 2.0) * b);
	else
		tmp = x + ((z * (1.0 - y)) + (a * (1.0 - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -1.6e+52], N[Not[LessEqual[b, 2.45e+70]], $MachinePrecision]], N[(x + N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision] + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.6e52 or 2.45000000000000014e70 < b

   1. Initial program 90.3%

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

   2. Taylor expanded in z around 0 85.1%

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

   3. Taylor expanded in a around 0 82.7%

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

   if -1.6e52 < b < 2.45000000000000014e70

   1. Initial program 98.6%

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

   2. Taylor expanded in b around 0 92.0%

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

4. Final simplification 88.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.6 \cdot 10^{+52} \lor \neg \left(b \leq 2.45 \cdot 10^{+70}\right):\\ \;\;\;\;x + \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;x + \left(z \cdot \left(1 - y\right) + a \cdot \left(1 - t\right)\right)\\ \end{array} \]

Alternative 20: 83.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{if}\;b \leq -1.04 \cdot 10^{+55}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 6.2 \cdot 10^{-22}:\\ \;\;\;\;x + \left(z \cdot \left(1 - y\right) + a \cdot \left(1 - t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1 - t \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* (- (+ y t) 2.0) b))))
   (if (<= b -1.04e+55)
     t_1
     (if (<= b 6.2e-22)
       (+ x (+ (* z (- 1.0 y)) (* a (- 1.0 t))))
       (- t_1 (* t a))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (((y + t) - 2.0) * b);
	double tmp;
	if (b <= -1.04e+55) {
		tmp = t_1;
	} else if (b <= 6.2e-22) {
		tmp = x + ((z * (1.0 - y)) + (a * (1.0 - t)));
	} else {
		tmp = t_1 - (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) :: t_1
    real(8) :: tmp
    t_1 = x + (((y + t) - 2.0d0) * b)
    if (b <= (-1.04d+55)) then
        tmp = t_1
    else if (b <= 6.2d-22) then
        tmp = x + ((z * (1.0d0 - y)) + (a * (1.0d0 - t)))
    else
        tmp = t_1 - (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 t_1 = x + (((y + t) - 2.0) * b);
	double tmp;
	if (b <= -1.04e+55) {
		tmp = t_1;
	} else if (b <= 6.2e-22) {
		tmp = x + ((z * (1.0 - y)) + (a * (1.0 - t)));
	} else {
		tmp = t_1 - (t * a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (((y + t) - 2.0) * b)
	tmp = 0
	if b <= -1.04e+55:
		tmp = t_1
	elif b <= 6.2e-22:
		tmp = x + ((z * (1.0 - y)) + (a * (1.0 - t)))
	else:
		tmp = t_1 - (t * a)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(Float64(Float64(y + t) - 2.0) * b))
	tmp = 0.0
	if (b <= -1.04e+55)
		tmp = t_1;
	elseif (b <= 6.2e-22)
		tmp = Float64(x + Float64(Float64(z * Float64(1.0 - y)) + Float64(a * Float64(1.0 - t))));
	else
		tmp = Float64(t_1 - Float64(t * a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (((y + t) - 2.0) * b);
	tmp = 0.0;
	if (b <= -1.04e+55)
		tmp = t_1;
	elseif (b <= 6.2e-22)
		tmp = x + ((z * (1.0 - y)) + (a * (1.0 - t)));
	else
		tmp = t_1 - (t * a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.04e+55], t$95$1, If[LessEqual[b, 6.2e-22], N[(x + N[(N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision] + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 - N[(t * a), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.04000000000000003e55

   1. Initial program 90.7%

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

   2. Taylor expanded in z around 0 83.2%

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

   3. Taylor expanded in a around 0 81.3%

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

   if -1.04000000000000003e55 < b < 6.20000000000000025e-22

   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 95.9%

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

   if 6.20000000000000025e-22 < b

   1. Initial program 91.2%

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

   2. Taylor expanded in z around 0 86.2%

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

   3. Taylor expanded in t around inf 80.4%

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

      1. *-commutative 80.4%

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

   5. Simplified 80.4%

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

4. Final simplification 88.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.04 \cdot 10^{+55}:\\ \;\;\;\;x + \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{elif}\;b \leq 6.2 \cdot 10^{-22}:\\ \;\;\;\;x + \left(z \cdot \left(1 - y\right) + a \cdot \left(1 - t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + \left(\left(y + t\right) - 2\right) \cdot b\right) - t \cdot a\\ \end{array} \]

