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

Percentage Accurate: 95.1% → 98.5%

Time: 16.0s

Alternatives: 24

Speedup: 0.5×

• 37.0% of points produce a very large (infinite) output. You may want to add a precondition.

• could not determine a ground truth

  1. x = 5.332601811673223e-213
  2. y = -4.6093146986044336e-29
  3. z = -3.246359326072706e-148
  4. t = 6.253864510696213e-87
  5. a = -2.33731935840241e-94
  6. b = 1.0495960852013063e-94

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 95.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.5% accurate, 0.1× speedup

Math

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

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))) (* b (- 2.0 (+ y t))))
        INFINITY)
     (fma t_1 b (- x (fma (+ y -1.0) z (* (+ t -1.0) a))))
     (* z (+ 1.0 (- (+ (/ x z) (* b (/ t_1 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))) - (b * (2.0 - (y + t)))) <= ((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))) - 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(b * Float64(2.0 - Float64(y + t)))) <= 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))) - 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[(b * N[(2.0 - N[(y + t), $MachinePrecision]), $MachinePrecision]), $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] - y), $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 a around 0 36.4%

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

   4. Taylor expanded in z around inf 72.7%

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

      1. associate--l+ 72.7%

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

      2. associate-/l* 100.0%

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

      3. sub-neg 100.0%

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

      4. +-commutative 100.0%

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

      5. metadata-eval 100.0%

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

      6. associate-+r+ 100.0%

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

   6. Simplified 100.0%

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

4. Final simplification 100.0%

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

Alternative 2: 98.5% accurate, 0.5× speedup

Math

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

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1
         (- (+ (+ x (* z (- 1.0 y))) (* a (- 1.0 t))) (* b (- 2.0 (+ y t))))))
   (if (<= t_1 INFINITY)
     t_1
     (* z (+ 1.0 (- (+ (/ x z) (* b (/ (+ y (+ t -2.0)) 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))) - (b * (2.0 - (y + t)));
	double tmp;
	if (t_1 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = z * (1.0 + (((x / z) + (b * ((y + (t + -2.0)) / 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))) - (b * (2.0 - (y + t)));
	double tmp;
	if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else {
		tmp = z * (1.0 + (((x / z) + (b * ((y + (t + -2.0)) / z))) - y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((x + (z * (1.0 - y))) + (a * (1.0 - t))) - (b * (2.0 - (y + t)))
	tmp = 0
	if t_1 <= math.inf:
		tmp = t_1
	else:
		tmp = z * (1.0 + (((x / z) + (b * ((y + (t + -2.0)) / 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(b * Float64(2.0 - Float64(y + t))))
	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))) - 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))) - (b * (2.0 - (y + t)));
	tmp = 0.0;
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = z * (1.0 + (((x / z) + (b * ((y + (t + -2.0)) / 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[(b * N[(2.0 - N[(y + t), $MachinePrecision]), $MachinePrecision]), $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] - y), $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 a around 0 36.4%

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

   4. Taylor expanded in z around inf 72.7%

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

      1. associate--l+ 72.7%

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

      2. associate-/l* 100.0%

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

      3. sub-neg 100.0%

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

      4. +-commutative 100.0%

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

      5. metadata-eval 100.0%

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

      6. associate-+r+ 100.0%

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

   6. Simplified 100.0%

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

4. Final simplification 100.0%

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

Alternative 3: 86.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(1 + \left(\left(\frac{x}{z} + b \cdot \frac{y + \left(t + -2\right)}{z}\right) - y\right)\right)\\ \mathbf{if}\;z \leq -6.8 \cdot 10^{+34}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.18 \cdot 10^{-23}:\\ \;\;\;\;\left(x - b \cdot \left(2 - \left(y + t\right)\right)\right) + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;z \leq 9.6 \cdot 10^{+84}:\\ \;\;\;\;z \cdot \left(1 - y\right) - \left(\left(t \cdot a - x\right) - a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (+ 1.0 (- (+ (/ x z) (* b (/ (+ y (+ t -2.0)) z))) y)))))
   (if (<= z -6.8e+34)
     t_1
     (if (<= z 1.18e-23)
       (+ (- x (* b (- 2.0 (+ y t)))) (* a (- 1.0 t)))
       (if (<= z 9.6e+84) (- (* z (- 1.0 y)) (- (- (* t a) x) a)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (1.0 + (((x / z) + (b * ((y + (t + -2.0)) / z))) - y));
	double tmp;
	if (z <= -6.8e+34) {
		tmp = t_1;
	} else if (z <= 1.18e-23) {
		tmp = (x - (b * (2.0 - (y + t)))) + (a * (1.0 - t));
	} else if (z <= 9.6e+84) {
		tmp = (z * (1.0 - y)) - (((t * a) - x) - a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z * (1.0d0 + (((x / z) + (b * ((y + (t + (-2.0d0))) / z))) - y))
    if (z <= (-6.8d+34)) then
        tmp = t_1
    else if (z <= 1.18d-23) then
        tmp = (x - (b * (2.0d0 - (y + t)))) + (a * (1.0d0 - t))
    else if (z <= 9.6d+84) then
        tmp = (z * (1.0d0 - y)) - (((t * a) - x) - a)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (1.0 + (((x / z) + (b * ((y + (t + -2.0)) / z))) - y));
	double tmp;
	if (z <= -6.8e+34) {
		tmp = t_1;
	} else if (z <= 1.18e-23) {
		tmp = (x - (b * (2.0 - (y + t)))) + (a * (1.0 - t));
	} else if (z <= 9.6e+84) {
		tmp = (z * (1.0 - y)) - (((t * a) - x) - a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * (1.0 + (((x / z) + (b * ((y + (t + -2.0)) / z))) - y))
	tmp = 0
	if z <= -6.8e+34:
		tmp = t_1
	elif z <= 1.18e-23:
		tmp = (x - (b * (2.0 - (y + t)))) + (a * (1.0 - t))
	elif z <= 9.6e+84:
		tmp = (z * (1.0 - y)) - (((t * a) - x) - a)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(1.0 + Float64(Float64(Float64(x / z) + Float64(b * Float64(Float64(y + Float64(t + -2.0)) / z))) - y)))
	tmp = 0.0
	if (z <= -6.8e+34)
		tmp = t_1;
	elseif (z <= 1.18e-23)
		tmp = Float64(Float64(x - Float64(b * Float64(2.0 - Float64(y + t)))) + Float64(a * Float64(1.0 - t)));
	elseif (z <= 9.6e+84)
		tmp = Float64(Float64(z * Float64(1.0 - y)) - Float64(Float64(Float64(t * a) - x) - a));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * (1.0 + (((x / z) + (b * ((y + (t + -2.0)) / z))) - y));
	tmp = 0.0;
	if (z <= -6.8e+34)
		tmp = t_1;
	elseif (z <= 1.18e-23)
		tmp = (x - (b * (2.0 - (y + t)))) + (a * (1.0 - t));
	elseif (z <= 9.6e+84)
		tmp = (z * (1.0 - y)) - (((t * a) - x) - a);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{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] - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6.8e+34], t$95$1, If[LessEqual[z, 1.18e-23], N[(N[(x - N[(b * N[(2.0 - N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9.6e+84], N[(N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(t * a), $MachinePrecision] - x), $MachinePrecision] - a), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.7999999999999999e34 or 9.5999999999999999e84 < z

