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

Percentage Accurate: 95.2% → 98.5%

Time: 17.4s

Alternatives: 23

Speedup: 0.5×

• 36.9% 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: 98.5% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(t + -2\right)\\ \mathbf{if}\;\left(\left(x + z \cdot \left(1 - y\right)\right) + a \cdot \left(1 - t\right)\right) + \left(\left(y + t\right) - 2\right) \cdot b \leq \infty:\\ \;\;\;\;\mathsf{fma}\left(t\_1, b, x - \mathsf{fma}\left(y + -1, z, \left(t + -1\right) \cdot a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(1 + \left(\left(\frac{x}{z} + b \cdot \frac{t\_1}{z}\right) + \left(a \cdot \frac{1 - t}{z} - y\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if (+.f64 (-.f64 (-.f64 x (*.f64 (-.f64 y #s(literal 1 binary64)) z)) (*.f64 (-.f64 t #s(literal 1 binary64)) a)) (*.f64 (-.f64 (+.f64 y t) #s(literal 2 binary64)) 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-define 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%

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

   if +inf.0 < (+.f64 (-.f64 (-.f64 x (*.f64 (-.f64 y #s(literal 1 binary64)) z)) (*.f64 (-.f64 t #s(literal 1 binary64)) a)) (*.f64 (-.f64 (+.f64 y t) #s(literal 2 binary64)) 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. Add Preprocessing

   3. Taylor expanded in z around inf 40.0%

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

      1. associate--l+ 40.0%

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

      2. sub-neg 40.0%

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

      3. metadata-eval 40.0%

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

      4. associate-+r+ 40.0%

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

      5. associate-/l* 60.0%

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

      6. associate-+r+ 60.0%

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

      7. metadata-eval 60.0%

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

      8. +-commutative 60.0%

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

      9. sub-neg 60.0%

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

      10. associate--l+ 60.0%

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

      11. sub-neg 60.0%

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

      12. metadata-eval 60.0%

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

   5. Simplified 86.7%

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

4. Final simplification 99.2%

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

Alternative 2: 98.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(x + z \cdot \left(1 - y\right)\right) + a \cdot \left(1 - t\right)\right) + \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{if}\;t\_1 \leq \infty:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(1 + \left(\left(\frac{x}{z} + b \cdot \frac{y + \left(t + -2\right)}{z}\right) + \left(a \cdot \frac{1 - t}{z} - y\right)\right)\right)\\ \end{array} \end{array} \]

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
     (*
      z
      (+
       1.0
       (+
        (+ (/ x z) (* b (/ (+ y (+ t -2.0)) z)))
        (- (* a (/ (- 1.0 t) z)) y)))))))

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 = z * (1.0 + (((x / z) + (b * ((y + (t + -2.0)) / z))) + ((a * ((1.0 - t) / z)) - y)));
	}
	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 = z * (1.0 + (((x / z) + (b * ((y + (t + -2.0)) / z))) + ((a * ((1.0 - t) / z)) - y)));
	}
	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 = z * (1.0 + (((x / z) + (b * ((y + (t + -2.0)) / z))) + ((a * ((1.0 - t) / z)) - y)))
	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(z * Float64(1.0 + Float64(Float64(Float64(x / z) + Float64(b * Float64(Float64(y + Float64(t + -2.0)) / z))) + Float64(Float64(a * Float64(Float64(1.0 - t) / z)) - y))));
	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 = z * (1.0 + (((x / z) + (b * ((y + (t + -2.0)) / z))) + ((a * ((1.0 - t) / z)) - y)));
	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[(z * N[(1.0 + N[(N[(N[(x / z), $MachinePrecision] + N[(b * N[(N[(y + N[(t + -2.0), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(a * N[(N[(1.0 - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 (-.f64 (-.f64 x (*.f64 (-.f64 y #s(literal 1 binary64)) z)) (*.f64 (-.f64 t #s(literal 1 binary64)) a)) (*.f64 (-.f64 (+.f64 y t) #s(literal 2 binary64)) 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. Add Preprocessing

   if +inf.0 < (+.f64 (-.f64 (-.f64 x (*.f64 (-.f64 y #s(literal 1 binary64)) z)) (*.f64 (-.f64 t #s(literal 1 binary64)) a)) (*.f64 (-.f64 (+.f64 y t) #s(literal 2 binary64)) 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. Add Preprocessing

   3. Taylor expanded in z around inf 40.0%

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

      1. associate--l+ 40.0%

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

      2. sub-neg 40.0%

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

      3. metadata-eval 40.0%

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

      4. associate-+r+ 40.0%

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

      5. associate-/l* 60.0%

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

      6. associate-+r+ 60.0%

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

      7. metadata-eval 60.0%

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

      8. +-commutative 60.0%

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

      9. sub-neg 60.0%

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

      10. associate--l+ 60.0%

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

      11. sub-neg 60.0%

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

      12. metadata-eval 60.0%

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

   5. Simplified 86.7%

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

4. Final simplification 99.2%

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

Alternative 3: 97.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(x + z \cdot \left(1 - y\right)\right) + a \cdot \left(1 - t\right)\right) + \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{if}\;t\_1 \leq \infty:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \end{array} \end{array} \]

FPCore

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

C

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

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((x + (z * (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 = y * (b - z);
	}
	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 = y * (b - z)
	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(y * Float64(b - z));
	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 = y * (b - z);
	end
	tmp_2 = tmp;
end

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if (+.f64 (-.f64 (-.f64 x (*.f64 (-.f64 y #s(literal 1 binary64)) z)) (*.f64 (-.f64 t #s(literal 1 binary64)) a)) (*.f64 (-.f64 (+.f64 y t) #s(literal 2 binary64)) 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. Add Preprocessing

   if +inf.0 < (+.f64 (-.f64 (-.f64 x (*.f64 (-.f64 y #s(literal 1 binary64)) z)) (*.f64 (-.f64 t #s(literal 1 binary64)) a)) (*.f64 (-.f64 (+.f64 y t) #s(literal 2 binary64)) 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. Add Preprocessing

   3. Taylor expanded in y around inf 73.8%

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

4. Final simplification 98.4%

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

Alternative 4: 88.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(1 - t\right)\\ \mathbf{if}\;b \leq -6.6 \cdot 10^{-7} \lor \neg \left(b \leq 2.6 \cdot 10^{-24}\right):\\ \;\;\;\;\left(x + \left(\left(y + t\right) - 2\right) \cdot b\right) + t\_1\\ \mathbf{else}:\\ \;\;\;\;\left(\left(x + z \cdot \left(1 - y\right)\right) + t\_1\right) + y \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (- 1.0 t))))
   (if (or (<= b -6.6e-7) (not (<= b 2.6e-24)))
     (+ (+ x (* (- (+ y t) 2.0) b)) t_1)
     (+ (+ (+ x (* z (- 1.0 y))) t_1) (* y b)))))