Alternative 21: 39.7% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t - 2\right)\\ \mathbf{if}\;b \leq -5.8 \cdot 10^{+88}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -2.3 \cdot 10^{-257}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;b \leq 2.2 \cdot 10^{-284}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 8.5 \cdot 10^{+36}:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- t 2.0))))
   (if (<= b -5.8e+88)
     t_1
     (if (<= b -2.3e-257)
       (+ x a)
       (if (<= b 2.2e-284) (* a (- 1.0 t)) (if (<= b 8.5e+36) (+ 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 <= -5.8e+88) {
		tmp = t_1;
	} else if (b <= -2.3e-257) {
		tmp = x + a;
	} else if (b <= 2.2e-284) {
		tmp = a * (1.0 - t);
	} else if (b <= 8.5e+36) {
		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 <= (-5.8d+88)) then
        tmp = t_1
    else if (b <= (-2.3d-257)) then
        tmp = x + a
    else if (b <= 2.2d-284) then
        tmp = a * (1.0d0 - t)
    else if (b <= 8.5d+36) 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 <= -5.8e+88) {
		tmp = t_1;
	} else if (b <= -2.3e-257) {
		tmp = x + a;
	} else if (b <= 2.2e-284) {
		tmp = a * (1.0 - t);
	} else if (b <= 8.5e+36) {
		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 <= -5.8e+88:
		tmp = t_1
	elif b <= -2.3e-257:
		tmp = x + a
	elif b <= 2.2e-284:
		tmp = a * (1.0 - t)
	elif b <= 8.5e+36:
		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 <= -5.8e+88)
		tmp = t_1;
	elseif (b <= -2.3e-257)
		tmp = Float64(x + a);
	elseif (b <= 2.2e-284)
		tmp = Float64(a * Float64(1.0 - t));
	elseif (b <= 8.5e+36)
		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 <= -5.8e+88)
		tmp = t_1;
	elseif (b <= -2.3e-257)
		tmp = x + a;
	elseif (b <= 2.2e-284)
		tmp = a * (1.0 - t);
	elseif (b <= 8.5e+36)
		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, -5.8e+88], t$95$1, If[LessEqual[b, -2.3e-257], N[(x + a), $MachinePrecision], If[LessEqual[b, 2.2e-284], N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 8.5e+36], N[(x + a), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -5.7999999999999999e88 or 8.50000000000000014e36 < b

   1. Initial program 89.2%

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

   2. Taylor expanded in b around inf 78.2%

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

   3. Taylor expanded in y around 0 53.6%

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

   if -5.7999999999999999e88 < b < -2.3e-257 or 2.2000000000000001e-284 < b < 8.50000000000000014e36

   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 z around 0 68.3%

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

   3. Taylor expanded in b around 0 57.2%

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

   4. Taylor expanded in t around 0 42.1%

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

      1. cancel-sign-sub-inv 42.1%

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

      2. metadata-eval 42.1%

         \[\leadsto x + \color{blue}{1} \cdot a \]

      3. *-lft-identity 42.1%

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

   6. Simplified 42.1%

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

   if -2.3e-257 < b < 2.2000000000000001e-284

   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 53.6%

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

4. Final simplification 47.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5.8 \cdot 10^{+88}:\\ \;\;\;\;b \cdot \left(t - 2\right)\\ \mathbf{elif}\;b \leq -2.3 \cdot 10^{-257}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;b \leq 2.2 \cdot 10^{-284}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 8.5 \cdot 10^{+36}:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t - 2\right)\\ \end{array} \]

