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

Percentage Accurate: 95.4% → 98.7%

Time: 12.3s

Alternatives: 20

Speedup: 0.5×

• 35.5% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 95.4% 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: 98.7% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(t + -1\right) \cdot a\\ t_2 := y + \left(t + -2\right)\\ \mathbf{if}\;\left(\left(x + z \cdot \left(1 - y\right)\right) - t\_1\right) + \left(\left(y + t\right) - 2\right) \cdot b \leq \infty:\\ \;\;\;\;\mathsf{fma}\left(t\_2, b, x - \mathsf{fma}\left(y + -1, z, t\_1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(\left(1 + \left(\frac{x}{z} + b \cdot \frac{t\_2}{z}\right)\right) + \left(a \cdot \frac{1 - t}{z} - y\right)\right)\\ \end{array} \end{array} \]

FPCore

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

C

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

Julia

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

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t + -1.0), $MachinePrecision] * a), $MachinePrecision]}, Block[{t$95$2 = N[(y + N[(t + -2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(N[(N[(x + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision] + N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision], Infinity], N[(t$95$2 * b + N[(x - N[(N[(y + -1.0), $MachinePrecision] * z + t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(N[(1.0 + N[(N[(x / z), $MachinePrecision] + N[(b * N[(t$95$2 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(a * N[(N[(1.0 - t), $MachinePrecision] / z), $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. fmm-def 100.0%

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

      9. sub-neg 100.0%

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

      10. metadata-eval 100.0%

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

      11. remove-double-neg 100.0%

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

      12. sub-neg 100.0%

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

      13. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in z around inf 31.3%

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

      1. associate-/l* 81.3%

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

      2. +-commutative 81.3%

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

      3. associate--l+ 81.3%

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

      4. sub-neg 81.3%

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

      5. metadata-eval 81.3%

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

      6. sub-neg 81.3%

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

      7. metadata-eval 81.3%

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

      8. associate-/l* 87.5%

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

      9. +-commutative 87.5%

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

   5. Simplified 87.5%

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

4. Final simplification 99.2%

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

Alternative 2: 98.6% accurate, 0.4× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(x + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(t + -1.0), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[(z * N[(N[(1.0 + N[(N[(x / z), $MachinePrecision] + N[(b * N[(N[(y + N[(t + -2.0), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(a * N[(N[(1.0 - t), $MachinePrecision] / z), $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 z around inf 31.3%

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

      1. associate-/l* 81.3%

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

      2. +-commutative 81.3%

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

      3. associate--l+ 81.3%

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

      4. sub-neg 81.3%

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

      5. metadata-eval 81.3%

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

      6. sub-neg 81.3%

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

      7. metadata-eval 81.3%

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

      8. associate-/l* 87.5%

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

      9. +-commutative 87.5%

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

   5. Simplified 87.5%

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

4. Final simplification 99.2%

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

Alternative 3: 98.7% accurate, 0.5× speedup

Math

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

FPCore

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

Python

def code(x, y, z, t, a, b):
	t_1 = ((x + (z * (1.0 - y))) - ((t + -1.0) * a)) + (((y + t) - 2.0) * b)
	tmp = 0
	if t_1 <= math.inf:
		tmp = t_1
	else:
		tmp = z * (1.0 + (((x / z) + (b * ((t + (y + -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(Float64(t + -1.0) * a)) + Float64(Float64(Float64(y + t) - 2.0) * b))
	tmp = 0.0
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = Float64(z * Float64(1.0 + Float64(Float64(Float64(x / z) + Float64(b * Float64(Float64(t + Float64(y + -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))) - ((t + -1.0) * a)) + (((y + t) - 2.0) * b);
	tmp = 0.0;
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = z * (1.0 + (((x / z) + (b * ((t + (y + -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[(N[(t + -1.0), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[(z * N[(1.0 + N[(N[(N[(x / z), $MachinePrecision] + N[(b * N[(N[(t + N[(y + -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 12.5%