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 <= -6.6e-7) || !(b <= 2.6e-24)) {
		tmp = (x + (((y + t) - 2.0) * b)) + t_1;
	} else {
		tmp = ((x + (z * (1.0 - y))) + t_1) + (y * b);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (1.0d0 - t)
    if ((b <= (-6.6d-7)) .or. (.not. (b <= 2.6d-24))) then
        tmp = (x + (((y + t) - 2.0d0) * b)) + t_1
    else
        tmp = ((x + (z * (1.0d0 - y))) + t_1) + (y * b)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double tmp;
	if ((b <= -6.6e-7) || !(b <= 2.6e-24)) {
		tmp = (x + (((y + t) - 2.0) * b)) + t_1;
	} else {
		tmp = ((x + (z * (1.0 - y))) + t_1) + (y * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (1.0 - t)
	tmp = 0
	if (b <= -6.6e-7) or not (b <= 2.6e-24):
		tmp = (x + (((y + t) - 2.0) * b)) + t_1
	else:
		tmp = ((x + (z * (1.0 - y))) + t_1) + (y * b)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(1.0 - t))
	tmp = 0.0
	if ((b <= -6.6e-7) || !(b <= 2.6e-24))
		tmp = Float64(Float64(x + Float64(Float64(Float64(y + t) - 2.0) * b)) + t_1);
	else
		tmp = Float64(Float64(Float64(x + Float64(z * Float64(1.0 - y))) + t_1) + Float64(y * b));
	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 <= -6.6e-7) || ~((b <= 2.6e-24)))
		tmp = (x + (((y + t) - 2.0) * b)) + t_1;
	else
		tmp = ((x + (z * (1.0 - y))) + t_1) + (y * b);
	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, -6.6e-7], N[Not[LessEqual[b, 2.6e-24]], $MachinePrecision]], N[(N[(x + N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], N[(N[(N[(x + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision] + N[(y * b), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if b < -6.6000000000000003e-7 or 2.6e-24 < b

   1. Initial program 90.6%

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

   3. Taylor expanded in z around 0 90.0%

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

   if -6.6000000000000003e-7 < b < 2.6e-24

   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. Add Preprocessing

   3. Taylor expanded in y around inf 96.4%

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

4. Final simplification 92.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -6.6 \cdot 10^{-7} \lor \neg \left(b \leq 2.6 \cdot 10^{-24}\right):\\ \;\;\;\;\left(x + \left(\left(y + t\right) - 2\right) \cdot b\right) + a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(x + z \cdot \left(1 - y\right)\right) + a \cdot \left(1 - t\right)\right) + y \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 53.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z + \left(x + a\right)\\ t_2 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -8.5 \cdot 10^{+41}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -1.1 \cdot 10^{-117}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 3.7 \cdot 10^{-222}:\\ \;\;\;\;b \cdot \left(y - 2\right)\\ \mathbf{elif}\;t \leq 12200000000:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ z (+ x a))) (t_2 (* t (- b a))))
   (if (<= t -8.5e+41)
     t_2
     (if (<= t -1.1e-117)
       t_1
       (if (<= t 3.7e-222)
         (* b (- y 2.0))
         (if (<= t 12200000000.0) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z + (x + a);
	double t_2 = t * (b - a);
	double tmp;
	if (t <= -8.5e+41) {
		tmp = t_2;
	} else if (t <= -1.1e-117) {
		tmp = t_1;
	} else if (t <= 3.7e-222) {
		tmp = b * (y - 2.0);
	} else if (t <= 12200000000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = z + (x + a)
    t_2 = t * (b - a)
    if (t <= (-8.5d+41)) then
        tmp = t_2
    else if (t <= (-1.1d-117)) then
        tmp = t_1
    else if (t <= 3.7d-222) then
        tmp = b * (y - 2.0d0)
    else if (t <= 12200000000.0d0) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z + (x + a);
	double t_2 = t * (b - a);
	double tmp;
	if (t <= -8.5e+41) {
		tmp = t_2;
	} else if (t <= -1.1e-117) {
		tmp = t_1;
	} else if (t <= 3.7e-222) {
		tmp = b * (y - 2.0);
	} else if (t <= 12200000000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z + (x + a)
	t_2 = t * (b - a)
	tmp = 0
	if t <= -8.5e+41:
		tmp = t_2
	elif t <= -1.1e-117:
		tmp = t_1
	elif t <= 3.7e-222:
		tmp = b * (y - 2.0)
	elif t <= 12200000000.0:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z + Float64(x + a))
	t_2 = Float64(t * Float64(b - a))
	tmp = 0.0
	if (t <= -8.5e+41)
		tmp = t_2;
	elseif (t <= -1.1e-117)
		tmp = t_1;
	elseif (t <= 3.7e-222)
		tmp = Float64(b * Float64(y - 2.0));
	elseif (t <= 12200000000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z + (x + a);
	t_2 = t * (b - a);
	tmp = 0.0;
	if (t <= -8.5e+41)
		tmp = t_2;
	elseif (t <= -1.1e-117)
		tmp = t_1;
	elseif (t <= 3.7e-222)
		tmp = b * (y - 2.0);
	elseif (t <= 12200000000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z + N[(x + a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -8.5e+41], t$95$2, If[LessEqual[t, -1.1e-117], t$95$1, If[LessEqual[t, 3.7e-222], N[(b * N[(y - 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 12200000000.0], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -8.49999999999999938e41 or 1.22e10 < t

   1. Initial program 91.3%

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

   3. Taylor expanded in t around inf 71.8%

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

   if -8.49999999999999938e41 < t < -1.1000000000000001e-117 or 3.6999999999999999e-222 < t < 1.22e10

   1. Initial program 98.7%

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

   3. Taylor expanded in y around inf 87.1%

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

   4. Taylor expanded in y around 0 56.3%

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

      1. sub-neg 56.3%

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

      2. neg-mul-1 56.3%

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

      3. sub-neg 56.3%

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

      4. metadata-eval 56.3%

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

      5. distribute-neg-in 56.3%

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

      6. remove-double-neg 56.3%

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

      7. distribute-rgt-neg-in 56.3%

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

      8. +-commutative 56.3%

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

      9. distribute-neg-in 56.3%

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

      10. metadata-eval 56.3%

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

      11. sub-neg 56.3%

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

   6. Simplified 56.3%

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

   7. Taylor expanded in t around 0 54.4%

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

      1. +-commutative 54.4%

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

      2. +-commutative 54.4%

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

      3. associate-+l+ 54.4%

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

   9. Simplified 54.4%

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

   if -1.1000000000000001e-117 < t < 3.6999999999999999e-222

   1. Initial program 94.4%

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

   3. Taylor expanded in t around inf 51.0%

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

      1. mul-1-neg 51.0%

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

      2. distribute-rgt-neg-in 51.0%

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

   5. Simplified 51.0%

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

   6. Taylor expanded in t around inf 32.0%

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

      1. associate-+r+ 32.0%

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

      2. neg-mul-1 32.0%

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

      3. sub-neg 32.0%

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

      4. sub-neg 32.0%

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

      5. metadata-eval 32.0%

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

   8. Simplified 32.0%

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

   9. Taylor expanded in t around 0 51.0%

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

Alternative 6: 86.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(1 - t\right)\\ \mathbf{if}\;b \leq -5.2 \cdot 10^{-6} \lor \neg \left(b \leq 6.8 \cdot 10^{-47}\right):\\ \;\;\;\;\left(x + \left(\left(y + t\right) - 2\right) \cdot b\right) + t\_1\\ \mathbf{else}:\\ \;\;\;\;x + \left(z \cdot \left(1 - y\right) + t\_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (- 1.0 t))))
   (if (or (<= b -5.2e-6) (not (<= b 6.8e-47)))
     (+ (+ 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 <= -5.2e-6) || !(b <= 6.8e-47)) {
		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 <= (-5.2d-6)) .or. (.not. (b <= 6.8d-47))) 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 <= -5.2e-6) || !(b <= 6.8e-47)) {
		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 <= -5.2e-6) or not (b <= 6.8e-47):
		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 <= -5.2e-6) || !(b <= 6.8e-47))
		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 <= -5.2e-6) || ~((b <= 6.8e-47)))
		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, -5.2e-6], N[Not[LessEqual[b, 6.8e-47]], $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 < -5.20000000000000019e-6 or 6.8000000000000003e-47 < b

   1. Initial program 90.8%

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

   3. Taylor expanded in z around 0 89.7%

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

   if -5.20000000000000019e-6 < b < 6.8000000000000003e-47

   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. Add Preprocessing

   3. 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. Recombined 2 regimes into one program.