   1. Initial program 91.0%

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

   3. Taylor expanded in a around 0 82.8%

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

   4. Taylor expanded in z around inf 86.4%

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

      1. associate--l+ 86.4%

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

      2. associate-/l* 89.0%

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

      3. sub-neg 89.0%

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

      4. +-commutative 89.0%

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

      5. metadata-eval 89.0%

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

      6. associate-+r+ 89.0%

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

   6. Simplified 89.0%

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

   if -6.7999999999999999e34 < z < 1.18e-23

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 97.3%

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

   if 1.18e-23 < z < 9.5999999999999999e84

   1. Initial program 95.2%

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

   3. Taylor expanded in t around 0 100.0%

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

   4. Taylor expanded in b around 0 86.0%

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

      1. associate-*r* 86.0%

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

      2. mul-1-neg 86.0%

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

   6. Simplified 86.0%

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

   7. Taylor expanded in x around 0 86.0%

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

      1. associate--r+ 86.0%

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

      2. sub-neg 86.0%

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

      3. +-commutative 86.0%

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

      4. mul-1-neg 86.0%

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

      5. distribute-rgt-neg-in 86.0%

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

      6. mul-1-neg 86.0%

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

      7. remove-double-neg 86.0%

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

      8. sub-neg 86.0%

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

      9. metadata-eval 86.0%

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

      10. +-commutative 86.0%

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

   9. Simplified 86.0%

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

4. Final simplification 92.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.8 \cdot 10^{+34}:\\ \;\;\;\;z \cdot \left(1 + \left(\left(\frac{x}{z} + b \cdot \frac{y + \left(t + -2\right)}{z}\right) - y\right)\right)\\ \mathbf{elif}\;z \leq 1.18 \cdot 10^{-23}:\\ \;\;\;\;\left(x - b \cdot \left(2 - \left(y + t\right)\right)\right) + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;z \leq 9.6 \cdot 10^{+84}:\\ \;\;\;\;z \cdot \left(1 - y\right) - \left(\left(t \cdot a - x\right) - a\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(1 + \left(\left(\frac{x}{z} + b \cdot \frac{y + \left(t + -2\right)}{z}\right) - y\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 34.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(-y\right)\\ t_2 := a \cdot \left(1 - t\right)\\ \mathbf{if}\;a \leq -4.9 \cdot 10^{+31}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq 1.9 \cdot 10^{-268}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 10^{-159}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 2.4 \cdot 10^{-76}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 4.6 \cdot 10^{+29}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (- y))) (t_2 (* a (- 1.0 t))))
   (if (<= a -4.9e+31)
     t_2
     (if (<= a 1.9e-268)
       x
       (if (<= a 1e-159)
         t_1
         (if (<= a 2.4e-76) x (if (<= a 4.6e+29) t_1 t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * -y;
	double t_2 = a * (1.0 - t);
	double tmp;
	if (a <= -4.9e+31) {
		tmp = t_2;
	} else if (a <= 1.9e-268) {
		tmp = x;
	} else if (a <= 1e-159) {
		tmp = t_1;
	} else if (a <= 2.4e-76) {
		tmp = x;
	} else if (a <= 4.6e+29) {
		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 * -y
    t_2 = a * (1.0d0 - t)
    if (a <= (-4.9d+31)) then
        tmp = t_2
    else if (a <= 1.9d-268) then
        tmp = x
    else if (a <= 1d-159) then
        tmp = t_1
    else if (a <= 2.4d-76) then
        tmp = x
    else if (a <= 4.6d+29) 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 * -y;
	double t_2 = a * (1.0 - t);
	double tmp;
	if (a <= -4.9e+31) {
		tmp = t_2;
	} else if (a <= 1.9e-268) {
		tmp = x;
	} else if (a <= 1e-159) {
		tmp = t_1;
	} else if (a <= 2.4e-76) {
		tmp = x;
	} else if (a <= 4.6e+29) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * -y
	t_2 = a * (1.0 - t)
	tmp = 0
	if a <= -4.9e+31:
		tmp = t_2
	elif a <= 1.9e-268:
		tmp = x
	elif a <= 1e-159:
		tmp = t_1
	elif a <= 2.4e-76:
		tmp = x
	elif a <= 4.6e+29:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(-y))
	t_2 = Float64(a * Float64(1.0 - t))
	tmp = 0.0
	if (a <= -4.9e+31)
		tmp = t_2;
	elseif (a <= 1.9e-268)
		tmp = x;
	elseif (a <= 1e-159)
		tmp = t_1;
	elseif (a <= 2.4e-76)
		tmp = x;
	elseif (a <= 4.6e+29)
		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 * -y;
	t_2 = a * (1.0 - t);
	tmp = 0.0;
	if (a <= -4.9e+31)
		tmp = t_2;
	elseif (a <= 1.9e-268)
		tmp = x;
	elseif (a <= 1e-159)
		tmp = t_1;
	elseif (a <= 2.4e-76)
		tmp = x;
	elseif (a <= 4.6e+29)
		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 * (-y)), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -4.9e+31], t$95$2, If[LessEqual[a, 1.9e-268], x, If[LessEqual[a, 1e-159], t$95$1, If[LessEqual[a, 2.4e-76], x, If[LessEqual[a, 4.6e+29], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -4.89999999999999996e31 or 4.6000000000000002e29 < a

   1. Initial program 93.0%

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

   3. Taylor expanded in a around inf 54.2%

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

   if -4.89999999999999996e31 < a < 1.9000000000000001e-268 or 9.99999999999999989e-160 < a < 2.40000000000000013e-76

   1. Initial program 97.2%

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

   3. Taylor expanded in x around inf 30.6%

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

   if 1.9000000000000001e-268 < a < 9.99999999999999989e-160 or 2.40000000000000013e-76 < a < 4.6000000000000002e29

   1. Initial program 97.8%

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

   3. Taylor expanded in t around 0 95.6%

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

   4. Taylor expanded in b around 0 67.9%

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

      1. associate-*r* 67.9%

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

      2. mul-1-neg 67.9%

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

   6. Simplified 67.9%

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

   7. Taylor expanded in y around inf 38.8%

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

      1. mul-1-neg 38.8%

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

      2. distribute-lft-neg-out 38.8%

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

      3. *-commutative 38.8%

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

   9. Simplified 38.8%

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

4. Final simplification 41.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.9 \cdot 10^{+31}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;a \leq 1.9 \cdot 10^{-268}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 10^{-159}:\\ \;\;\;\;z \cdot \left(-y\right)\\ \mathbf{elif}\;a \leq 2.4 \cdot 10^{-76}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 4.6 \cdot 10^{+29}:\\ \;\;\;\;z \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 49.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + b \cdot -2\\ t_2 := y \cdot \left(b - z\right)\\ t_3 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -5.2 \cdot 10^{+45}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t \leq -6.8 \cdot 10^{-119}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -2.9 \cdot 10^{-153}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{-195}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.42 \cdot 10^{+66}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* b -2.0))) (t_2 (* y (- b z))) (t_3 (* t (- b a))))
   (if (<= t -5.2e+45)
     t_3
     (if (<= t -6.8e-119)
       t_1
       (if (<= t -2.9e-153)
         t_2
         (if (<= t 2.2e-195) t_1 (if (<= t 1.42e+66) t_2 t_3)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (b * -2.0);
	double t_2 = y * (b - z);
	double t_3 = t * (b - a);
	double tmp;
	if (t <= -5.2e+45) {
		tmp = t_3;
	} else if (t <= -6.8e-119) {
		tmp = t_1;
	} else if (t <= -2.9e-153) {
		tmp = t_2;
	} else if (t <= 2.2e-195) {
		tmp = t_1;
	} else if (t <= 1.42e+66) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = x + (b * (-2.0d0))
    t_2 = y * (b - z)
    t_3 = t * (b - a)
    if (t <= (-5.2d+45)) then
        tmp = t_3
    else if (t <= (-6.8d-119)) then
        tmp = t_1
    else if (t <= (-2.9d-153)) then
        tmp = t_2
    else if (t <= 2.2d-195) then
        tmp = t_1
    else if (t <= 1.42d+66) then
        tmp = t_2
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (b * -2.0);
	double t_2 = y * (b - z);
	double t_3 = t * (b - a);
	double tmp;
	if (t <= -5.2e+45) {
		tmp = t_3;
	} else if (t <= -6.8e-119) {
		tmp = t_1;
	} else if (t <= -2.9e-153) {
		tmp = t_2;
	} else if (t <= 2.2e-195) {
		tmp = t_1;
	} else if (t <= 1.42e+66) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (b * -2.0)
	t_2 = y * (b - z)
	t_3 = t * (b - a)
	tmp = 0
	if t <= -5.2e+45:
		tmp = t_3
	elif t <= -6.8e-119:
		tmp = t_1
	elif t <= -2.9e-153:
		tmp = t_2
	elif t <= 2.2e-195:
		tmp = t_1
	elif t <= 1.42e+66:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(b * -2.0))
	t_2 = Float64(y * Float64(b - z))
	t_3 = Float64(t * Float64(b - a))
	tmp = 0.0
	if (t <= -5.2e+45)
		tmp = t_3;
	elseif (t <= -6.8e-119)
		tmp = t_1;
	elseif (t <= -2.9e-153)
		tmp = t_2;
	elseif (t <= 2.2e-195)
		tmp = t_1;
	elseif (t <= 1.42e+66)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (b * -2.0);
	t_2 = y * (b - z);
	t_3 = t * (b - a);
	tmp = 0.0;
	if (t <= -5.2e+45)
		tmp = t_3;
	elseif (t <= -6.8e-119)
		tmp = t_1;
	elseif (t <= -2.9e-153)
		tmp = t_2;
	elseif (t <= 2.2e-195)
		tmp = t_1;
	elseif (t <= 1.42e+66)
		tmp = t_2;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(b * -2.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -5.2e+45], t$95$3, If[LessEqual[t, -6.8e-119], t$95$1, If[LessEqual[t, -2.9e-153], t$95$2, If[LessEqual[t, 2.2e-195], t$95$1, If[LessEqual[t, 1.42e+66], t$95$2, t$95$3]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -5.20000000000000014e45 or 1.4200000000000001e66 < t

   1. Initial program 93.4%

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

   3. Taylor expanded in t around inf 67.0%

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

   if -5.20000000000000014e45 < t < -6.80000000000000047e-119 or -2.90000000000000002e-153 < t < 2.20000000000000005e-195

   1. Initial program 99.9%

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

   3. Taylor expanded in a around 0 82.0%

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

   4. Taylor expanded in z around 0 55.8%

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

   5. Taylor expanded in t around 0 55.4%

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

   6. Taylor expanded in y around 0 41.8%

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

      1. *-commutative 41.8%

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

   8. Simplified 41.8%

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

   if -6.80000000000000047e-119 < t < -2.90000000000000002e-153 or 2.20000000000000005e-195 < t < 1.4200000000000001e66