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

   4. Taylor expanded in z around inf 43.8%

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

      1. associate--l+ 43.8%

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

      2. sub-neg 43.8%

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

      3. metadata-eval 43.8%

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

      4. associate-+r+ 43.8%

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

      5. associate-/l* 75.0%

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

   6. Simplified 75.0%

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

4. Final simplification 98.4%

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

Alternative 4: 63.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(t + -1\right) \cdot a\\ t_2 := x - b \cdot \left(2 - \left(y + t\right)\right)\\ \mathbf{if}\;b \leq -7.8 \cdot 10^{+104}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -1.9 \cdot 10^{+42}:\\ \;\;\;\;z - t\_1\\ \mathbf{elif}\;b \leq -9 \cdot 10^{-187}:\\ \;\;\;\;x + z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq 1.58 \cdot 10^{+60}:\\ \;\;\;\;x - t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (+ t -1.0) a)) (t_2 (- x (* b (- 2.0 (+ y t))))))
   (if (<= b -7.8e+104)
     t_2
     (if (<= b -1.9e+42)
       (- z t_1)
       (if (<= b -9e-187)
         (+ x (* z (- 1.0 y)))
         (if (<= b 1.58e+60) (- x t_1) t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t + -1.0) * a;
	double t_2 = x - (b * (2.0 - (y + t)));
	double tmp;
	if (b <= -7.8e+104) {
		tmp = t_2;
	} else if (b <= -1.9e+42) {
		tmp = z - t_1;
	} else if (b <= -9e-187) {
		tmp = x + (z * (1.0 - y));
	} else if (b <= 1.58e+60) {
		tmp = x - t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (t + (-1.0d0)) * a
    t_2 = x - (b * (2.0d0 - (y + t)))
    if (b <= (-7.8d+104)) then
        tmp = t_2
    else if (b <= (-1.9d+42)) then
        tmp = z - t_1
    else if (b <= (-9d-187)) then
        tmp = x + (z * (1.0d0 - y))
    else if (b <= 1.58d+60) then
        tmp = x - t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t + -1.0) * a;
	double t_2 = x - (b * (2.0 - (y + t)));
	double tmp;
	if (b <= -7.8e+104) {
		tmp = t_2;
	} else if (b <= -1.9e+42) {
		tmp = z - t_1;
	} else if (b <= -9e-187) {
		tmp = x + (z * (1.0 - y));
	} else if (b <= 1.58e+60) {
		tmp = x - t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (t + -1.0) * a
	t_2 = x - (b * (2.0 - (y + t)))
	tmp = 0
	if b <= -7.8e+104:
		tmp = t_2
	elif b <= -1.9e+42:
		tmp = z - t_1
	elif b <= -9e-187:
		tmp = x + (z * (1.0 - y))
	elif b <= 1.58e+60:
		tmp = x - t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t + -1.0) * a)
	t_2 = Float64(x - Float64(b * Float64(2.0 - Float64(y + t))))
	tmp = 0.0
	if (b <= -7.8e+104)
		tmp = t_2;
	elseif (b <= -1.9e+42)
		tmp = Float64(z - t_1);
	elseif (b <= -9e-187)
		tmp = Float64(x + Float64(z * Float64(1.0 - y)));
	elseif (b <= 1.58e+60)
		tmp = Float64(x - t_1);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (t + -1.0) * a;
	t_2 = x - (b * (2.0 - (y + t)));
	tmp = 0.0;
	if (b <= -7.8e+104)
		tmp = t_2;
	elseif (b <= -1.9e+42)
		tmp = z - t_1;
	elseif (b <= -9e-187)
		tmp = x + (z * (1.0 - y));
	elseif (b <= 1.58e+60)
		tmp = x - t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t + -1.0), $MachinePrecision] * a), $MachinePrecision]}, Block[{t$95$2 = N[(x - N[(b * N[(2.0 - N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -7.8e+104], t$95$2, If[LessEqual[b, -1.9e+42], N[(z - t$95$1), $MachinePrecision], If[LessEqual[b, -9e-187], N[(x + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.58e+60], N[(x - t$95$1), $MachinePrecision], t$95$2]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -7.80000000000000033e104 or 1.58e60 < b

   1. Initial program 85.4%

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

   3. Taylor expanded in z around 0 85.6%

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

   4. Taylor expanded in a around 0 83.4%

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

   if -7.80000000000000033e104 < b < -1.8999999999999999e42

   1. Initial program 84.6%

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

   3. Taylor expanded in b around 0 77.9%

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

   4. Taylor expanded in y around 0 77.9%

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

      1. +-commutative 77.9%

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

      2. sub-neg 77.9%

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

      3. metadata-eval 77.9%

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

      4. mul-1-neg 77.9%

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

      5. unsub-neg 77.9%

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

      6. +-commutative 77.9%

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

   6. Simplified 77.9%

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

   7. Taylor expanded in x around 0 77.9%

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

   if -1.8999999999999999e42 < b < -8.9999999999999996e-187

   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 b around 0 86.2%

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

   4. Taylor expanded in a around 0 63.5%

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

   if -8.9999999999999996e-187 < b < 1.58e60

   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 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 z around 0 64.5%