4. Final simplification 91.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5.2 \cdot 10^{-6} \lor \neg \left(b \leq 6.8 \cdot 10^{-47}\right):\\ \;\;\;\;\left(x + \left(\left(y + t\right) - 2\right) \cdot b\right) + a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(z \cdot \left(1 - y\right) + a \cdot \left(1 - t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 35.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{+50}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;y \leq 6 \cdot 10^{-5}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;y \leq 2 \cdot 10^{+55}:\\ \;\;\;\;t \cdot \left(-a\right)\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{+174}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -1.1e+50)
   (* y b)
   (if (<= y 6e-5)
     (+ x z)
     (if (<= y 2e+55) (* t (- a)) (if (<= y 6.2e+174) (* y (- z)) (* y b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1.1e+50) {
		tmp = y * b;
	} else if (y <= 6e-5) {
		tmp = x + z;
	} else if (y <= 2e+55) {
		tmp = t * -a;
	} else if (y <= 6.2e+174) {
		tmp = y * -z;
	} 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 (y <= (-1.1d+50)) then
        tmp = y * b
    else if (y <= 6d-5) then
        tmp = x + z
    else if (y <= 2d+55) then
        tmp = t * -a
    else if (y <= 6.2d+174) then
        tmp = y * -z
    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 (y <= -1.1e+50) {
		tmp = y * b;
	} else if (y <= 6e-5) {
		tmp = x + z;
	} else if (y <= 2e+55) {
		tmp = t * -a;
	} else if (y <= 6.2e+174) {
		tmp = y * -z;
	} else {
		tmp = y * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -1.1e+50:
		tmp = y * b
	elif y <= 6e-5:
		tmp = x + z
	elif y <= 2e+55:
		tmp = t * -a
	elif y <= 6.2e+174:
		tmp = y * -z
	else:
		tmp = y * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -1.1e+50)
		tmp = Float64(y * b);
	elseif (y <= 6e-5)
		tmp = Float64(x + z);
	elseif (y <= 2e+55)
		tmp = Float64(t * Float64(-a));
	elseif (y <= 6.2e+174)
		tmp = Float64(y * Float64(-z));
	else
		tmp = Float64(y * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -1.1e+50)
		tmp = y * b;
	elseif (y <= 6e-5)
		tmp = x + z;
	elseif (y <= 2e+55)
		tmp = t * -a;
	elseif (y <= 6.2e+174)
		tmp = y * -z;
	else
		tmp = y * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -1.1e+50], N[(y * b), $MachinePrecision], If[LessEqual[y, 6e-5], N[(x + z), $MachinePrecision], If[LessEqual[y, 2e+55], N[(t * (-a)), $MachinePrecision], If[LessEqual[y, 6.2e+174], N[(y * (-z)), $MachinePrecision], N[(y * b), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.10000000000000008e50 or 6.2e174 < y

   1. Initial program 88.7%

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

   3. Taylor expanded in y around inf 72.9%

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

   4. Taylor expanded in b around inf 50.5%

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

   if -1.10000000000000008e50 < y < 6.00000000000000015e-5

   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. Add Preprocessing

   3. Taylor expanded in a around 0 73.8%

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

   4. Taylor expanded in b around 0 36.7%

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

   5. Taylor expanded in y around 0 36.3%

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

      1. sub-neg 36.3%

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

      2. neg-mul-1 36.3%

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

      3. remove-double-neg 36.3%

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

      4. +-commutative 36.3%

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

   7. Simplified 36.3%

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

   if 6.00000000000000015e-5 < y < 2.00000000000000002e55

   1. Initial program 92.9%

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

   3. Taylor expanded in t around inf 78.6%

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

      1. mul-1-neg 78.6%

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

      2. distribute-rgt-neg-in 78.6%

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

   5. Simplified 78.6%

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

   6. Taylor expanded in a around inf 57.9%

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

      1. mul-1-neg 57.9%

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

      2. *-commutative 57.9%

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

      3. distribute-rgt-neg-in 57.9%

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

   8. Simplified 57.9%

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

   if 2.00000000000000002e55 < y < 6.2e174

   1. Initial program 83.3%

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

   3. Taylor expanded in y around inf 72.3%

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

   4. Taylor expanded in b around 0 50.8%

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

      1. associate-*r* 50.8%

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

      2. mul-1-neg 50.8%

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

   6. Simplified 50.8%

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

4. Final simplification 42.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{+50}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;y \leq 6 \cdot 10^{-5}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;y \leq 2 \cdot 10^{+55}:\\ \;\;\;\;t \cdot \left(-a\right)\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{+174}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 70.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{if}\;b \leq -35:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -1.55 \cdot 10^{-87}:\\ \;\;\;\;t \cdot b + z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq 5.1 \cdot 10^{+67}:\\ \;\;\;\;x + \left(z + a \cdot \left(1 - t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* (- (+ y t) 2.0) b))))
   (if (<= b -35.0)
     t_1
     (if (<= b -1.55e-87)
       (+ (* t b) (* z (- 1.0 y)))
       (if (<= b 5.1e+67) (+ x (+ z (* a (- 1.0 t)))) t_1)))))

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 <= -35.0) {
		tmp = t_1;
	} else if (b <= -1.55e-87) {
		tmp = (t * b) + (z * (1.0 - y));
	} else if (b <= 5.1e+67) {
		tmp = x + (z + (a * (1.0 - t)));
	} 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 = x + (((y + t) - 2.0d0) * b)
    if (b <= (-35.0d0)) then
        tmp = t_1
    else if (b <= (-1.55d-87)) then
        tmp = (t * b) + (z * (1.0d0 - y))
    else if (b <= 5.1d+67) then
        tmp = x + (z + (a * (1.0d0 - t)))
    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 = x + (((y + t) - 2.0) * b);
	double tmp;
	if (b <= -35.0) {
		tmp = t_1;
	} else if (b <= -1.55e-87) {
		tmp = (t * b) + (z * (1.0 - y));
	} else if (b <= 5.1e+67) {
		tmp = x + (z + (a * (1.0 - t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (((y + t) - 2.0) * b)
	tmp = 0
	if b <= -35.0:
		tmp = t_1
	elif b <= -1.55e-87:
		tmp = (t * b) + (z * (1.0 - y))
	elif b <= 5.1e+67:
		tmp = x + (z + (a * (1.0 - t)))
	else:
		tmp = t_1
	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 <= -35.0)
		tmp = t_1;
	elseif (b <= -1.55e-87)
		tmp = Float64(Float64(t * b) + Float64(z * Float64(1.0 - y)));
	elseif (b <= 5.1e+67)
		tmp = Float64(x + Float64(z + Float64(a * Float64(1.0 - t))));
	else
		tmp = t_1;
	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 <= -35.0)
		tmp = t_1;
	elseif (b <= -1.55e-87)
		tmp = (t * b) + (z * (1.0 - y));
	elseif (b <= 5.1e+67)
		tmp = x + (z + (a * (1.0 - t)));
	else
		tmp = t_1;
	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, -35.0], t$95$1, If[LessEqual[b, -1.55e-87], N[(N[(t * b), $MachinePrecision] + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 5.1e+67], N[(x + N[(z + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -35 or 5.1000000000000002e67 < 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. Add Preprocessing