   1. Initial program 93.8%

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

   3. Taylor expanded in y around inf 44.8%

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

4. Final simplification 53.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.2 \cdot 10^{+45}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq -6.8 \cdot 10^{-119}:\\ \;\;\;\;x + b \cdot -2\\ \mathbf{elif}\;t \leq -2.9 \cdot 10^{-153}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{-195}:\\ \;\;\;\;x + b \cdot -2\\ \mathbf{elif}\;t \leq 1.42 \cdot 10^{+66}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 43.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - y \cdot z\\ t_2 := b \cdot \left(y - 2\right)\\ \mathbf{if}\;b \leq -2.7 \cdot 10^{+167}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -49000:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;b \leq -1.6 \cdot 10^{-256}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 3.3 \cdot 10^{-250}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 2.25 \cdot 10^{+129}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- x (* y z))) (t_2 (* b (- y 2.0))))
   (if (<= b -2.7e+167)
     t_2
     (if (<= b -49000.0)
       (* t (- b a))
       (if (<= b -1.6e-256)
         t_1
         (if (<= b 3.3e-250)
           (* a (- 1.0 t))
           (if (<= b 2.25e+129) t_1 t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x - (y * z);
	double t_2 = b * (y - 2.0);
	double tmp;
	if (b <= -2.7e+167) {
		tmp = t_2;
	} else if (b <= -49000.0) {
		tmp = t * (b - a);
	} else if (b <= -1.6e-256) {
		tmp = t_1;
	} else if (b <= 3.3e-250) {
		tmp = a * (1.0 - t);
	} else if (b <= 2.25e+129) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x - (y * z)
    t_2 = b * (y - 2.0d0)
    if (b <= (-2.7d+167)) then
        tmp = t_2
    else if (b <= (-49000.0d0)) then
        tmp = t * (b - a)
    else if (b <= (-1.6d-256)) then
        tmp = t_1
    else if (b <= 3.3d-250) then
        tmp = a * (1.0d0 - t)
    else if (b <= 2.25d+129) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x - (y * z);
	double t_2 = b * (y - 2.0);
	double tmp;
	if (b <= -2.7e+167) {
		tmp = t_2;
	} else if (b <= -49000.0) {
		tmp = t * (b - a);
	} else if (b <= -1.6e-256) {
		tmp = t_1;
	} else if (b <= 3.3e-250) {
		tmp = a * (1.0 - t);
	} else if (b <= 2.25e+129) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x - (y * z)
	t_2 = b * (y - 2.0)
	tmp = 0
	if b <= -2.7e+167:
		tmp = t_2
	elif b <= -49000.0:
		tmp = t * (b - a)
	elif b <= -1.6e-256:
		tmp = t_1
	elif b <= 3.3e-250:
		tmp = a * (1.0 - t)
	elif b <= 2.25e+129:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x - Float64(y * z))
	t_2 = Float64(b * Float64(y - 2.0))
	tmp = 0.0
	if (b <= -2.7e+167)
		tmp = t_2;
	elseif (b <= -49000.0)
		tmp = Float64(t * Float64(b - a));
	elseif (b <= -1.6e-256)
		tmp = t_1;
	elseif (b <= 3.3e-250)
		tmp = Float64(a * Float64(1.0 - t));
	elseif (b <= 2.25e+129)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x - (y * z);
	t_2 = b * (y - 2.0);
	tmp = 0.0;
	if (b <= -2.7e+167)
		tmp = t_2;
	elseif (b <= -49000.0)
		tmp = t * (b - a);
	elseif (b <= -1.6e-256)
		tmp = t_1;
	elseif (b <= 3.3e-250)
		tmp = a * (1.0 - t);
	elseif (b <= 2.25e+129)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(y - 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2.7e+167], t$95$2, If[LessEqual[b, -49000.0], N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -1.6e-256], t$95$1, If[LessEqual[b, 3.3e-250], N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.25e+129], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -2.70000000000000005e167 or 2.2500000000000001e129 < b

   1. Initial program 86.5%

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

   3. Taylor expanded in b around inf 84.0%

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

   4. Taylor expanded in t around 0 60.6%

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

   if -2.70000000000000005e167 < b < -49000

   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 50.6%

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

   if -49000 < b < -1.6e-256 or 3.3e-250 < b < 2.2500000000000001e129

   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 90.9%

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

   4. Taylor expanded in y around inf 51.2%

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

      1. *-commutative 51.2%

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

   6. Simplified 51.2%

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

   if -1.6e-256 < b < 3.3e-250

   1. Initial program 99.9%

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

   3. Taylor expanded in a around inf 52.8%

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

4. Final simplification 53.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.7 \cdot 10^{+167}:\\ \;\;\;\;b \cdot \left(y - 2\right)\\ \mathbf{elif}\;b \leq -49000:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;b \leq -1.6 \cdot 10^{-256}:\\ \;\;\;\;x - y \cdot z\\ \mathbf{elif}\;b \leq 3.3 \cdot 10^{-250}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 2.25 \cdot 10^{+129}:\\ \;\;\;\;x - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(y - 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 64.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + z \cdot \left(1 - y\right)\\ t_2 := x - b \cdot \left(2 - \left(y + t\right)\right)\\ \mathbf{if}\;b \leq -750000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 6.6 \cdot 10^{-99}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1.15 \cdot 10^{-29}:\\ \;\;\;\;x - \left(t + -1\right) \cdot a\\ \mathbf{elif}\;b \leq 2.25 \cdot 10^{+129}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* z (- 1.0 y)))) (t_2 (- x (* b (- 2.0 (+ y t))))))
   (if (<= b -750000.0)
     t_2
     (if (<= b 6.6e-99)
       t_1
       (if (<= b 1.15e-29)
         (- x (* (+ t -1.0) a))
         (if (<= b 2.25e+129) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (z * (1.0 - y));
	double t_2 = x - (b * (2.0 - (y + t)));
	double tmp;
	if (b <= -750000.0) {
		tmp = t_2;
	} else if (b <= 6.6e-99) {
		tmp = t_1;
	} else if (b <= 1.15e-29) {
		tmp = x - ((t + -1.0) * a);
	} else if (b <= 2.25e+129) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + (z * (1.0d0 - y))
    t_2 = x - (b * (2.0d0 - (y + t)))
    if (b <= (-750000.0d0)) then
        tmp = t_2
    else if (b <= 6.6d-99) then
        tmp = t_1
    else if (b <= 1.15d-29) then
        tmp = x - ((t + (-1.0d0)) * a)
    else if (b <= 2.25d+129) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (z * (1.0 - y));
	double t_2 = x - (b * (2.0 - (y + t)));
	double tmp;
	if (b <= -750000.0) {
		tmp = t_2;
	} else if (b <= 6.6e-99) {
		tmp = t_1;
	} else if (b <= 1.15e-29) {
		tmp = x - ((t + -1.0) * a);
	} else if (b <= 2.25e+129) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (z * (1.0 - y))
	t_2 = x - (b * (2.0 - (y + t)))
	tmp = 0
	if b <= -750000.0:
		tmp = t_2
	elif b <= 6.6e-99:
		tmp = t_1
	elif b <= 1.15e-29:
		tmp = x - ((t + -1.0) * a)
	elif b <= 2.25e+129:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(z * Float64(1.0 - y)))
	t_2 = Float64(x - Float64(b * Float64(2.0 - Float64(y + t))))
	tmp = 0.0
	if (b <= -750000.0)
		tmp = t_2;
	elseif (b <= 6.6e-99)
		tmp = t_1;
	elseif (b <= 1.15e-29)
		tmp = Float64(x - Float64(Float64(t + -1.0) * a));
	elseif (b <= 2.25e+129)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (z * (1.0 - y));
	t_2 = x - (b * (2.0 - (y + t)));
	tmp = 0.0;
	if (b <= -750000.0)
		tmp = t_2;
	elseif (b <= 6.6e-99)
		tmp = t_1;
	elseif (b <= 1.15e-29)
		tmp = x - ((t + -1.0) * a);
	elseif (b <= 2.25e+129)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x - N[(b * N[(2.0 - N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -750000.0], t$95$2, If[LessEqual[b, 6.6e-99], t$95$1, If[LessEqual[b, 1.15e-29], N[(x - N[(N[(t + -1.0), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.25e+129], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -7.5e5 or 2.2500000000000001e129 < b

   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 a around 0 84.8%

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

   4. Taylor expanded in z around 0 81.5%

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

   if -7.5e5 < b < 6.59999999999999973e-99 or 1.14999999999999996e-29 < b < 2.2500000000000001e129

   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 a around 0 72.1%

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

   4. Taylor expanded in b around 0 65.8%

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

   if 6.59999999999999973e-99 < b < 1.14999999999999996e-29

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 85.3%

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

   4. Taylor expanded in b around 0 70.4%

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

4. Final simplification 72.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -750000:\\ \;\;\;\;x - b \cdot \left(2 - \left(y + t\right)\right)\\ \mathbf{elif}\;b \leq 6.6 \cdot 10^{-99}:\\ \;\;\;\;x + z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq 1.15 \cdot 10^{-29}:\\ \;\;\;\;x - \left(t + -1\right) \cdot a\\ \mathbf{elif}\;b \leq 2.25 \cdot 10^{+129}:\\ \;\;\;\;x + z \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;x - b \cdot \left(2 - \left(y + t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 53.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{if}\;b \leq -340000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -6.8 \cdot 10^{-254}:\\ \;\;\;\;x - t \cdot a\\ \mathbf{elif}\;b \leq 5.5 \cdot 10^{-233}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq 2.25 \cdot 10^{+129}:\\ \;\;\;\;x - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- (+ y t) 2.0) b)))
   (if (<= b -340000.0)
     t_1
     (if (<= b -6.8e-254)
       (- x (* t a))
       (if (<= b 5.5e-233)
         (* z (- 1.0 y))
         (if (<= b 2.25e+129) (- x (* y z)) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((y + t) - 2.0) * b;
	double tmp;
	if (b <= -340000.0) {
		tmp = t_1;
	} else if (b <= -6.8e-254) {
		tmp = x - (t * a);
	} else if (b <= 5.5e-233) {
		tmp = z * (1.0 - y);
	} else if (b <= 2.25e+129) {
		tmp = x - (y * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((y + t) - 2.0d0) * b
    if (b <= (-340000.0d0)) then
        tmp = t_1
    else if (b <= (-6.8d-254)) then
        tmp = x - (t * a)
    else if (b <= 5.5d-233) then
        tmp = z * (1.0d0 - y)
    else if (b <= 2.25d+129) then
        tmp = x - (y * z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((y + t) - 2.0) * b;
	double tmp;
	if (b <= -340000.0) {
		tmp = t_1;
	} else if (b <= -6.8e-254) {
		tmp = x - (t * a);
	} else if (b <= 5.5e-233) {
		tmp = z * (1.0 - y);
	} else if (b <= 2.25e+129) {
		tmp = x - (y * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((y + t) - 2.0) * b
	tmp = 0
	if b <= -340000.0:
		tmp = t_1
	elif b <= -6.8e-254:
		tmp = x - (t * a)
	elif b <= 5.5e-233:
		tmp = z * (1.0 - y)
	elif b <= 2.25e+129:
		tmp = x - (y * z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(y + t) - 2.0) * b)
	tmp = 0.0
	if (b <= -340000.0)
		tmp = t_1;
	elseif (b <= -6.8e-254)
		tmp = Float64(x - Float64(t * a));
	elseif (b <= 5.5e-233)
		tmp = Float64(z * Float64(1.0 - y));
	elseif (b <= 2.25e+129)
		tmp = Float64(x - Float64(y * z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((y + t) - 2.0) * b;
	tmp = 0.0;
	if (b <= -340000.0)
		tmp = t_1;
	elseif (b <= -6.8e-254)
		tmp = x - (t * a);
	elseif (b <= 5.5e-233)
		tmp = z * (1.0 - y);
	elseif (b <= 2.25e+129)
		tmp = x - (y * z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[b, -340000.0], t$95$1, If[LessEqual[b, -6.8e-254], N[(x - N[(t * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 5.5e-233], N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.25e+129], N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -3.4e5 or 2.2500000000000001e129 < b