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

4. Final simplification 72.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -7.8 \cdot 10^{+104}:\\ \;\;\;\;x - b \cdot \left(2 - \left(y + t\right)\right)\\ \mathbf{elif}\;b \leq -1.9 \cdot 10^{+42}:\\ \;\;\;\;z - \left(t + -1\right) \cdot a\\ \mathbf{elif}\;b \leq -9 \cdot 10^{-187}:\\ \;\;\;\;x + z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq 1.58 \cdot 10^{+60}:\\ \;\;\;\;x - \left(t + -1\right) \cdot a\\ \mathbf{else}:\\ \;\;\;\;x - b \cdot \left(2 - \left(y + t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 49.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(b - z\right)\\ t_2 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -7.8 \cdot 10^{+25}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -3.2 \cdot 10^{-232}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -2.3 \cdot 10^{-292}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{+62}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (- b z))) (t_2 (* t (- b a))))
   (if (<= t -7.8e+25)
     t_2
     (if (<= t -3.2e-232)
       t_1
       (if (<= t -2.3e-292) (+ x a) (if (<= t 5.2e+62) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (b - z);
	double t_2 = t * (b - a);
	double tmp;
	if (t <= -7.8e+25) {
		tmp = t_2;
	} else if (t <= -3.2e-232) {
		tmp = t_1;
	} else if (t <= -2.3e-292) {
		tmp = x + a;
	} else if (t <= 5.2e+62) {
		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 = y * (b - z)
    t_2 = t * (b - a)
    if (t <= (-7.8d+25)) then
        tmp = t_2
    else if (t <= (-3.2d-232)) then
        tmp = t_1
    else if (t <= (-2.3d-292)) then
        tmp = x + a
    else if (t <= 5.2d+62) 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 = y * (b - z);
	double t_2 = t * (b - a);
	double tmp;
	if (t <= -7.8e+25) {
		tmp = t_2;
	} else if (t <= -3.2e-232) {
		tmp = t_1;
	} else if (t <= -2.3e-292) {
		tmp = x + a;
	} else if (t <= 5.2e+62) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y * (b - z)
	t_2 = t * (b - a)
	tmp = 0
	if t <= -7.8e+25:
		tmp = t_2
	elif t <= -3.2e-232:
		tmp = t_1
	elif t <= -2.3e-292:
		tmp = x + a
	elif t <= 5.2e+62:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y * Float64(b - z))
	t_2 = Float64(t * Float64(b - a))
	tmp = 0.0
	if (t <= -7.8e+25)
		tmp = t_2;
	elseif (t <= -3.2e-232)
		tmp = t_1;
	elseif (t <= -2.3e-292)
		tmp = Float64(x + a);
	elseif (t <= 5.2e+62)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y * (b - z);
	t_2 = t * (b - a);
	tmp = 0.0;
	if (t <= -7.8e+25)
		tmp = t_2;
	elseif (t <= -3.2e-232)
		tmp = t_1;
	elseif (t <= -2.3e-292)
		tmp = x + a;
	elseif (t <= 5.2e+62)
		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[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -7.8e+25], t$95$2, If[LessEqual[t, -3.2e-232], t$95$1, If[LessEqual[t, -2.3e-292], N[(x + a), $MachinePrecision], If[LessEqual[t, 5.2e+62], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -7.8000000000000004e25 or 5.19999999999999968e62 < t

   1. Initial program 89.9%

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

   3. Taylor expanded in t around inf 76.4%

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

   if -7.8000000000000004e25 < t < -3.19999999999999987e-232 or -2.2999999999999999e-292 < t < 5.19999999999999968e62

   1. Initial program 96.1%

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

   3. Taylor expanded in y around inf 53.8%

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

   if -3.19999999999999987e-232 < t < -2.2999999999999999e-292

   1. Initial program 100.0%

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

   3. Taylor expanded in b around 0 78.3%

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

   4. Taylor expanded in z around 0 72.8%

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

   5. Taylor expanded in t around 0 72.8%

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

      1. cancel-sign-sub-inv 72.8%

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

      2. metadata-eval 72.8%

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

      3. *-lft-identity 72.8%

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

   7. Simplified 72.8%

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

Alternative 6: 82.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{-147} \lor \neg \left(z \leq 8 \cdot 10^{+120}\right):\\ \;\;\;\;x + \left(z \cdot \left(1 - y\right) - \left(t + -1\right) \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x - b \cdot \left(2 - \left(y + t\right)\right)\right) + a \cdot \left(1 - t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -1.05e-147) (not (<= z 8e+120)))
   (+ x (- (* z (- 1.0 y)) (* (+ t -1.0) a)))
   (+ (- x (* b (- 2.0 (+ y t)))) (* a (- 1.0 t)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.05e-147) || !(z <= 8e+120)) {
		tmp = x + ((z * (1.0 - y)) - ((t + -1.0) * a));
	} else {
		tmp = (x - (b * (2.0 - (y + t)))) + (a * (1.0 - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-1.05d-147)) .or. (.not. (z <= 8d+120))) then
        tmp = x + ((z * (1.0d0 - y)) - ((t + (-1.0d0)) * a))
    else
        tmp = (x - (b * (2.0d0 - (y + t)))) + (a * (1.0d0 - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.05e-147) || !(z <= 8e+120)) {
		tmp = x + ((z * (1.0 - y)) - ((t + -1.0) * a));
	} else {
		tmp = (x - (b * (2.0 - (y + t)))) + (a * (1.0 - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -1.05e-147) or not (z <= 8e+120):
		tmp = x + ((z * (1.0 - y)) - ((t + -1.0) * a))
	else:
		tmp = (x - (b * (2.0 - (y + t)))) + (a * (1.0 - t))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -1.05e-147) || !(z <= 8e+120))
		tmp = Float64(x + Float64(Float64(z * Float64(1.0 - y)) - Float64(Float64(t + -1.0) * a)));
	else
		tmp = Float64(Float64(x - Float64(b * Float64(2.0 - Float64(y + t)))) + Float64(a * Float64(1.0 - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -1.05e-147) || ~((z <= 8e+120)))
		tmp = x + ((z * (1.0 - y)) - ((t + -1.0) * a));
	else
		tmp = (x - (b * (2.0 - (y + t)))) + (a * (1.0 - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -1.05e-147], N[Not[LessEqual[z, 8e+120]], $MachinePrecision]], N[(x + N[(N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision] - N[(N[(t + -1.0), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x - N[(b * N[(2.0 - N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.05e-147 or 7.9999999999999998e120 < z