Alternative 22: 72.0% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2.8 \cdot 10^{+51} \lor \neg \left(b \leq 5.2 \cdot 10^{-21}\right):\\ \;\;\;\;x + \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;x + \left(a + z \cdot \left(1 - y\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -2.8e+51) (not (<= b 5.2e-21)))
   (+ x (* (- (+ y t) 2.0) b))
   (+ x (+ a (* z (- 1.0 y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -2.8e+51) || !(b <= 5.2e-21)) {
		tmp = x + (((y + t) - 2.0) * b);
	} else {
		tmp = x + (a + (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 <= (-2.8d+51)) .or. (.not. (b <= 5.2d-21))) then
        tmp = x + (((y + t) - 2.0d0) * b)
    else
        tmp = x + (a + (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 <= -2.8e+51) || !(b <= 5.2e-21)) {
		tmp = x + (((y + t) - 2.0) * b);
	} else {
		tmp = x + (a + (z * (1.0 - y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -2.8e+51) or not (b <= 5.2e-21):
		tmp = x + (((y + t) - 2.0) * b)
	else:
		tmp = x + (a + (z * (1.0 - y)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -2.8e+51) || !(b <= 5.2e-21))
		tmp = Float64(x + Float64(Float64(Float64(y + t) - 2.0) * b));
	else
		tmp = Float64(x + Float64(a + 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 <= -2.8e+51) || ~((b <= 5.2e-21)))
		tmp = x + (((y + t) - 2.0) * b);
	else
		tmp = x + (a + (z * (1.0 - y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -2.8e+51], N[Not[LessEqual[b, 5.2e-21]], $MachinePrecision]], N[(x + N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision], N[(x + N[(a + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -2.80000000000000005e51 or 5.20000000000000035e-21 < b

   1. Initial program 91.0%

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

   2. Taylor expanded in z around 0 85.2%

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

   3. Taylor expanded in a around 0 77.5%

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

   if -2.80000000000000005e51 < b < 5.20000000000000035e-21

   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 95.9%

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

   3. Taylor expanded in t around 0 76.6%

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

      1. neg-mul-1 76.6%

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

   5. Simplified 76.6%

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

4. Final simplification 77.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.8 \cdot 10^{+51} \lor \neg \left(b \leq 5.2 \cdot 10^{-21}\right):\\ \;\;\;\;x + \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;x + \left(a + z \cdot \left(1 - y\right)\right)\\ \end{array} \]

Alternative 23: 34.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -5.2 \cdot 10^{+114}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;b \leq 1.65 \cdot 10^{+35}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;b \leq 9.5 \cdot 10^{+162} \lor \neg \left(b \leq 1.05 \cdot 10^{+270}\right):\\ \;\;\;\;t \cdot b\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -5.2e+114)
   (* t b)
   (if (<= b 1.65e+35)
     (+ x a)
     (if (or (<= b 9.5e+162) (not (<= b 1.05e+270))) (* t b) (* y b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -5.2e+114) {
		tmp = t * b;
	} else if (b <= 1.65e+35) {
		tmp = x + a;
	} else if ((b <= 9.5e+162) || !(b <= 1.05e+270)) {
		tmp = t * b;
	} else {
		tmp = y * b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-5.2d+114)) then
        tmp = t * b
    else if (b <= 1.65d+35) then
        tmp = x + a
    else if ((b <= 9.5d+162) .or. (.not. (b <= 1.05d+270))) then
        tmp = t * b
    else
        tmp = y * b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -5.2e+114) {
		tmp = t * b;
	} else if (b <= 1.65e+35) {
		tmp = x + a;
	} else if ((b <= 9.5e+162) || !(b <= 1.05e+270)) {
		tmp = t * b;
	} else {
		tmp = y * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -5.2e+114:
		tmp = t * b
	elif b <= 1.65e+35:
		tmp = x + a
	elif (b <= 9.5e+162) or not (b <= 1.05e+270):
		tmp = t * b
	else:
		tmp = y * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -5.2e+114)
		tmp = Float64(t * b);
	elseif (b <= 1.65e+35)
		tmp = Float64(x + a);
	elseif ((b <= 9.5e+162) || !(b <= 1.05e+270))
		tmp = Float64(t * b);
	else
		tmp = Float64(y * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -5.2e+114)
		tmp = t * b;
	elseif (b <= 1.65e+35)
		tmp = x + a;
	elseif ((b <= 9.5e+162) || ~((b <= 1.05e+270)))
		tmp = t * b;
	else
		tmp = y * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -5.2e+114], N[(t * b), $MachinePrecision], If[LessEqual[b, 1.65e+35], N[(x + a), $MachinePrecision], If[Or[LessEqual[b, 9.5e+162], N[Not[LessEqual[b, 1.05e+270]], $MachinePrecision]], N[(t * b), $MachinePrecision], N[(y * b), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if b < -5.2000000000000001e114 or 1.6500000000000001e35 < b < 9.50000000000000021e162 or 1.05000000000000005e270 < b