   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 b around inf 77.0%

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

   if -3.4e5 < b < -6.79999999999999986e-254

   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 b around 0 92.8%

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

   4. Taylor expanded in t around inf 56.6%

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

   if -6.79999999999999986e-254 < b < 5.50000000000000005e-233

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 51.2%

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

   if 5.50000000000000005e-233 < b < 2.2500000000000001e129

   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 88.2%

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

   4. Taylor expanded in y around inf 46.6%

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

      1. *-commutative 46.6%

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

   6. Simplified 46.6%

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

4. Final simplification 62.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -340000:\\ \;\;\;\;\left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{elif}\;b \leq -6.8 \cdot 10^{-254}:\\ \;\;\;\;x - t \cdot a\\ \mathbf{elif}\;b \leq 5.5 \cdot 10^{-233}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq 2.25 \cdot 10^{+129}:\\ \;\;\;\;x - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;\left(\left(y + t\right) - 2\right) \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 61.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \left(t + -1\right) \cdot a\\ t_2 := \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{if}\;b \leq -210000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 1.6 \cdot 10^{-250}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 9.4 \cdot 10^{-211}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq 7 \cdot 10^{+99}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- x (* (+ t -1.0) a))) (t_2 (* (- (+ y t) 2.0) b)))
   (if (<= b -210000.0)
     t_2
     (if (<= b 1.6e-250)
       t_1
       (if (<= b 9.4e-211) (* z (- 1.0 y)) (if (<= b 7e+99) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x - ((t + -1.0) * a);
	double t_2 = ((y + t) - 2.0) * b;
	double tmp;
	if (b <= -210000.0) {
		tmp = t_2;
	} else if (b <= 1.6e-250) {
		tmp = t_1;
	} else if (b <= 9.4e-211) {
		tmp = z * (1.0 - y);
	} else if (b <= 7e+99) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x - ((t + (-1.0d0)) * a)
    t_2 = ((y + t) - 2.0d0) * b
    if (b <= (-210000.0d0)) then
        tmp = t_2
    else if (b <= 1.6d-250) then
        tmp = t_1
    else if (b <= 9.4d-211) then
        tmp = z * (1.0d0 - y)
    else if (b <= 7d+99) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x - ((t + -1.0) * a);
	double t_2 = ((y + t) - 2.0) * b;
	double tmp;
	if (b <= -210000.0) {
		tmp = t_2;
	} else if (b <= 1.6e-250) {
		tmp = t_1;
	} else if (b <= 9.4e-211) {
		tmp = z * (1.0 - y);
	} else if (b <= 7e+99) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x - ((t + -1.0) * a)
	t_2 = ((y + t) - 2.0) * b
	tmp = 0
	if b <= -210000.0:
		tmp = t_2
	elif b <= 1.6e-250:
		tmp = t_1
	elif b <= 9.4e-211:
		tmp = z * (1.0 - y)
	elif b <= 7e+99:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x - Float64(Float64(t + -1.0) * a))
	t_2 = Float64(Float64(Float64(y + t) - 2.0) * b)
	tmp = 0.0
	if (b <= -210000.0)
		tmp = t_2;
	elseif (b <= 1.6e-250)
		tmp = t_1;
	elseif (b <= 9.4e-211)
		tmp = Float64(z * Float64(1.0 - y));
	elseif (b <= 7e+99)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x - ((t + -1.0) * a);
	t_2 = ((y + t) - 2.0) * b;
	tmp = 0.0;
	if (b <= -210000.0)
		tmp = t_2;
	elseif (b <= 1.6e-250)
		tmp = t_1;
	elseif (b <= 9.4e-211)
		tmp = z * (1.0 - y);
	elseif (b <= 7e+99)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x - N[(N[(t + -1.0), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[b, -210000.0], t$95$2, If[LessEqual[b, 1.6e-250], t$95$1, If[LessEqual[b, 9.4e-211], N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 7e+99], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -2.1e5 or 6.9999999999999995e99 < b

   1. Initial program 90.7%

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

   3. Taylor expanded in b around inf 75.6%

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

   if -2.1e5 < b < 1.60000000000000002e-250 or 9.3999999999999993e-211 < b < 6.9999999999999995e99

   1. Initial program 99.2%

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

   3. Taylor expanded in z around 0 66.6%

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

   4. Taylor expanded in b around 0 59.8%

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

   if 1.60000000000000002e-250 < b < 9.3999999999999993e-211

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 69.9%

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

4. Final simplification 67.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -210000:\\ \;\;\;\;\left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{elif}\;b \leq 1.6 \cdot 10^{-250}:\\ \;\;\;\;x - \left(t + -1\right) \cdot a\\ \mathbf{elif}\;b \leq 9.4 \cdot 10^{-211}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq 7 \cdot 10^{+99}:\\ \;\;\;\;x - \left(t + -1\right) \cdot a\\ \mathbf{else}:\\ \;\;\;\;\left(\left(y + t\right) - 2\right) \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 61.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + z \cdot \left(1 - y\right)\\ t_2 := \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{if}\;b \leq -235000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 3.2 \cdot 10^{-90}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1.9 \cdot 10^{-29}:\\ \;\;\;\;x - \left(t + -1\right) \cdot a\\ \mathbf{elif}\;b \leq 2.3 \cdot 10^{+129}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* z (- 1.0 y)))) (t_2 (* (- (+ y t) 2.0) b)))
   (if (<= b -235000.0)
     t_2
     (if (<= b 3.2e-90)
       t_1
       (if (<= b 1.9e-29)
         (- x (* (+ t -1.0) a))
         (if (<= b 2.3e+129) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (z * (1.0 - y));
	double t_2 = ((y + t) - 2.0) * b;
	double tmp;
	if (b <= -235000.0) {
		tmp = t_2;
	} else if (b <= 3.2e-90) {
		tmp = t_1;
	} else if (b <= 1.9e-29) {
		tmp = x - ((t + -1.0) * a);
	} else if (b <= 2.3e+129) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + (z * (1.0d0 - y))
    t_2 = ((y + t) - 2.0d0) * b
    if (b <= (-235000.0d0)) then
        tmp = t_2
    else if (b <= 3.2d-90) then
        tmp = t_1
    else if (b <= 1.9d-29) then
        tmp = x - ((t + (-1.0d0)) * a)
    else if (b <= 2.3d+129) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (z * (1.0 - y));
	double t_2 = ((y + t) - 2.0) * b;
	double tmp;
	if (b <= -235000.0) {
		tmp = t_2;
	} else if (b <= 3.2e-90) {
		tmp = t_1;
	} else if (b <= 1.9e-29) {
		tmp = x - ((t + -1.0) * a);
	} else if (b <= 2.3e+129) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (z * (1.0 - y))
	t_2 = ((y + t) - 2.0) * b
	tmp = 0
	if b <= -235000.0:
		tmp = t_2
	elif b <= 3.2e-90:
		tmp = t_1
	elif b <= 1.9e-29:
		tmp = x - ((t + -1.0) * a)
	elif b <= 2.3e+129:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(z * Float64(1.0 - y)))
	t_2 = Float64(Float64(Float64(y + t) - 2.0) * b)
	tmp = 0.0
	if (b <= -235000.0)
		tmp = t_2;
	elseif (b <= 3.2e-90)
		tmp = t_1;
	elseif (b <= 1.9e-29)
		tmp = Float64(x - Float64(Float64(t + -1.0) * a));
	elseif (b <= 2.3e+129)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (z * (1.0 - y));
	t_2 = ((y + t) - 2.0) * b;
	tmp = 0.0;
	if (b <= -235000.0)
		tmp = t_2;
	elseif (b <= 3.2e-90)
		tmp = t_1;
	elseif (b <= 1.9e-29)
		tmp = x - ((t + -1.0) * a);
	elseif (b <= 2.3e+129)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[b, -235000.0], t$95$2, If[LessEqual[b, 3.2e-90], t$95$1, If[LessEqual[b, 1.9e-29], N[(x - N[(N[(t + -1.0), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.3e+129], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -235000 or 2.2999999999999999e129 < b