   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 0 84.9%

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

   if -1.05e-147 < z < 7.9999999999999998e120

   1. Initial program 96.8%

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

   3. Taylor expanded in z around 0 95.6%

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

4. Final simplification 90.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{-147} \lor \neg \left(z \leq 8 \cdot 10^{+120}\right):\\ \;\;\;\;x + \left(z \cdot \left(1 - y\right) - \left(t + -1\right) \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x - b \cdot \left(2 - \left(y + t\right)\right)\right) + a \cdot \left(1 - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 86.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{-39}:\\ \;\;\;\;z \cdot \left(1 + \left(\left(\frac{x}{z} + b \cdot \frac{t + \left(y + -2\right)}{z}\right) - y\right)\right)\\ \mathbf{elif}\;z \leq 8 \cdot 10^{+120}:\\ \;\;\;\;\left(x - b \cdot \left(2 - \left(y + t\right)\right)\right) + a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(z \cdot \left(1 - y\right) - \left(t + -1\right) \cdot a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -2.4e-39)
   (* z (+ 1.0 (- (+ (/ x z) (* b (/ (+ t (+ y -2.0)) z))) y)))
   (if (<= z 8e+120)
     (+ (- x (* b (- 2.0 (+ y t)))) (* a (- 1.0 t)))
     (+ x (- (* z (- 1.0 y)) (* (+ t -1.0) a))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -2.4e-39) {
		tmp = z * (1.0 + (((x / z) + (b * ((t + (y + -2.0)) / z))) - y));
	} else if (z <= 8e+120) {
		tmp = (x - (b * (2.0 - (y + t)))) + (a * (1.0 - t));
	} else {
		tmp = x + ((z * (1.0 - y)) - ((t + -1.0) * 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 (z <= (-2.4d-39)) then
        tmp = z * (1.0d0 + (((x / z) + (b * ((t + (y + (-2.0d0))) / z))) - y))
    else if (z <= 8d+120) then
        tmp = (x - (b * (2.0d0 - (y + t)))) + (a * (1.0d0 - t))
    else
        tmp = x + ((z * (1.0d0 - y)) - ((t + (-1.0d0)) * 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 (z <= -2.4e-39) {
		tmp = z * (1.0 + (((x / z) + (b * ((t + (y + -2.0)) / z))) - y));
	} else if (z <= 8e+120) {
		tmp = (x - (b * (2.0 - (y + t)))) + (a * (1.0 - t));
	} else {
		tmp = x + ((z * (1.0 - y)) - ((t + -1.0) * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -2.4e-39:
		tmp = z * (1.0 + (((x / z) + (b * ((t + (y + -2.0)) / z))) - y))
	elif z <= 8e+120:
		tmp = (x - (b * (2.0 - (y + t)))) + (a * (1.0 - t))
	else:
		tmp = x + ((z * (1.0 - y)) - ((t + -1.0) * a))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -2.4e-39)
		tmp = Float64(z * Float64(1.0 + Float64(Float64(Float64(x / z) + Float64(b * Float64(Float64(t + Float64(y + -2.0)) / z))) - y)));
	elseif (z <= 8e+120)
		tmp = Float64(Float64(x - Float64(b * Float64(2.0 - Float64(y + t)))) + Float64(a * Float64(1.0 - t)));
	else
		tmp = Float64(x + Float64(Float64(z * Float64(1.0 - y)) - Float64(Float64(t + -1.0) * a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -2.4e-39)
		tmp = z * (1.0 + (((x / z) + (b * ((t + (y + -2.0)) / z))) - y));
	elseif (z <= 8e+120)
		tmp = (x - (b * (2.0 - (y + t)))) + (a * (1.0 - t));
	else
		tmp = x + ((z * (1.0 - y)) - ((t + -1.0) * a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -2.4e-39], N[(z * N[(1.0 + N[(N[(N[(x / z), $MachinePrecision] + N[(b * N[(N[(t + N[(y + -2.0), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8e+120], N[(N[(x - N[(b * N[(2.0 - N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision] - N[(N[(t + -1.0), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.40000000000000016e-39