   1. Initial program 86.8%

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

   2. Taylor expanded in a around 0 80.0%

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

   3. Taylor expanded in t around inf 42.0%

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

   if -5.2000000000000001e114 < b < 1.6500000000000001e35

   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 z around 0 69.7%

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

   3. Taylor expanded in b around 0 59.7%

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

   4. Taylor expanded in t around 0 40.6%

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

      1. cancel-sign-sub-inv 40.6%

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

      2. metadata-eval 40.6%

         \[\leadsto x + \color{blue}{1} \cdot a \]

      3. *-lft-identity 40.6%

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

   6. Simplified 40.6%

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

   if 9.50000000000000021e162 < b < 1.05000000000000005e270

   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 83.6%

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

   3. Taylor expanded in t around inf 83.6%

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

      1. *-commutative 83.6%

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

   5. Simplified 83.6%

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

   6. Taylor expanded in y around inf 48.8%

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

4. Final simplification 41.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5.2 \cdot 10^{+114}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;b \leq 1.65 \cdot 10^{+35}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;b \leq 9.5 \cdot 10^{+162} \lor \neg \left(b \leq 1.05 \cdot 10^{+270}\right):\\ \;\;\;\;t \cdot b\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \]

Alternative 24: 27.5% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2.25 \cdot 10^{+51} \lor \neg \left(b \leq 2.3 \cdot 10^{+22}\right):\\ \;\;\;\;t \cdot b\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -2.25e+51) (not (<= b 2.3e+22))) (* t b) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -2.25e+51) || !(b <= 2.3e+22)) {
		tmp = t * 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 <= (-2.25d+51)) .or. (.not. (b <= 2.3d+22))) then
        tmp = t * 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 <= -2.25e+51) || !(b <= 2.3e+22)) {
		tmp = t * b;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -2.25e+51) or not (b <= 2.3e+22):
		tmp = t * b
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -2.25e+51) || !(b <= 2.3e+22))
		tmp = Float64(t * b);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -2.25e+51) || ~((b <= 2.3e+22)))
		tmp = t * b;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -2.25e+51], N[Not[LessEqual[b, 2.3e+22]], $MachinePrecision]], N[(t * b), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if b < -2.25e51 or 2.3000000000000002e22 < b

   1. Initial program 90.2%

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

   2. Taylor expanded in a around 0 83.5%

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

   3. Taylor expanded in t around inf 37.7%

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

   if -2.25e51 < b < 2.3000000000000002e22

   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 x around inf 24.7%

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

4. Final simplification 30.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.25 \cdot 10^{+51} \lor \neg \left(b \leq 2.3 \cdot 10^{+22}\right):\\ \;\;\;\;t \cdot b\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 25: 20.6% accurate, 4.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.65 \cdot 10^{+162}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 4.8 \cdot 10^{-26}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -1.65e+162) x (if (<= x 4.8e-26) a x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -1.65e+162) {
		tmp = x;
	} else if (x <= 4.8e-26) {
		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 <= (-1.65d+162)) then
        tmp = x
    else if (x <= 4.8d-26) 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 <= -1.65e+162) {
		tmp = x;
	} else if (x <= 4.8e-26) {
		tmp = a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -1.65e+162:
		tmp = x
	elif x <= 4.8e-26:
		tmp = a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -1.65e+162)
		tmp = x;
	elseif (x <= 4.8e-26)
		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 <= -1.65e+162)
		tmp = x;
	elseif (x <= 4.8e-26)
		tmp = a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -1.65e+162], x, If[LessEqual[x, 4.8e-26], a, x]]

Derivation

1. Split input into 2 regimes

2. if x < -1.64999999999999994e162 or 4.8000000000000002e-26 < x

   1. Initial program 92.8%

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

   2. Taylor expanded in x around inf 36.6%

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

   if -1.64999999999999994e162 < x < 4.8000000000000002e-26

   1. Initial program 96.8%

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

   2. Taylor expanded in a around inf 34.3%

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

   3. Taylor expanded in t around 0 19.8%

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

4. Final simplification 26.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.65 \cdot 10^{+162}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 4.8 \cdot 10^{-26}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 26: 10.6% 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 95.3%

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

2. Taylor expanded in a around inf 28.6%

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

3. Taylor expanded in t around 0 14.3%

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

4. Final simplification 14.3%

   \[\leadsto a \]

Reproduce

herbie shell --seed 2023318 
(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)))