   3. Taylor expanded in z around 0 90.4%

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

   4. Taylor expanded in a around 0 86.8%

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

   if -35 < b < -1.54999999999999999e-87

   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. Add Preprocessing

   3. Taylor expanded in a around 0 78.8%

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

   4. Taylor expanded in t around inf 74.7%

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

   if -1.54999999999999999e-87 < b < 5.1000000000000002e67

   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. Add Preprocessing

   3. Taylor expanded in y around inf 95.5%

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

   4. Taylor expanded in y around 0 79.4%

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

      1. sub-neg 79.4%

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

      2. neg-mul-1 79.4%

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

      3. sub-neg 79.4%

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

      4. metadata-eval 79.4%

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

      5. distribute-neg-in 79.4%

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

      6. remove-double-neg 79.4%

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

      7. distribute-rgt-neg-in 79.4%

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

      8. +-commutative 79.4%

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

      9. distribute-neg-in 79.4%

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

      10. metadata-eval 79.4%

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

      11. sub-neg 79.4%

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

   6. Simplified 79.4%

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

4. Final simplification 82.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -35:\\ \;\;\;\;x + \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{elif}\;b \leq -1.55 \cdot 10^{-87}:\\ \;\;\;\;t \cdot b + z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq 5.1 \cdot 10^{+67}:\\ \;\;\;\;x + \left(z + a \cdot \left(1 - t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(\left(y + t\right) - 2\right) \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 65.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{if}\;b \leq -8 \cdot 10^{-8}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -2.1 \cdot 10^{-89}:\\ \;\;\;\;x + z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq 2.5 \cdot 10^{+68}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* (- (+ y t) 2.0) b))))
   (if (<= b -8e-8)
     t_1
     (if (<= b -2.1e-89)
       (+ x (* z (- 1.0 y)))
       (if (<= b 2.5e+68) (+ x (* a (- 1.0 t))) t_1)))))

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 <= -8e-8) {
		tmp = t_1;
	} else if (b <= -2.1e-89) {
		tmp = x + (z * (1.0 - y));
	} else if (b <= 2.5e+68) {
		tmp = x + (a * (1.0 - t));
	} 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 = x + (((y + t) - 2.0d0) * b)
    if (b <= (-8d-8)) then
        tmp = t_1
    else if (b <= (-2.1d-89)) then
        tmp = x + (z * (1.0d0 - y))
    else if (b <= 2.5d+68) then
        tmp = x + (a * (1.0d0 - t))
    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 = x + (((y + t) - 2.0) * b);
	double tmp;
	if (b <= -8e-8) {
		tmp = t_1;
	} else if (b <= -2.1e-89) {
		tmp = x + (z * (1.0 - y));
	} else if (b <= 2.5e+68) {
		tmp = x + (a * (1.0 - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (((y + t) - 2.0) * b)
	tmp = 0
	if b <= -8e-8:
		tmp = t_1
	elif b <= -2.1e-89:
		tmp = x + (z * (1.0 - y))
	elif b <= 2.5e+68:
		tmp = x + (a * (1.0 - t))
	else:
		tmp = t_1
	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 <= -8e-8)
		tmp = t_1;
	elseif (b <= -2.1e-89)
		tmp = Float64(x + Float64(z * Float64(1.0 - y)));
	elseif (b <= 2.5e+68)
		tmp = Float64(x + Float64(a * Float64(1.0 - t)));
	else
		tmp = t_1;
	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 <= -8e-8)
		tmp = t_1;
	elseif (b <= -2.1e-89)
		tmp = x + (z * (1.0 - y));
	elseif (b <= 2.5e+68)
		tmp = x + (a * (1.0 - t));
	else
		tmp = t_1;
	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, -8e-8], t$95$1, If[LessEqual[b, -2.1e-89], N[(x + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.5e+68], N[(x + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -8.0000000000000002e-8 or 2.5000000000000002e68 < b

   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. Add Preprocessing

   3. Taylor expanded in z around 0 90.6%

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

   4. Taylor expanded in a around 0 86.3%

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

   if -8.0000000000000002e-8 < b < -2.1000000000000001e-89

   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. Add Preprocessing

   3. Taylor expanded in a around 0 78.8%

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

   4. Taylor expanded in b around 0 61.9%

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

   if -2.1000000000000001e-89 < b < 2.5000000000000002e68

   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. Add Preprocessing

   3. Taylor expanded in z around 0 74.1%

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

   4. Taylor expanded in b around 0 67.0%

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

4. Final simplification 76.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -8 \cdot 10^{-8}:\\ \;\;\;\;x + \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{elif}\;b \leq -2.1 \cdot 10^{-89}:\\ \;\;\;\;x + z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq 2.5 \cdot 10^{+68}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(\left(y + t\right) - 2\right) \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 83.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1 \cdot 10^{-5} \lor \neg \left(b \leq 2.7 \cdot 10^{+68}\right):\\ \;\;\;\;x + \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;x + \left(z \cdot \left(1 - y\right) + a \cdot \left(1 - t\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -1e-5) (not (<= b 2.7e+68)))
   (+ 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 <= -1e-5) || !(b <= 2.7e+68)) {
		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 <= (-1d-5)) .or. (.not. (b <= 2.7d+68))) 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 <= -1e-5) || !(b <= 2.7e+68)) {
		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 <= -1e-5) or not (b <= 2.7e+68):
		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 <= -1e-5) || !(b <= 2.7e+68))
		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 <= -1e-5) || ~((b <= 2.7e+68)))
		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, -1e-5], N[Not[LessEqual[b, 2.7e+68]], $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 < -1.00000000000000008e-5 or 2.69999999999999991e68 < b

   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. Add Preprocessing

   3. Taylor expanded in z around 0 90.6%

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

   4. Taylor expanded in a around 0 86.3%

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

   if -1.00000000000000008e-5 < b < 2.69999999999999991e68

   1. Initial program 98.4%

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

   3. 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. Recombined 2 regimes into one program.