   1. Initial program 90.5%

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

   3. Taylor expanded in a around 0 78.5%

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

   4. Taylor expanded in z around inf 81.2%

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

      1. associate--l+ 81.2%

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

      2. sub-neg 81.2%

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

      3. metadata-eval 81.2%

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

      4. associate-+r+ 81.2%

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

      5. associate-/l* 82.6%

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

   6. Simplified 82.6%

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

   if -2.40000000000000016e-39 < z < 7.9999999999999998e120

   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 z around 0 94.8%

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

   if 7.9999999999999998e120 < z

   1. Initial program 86.8%

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

   3. Taylor expanded in b around 0 89.7%

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

4. Final simplification 90.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{-39}:\\ \;\;\;\;z \cdot \left(1 + \left(\left(\frac{x}{z} + b \cdot \frac{t + \left(y + -2\right)}{z}\right) - y\right)\right)\\ \mathbf{elif}\;z \leq 8 \cdot 10^{+120}:\\ \;\;\;\;\left(x - b \cdot \left(2 - \left(y + t\right)\right)\right) + a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(z \cdot \left(1 - y\right) - \left(t + -1\right) \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 34.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(-a\right)\\ \mathbf{if}\;t \leq -6 \cdot 10^{+31}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -7.5 \cdot 10^{-232}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;t \leq 1.22 \cdot 10^{+14}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq 4.4 \cdot 10^{+134}:\\ \;\;\;\;t \cdot b\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (- a))))
   (if (<= t -6e+31)
     t_1
     (if (<= t -7.5e-232)
       (* y (- z))
       (if (<= t 1.22e+14) (+ x a) (if (<= t 4.4e+134) (* t b) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * -a;
	double tmp;
	if (t <= -6e+31) {
		tmp = t_1;
	} else if (t <= -7.5e-232) {
		tmp = y * -z;
	} else if (t <= 1.22e+14) {
		tmp = x + a;
	} else if (t <= 4.4e+134) {
		tmp = t * b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * -a
    if (t <= (-6d+31)) then
        tmp = t_1
    else if (t <= (-7.5d-232)) then
        tmp = y * -z
    else if (t <= 1.22d+14) then
        tmp = x + a
    else if (t <= 4.4d+134) then
        tmp = t * b
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * -a;
	double tmp;
	if (t <= -6e+31) {
		tmp = t_1;
	} else if (t <= -7.5e-232) {
		tmp = y * -z;
	} else if (t <= 1.22e+14) {
		tmp = x + a;
	} else if (t <= 4.4e+134) {
		tmp = t * b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t * -a
	tmp = 0
	if t <= -6e+31:
		tmp = t_1
	elif t <= -7.5e-232:
		tmp = y * -z
	elif t <= 1.22e+14:
		tmp = x + a
	elif t <= 4.4e+134:
		tmp = t * b
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t * Float64(-a))
	tmp = 0.0
	if (t <= -6e+31)
		tmp = t_1;
	elseif (t <= -7.5e-232)
		tmp = Float64(y * Float64(-z));
	elseif (t <= 1.22e+14)
		tmp = Float64(x + a);
	elseif (t <= 4.4e+134)
		tmp = Float64(t * b);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t * -a;
	tmp = 0.0;
	if (t <= -6e+31)
		tmp = t_1;
	elseif (t <= -7.5e-232)
		tmp = y * -z;
	elseif (t <= 1.22e+14)
		tmp = x + a;
	elseif (t <= 4.4e+134)
		tmp = t * b;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t * (-a)), $MachinePrecision]}, If[LessEqual[t, -6e+31], t$95$1, If[LessEqual[t, -7.5e-232], N[(y * (-z)), $MachinePrecision], If[LessEqual[t, 1.22e+14], N[(x + a), $MachinePrecision], If[LessEqual[t, 4.4e+134], N[(t * b), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -5.99999999999999978e31 or 4.4e134 < t