   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 b around inf 77.0%

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

   if -235000 < b < 3.20000000000000007e-90 or 1.89999999999999988e-29 < b < 2.2999999999999999e129

   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 a around 0 72.1%

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

   4. Taylor expanded in b around 0 65.8%

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

   if 3.20000000000000007e-90 < b < 1.89999999999999988e-29

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 85.3%

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

   4. Taylor expanded in b around 0 70.4%

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

4. Final simplification 70.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -235000:\\ \;\;\;\;\left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{elif}\;b \leq 3.2 \cdot 10^{-90}:\\ \;\;\;\;x + z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq 1.9 \cdot 10^{-29}:\\ \;\;\;\;x - \left(t + -1\right) \cdot a\\ \mathbf{elif}\;b \leq 2.3 \cdot 10^{+129}:\\ \;\;\;\;x + z \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(y + t\right) - 2\right) \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 39.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(1 - t\right)\\ t_2 := b \cdot \left(y - 2\right)\\ \mathbf{if}\;b \leq -1 \cdot 10^{+33}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 2.35 \cdot 10^{-198}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 2.1 \cdot 10^{-108}:\\ \;\;\;\;x\\ \mathbf{elif}\;b \leq 4.1 \cdot 10^{+99}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (- 1.0 t))) (t_2 (* b (- y 2.0))))
   (if (<= b -1e+33)
     t_2
     (if (<= b 2.35e-198)
       t_1
       (if (<= b 2.1e-108) x (if (<= b 4.1e+99) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double t_2 = b * (y - 2.0);
	double tmp;
	if (b <= -1e+33) {
		tmp = t_2;
	} else if (b <= 2.35e-198) {
		tmp = t_1;
	} else if (b <= 2.1e-108) {
		tmp = x;
	} else if (b <= 4.1e+99) {
		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 = a * (1.0d0 - t)
    t_2 = b * (y - 2.0d0)
    if (b <= (-1d+33)) then
        tmp = t_2
    else if (b <= 2.35d-198) then
        tmp = t_1
    else if (b <= 2.1d-108) then
        tmp = x
    else if (b <= 4.1d+99) 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 = a * (1.0 - t);
	double t_2 = b * (y - 2.0);
	double tmp;
	if (b <= -1e+33) {
		tmp = t_2;
	} else if (b <= 2.35e-198) {
		tmp = t_1;
	} else if (b <= 2.1e-108) {
		tmp = x;
	} else if (b <= 4.1e+99) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (1.0 - t)
	t_2 = b * (y - 2.0)
	tmp = 0
	if b <= -1e+33:
		tmp = t_2
	elif b <= 2.35e-198:
		tmp = t_1
	elif b <= 2.1e-108:
		tmp = x
	elif b <= 4.1e+99:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(1.0 - t))
	t_2 = Float64(b * Float64(y - 2.0))
	tmp = 0.0
	if (b <= -1e+33)
		tmp = t_2;
	elseif (b <= 2.35e-198)
		tmp = t_1;
	elseif (b <= 2.1e-108)
		tmp = x;
	elseif (b <= 4.1e+99)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (1.0 - t);
	t_2 = b * (y - 2.0);
	tmp = 0.0;
	if (b <= -1e+33)
		tmp = t_2;
	elseif (b <= 2.35e-198)
		tmp = t_1;
	elseif (b <= 2.1e-108)
		tmp = x;
	elseif (b <= 4.1e+99)
		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[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(y - 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1e+33], t$95$2, If[LessEqual[b, 2.35e-198], t$95$1, If[LessEqual[b, 2.1e-108], x, If[LessEqual[b, 4.1e+99], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -9.9999999999999995e32 or 4.09999999999999979e99 < b

   1. Initial program 90.1%

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

   3. Taylor expanded in b around inf 76.9%

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

   4. Taylor expanded in t around 0 48.7%

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

   if -9.9999999999999995e32 < b < 2.35e-198 or 2.0999999999999999e-108 < b < 4.09999999999999979e99

   1. Initial program 99.2%

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

   3. Taylor expanded in a around inf 35.1%

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

   if 2.35e-198 < b < 2.0999999999999999e-108

   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 x around inf 48.0%

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

4. Final simplification 41.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1 \cdot 10^{+33}:\\ \;\;\;\;b \cdot \left(y - 2\right)\\ \mathbf{elif}\;b \leq 2.35 \cdot 10^{-198}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 2.1 \cdot 10^{-108}:\\ \;\;\;\;x\\ \mathbf{elif}\;b \leq 4.1 \cdot 10^{+99}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(y - 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 47.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(y - 2\right)\\ t_2 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -7.5 \cdot 10^{+54}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -9.6 \cdot 10^{-191}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.3 \cdot 10^{-240}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 6.8 \cdot 10^{+65}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- y 2.0))) (t_2 (* t (- b a))))
   (if (<= t -7.5e+54)
     t_2
     (if (<= t -9.6e-191)
       t_1
       (if (<= t -1.3e-240) x (if (<= t 6.8e+65) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (y - 2.0);
	double t_2 = t * (b - a);
	double tmp;
	if (t <= -7.5e+54) {
		tmp = t_2;
	} else if (t <= -9.6e-191) {
		tmp = t_1;
	} else if (t <= -1.3e-240) {
		tmp = x;
	} else if (t <= 6.8e+65) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = b * (y - 2.0d0)
    t_2 = t * (b - a)
    if (t <= (-7.5d+54)) then
        tmp = t_2
    else if (t <= (-9.6d-191)) then
        tmp = t_1
    else if (t <= (-1.3d-240)) then
        tmp = x
    else if (t <= 6.8d+65) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (y - 2.0);
	double t_2 = t * (b - a);
	double tmp;
	if (t <= -7.5e+54) {
		tmp = t_2;
	} else if (t <= -9.6e-191) {
		tmp = t_1;
	} else if (t <= -1.3e-240) {
		tmp = x;
	} else if (t <= 6.8e+65) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * (y - 2.0)
	t_2 = t * (b - a)
	tmp = 0
	if t <= -7.5e+54:
		tmp = t_2
	elif t <= -9.6e-191:
		tmp = t_1
	elif t <= -1.3e-240:
		tmp = x
	elif t <= 6.8e+65:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(y - 2.0))
	t_2 = Float64(t * Float64(b - a))
	tmp = 0.0
	if (t <= -7.5e+54)
		tmp = t_2;
	elseif (t <= -9.6e-191)
		tmp = t_1;
	elseif (t <= -1.3e-240)
		tmp = x;
	elseif (t <= 6.8e+65)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * (y - 2.0);
	t_2 = t * (b - a);
	tmp = 0.0;
	if (t <= -7.5e+54)
		tmp = t_2;
	elseif (t <= -9.6e-191)
		tmp = t_1;
	elseif (t <= -1.3e-240)
		tmp = x;
	elseif (t <= 6.8e+65)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(y - 2.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -7.5e+54], t$95$2, If[LessEqual[t, -9.6e-191], t$95$1, If[LessEqual[t, -1.3e-240], x, If[LessEqual[t, 6.8e+65], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -7.50000000000000042e54 or 6.7999999999999999e65 < t

   1. Initial program 93.1%

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

   3. Taylor expanded in t around inf 68.5%

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

   if -7.50000000000000042e54 < t < -9.5999999999999997e-191 or -1.29999999999999996e-240 < t < 6.7999999999999999e65

   1. Initial program 97.1%

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

   3. Taylor expanded in b around inf 34.5%

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

   4. Taylor expanded in t around 0 32.9%

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

   if -9.5999999999999997e-191 < t < -1.29999999999999996e-240

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 44.5%

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

4. Final simplification 47.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.5 \cdot 10^{+54}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq -9.6 \cdot 10^{-191}:\\ \;\;\;\;b \cdot \left(y - 2\right)\\ \mathbf{elif}\;t \leq -1.3 \cdot 10^{-240}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 6.8 \cdot 10^{+65}:\\ \;\;\;\;b \cdot \left(y - 2\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 72.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - b \cdot \left(2 - \left(y + t\right)\right)\\ \mathbf{if}\;b \leq -195000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -1.6 \cdot 10^{-216}:\\ \;\;\;\;x - \left(\left(t + -1\right) \cdot a + y \cdot z\right)\\ \mathbf{elif}\;b \leq 2.3 \cdot 10^{+129}:\\ \;\;\;\;x + \left(a + z \cdot \left(1 - y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- x (* b (- 2.0 (+ y t))))))
   (if (<= b -195000.0)
     t_1
     (if (<= b -1.6e-216)
       (- x (+ (* (+ t -1.0) a) (* y z)))
       (if (<= b 2.3e+129) (+ x (+ a (* z (- 1.0 y)))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x - (b * (2.0 - (y + t)));
	double tmp;
	if (b <= -195000.0) {
		tmp = t_1;
	} else if (b <= -1.6e-216) {
		tmp = x - (((t + -1.0) * a) + (y * z));
	} else if (b <= 2.3e+129) {
		tmp = x + (a + (z * (1.0 - y)));
	} 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 - (b * (2.0d0 - (y + t)))
    if (b <= (-195000.0d0)) then
        tmp = t_1
    else if (b <= (-1.6d-216)) then
        tmp = x - (((t + (-1.0d0)) * a) + (y * z))
    else if (b <= 2.3d+129) then
        tmp = x + (a + (z * (1.0d0 - y)))
    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 - (b * (2.0 - (y + t)));
	double tmp;
	if (b <= -195000.0) {
		tmp = t_1;
	} else if (b <= -1.6e-216) {
		tmp = x - (((t + -1.0) * a) + (y * z));
	} else if (b <= 2.3e+129) {
		tmp = x + (a + (z * (1.0 - y)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x - (b * (2.0 - (y + t)))
	tmp = 0
	if b <= -195000.0:
		tmp = t_1
	elif b <= -1.6e-216:
		tmp = x - (((t + -1.0) * a) + (y * z))
	elif b <= 2.3e+129:
		tmp = x + (a + (z * (1.0 - y)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x - Float64(b * Float64(2.0 - Float64(y + t))))
	tmp = 0.0
	if (b <= -195000.0)
		tmp = t_1;
	elseif (b <= -1.6e-216)
		tmp = Float64(x - Float64(Float64(Float64(t + -1.0) * a) + Float64(y * z)));
	elseif (b <= 2.3e+129)
		tmp = Float64(x + Float64(a + Float64(z * Float64(1.0 - y))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x - (b * (2.0 - (y + t)));
	tmp = 0.0;
	if (b <= -195000.0)
		tmp = t_1;
	elseif (b <= -1.6e-216)
		tmp = x - (((t + -1.0) * a) + (y * z));
	elseif (b <= 2.3e+129)
		tmp = x + (a + (z * (1.0 - y)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x - N[(b * N[(2.0 - N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -195000.0], t$95$1, If[LessEqual[b, -1.6e-216], N[(x - N[(N[(N[(t + -1.0), $MachinePrecision] * a), $MachinePrecision] + N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.3e+129], N[(x + N[(a + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -195000 or 2.2999999999999999e129 < b