4. Final simplification 88.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1 \cdot 10^{-5} \lor \neg \left(b \leq 2.7 \cdot 10^{+68}\right):\\ \;\;\;\;x + \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;x + \left(z \cdot \left(1 - y\right) + a \cdot \left(1 - t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 62.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{if}\;b \leq -5.5 \cdot 10^{+16}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -2.75 \cdot 10^{-89}:\\ \;\;\;\;x + z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq 7.5 \cdot 10^{+72}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- (+ y t) 2.0) b)))
   (if (<= b -5.5e+16)
     t_1
     (if (<= b -2.75e-89)
       (+ x (* z (- 1.0 y)))
       (if (<= b 7.5e+72) (+ x (* a (- 1.0 t))) 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 <= -5.5e+16) {
		tmp = t_1;
	} else if (b <= -2.75e-89) {
		tmp = x + (z * (1.0 - y));
	} else if (b <= 7.5e+72) {
		tmp = x + (a * (1.0 - t));
	} 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 <= (-5.5d+16)) then
        tmp = t_1
    else if (b <= (-2.75d-89)) then
        tmp = x + (z * (1.0d0 - y))
    else if (b <= 7.5d+72) then
        tmp = x + (a * (1.0d0 - t))
    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 <= -5.5e+16) {
		tmp = t_1;
	} else if (b <= -2.75e-89) {
		tmp = x + (z * (1.0 - y));
	} else if (b <= 7.5e+72) {
		tmp = x + (a * (1.0 - t));
	} 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 <= -5.5e+16:
		tmp = t_1
	elif b <= -2.75e-89:
		tmp = x + (z * (1.0 - y))
	elif b <= 7.5e+72:
		tmp = x + (a * (1.0 - t))
	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 <= -5.5e+16)
		tmp = t_1;
	elseif (b <= -2.75e-89)
		tmp = Float64(x + Float64(z * Float64(1.0 - y)));
	elseif (b <= 7.5e+72)
		tmp = Float64(x + Float64(a * Float64(1.0 - t)));
	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 <= -5.5e+16)
		tmp = t_1;
	elseif (b <= -2.75e-89)
		tmp = x + (z * (1.0 - y));
	elseif (b <= 7.5e+72)
		tmp = x + (a * (1.0 - t));
	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, -5.5e+16], t$95$1, If[LessEqual[b, -2.75e-89], N[(x + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 7.5e+72], N[(x + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -5.5e16 or 7.50000000000000027e72 < b

   1. Initial program 89.5%

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

   3. Taylor expanded in b around inf 78.0%

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

   if -5.5e16 < b < -2.75000000000000006e-89

   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. Add Preprocessing

   3. Taylor expanded in a around 0 78.3%

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

   4. Taylor expanded in b around 0 59.8%

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

   if -2.75000000000000006e-89 < b < 7.50000000000000027e72

   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. Add Preprocessing

   3. Taylor expanded in z around 0 74.6%

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

   4. Taylor expanded in b around 0 67.5%

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

4. Final simplification 72.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5.5 \cdot 10^{+16}:\\ \;\;\;\;\left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{elif}\;b \leq -2.75 \cdot 10^{-89}:\\ \;\;\;\;x + z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq 7.5 \cdot 10^{+72}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(y + t\right) - 2\right) \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 61.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{if}\;b \leq -6.4 \cdot 10^{-6}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -6.5 \cdot 10^{-89}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq 2.8 \cdot 10^{+74}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- (+ y t) 2.0) b)))
   (if (<= b -6.4e-6)
     t_1
     (if (<= b -6.5e-89)
       (* z (- 1.0 y))
       (if (<= b 2.8e+74) (+ x (* a (- 1.0 t))) 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 <= -6.4e-6) {
		tmp = t_1;
	} else if (b <= -6.5e-89) {
		tmp = z * (1.0 - y);
	} else if (b <= 2.8e+74) {
		tmp = x + (a * (1.0 - t));
	} 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 <= (-6.4d-6)) then
        tmp = t_1
    else if (b <= (-6.5d-89)) then
        tmp = z * (1.0d0 - y)
    else if (b <= 2.8d+74) then
        tmp = x + (a * (1.0d0 - t))
    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 <= -6.4e-6) {
		tmp = t_1;
	} else if (b <= -6.5e-89) {
		tmp = z * (1.0 - y);
	} else if (b <= 2.8e+74) {
		tmp = x + (a * (1.0 - t));
	} 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 <= -6.4e-6:
		tmp = t_1
	elif b <= -6.5e-89:
		tmp = z * (1.0 - y)
	elif b <= 2.8e+74:
		tmp = x + (a * (1.0 - t))
	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 <= -6.4e-6)
		tmp = t_1;
	elseif (b <= -6.5e-89)
		tmp = Float64(z * Float64(1.0 - y));
	elseif (b <= 2.8e+74)
		tmp = Float64(x + Float64(a * Float64(1.0 - t)));
	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 <= -6.4e-6)
		tmp = t_1;
	elseif (b <= -6.5e-89)
		tmp = z * (1.0 - y);
	elseif (b <= 2.8e+74)
		tmp = x + (a * (1.0 - t));
	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, -6.4e-6], t$95$1, If[LessEqual[b, -6.5e-89], N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.8e+74], N[(x + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -6.3999999999999997e-6 or 2.80000000000000002e74 < 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. Add Preprocessing

   3. Taylor expanded in b around inf 76.5%

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

   if -6.3999999999999997e-6 < b < -6.50000000000000034e-89

   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. Add Preprocessing

   3. Taylor expanded in z around inf 61.3%

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

   if -6.50000000000000034e-89 < b < 2.80000000000000002e74

   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. Add Preprocessing

   3. Taylor expanded in z around 0 74.6%

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

   4. Taylor expanded in b around 0 67.5%

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

4. Final simplification 71.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -6.4 \cdot 10^{-6}:\\ \;\;\;\;\left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{elif}\;b \leq -6.5 \cdot 10^{-89}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq 2.8 \cdot 10^{+74}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(y + t\right) - 2\right) \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 49.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -1.85 \cdot 10^{+42}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.1 \cdot 10^{-46}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{+14}:\\ \;\;\;\;b \cdot \left(y - 2\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (- b a))))
   (if (<= t -1.85e+42)
     t_1
     (if (<= t -1.1e-46) (+ x z) (if (<= t 1.6e+14) (* b (- y 2.0)) 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 <= -1.85e+42) {
		tmp = t_1;
	} else if (t <= -1.1e-46) {
		tmp = x + z;
	} else if (t <= 1.6e+14) {
		tmp = b * (y - 2.0);
	} 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 <= (-1.85d+42)) then
        tmp = t_1
    else if (t <= (-1.1d-46)) then
        tmp = x + z
    else if (t <= 1.6d+14) then
        tmp = b * (y - 2.0d0)
    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 <= -1.85e+42) {
		tmp = t_1;
	} else if (t <= -1.1e-46) {
		tmp = x + z;
	} else if (t <= 1.6e+14) {
		tmp = b * (y - 2.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t * (b - a)
	tmp = 0
	if t <= -1.85e+42:
		tmp = t_1
	elif t <= -1.1e-46:
		tmp = x + z
	elif t <= 1.6e+14:
		tmp = b * (y - 2.0)
	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 <= -1.85e+42)
		tmp = t_1;
	elseif (t <= -1.1e-46)
		tmp = Float64(x + z);
	elseif (t <= 1.6e+14)
		tmp = Float64(b * Float64(y - 2.0));
	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 <= -1.85e+42)
		tmp = t_1;
	elseif (t <= -1.1e-46)
		tmp = x + z;
	elseif (t <= 1.6e+14)
		tmp = b * (y - 2.0);
	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, -1.85e+42], t$95$1, If[LessEqual[t, -1.1e-46], N[(x + z), $MachinePrecision], If[LessEqual[t, 1.6e+14], N[(b * N[(y - 2.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.84999999999999998e42 or 1.6e14 < t