   1. Initial program 92.4%

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

   3. Taylor expanded in t around inf 78.4%

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

   4. Taylor expanded in b around 0 53.7%

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

      1. associate-*r* 53.7%

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

      2. neg-mul-1 53.7%

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

   6. Simplified 53.7%

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

   if -5.99999999999999978e31 < t < -7.5000000000000006e-232

   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 z around inf 54.0%

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

   4. Taylor expanded in y around inf 41.2%

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

      1. associate-*r* 41.2%

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

      2. neg-mul-1 41.2%

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

   6. Simplified 41.2%

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

   if -7.5000000000000006e-232 < t < 1.22e14

   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 b around 0 70.1%

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

   4. Taylor expanded in z around 0 44.6%

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

   5. Taylor expanded in t around 0 44.6%

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

      1. cancel-sign-sub-inv 44.6%

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

      2. metadata-eval 44.6%

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

      3. *-lft-identity 44.6%

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

   7. Simplified 44.6%

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

   if 1.22e14 < t < 4.4e134

   1. Initial program 84.0%

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

   3. Taylor expanded in t around inf 53.7%

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

   4. Taylor expanded in b around inf 41.2%

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

      1. *-commutative 41.2%

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

   6. Simplified 41.2%

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

4. Final simplification 47.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6 \cdot 10^{+31}:\\ \;\;\;\;t \cdot \left(-a\right)\\ \mathbf{elif}\;t \leq -7.5 \cdot 10^{-232}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;t \leq 1.22 \cdot 10^{+14}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq 4.4 \cdot 10^{+134}:\\ \;\;\;\;t \cdot b\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 69.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - b \cdot \left(2 - \left(y + t\right)\right)\\ \mathbf{if}\;b \leq -2.3 \cdot 10^{+121}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 3 \cdot 10^{-267}:\\ \;\;\;\;x - \left(y \cdot z + t \cdot a\right)\\ \mathbf{elif}\;b \leq 1.52 \cdot 10^{+60}:\\ \;\;\;\;x - \left(\left(t + -1\right) \cdot a - z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- x (* b (- 2.0 (+ y t))))))
   (if (<= b -2.3e+121)
     t_1
     (if (<= b 3e-267)
       (- x (+ (* y z) (* t a)))
       (if (<= b 1.52e+60) (- x (- (* (+ t -1.0) a) z)) 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 <= -2.3e+121) {
		tmp = t_1;
	} else if (b <= 3e-267) {
		tmp = x - ((y * z) + (t * a));
	} else if (b <= 1.52e+60) {
		tmp = x - (((t + -1.0) * a) - 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 = x - (b * (2.0d0 - (y + t)))
    if (b <= (-2.3d+121)) then
        tmp = t_1
    else if (b <= 3d-267) then
        tmp = x - ((y * z) + (t * a))
    else if (b <= 1.52d+60) then
        tmp = x - (((t + (-1.0d0)) * a) - 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 = x - (b * (2.0 - (y + t)));
	double tmp;
	if (b <= -2.3e+121) {
		tmp = t_1;
	} else if (b <= 3e-267) {
		tmp = x - ((y * z) + (t * a));
	} else if (b <= 1.52e+60) {
		tmp = x - (((t + -1.0) * a) - z);
	} 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 <= -2.3e+121:
		tmp = t_1
	elif b <= 3e-267:
		tmp = x - ((y * z) + (t * a))
	elif b <= 1.52e+60:
		tmp = x - (((t + -1.0) * a) - z)
	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 <= -2.3e+121)
		tmp = t_1;
	elseif (b <= 3e-267)
		tmp = Float64(x - Float64(Float64(y * z) + Float64(t * a)));
	elseif (b <= 1.52e+60)
		tmp = Float64(x - Float64(Float64(Float64(t + -1.0) * a) - z));
	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 <= -2.3e+121)
		tmp = t_1;
	elseif (b <= 3e-267)
		tmp = x - ((y * z) + (t * a));
	elseif (b <= 1.52e+60)
		tmp = x - (((t + -1.0) * a) - z);
	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, -2.3e+121], t$95$1, If[LessEqual[b, 3e-267], N[(x - N[(N[(y * z), $MachinePrecision] + N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.52e+60], N[(x - N[(N[(N[(t + -1.0), $MachinePrecision] * a), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -2.2999999999999999e121 or 1.52e60 < b