   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 a around 0 84.8%

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

   4. Taylor expanded in z around 0 81.5%

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

   if -195000 < b < -1.60000000000000013e-216

   1. Initial program 97.7%

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

   3. Taylor expanded in b around 0 90.9%

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

   4. Taylor expanded in y around inf 82.4%

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

   if -1.60000000000000013e-216 < b < 2.2999999999999999e129

   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 92.7%

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

   4. Taylor expanded in t around 0 78.4%

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

      1. +-commutative 78.4%

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

      2. sub-neg 78.4%

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

      3. metadata-eval 78.4%

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

      4. mul-1-neg 78.4%

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

      5. unsub-neg 78.4%

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

      6. +-commutative 78.4%

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

   6. Simplified 78.4%

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

4. Final simplification 80.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -195000:\\ \;\;\;\;x - b \cdot \left(2 - \left(y + t\right)\right)\\ \mathbf{elif}\;b \leq -1.6 \cdot 10^{-216}:\\ \;\;\;\;x - \left(\left(t + -1\right) \cdot a + y \cdot z\right)\\ \mathbf{elif}\;b \leq 2.3 \cdot 10^{+129}:\\ \;\;\;\;x + \left(a + z \cdot \left(1 - y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x - b \cdot \left(2 - \left(y + t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 83.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -800000 \lor \neg \left(b \leq 2.5 \cdot 10^{+129}\right):\\ \;\;\;\;x - b \cdot \left(2 - \left(y + t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(a \cdot \left(1 - t\right) + z \cdot \left(1 - y\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -800000.0) (not (<= b 2.5e+129)))
   (- x (* b (- 2.0 (+ y t))))
   (+ x (+ (* a (- 1.0 t)) (* z (- 1.0 y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -800000.0) || !(b <= 2.5e+129)) {
		tmp = x - (b * (2.0 - (y + t)));
	} else {
		tmp = x + ((a * (1.0 - t)) + (z * (1.0 - y)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-800000.0d0)) .or. (.not. (b <= 2.5d+129))) then
        tmp = x - (b * (2.0d0 - (y + t)))
    else
        tmp = x + ((a * (1.0d0 - t)) + (z * (1.0d0 - y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -800000.0) || !(b <= 2.5e+129)) {
		tmp = x - (b * (2.0 - (y + t)));
	} else {
		tmp = x + ((a * (1.0 - t)) + (z * (1.0 - y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -800000.0) or not (b <= 2.5e+129):
		tmp = x - (b * (2.0 - (y + t)))
	else:
		tmp = x + ((a * (1.0 - t)) + (z * (1.0 - y)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -800000.0) || !(b <= 2.5e+129))
		tmp = Float64(x - Float64(b * Float64(2.0 - Float64(y + t))));
	else
		tmp = Float64(x + Float64(Float64(a * Float64(1.0 - t)) + Float64(z * Float64(1.0 - y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -800000.0) || ~((b <= 2.5e+129)))
		tmp = x - (b * (2.0 - (y + t)));
	else
		tmp = x + ((a * (1.0 - t)) + (z * (1.0 - y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -800000.0], N[Not[LessEqual[b, 2.5e+129]], $MachinePrecision]], N[(x - N[(b * N[(2.0 - N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision] + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -8e5 or 2.5000000000000001e129 < b

   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 a around 0 84.8%

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

   4. Taylor expanded in z around 0 81.5%

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

   if -8e5 < b < 2.5000000000000001e129

   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 b around 0 92.1%

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

4. Final simplification 87.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -800000 \lor \neg \left(b \leq 2.5 \cdot 10^{+129}\right):\\ \;\;\;\;x - b \cdot \left(2 - \left(y + t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(a \cdot \left(1 - t\right) + z \cdot \left(1 - y\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 84.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - b \cdot \left(2 - \left(y + t\right)\right)\\ \mathbf{if}\;b \leq -500000:\\ \;\;\;\;t\_1 - t \cdot a\\ \mathbf{elif}\;b \leq 2.25 \cdot 10^{+129}:\\ \;\;\;\;x + \left(a \cdot \left(1 - t\right) + z \cdot \left(1 - y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- x (* b (- 2.0 (+ y t))))))
   (if (<= b -500000.0)
     (- t_1 (* t a))
     (if (<= b 2.25e+129) (+ x (+ (* a (- 1.0 t)) (* z (- 1.0 y)))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x - (b * (2.0 - (y + t)));
	double tmp;
	if (b <= -500000.0) {
		tmp = t_1 - (t * a);
	} else if (b <= 2.25e+129) {
		tmp = x + ((a * (1.0 - t)) + (z * (1.0 - y)));
	} 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 - (b * (2.0d0 - (y + t)))
    if (b <= (-500000.0d0)) then
        tmp = t_1 - (t * a)
    else if (b <= 2.25d+129) then
        tmp = x + ((a * (1.0d0 - t)) + (z * (1.0d0 - y)))
    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 - (b * (2.0 - (y + t)));
	double tmp;
	if (b <= -500000.0) {
		tmp = t_1 - (t * a);
	} else if (b <= 2.25e+129) {
		tmp = x + ((a * (1.0 - t)) + (z * (1.0 - y)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x - (b * (2.0 - (y + t)))
	tmp = 0
	if b <= -500000.0:
		tmp = t_1 - (t * a)
	elif b <= 2.25e+129:
		tmp = x + ((a * (1.0 - t)) + (z * (1.0 - y)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x - Float64(b * Float64(2.0 - Float64(y + t))))
	tmp = 0.0
	if (b <= -500000.0)
		tmp = Float64(t_1 - Float64(t * a));
	elseif (b <= 2.25e+129)
		tmp = Float64(x + Float64(Float64(a * Float64(1.0 - t)) + Float64(z * Float64(1.0 - y))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x - (b * (2.0 - (y + t)));
	tmp = 0.0;
	if (b <= -500000.0)
		tmp = t_1 - (t * a);
	elseif (b <= 2.25e+129)
		tmp = x + ((a * (1.0 - t)) + (z * (1.0 - y)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x - N[(b * N[(2.0 - N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -500000.0], N[(t$95$1 - N[(t * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.25e+129], N[(x + N[(N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision] + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 3 regimes