   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. Add Preprocessing

   3. Taylor expanded in t around inf 72.3%

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

   if -1.84999999999999998e42 < t < -1.1e-46

   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. Add Preprocessing

   3. Taylor expanded in a around 0 77.2%

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

   4. Taylor expanded in b around 0 65.8%

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

   5. Taylor expanded in y around 0 45.9%

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

      1. sub-neg 45.9%

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

      2. neg-mul-1 45.9%

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

      3. remove-double-neg 45.9%

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

      4. +-commutative 45.9%

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

   7. Simplified 45.9%

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

   if -1.1e-46 < t < 1.6e14

   1. Initial program 96.5%

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

   3. Taylor expanded in t around inf 44.6%

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

      1. mul-1-neg 44.6%

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

      2. distribute-rgt-neg-in 44.6%

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

   5. Simplified 44.6%

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

   6. Taylor expanded in t around inf 32.4%

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

      1. associate-+r+ 32.4%

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

      2. neg-mul-1 32.4%

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

      3. sub-neg 32.4%

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

      4. sub-neg 32.4%

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

      5. metadata-eval 32.4%

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

   8. Simplified 32.4%

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

   9. Taylor expanded in t around 0 44.6%

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

4. Final simplification 58.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.85 \cdot 10^{+42}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq -1.1 \cdot 10^{-46}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{+14}:\\ \;\;\;\;b \cdot \left(y - 2\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 40.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(y - 2\right)\\ \mathbf{if}\;b \leq -1.4 \cdot 10^{+105}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -2.6 \cdot 10^{-6}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;b \leq 1.15 \cdot 10^{+70}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- y 2.0))))
   (if (<= b -1.4e+105)
     t_1
     (if (<= b -2.6e-6) (* t b) (if (<= b 1.15e+70) (* a (- 1.0 t)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (y - 2.0);
	double tmp;
	if (b <= -1.4e+105) {
		tmp = t_1;
	} else if (b <= -2.6e-6) {
		tmp = t * b;
	} else if (b <= 1.15e+70) {
		tmp = a * (1.0 - t);
	} 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 * (y - 2.0d0)
    if (b <= (-1.4d+105)) then
        tmp = t_1
    else if (b <= (-2.6d-6)) then
        tmp = t * b
    else if (b <= 1.15d+70) then
        tmp = a * (1.0d0 - t)
    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 * (y - 2.0);
	double tmp;
	if (b <= -1.4e+105) {
		tmp = t_1;
	} else if (b <= -2.6e-6) {
		tmp = t * b;
	} else if (b <= 1.15e+70) {
		tmp = a * (1.0 - t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * (y - 2.0)
	tmp = 0
	if b <= -1.4e+105:
		tmp = t_1
	elif b <= -2.6e-6:
		tmp = t * b
	elif b <= 1.15e+70:
		tmp = a * (1.0 - t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(y - 2.0))
	tmp = 0.0
	if (b <= -1.4e+105)
		tmp = t_1;
	elseif (b <= -2.6e-6)
		tmp = Float64(t * b);
	elseif (b <= 1.15e+70)
		tmp = Float64(a * Float64(1.0 - t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * (y - 2.0);
	tmp = 0.0;
	if (b <= -1.4e+105)
		tmp = t_1;
	elseif (b <= -2.6e-6)
		tmp = t * b;
	elseif (b <= 1.15e+70)
		tmp = a * (1.0 - t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(y - 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.4e+105], t$95$1, If[LessEqual[b, -2.6e-6], N[(t * b), $MachinePrecision], If[LessEqual[b, 1.15e+70], N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.4000000000000001e105 or 1.14999999999999997e70 < b

   1. Initial program 87.8%

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

   3. Taylor expanded in t around inf 76.2%

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

      1. mul-1-neg 76.2%

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

      2. distribute-rgt-neg-in 76.2%

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

   5. Simplified 76.2%

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

   6. Taylor expanded in t around inf 66.1%

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

      1. associate-+r+ 66.1%

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

      2. neg-mul-1 66.1%

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

      3. sub-neg 66.1%

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

      4. sub-neg 66.1%

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

      5. metadata-eval 66.1%

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

   8. Simplified 66.1%

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

   9. Taylor expanded in t around 0 55.7%

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

   if -1.4000000000000001e105 < b < -2.60000000000000009e-6

   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. Add Preprocessing

   3. Taylor expanded in t around inf 67.9%

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

   4. Taylor expanded in b around inf 59.6%

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

   if -2.60000000000000009e-6 < b < 1.14999999999999997e70

   1. Initial program 98.4%

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

   3. Taylor expanded in a around inf 40.6%

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

Alternative 15: 39.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(1 - t\right)\\ \mathbf{if}\;a \leq -5.4 \cdot 10^{+34}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 8 \cdot 10^{-270}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;a \leq 540000000000:\\ \;\;\;\;t \cdot b\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (- 1.0 t))))
   (if (<= a -5.4e+34)
     t_1
     (if (<= a 8e-270) (+ x z) (if (<= a 540000000000.0) (* t b) 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 <= -5.4e+34) {
		tmp = t_1;
	} else if (a <= 8e-270) {
		tmp = x + z;
	} else if (a <= 540000000000.0) {
		tmp = t * b;
	} 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 <= (-5.4d+34)) then
        tmp = t_1
    else if (a <= 8d-270) then
        tmp = x + z
    else if (a <= 540000000000.0d0) then
        tmp = t * b
    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 <= -5.4e+34) {
		tmp = t_1;
	} else if (a <= 8e-270) {
		tmp = x + z;
	} else if (a <= 540000000000.0) {
		tmp = t * b;
	} 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 <= -5.4e+34:
		tmp = t_1
	elif a <= 8e-270:
		tmp = x + z
	elif a <= 540000000000.0:
		tmp = t * b
	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 <= -5.4e+34)
		tmp = t_1;
	elseif (a <= 8e-270)
		tmp = Float64(x + z);
	elseif (a <= 540000000000.0)
		tmp = Float64(t * b);
	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 <= -5.4e+34)
		tmp = t_1;
	elseif (a <= 8e-270)
		tmp = x + z;
	elseif (a <= 540000000000.0)
		tmp = t * b;
	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, -5.4e+34], t$95$1, If[LessEqual[a, 8e-270], N[(x + z), $MachinePrecision], If[LessEqual[a, 540000000000.0], N[(t * b), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -5.4000000000000001e34 or 5.4e11 < a