   1. Initial program 85.4%

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

   3. Taylor expanded in z around 0 88.8%

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

   4. Taylor expanded in a around 0 86.4%

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

   if -2.2999999999999999e121 < b < 3e-267

   1. Initial program 96.8%

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

   3. Taylor expanded in b around 0 89.0%

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

   4. Taylor expanded in y around inf 80.1%

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

      1. *-commutative 80.1%

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

   6. Simplified 80.1%

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

   7. Taylor expanded in t around inf 69.8%

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

   if 3e-267 < b < 1.52e60

   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 b around 0 90.6%

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

   4. Taylor expanded in y around 0 73.2%

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

      1. +-commutative 73.2%

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

      2. sub-neg 73.2%

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

      3. metadata-eval 73.2%

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

      4. mul-1-neg 73.2%

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

      5. unsub-neg 73.2%

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

      6. +-commutative 73.2%

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

   6. Simplified 73.2%

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

4. Final simplification 76.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.3 \cdot 10^{+121}:\\ \;\;\;\;x - b \cdot \left(2 - \left(y + t\right)\right)\\ \mathbf{elif}\;b \leq 3 \cdot 10^{-267}:\\ \;\;\;\;x - \left(y \cdot z + t \cdot a\right)\\ \mathbf{elif}\;b \leq 1.52 \cdot 10^{+60}:\\ \;\;\;\;x - \left(\left(t + -1\right) \cdot a - z\right)\\ \mathbf{else}:\\ \;\;\;\;x - b \cdot \left(2 - \left(y + t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 83.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.5 \cdot 10^{+131} \lor \neg \left(b \leq 8.5 \cdot 10^{+56}\right):\\ \;\;\;\;x - b \cdot \left(2 - \left(y + t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(z \cdot \left(1 - y\right) - \left(t + -1\right) \cdot a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -1.5e+131) (not (<= b 8.5e+56)))
   (- x (* b (- 2.0 (+ y t))))
   (+ x (- (* z (- 1.0 y)) (* (+ t -1.0) a)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -1.5e+131) || !(b <= 8.5e+56)) {
		tmp = x - (b * (2.0 - (y + t)));
	} else {
		tmp = x + ((z * (1.0 - y)) - ((t + -1.0) * a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-1.5d+131)) .or. (.not. (b <= 8.5d+56))) then
        tmp = x - (b * (2.0d0 - (y + t)))
    else
        tmp = x + ((z * (1.0d0 - y)) - ((t + (-1.0d0)) * a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -1.5e+131) || !(b <= 8.5e+56)) {
		tmp = x - (b * (2.0 - (y + t)));
	} else {
		tmp = x + ((z * (1.0 - y)) - ((t + -1.0) * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -1.5e+131) or not (b <= 8.5e+56):
		tmp = x - (b * (2.0 - (y + t)))
	else:
		tmp = x + ((z * (1.0 - y)) - ((t + -1.0) * a))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -1.5e+131) || !(b <= 8.5e+56))
		tmp = Float64(x - Float64(b * Float64(2.0 - Float64(y + t))));
	else
		tmp = Float64(x + Float64(Float64(z * Float64(1.0 - y)) - Float64(Float64(t + -1.0) * a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -1.5e+131) || ~((b <= 8.5e+56)))
		tmp = x - (b * (2.0 - (y + t)));
	else
		tmp = x + ((z * (1.0 - y)) - ((t + -1.0) * a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -1.5e+131], N[Not[LessEqual[b, 8.5e+56]], $MachinePrecision]], N[(x - N[(b * N[(2.0 - N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision] - N[(N[(t + -1.0), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.5000000000000001e131 or 8.4999999999999998e56 < b

   1. Initial program 85.1%

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

   3. Taylor expanded in z around 0 88.5%

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

   4. Taylor expanded in a around 0 87.2%

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

   if -1.5000000000000001e131 < b < 8.4999999999999998e56

   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 89.8%

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

4. Final simplification 88.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.5 \cdot 10^{+131} \lor \neg \left(b \leq 8.5 \cdot 10^{+56}\right):\\ \;\;\;\;x - b \cdot \left(2 - \left(y + t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(z \cdot \left(1 - y\right) - \left(t + -1\right) \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 56.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(b - z\right)\\ \mathbf{if}\;y \leq -1.3 \cdot 10^{+25}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.28 \cdot 10^{-48}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{+137}:\\ \;\;\;\;x - \left(t + -1\right) \cdot a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (- b z))))
   (if (<= y -1.3e+25)
     t_1
     (if (<= y -1.28e-48)
       (* t (- b a))
       (if (<= y 8.2e+137) (- x (* (+ t -1.0) a)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (b - z);
	double tmp;
	if (y <= -1.3e+25) {
		tmp = t_1;
	} else if (y <= -1.28e-48) {
		tmp = t * (b - a);
	} else if (y <= 8.2e+137) {
		tmp = x - ((t + -1.0) * a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (b - z)
    if (y <= (-1.3d+25)) then
        tmp = t_1
    else if (y <= (-1.28d-48)) then
        tmp = t * (b - a)
    else if (y <= 8.2d+137) then
        tmp = x - ((t + (-1.0d0)) * a)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (b - z);
	double tmp;
	if (y <= -1.3e+25) {
		tmp = t_1;
	} else if (y <= -1.28e-48) {
		tmp = t * (b - a);
	} else if (y <= 8.2e+137) {
		tmp = x - ((t + -1.0) * a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y * (b - z)
	tmp = 0
	if y <= -1.3e+25:
		tmp = t_1
	elif y <= -1.28e-48:
		tmp = t * (b - a)
	elif y <= 8.2e+137:
		tmp = x - ((t + -1.0) * a)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y * Float64(b - z))
	tmp = 0.0
	if (y <= -1.3e+25)
		tmp = t_1;
	elseif (y <= -1.28e-48)
		tmp = Float64(t * Float64(b - a));
	elseif (y <= 8.2e+137)
		tmp = Float64(x - Float64(Float64(t + -1.0) * a));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y * (b - z);
	tmp = 0.0;
	if (y <= -1.3e+25)
		tmp = t_1;
	elseif (y <= -1.28e-48)
		tmp = t * (b - a);
	elseif (y <= 8.2e+137)
		tmp = x - ((t + -1.0) * a);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.3e+25], t$95$1, If[LessEqual[y, -1.28e-48], N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 8.2e+137], N[(x - N[(N[(t + -1.0), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.2999999999999999e25 or 8.19999999999999994e137 < y