2. if b < -5e5

   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 z around 0 87.7%

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

   4. Taylor expanded in t around inf 79.6%

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

      1. *-commutative 79.6%

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

   6. Simplified 79.6%

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

   if -5e5 < b < 2.2500000000000001e129

   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 b around 0 92.1%

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

   if 2.2500000000000001e129 < b

   1. Initial program 85.3%

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

   3. Taylor expanded in a around 0 85.3%

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

   4. Taylor expanded in z around 0 88.3%

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

4. Final simplification 88.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -500000:\\ \;\;\;\;\left(x - b \cdot \left(2 - \left(y + t\right)\right)\right) - t \cdot a\\ \mathbf{elif}\;b \leq 2.25 \cdot 10^{+129}:\\ \;\;\;\;x + \left(a \cdot \left(1 - t\right) + z \cdot \left(1 - y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x - b \cdot \left(2 - \left(y + t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 84.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - b \cdot \left(2 - \left(y + t\right)\right)\\ \mathbf{if}\;b \leq -195000:\\ \;\;\;\;t\_1 - t \cdot a\\ \mathbf{elif}\;b \leq 8.5 \cdot 10^{+129}:\\ \;\;\;\;z \cdot \left(1 - y\right) - \left(\left(t \cdot a - x\right) - a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- x (* b (- 2.0 (+ y t))))))
   (if (<= b -195000.0)
     (- t_1 (* t a))
     (if (<= b 8.5e+129) (- (* z (- 1.0 y)) (- (- (* t a) x) a)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x - (b * (2.0 - (y + t)));
	double tmp;
	if (b <= -195000.0) {
		tmp = t_1 - (t * a);
	} else if (b <= 8.5e+129) {
		tmp = (z * (1.0 - y)) - (((t * a) - x) - a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x - (b * (2.0d0 - (y + t)))
    if (b <= (-195000.0d0)) then
        tmp = t_1 - (t * a)
    else if (b <= 8.5d+129) then
        tmp = (z * (1.0d0 - y)) - (((t * a) - x) - a)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x - (b * (2.0 - (y + t)));
	double tmp;
	if (b <= -195000.0) {
		tmp = t_1 - (t * a);
	} else if (b <= 8.5e+129) {
		tmp = (z * (1.0 - y)) - (((t * a) - x) - a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x - (b * (2.0 - (y + t)))
	tmp = 0
	if b <= -195000.0:
		tmp = t_1 - (t * a)
	elif b <= 8.5e+129:
		tmp = (z * (1.0 - y)) - (((t * a) - x) - a)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x - Float64(b * Float64(2.0 - Float64(y + t))))
	tmp = 0.0
	if (b <= -195000.0)
		tmp = Float64(t_1 - Float64(t * a));
	elseif (b <= 8.5e+129)
		tmp = Float64(Float64(z * Float64(1.0 - y)) - Float64(Float64(Float64(t * a) - x) - a));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x - (b * (2.0 - (y + t)));
	tmp = 0.0;
	if (b <= -195000.0)
		tmp = t_1 - (t * a);
	elseif (b <= 8.5e+129)
		tmp = (z * (1.0 - y)) - (((t * a) - x) - a);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x - N[(b * N[(2.0 - N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -195000.0], N[(t$95$1 - N[(t * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 8.5e+129], N[(N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(t * a), $MachinePrecision] - x), $MachinePrecision] - a), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 3 regimes

2. if b < -195000

   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 z around 0 87.7%

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

   4. Taylor expanded in t around inf 79.6%

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

      1. *-commutative 79.6%

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

   6. Simplified 79.6%

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

   if -195000 < b < 8.5000000000000001e129

   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 0 98.6%

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

   4. Taylor expanded in b around 0 92.2%

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

      1. associate-*r* 92.2%

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

      2. mul-1-neg 92.2%

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

   6. Simplified 92.2%

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

   7. Taylor expanded in x around 0 92.2%

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

      1. associate--r+ 92.2%

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

      2. sub-neg 92.2%

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

      3. +-commutative 92.2%

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

      4. mul-1-neg 92.2%

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

      5. distribute-rgt-neg-in 92.2%

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

      6. mul-1-neg 92.2%

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

      7. remove-double-neg 92.2%

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

      8. sub-neg 92.2%

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

      9. metadata-eval 92.2%

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

      10. +-commutative 92.2%

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

   9. Simplified 92.2%

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

   if 8.5000000000000001e129 < b

   1. Initial program 85.3%

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

   3. Taylor expanded in a around 0 85.3%

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

   4. Taylor expanded in z around 0 88.3%

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

4. Final simplification 88.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -195000:\\ \;\;\;\;\left(x - b \cdot \left(2 - \left(y + t\right)\right)\right) - t \cdot a\\ \mathbf{elif}\;b \leq 8.5 \cdot 10^{+129}:\\ \;\;\;\;z \cdot \left(1 - y\right) - \left(\left(t \cdot a - x\right) - a\right)\\ \mathbf{else}:\\ \;\;\;\;x - b \cdot \left(2 - \left(y + t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 85.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - b \cdot \left(2 - \left(y + t\right)\right)\\ \mathbf{if}\;b \leq -620000:\\ \;\;\;\;t\_1 + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 6.5 \cdot 10^{+131}:\\ \;\;\;\;z \cdot \left(1 - y\right) - \left(\left(t \cdot a - x\right) - a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- x (* b (- 2.0 (+ y t))))))
   (if (<= b -620000.0)
     (+ t_1 (* a (- 1.0 t)))
     (if (<= b 6.5e+131) (- (* z (- 1.0 y)) (- (- (* t a) x) a)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x - (b * (2.0 - (y + t)));
	double tmp;
	if (b <= -620000.0) {
		tmp = t_1 + (a * (1.0 - t));
	} else if (b <= 6.5e+131) {
		tmp = (z * (1.0 - y)) - (((t * a) - x) - a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x - (b * (2.0d0 - (y + t)))
    if (b <= (-620000.0d0)) then
        tmp = t_1 + (a * (1.0d0 - t))
    else if (b <= 6.5d+131) then
        tmp = (z * (1.0d0 - y)) - (((t * a) - x) - a)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x - (b * (2.0 - (y + t)));
	double tmp;
	if (b <= -620000.0) {
		tmp = t_1 + (a * (1.0 - t));
	} else if (b <= 6.5e+131) {
		tmp = (z * (1.0 - y)) - (((t * a) - x) - a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x - (b * (2.0 - (y + t)))
	tmp = 0
	if b <= -620000.0:
		tmp = t_1 + (a * (1.0 - t))
	elif b <= 6.5e+131:
		tmp = (z * (1.0 - y)) - (((t * a) - x) - a)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x - Float64(b * Float64(2.0 - Float64(y + t))))
	tmp = 0.0
	if (b <= -620000.0)
		tmp = Float64(t_1 + Float64(a * Float64(1.0 - t)));
	elseif (b <= 6.5e+131)
		tmp = Float64(Float64(z * Float64(1.0 - y)) - Float64(Float64(Float64(t * a) - x) - a));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x - (b * (2.0 - (y + t)));
	tmp = 0.0;
	if (b <= -620000.0)
		tmp = t_1 + (a * (1.0 - t));
	elseif (b <= 6.5e+131)
		tmp = (z * (1.0 - y)) - (((t * a) - x) - a);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x - N[(b * N[(2.0 - N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -620000.0], N[(t$95$1 + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 6.5e+131], N[(N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(t * a), $MachinePrecision] - x), $MachinePrecision] - a), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 3 regimes

2. if b < -6.2e5

   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 z around 0 87.7%

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

   if -6.2e5 < b < 6.5e131

   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 0 98.6%

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

   4. Taylor expanded in b around 0 92.2%

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

      1. associate-*r* 92.2%

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

      2. mul-1-neg 92.2%

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

   6. Simplified 92.2%

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

   7. Taylor expanded in x around 0 92.2%

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

      1. associate--r+ 92.2%

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

      2. sub-neg 92.2%

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

      3. +-commutative 92.2%

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

      4. mul-1-neg 92.2%

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

      5. distribute-rgt-neg-in 92.2%

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

      6. mul-1-neg 92.2%

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

      7. remove-double-neg 92.2%

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

      8. sub-neg 92.2%

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

      9. metadata-eval 92.2%

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

      10. +-commutative 92.2%

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

   9. Simplified 92.2%

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

   if 6.5e131 < b

   1. Initial program 85.3%

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

   3. Taylor expanded in a around 0 85.3%

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

   4. Taylor expanded in z around 0 88.3%

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

4. Final simplification 90.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -620000:\\ \;\;\;\;\left(x - b \cdot \left(2 - \left(y + t\right)\right)\right) + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 6.5 \cdot 10^{+131}:\\ \;\;\;\;z \cdot \left(1 - y\right) - \left(\left(t \cdot a - x\right) - a\right)\\ \mathbf{else}:\\ \;\;\;\;x - b \cdot \left(2 - \left(y + t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 47.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -1.7 \cdot 10^{+43}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 420000:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{elif}\;t \leq 1.34 \cdot 10^{+67}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (- b a))))
   (if (<= t -1.7e+43)
     t_1
     (if (<= t 420000.0)
       (* z (- 1.0 y))
       (if (<= t 1.34e+67) (* y (- b z)) 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 <= -1.7e+43) {
		tmp = t_1;
	} else if (t <= 420000.0) {
		tmp = z * (1.0 - y);
	} else if (t <= 1.34e+67) {
		tmp = y * (b - z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (b - a)
    if (t <= (-1.7d+43)) then
        tmp = t_1
    else if (t <= 420000.0d0) then
        tmp = z * (1.0d0 - y)
    else if (t <= 1.34d+67) then
        tmp = y * (b - z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (b - a);
	double tmp;
	if (t <= -1.7e+43) {
		tmp = t_1;
	} else if (t <= 420000.0) {
		tmp = z * (1.0 - y);
	} else if (t <= 1.34e+67) {
		tmp = y * (b - z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t * (b - a)
	tmp = 0
	if t <= -1.7e+43:
		tmp = t_1
	elif t <= 420000.0:
		tmp = z * (1.0 - y)
	elif t <= 1.34e+67:
		tmp = y * (b - z)
	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 <= -1.7e+43)
		tmp = t_1;
	elseif (t <= 420000.0)
		tmp = Float64(z * Float64(1.0 - y));
	elseif (t <= 1.34e+67)
		tmp = Float64(y * Float64(b - z));
	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 <= -1.7e+43)
		tmp = t_1;
	elseif (t <= 420000.0)
		tmp = z * (1.0 - y);
	elseif (t <= 1.34e+67)
		tmp = y * (b - z);
	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, -1.7e+43], t$95$1, If[LessEqual[t, 420000.0], N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.34e+67], N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.70000000000000006e43 or 1.33999999999999994e67 < t