   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. Add Preprocessing

   3. Taylor expanded in a around inf 53.7%

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

   if -5.4000000000000001e34 < a < 8.0000000000000003e-270

   1. Initial program 97.3%

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

   3. Taylor expanded in a around 0 92.6%

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

   4. Taylor expanded in b around 0 52.1%

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

   5. Taylor expanded in y around 0 40.4%

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

      1. sub-neg 40.4%

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

      2. neg-mul-1 40.4%

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

      3. remove-double-neg 40.4%

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

      4. +-commutative 40.4%

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

   7. Simplified 40.4%

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

   if 8.0000000000000003e-270 < a < 5.4e11

   1. Initial program 97.0%

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

   3. Taylor expanded in t around inf 40.2%

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

   4. Taylor expanded in b around inf 38.6%

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

4. Final simplification 45.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.4 \cdot 10^{+34}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;a \leq 8 \cdot 10^{-270}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;a \leq 540000000000:\\ \;\;\;\;t \cdot b\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 72.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -4.4 \cdot 10^{-7} \lor \neg \left(b \leq 3.3 \cdot 10^{+67}\right):\\ \;\;\;\;x + \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;x + \left(z + a \cdot \left(1 - t\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -4.4e-7) (not (<= b 3.3e+67)))
   (+ x (* (- (+ y t) 2.0) b))
   (+ x (+ z (* a (- 1.0 t))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -4.4e-7) || !(b <= 3.3e+67)) {
		tmp = x + (((y + t) - 2.0) * b);
	} else {
		tmp = x + (z + (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 <= (-4.4d-7)) .or. (.not. (b <= 3.3d+67))) then
        tmp = x + (((y + t) - 2.0d0) * b)
    else
        tmp = x + (z + (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 <= -4.4e-7) || !(b <= 3.3e+67)) {
		tmp = x + (((y + t) - 2.0) * b);
	} else {
		tmp = x + (z + (a * (1.0 - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -4.4e-7) or not (b <= 3.3e+67):
		tmp = x + (((y + t) - 2.0) * b)
	else:
		tmp = x + (z + (a * (1.0 - t)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -4.4e-7) || !(b <= 3.3e+67))
		tmp = Float64(x + Float64(Float64(Float64(y + t) - 2.0) * b));
	else
		tmp = Float64(x + Float64(z + 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 <= -4.4e-7) || ~((b <= 3.3e+67)))
		tmp = x + (((y + t) - 2.0) * b);
	else
		tmp = x + (z + (a * (1.0 - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -4.4e-7], N[Not[LessEqual[b, 3.3e+67]], $MachinePrecision]], N[(x + N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision], N[(x + N[(z + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -4.4000000000000002e-7 or 3.3000000000000003e67 < b

   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. Add Preprocessing

   3. Taylor expanded in z around 0 90.6%

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

   4. Taylor expanded in a around 0 86.3%

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

   if -4.4000000000000002e-7 < b < 3.3000000000000003e67

   1. Initial program 98.4%

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

   3. Taylor expanded in y around inf 93.8%

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

   4. Taylor expanded in y around 0 75.0%

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

      1. sub-neg 75.0%

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

      2. neg-mul-1 75.0%

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

      3. sub-neg 75.0%

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

      4. metadata-eval 75.0%

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

      5. distribute-neg-in 75.0%

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

      6. remove-double-neg 75.0%

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

      7. distribute-rgt-neg-in 75.0%

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

      8. +-commutative 75.0%

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

      9. distribute-neg-in 75.0%

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

      10. metadata-eval 75.0%

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

      11. sub-neg 75.0%

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

   6. Simplified 75.0%

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

4. Final simplification 80.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.4 \cdot 10^{-7} \lor \neg \left(b \leq 3.3 \cdot 10^{+67}\right):\\ \;\;\;\;x + \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;x + \left(z + a \cdot \left(1 - t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 58.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.75 \cdot 10^{-6} \lor \neg \left(b \leq 5.1 \cdot 10^{+67}\right):\\ \;\;\;\;\left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;z + a \cdot \left(1 - t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -1.75e-6) (not (<= b 5.1e+67)))
   (* (- (+ y t) 2.0) b)
   (+ z (* a (- 1.0 t)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -1.75e-6) || !(b <= 5.1e+67)) {
		tmp = ((y + t) - 2.0) * b;
	} else {
		tmp = z + (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 <= (-1.75d-6)) .or. (.not. (b <= 5.1d+67))) then
        tmp = ((y + t) - 2.0d0) * b
    else
        tmp = z + (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 <= -1.75e-6) || !(b <= 5.1e+67)) {
		tmp = ((y + t) - 2.0) * b;
	} else {
		tmp = z + (a * (1.0 - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -1.75e-6) or not (b <= 5.1e+67):
		tmp = ((y + t) - 2.0) * b
	else:
		tmp = z + (a * (1.0 - t))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -1.75e-6) || !(b <= 5.1e+67))
		tmp = Float64(Float64(Float64(y + t) - 2.0) * b);
	else
		tmp = Float64(z + 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 <= -1.75e-6) || ~((b <= 5.1e+67)))
		tmp = ((y + t) - 2.0) * b;
	else
		tmp = z + (a * (1.0 - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -1.75e-6], N[Not[LessEqual[b, 5.1e+67]], $MachinePrecision]], N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision], N[(z + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.74999999999999997e-6 or 5.1000000000000002e67 < b

   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. Add Preprocessing

   3. Taylor expanded in b around inf 75.4%

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

   if -1.74999999999999997e-6 < b < 5.1000000000000002e67

   1. Initial program 98.4%

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

   3. Taylor expanded in y around inf 93.8%

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

   4. Taylor expanded in y around 0 75.0%

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

      1. sub-neg 75.0%

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

      2. neg-mul-1 75.0%

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

      3. sub-neg 75.0%

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

      4. metadata-eval 75.0%

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

      5. distribute-neg-in 75.0%

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

      6. remove-double-neg 75.0%

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

      7. distribute-rgt-neg-in 75.0%

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

      8. +-commutative 75.0%

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

      9. distribute-neg-in 75.0%

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

      10. metadata-eval 75.0%

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

      11. sub-neg 75.0%

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

   6. Simplified 75.0%

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

   7. Taylor expanded in x around 0 54.7%

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

4. Final simplification 65.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.75 \cdot 10^{-6} \lor \neg \left(b \leq 5.1 \cdot 10^{+67}\right):\\ \;\;\;\;\left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;z + a \cdot \left(1 - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 57.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2.7 \cdot 10^{+15} \lor \neg \left(b \leq 5.6 \cdot 10^{+73}\right):\\ \;\;\;\;\left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;z + \left(x + a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -2.7e+15) (not (<= b 5.6e+73)))
   (* (- (+ y t) 2.0) b)
   (+ z (+ x a))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -2.7e+15) || !(b <= 5.6e+73)) {
		tmp = ((y + t) - 2.0) * b;
	} else {
		tmp = z + (x + a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-2.7d+15)) .or. (.not. (b <= 5.6d+73))) then
        tmp = ((y + t) - 2.0d0) * b
    else
        tmp = z + (x + a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -2.7e+15) || !(b <= 5.6e+73)) {
		tmp = ((y + t) - 2.0) * b;
	} else {
		tmp = z + (x + a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -2.7e+15) or not (b <= 5.6e+73):
		tmp = ((y + t) - 2.0) * b
	else:
		tmp = z + (x + a)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -2.7e+15) || !(b <= 5.6e+73))
		tmp = Float64(Float64(Float64(y + t) - 2.0) * b);
	else
		tmp = Float64(z + Float64(x + a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -2.7e+15) || ~((b <= 5.6e+73)))
		tmp = ((y + t) - 2.0) * b;
	else
		tmp = z + (x + a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -2.7e+15], N[Not[LessEqual[b, 5.6e+73]], $MachinePrecision]], N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision], N[(z + N[(x + a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -2.7e15 or 5.60000000000000016e73 < b