   1. Initial program 93.4%

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

   3. Taylor expanded in t around inf 67.0%

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

   if -1.70000000000000006e43 < t < 4.2e5

   1. Initial program 97.7%

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

   3. Taylor expanded in z around inf 36.5%

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

   if 4.2e5 < t < 1.33999999999999994e67

   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 y around inf 65.4%

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

4. Final simplification 50.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.7 \cdot 10^{+43}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq 420000:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{elif}\;t \leq 1.34 \cdot 10^{+67}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 71.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -720000 \lor \neg \left(b \leq 2.25 \cdot 10^{+129}\right):\\ \;\;\;\;x - b \cdot \left(2 - \left(y + t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(a + z \cdot \left(1 - y\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -720000.0) (not (<= b 2.25e+129)))
   (- x (* b (- 2.0 (+ y t))))
   (+ x (+ a (* z (- 1.0 y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -720000.0) || !(b <= 2.25e+129)) {
		tmp = x - (b * (2.0 - (y + t)));
	} else {
		tmp = x + (a + (z * (1.0 - y)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-720000.0d0)) .or. (.not. (b <= 2.25d+129))) then
        tmp = x - (b * (2.0d0 - (y + t)))
    else
        tmp = x + (a + (z * (1.0d0 - y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -720000.0) || !(b <= 2.25e+129)) {
		tmp = x - (b * (2.0 - (y + t)));
	} else {
		tmp = x + (a + (z * (1.0 - y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -720000.0) or not (b <= 2.25e+129):
		tmp = x - (b * (2.0 - (y + t)))
	else:
		tmp = x + (a + (z * (1.0 - y)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -720000.0) || !(b <= 2.25e+129))
		tmp = Float64(x - Float64(b * Float64(2.0 - Float64(y + t))));
	else
		tmp = Float64(x + Float64(a + Float64(z * Float64(1.0 - y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -720000.0) || ~((b <= 2.25e+129)))
		tmp = x - (b * (2.0 - (y + t)));
	else
		tmp = x + (a + (z * (1.0 - y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -720000.0], N[Not[LessEqual[b, 2.25e+129]], $MachinePrecision]], N[(x - N[(b * N[(2.0 - N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(a + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -7.2e5 or 2.2500000000000001e129 < b

   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 a around 0 84.8%

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

   4. Taylor expanded in z around 0 81.5%

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

   if -7.2e5 < b < 2.2500000000000001e129

   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 b around 0 92.1%

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

   4. Taylor expanded in t around 0 74.2%

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

      1. +-commutative 74.2%

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

      2. sub-neg 74.2%

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

      3. metadata-eval 74.2%

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

      4. mul-1-neg 74.2%

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

      5. unsub-neg 74.2%

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

      6. +-commutative 74.2%

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

   6. Simplified 74.2%

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

4. Final simplification 77.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -720000 \lor \neg \left(b \leq 2.25 \cdot 10^{+129}\right):\\ \;\;\;\;x - b \cdot \left(2 - \left(y + t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(a + z \cdot \left(1 - y\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 50.9% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.92 \cdot 10^{+28} \lor \neg \left(y \leq 9.6 \cdot 10^{+58}\right):\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1.92e+28) (not (<= y 9.6e+58))) (* y (- b z)) (* t (- b a))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.92e+28) || !(y <= 9.6e+58)) {
		tmp = y * (b - z);
	} else {
		tmp = t * (b - 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 ((y <= (-1.92d+28)) .or. (.not. (y <= 9.6d+58))) then
        tmp = y * (b - z)
    else
        tmp = t * (b - 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 ((y <= -1.92e+28) || !(y <= 9.6e+58)) {
		tmp = y * (b - z);
	} else {
		tmp = t * (b - a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -1.92e+28) or not (y <= 9.6e+58):
		tmp = y * (b - z)
	else:
		tmp = t * (b - a)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -1.92e+28) || !(y <= 9.6e+58))
		tmp = Float64(y * Float64(b - z));
	else
		tmp = Float64(t * Float64(b - a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -1.92e+28) || ~((y <= 9.6e+58)))
		tmp = y * (b - z);
	else
		tmp = t * (b - a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -1.92e+28], N[Not[LessEqual[y, 9.6e+58]], $MachinePrecision]], N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision], N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.91999999999999998e28 or 9.5999999999999999e58 < y

   1. Initial program 92.0%

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

   3. Taylor expanded in y around inf 67.8%

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

   if -1.91999999999999998e28 < y < 9.5999999999999999e58

   1. Initial program 98.0%

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

   3. Taylor expanded in t around inf 35.5%

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

4. Final simplification 48.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.92 \cdot 10^{+28} \lor \neg \left(y \leq 9.6 \cdot 10^{+58}\right):\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 27.1% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.08 \cdot 10^{+95}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{+53}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -1.08e+95) (* y b) (if (<= y 2.7e+53) x (* z (- y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1.08e+95) {
		tmp = y * b;
	} else if (y <= 2.7e+53) {
		tmp = x;
	} else {
		tmp = z * -y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-1.08d+95)) then
        tmp = y * b
    else if (y <= 2.7d+53) then
        tmp = x
    else
        tmp = z * -y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1.08e+95) {
		tmp = y * b;
	} else if (y <= 2.7e+53) {
		tmp = x;
	} else {
		tmp = z * -y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -1.08e+95:
		tmp = y * b
	elif y <= 2.7e+53:
		tmp = x
	else:
		tmp = z * -y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -1.08e+95)
		tmp = Float64(y * b);
	elseif (y <= 2.7e+53)
		tmp = x;
	else
		tmp = Float64(z * Float64(-y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -1.08e+95)
		tmp = y * b;
	elseif (y <= 2.7e+53)
		tmp = x;
	else
		tmp = z * -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -1.08e+95], N[(y * b), $MachinePrecision], If[LessEqual[y, 2.7e+53], x, N[(z * (-y)), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.0800000000000001e95

   1. Initial program 88.1%

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

   3. Taylor expanded in y around inf 71.2%

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

   4. Taylor expanded in b around inf 42.6%

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

      1. *-commutative 42.6%

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

   6. Simplified 42.6%

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

   if -1.0800000000000001e95 < y < 2.70000000000000019e53

   1. Initial program 98.1%

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

   3. Taylor expanded in x around inf 23.1%

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

   if 2.70000000000000019e53 < y

   1. Initial program 93.7%

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

   3. Taylor expanded in t around 0 93.8%

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

   4. Taylor expanded in b around 0 73.4%

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

      1. associate-*r* 73.4%

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

      2. mul-1-neg 73.4%

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

   6. Simplified 73.4%

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

   7. Taylor expanded in y around inf 48.8%

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

      1. mul-1-neg 48.8%

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

      2. distribute-lft-neg-out 48.8%

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

      3. *-commutative 48.8%

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

   9. Simplified 48.8%

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

4. Final simplification 31.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.08 \cdot 10^{+95}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{+53}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 26.2% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -320000000 \lor \neg \left(b \leq 3.3 \cdot 10^{+100}\right):\\ \;\;\;\;y \cdot b\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -320000000.0) (not (<= b 3.3e+100))) (* y b) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -320000000.0) || !(b <= 3.3e+100)) {
		tmp = y * b;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-320000000.0d0)) .or. (.not. (b <= 3.3d+100))) then
        tmp = y * b
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -320000000.0) || !(b <= 3.3e+100)) {
		tmp = y * b;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -320000000.0) or not (b <= 3.3e+100):
		tmp = y * b
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -320000000.0) || !(b <= 3.3e+100))
		tmp = Float64(y * b);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -320000000.0) || ~((b <= 3.3e+100)))
		tmp = y * b;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -320000000.0], N[Not[LessEqual[b, 3.3e+100]], $MachinePrecision]], N[(y * b), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if b < -3.2e8 or 3.3000000000000001e100 < 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 y around inf 37.8%

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

   4. Taylor expanded in b around inf 33.1%

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

      1. *-commutative 33.1%

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

   6. Simplified 33.1%

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

   if -3.2e8 < b < 3.3000000000000001e100

   1. Initial program 99.3%

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

   3. Taylor expanded in x around inf 26.5%

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

4. Final simplification 29.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -320000000 \lor \neg \left(b \leq 3.3 \cdot 10^{+100}\right):\\ \;\;\;\;y \cdot b\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 20.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.15 \cdot 10^{+34}:\\ \;\;\;\;a\\ \mathbf{elif}\;a \leq 4.6 \cdot 10^{+103}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -1.15e+34) a (if (<= a 4.6e+103) x a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -1.15e+34) {
		tmp = a;
	} else if (a <= 4.6e+103) {
		tmp = x;
	} else {
		tmp = a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (a <= (-1.15d+34)) then
        tmp = a
    else if (a <= 4.6d+103) then
        tmp = x
    else
        tmp = a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -1.15e+34) {
		tmp = a;
	} else if (a <= 4.6e+103) {
		tmp = x;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -1.15e+34:
		tmp = a
	elif a <= 4.6e+103:
		tmp = x
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -1.15e+34)
		tmp = a;
	elseif (a <= 4.6e+103)
		tmp = x;
	else
		tmp = a;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= -1.15e+34)
		tmp = a;
	elseif (a <= 4.6e+103)
		tmp = x;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -1.15e+34], a, If[LessEqual[a, 4.6e+103], x, a]]

Derivation

1. Split input into 2 regimes

2. if a < -1.1499999999999999e34 or 4.60000000000000017e103 < a

   1. Initial program 92.7%

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

   3. Taylor expanded in a around inf 60.5%

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

   4. Taylor expanded in t around 0 28.9%

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

   if -1.1499999999999999e34 < a < 4.60000000000000017e103

   1. Initial program 97.1%

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

   3. Taylor expanded in x around inf 24.0%

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

4. Final simplification 25.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.15 \cdot 10^{+34}:\\ \;\;\;\;a\\ \mathbf{elif}\;a \leq 4.6 \cdot 10^{+103}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 10.4% accurate, 21.0× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = a
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 95.7%

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

3. Taylor expanded in a around inf 25.2%

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

4. Taylor expanded in t around 0 11.0%

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

5. Final simplification 11.0%

   \[\leadsto a \]
6. Add Preprocessing

Reproduce

herbie shell --seed 2024079 
(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)))