   1. Initial program 89.5%

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

   3. Taylor expanded in b around inf 78.0%

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

   if -2.7e15 < b < 5.60000000000000016e73

   1. Initial program 98.5%

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

   3. Taylor expanded in y around inf 93.3%

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

   4. Taylor expanded in y around 0 75.4%

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

      1. sub-neg 75.4%

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

      2. neg-mul-1 75.4%

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

      3. sub-neg 75.4%

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

      4. metadata-eval 75.4%

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

      5. distribute-neg-in 75.4%

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

      6. remove-double-neg 75.4%

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

      7. distribute-rgt-neg-in 75.4%

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

      8. +-commutative 75.4%

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

      9. distribute-neg-in 75.4%

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

      10. metadata-eval 75.4%

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

      11. sub-neg 75.4%

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

   6. Simplified 75.4%

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

   7. Taylor expanded in t around 0 47.0%

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

      1. +-commutative 47.0%

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

      2. +-commutative 47.0%

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

      3. associate-+l+ 47.0%

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

   9. Simplified 47.0%

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

4. Final simplification 62.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.7 \cdot 10^{+15} \lor \neg \left(b \leq 5.6 \cdot 10^{+73}\right):\\ \;\;\;\;\left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;z + \left(x + a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 35.0% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{+51} \lor \neg \left(y \leq 0.000105\right):\\ \;\;\;\;y \cdot b\\ \mathbf{else}:\\ \;\;\;\;x + z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1.05e+51) (not (<= y 0.000105))) (* y b) (+ x z)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.05e+51) || !(y <= 0.000105)) {
		tmp = y * b;
	} else {
		tmp = x + z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-1.05d+51)) .or. (.not. (y <= 0.000105d0))) then
        tmp = y * b
    else
        tmp = x + z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.05e+51) || !(y <= 0.000105)) {
		tmp = y * b;
	} else {
		tmp = x + z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -1.05e+51) or not (y <= 0.000105):
		tmp = y * b
	else:
		tmp = x + z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -1.05e+51) || !(y <= 0.000105))
		tmp = Float64(y * b);
	else
		tmp = Float64(x + z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -1.05e+51) || ~((y <= 0.000105)))
		tmp = y * b;
	else
		tmp = x + z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -1.05e+51], N[Not[LessEqual[y, 0.000105]], $MachinePrecision]], N[(y * b), $MachinePrecision], N[(x + z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.0500000000000001e51 or 1.05e-4 < y

   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. Add Preprocessing

   3. Taylor expanded in y around inf 69.2%

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

   4. Taylor expanded in b around inf 43.5%

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

   if -1.0500000000000001e51 < y < 1.05e-4

   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. Add Preprocessing

   3. Taylor expanded in a around 0 73.8%

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

   4. Taylor expanded in b around 0 36.7%

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

   5. Taylor expanded in y around 0 36.3%

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

      1. sub-neg 36.3%

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

      2. neg-mul-1 36.3%

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

      3. remove-double-neg 36.3%

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

      4. +-commutative 36.3%

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

   7. Simplified 36.3%

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

4. Final simplification 39.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{+51} \lor \neg \left(y \leq 0.000105\right):\\ \;\;\;\;y \cdot b\\ \mathbf{else}:\\ \;\;\;\;x + z\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 27.5% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.62 \cdot 10^{+63} \lor \neg \left(y \leq 9.2 \cdot 10^{+16}\right):\\ \;\;\;\;y \cdot b\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1.62e+63) (not (<= y 9.2e+16))) (* y b) (* t b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.62e+63) || !(y <= 9.2e+16)) {
		tmp = y * b;
	} else {
		tmp = t * b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-1.62d+63)) .or. (.not. (y <= 9.2d+16))) then
        tmp = y * b
    else
        tmp = t * b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.62e+63) || !(y <= 9.2e+16)) {
		tmp = y * b;
	} else {
		tmp = t * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -1.62e+63) or not (y <= 9.2e+16):
		tmp = y * b
	else:
		tmp = t * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -1.62e+63) || !(y <= 9.2e+16))
		tmp = Float64(y * b);
	else
		tmp = Float64(t * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -1.62e+63) || ~((y <= 9.2e+16)))
		tmp = y * b;
	else
		tmp = t * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -1.62e+63], N[Not[LessEqual[y, 9.2e+16]], $MachinePrecision]], N[(y * b), $MachinePrecision], N[(t * b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.62e63 or 9.2e16 < y

   1. Initial program 87.7%

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

   3. Taylor expanded in y around inf 72.0%

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

   4. Taylor expanded in b around inf 44.9%

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

   if -1.62e63 < y < 9.2e16

   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. Add Preprocessing

   3. Taylor expanded in t around inf 43.9%

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

   4. Taylor expanded in b around inf 26.5%

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

4. Final simplification 34.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.62 \cdot 10^{+63} \lor \neg \left(y \leq 9.2 \cdot 10^{+16}\right):\\ \;\;\;\;y \cdot b\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 26.9% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5.4 \cdot 10^{+34} \lor \neg \left(t \leq 2800000\right):\\ \;\;\;\;t \cdot b\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -5.4e+34) (not (<= t 2800000.0))) (* t b) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -5.4e+34) || !(t <= 2800000.0)) {
		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 ((t <= (-5.4d+34)) .or. (.not. (t <= 2800000.0d0))) 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 ((t <= -5.4e+34) || !(t <= 2800000.0)) {
		tmp = t * b;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -5.4e+34) or not (t <= 2800000.0):
		tmp = t * b
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -5.4e+34) || !(t <= 2800000.0))
		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 ((t <= -5.4e+34) || ~((t <= 2800000.0)))
		tmp = t * b;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -5.4e+34], N[Not[LessEqual[t, 2800000.0]], $MachinePrecision]], N[(t * b), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if t < -5.4000000000000001e34 or 2.8e6 < t

   1. Initial program 91.5%

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

   3. Taylor expanded in t around inf 70.9%

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

   4. Taylor expanded in b around inf 40.1%

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

   if -5.4000000000000001e34 < t < 2.8e6

   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. Add Preprocessing

   3. Taylor expanded in x around inf 23.0%

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

4. Final simplification 31.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.4 \cdot 10^{+34} \lor \neg \left(t \leq 2800000\right):\\ \;\;\;\;t \cdot b\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 20.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.000242:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 7 \cdot 10^{-20}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -0.000242) x (if (<= x 7e-20) z x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -0.000242) {
		tmp = x;
	} else if (x <= 7e-20) {
		tmp = z;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= (-0.000242d0)) then
        tmp = x
    else if (x <= 7d-20) then
        tmp = z
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -0.000242) {
		tmp = x;
	} else if (x <= 7e-20) {
		tmp = z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -0.000242:
		tmp = x
	elif x <= 7e-20:
		tmp = z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -0.000242)
		tmp = x;
	elseif (x <= 7e-20)
		tmp = z;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -0.000242)
		tmp = x;
	elseif (x <= 7e-20)
		tmp = z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -0.000242], x, If[LessEqual[x, 7e-20], z, x]]

Derivation

1. Split input into 2 regimes

2. if x < -2.42e-4 or 7.00000000000000007e-20 < x

   1. Initial program 94.1%

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

   3. Taylor expanded in x around inf 30.1%

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

   if -2.42e-4 < x < 7.00000000000000007e-20

   1. Initial program 94.1%

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

   3. Taylor expanded in y around inf 72.0%

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

   4. Taylor expanded in y around 0 44.1%

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

      1. sub-neg 44.1%

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

      2. neg-mul-1 44.1%

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

      3. sub-neg 44.1%

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

      4. metadata-eval 44.1%

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

      5. distribute-neg-in 44.1%

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

      6. remove-double-neg 44.1%

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

      7. distribute-rgt-neg-in 44.1%

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

      8. +-commutative 44.1%

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

      9. distribute-neg-in 44.1%

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

      10. metadata-eval 44.1%

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

      11. sub-neg 44.1%

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

   6. Simplified 44.1%

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

   7. Taylor expanded in z around inf 14.5%

      \[\leadsto \color{blue}{z} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 23: 15.6% accurate, 21.0× speedup

Math

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

FPCore

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

C

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

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
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 94.1%

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

3. Taylor expanded in x around inf 17.1%

   \[\leadsto \color{blue}{x} \]
4. Add Preprocessing

Reproduce

herbie shell --seed 2024116 
(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)))