   1. Initial program 89.1%

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

   3. Taylor expanded in y around inf 76.3%

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

   if -1.2999999999999999e25 < y < -1.28000000000000001e-48

   1. Initial program 88.2%

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

   3. Taylor expanded in t around inf 74.5%

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

   if -1.28000000000000001e-48 < y < 8.19999999999999994e137

   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 77.2%

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

   4. Taylor expanded in z around 0 60.1%

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

4. Final simplification 68.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{+25}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;y \leq -1.28 \cdot 10^{-48}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{+137}:\\ \;\;\;\;x - \left(t + -1\right) \cdot a\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 76.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -5.5 \cdot 10^{+129} \lor \neg \left(b \leq 6 \cdot 10^{+60}\right):\\ \;\;\;\;x - b \cdot \left(2 - \left(y + t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x - \left(\left(t + -1\right) \cdot a + y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -5.5e+129) (not (<= b 6e+60)))
   (- x (* b (- 2.0 (+ y t))))
   (- x (+ (* (+ t -1.0) a) (* y z)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -5.5e+129) || !(b <= 6e+60)) {
		tmp = x - (b * (2.0 - (y + t)));
	} else {
		tmp = x - (((t + -1.0) * a) + (y * z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-5.5d+129)) .or. (.not. (b <= 6d+60))) then
        tmp = x - (b * (2.0d0 - (y + t)))
    else
        tmp = x - (((t + (-1.0d0)) * a) + (y * z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -5.5e+129) || !(b <= 6e+60)) {
		tmp = x - (b * (2.0 - (y + t)));
	} else {
		tmp = x - (((t + -1.0) * a) + (y * z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -5.5e+129) or not (b <= 6e+60):
		tmp = x - (b * (2.0 - (y + t)))
	else:
		tmp = x - (((t + -1.0) * a) + (y * z))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -5.5e+129) || !(b <= 6e+60))
		tmp = Float64(x - Float64(b * Float64(2.0 - Float64(y + t))));
	else
		tmp = Float64(x - Float64(Float64(Float64(t + -1.0) * a) + Float64(y * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -5.5e+129) || ~((b <= 6e+60)))
		tmp = x - (b * (2.0 - (y + t)));
	else
		tmp = x - (((t + -1.0) * a) + (y * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -5.5e+129], N[Not[LessEqual[b, 6e+60]], $MachinePrecision]], N[(x - N[(b * N[(2.0 - N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(N[(t + -1.0), $MachinePrecision] * a), $MachinePrecision] + N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -5.49999999999999984e129 or 5.9999999999999997e60 < b

   1. Initial program 85.1%

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

   3. Taylor expanded in z around 0 88.5%

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

   4. Taylor expanded in a around 0 87.2%

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

   if -5.49999999999999984e129 < b < 5.9999999999999997e60

   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 89.8%

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

   4. Taylor expanded in y around inf 80.4%

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

      1. *-commutative 80.4%

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

   6. Simplified 80.4%

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

4. Final simplification 82.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5.5 \cdot 10^{+129} \lor \neg \left(b \leq 6 \cdot 10^{+60}\right):\\ \;\;\;\;x - b \cdot \left(2 - \left(y + t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x - \left(\left(t + -1\right) \cdot a + y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 47.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -1.05 \cdot 10^{+27}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -9 \cdot 10^{-232}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;t \leq 7800000000:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (- b a))))
   (if (<= t -1.05e+27)
     t_1
     (if (<= t -9e-232) (* y (- z)) (if (<= t 7800000000.0) (+ x a) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (b - a);
	double tmp;
	if (t <= -1.05e+27) {
		tmp = t_1;
	} else if (t <= -9e-232) {
		tmp = y * -z;
	} else if (t <= 7800000000.0) {
		tmp = x + a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (b - a)
    if (t <= (-1.05d+27)) then
        tmp = t_1
    else if (t <= (-9d-232)) then
        tmp = y * -z
    else if (t <= 7800000000.0d0) then
        tmp = x + a
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (b - a);
	double tmp;
	if (t <= -1.05e+27) {
		tmp = t_1;
	} else if (t <= -9e-232) {
		tmp = y * -z;
	} else if (t <= 7800000000.0) {
		tmp = x + a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t * (b - a)
	tmp = 0
	if t <= -1.05e+27:
		tmp = t_1
	elif t <= -9e-232:
		tmp = y * -z
	elif t <= 7800000000.0:
		tmp = x + a
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t * Float64(b - a))
	tmp = 0.0
	if (t <= -1.05e+27)
		tmp = t_1;
	elseif (t <= -9e-232)
		tmp = Float64(y * Float64(-z));
	elseif (t <= 7800000000.0)
		tmp = Float64(x + a);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t * (b - a);
	tmp = 0.0;
	if (t <= -1.05e+27)
		tmp = t_1;
	elseif (t <= -9e-232)
		tmp = y * -z;
	elseif (t <= 7800000000.0)
		tmp = x + a;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.05e+27], t$95$1, If[LessEqual[t, -9e-232], N[(y * (-z)), $MachinePrecision], If[LessEqual[t, 7800000000.0], N[(x + a), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.04999999999999997e27 or 7.8e9 < t

   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 t around inf 73.1%

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

   if -1.04999999999999997e27 < t < -8.99999999999999933e-232

   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 z around inf 54.0%

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

   4. Taylor expanded in y around inf 41.2%

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

      1. associate-*r* 41.2%

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

      2. neg-mul-1 41.2%

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

   6. Simplified 41.2%

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

   if -8.99999999999999933e-232 < t < 7.8e9

   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 b around 0 70.1%

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

   4. Taylor expanded in z around 0 44.6%

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

   5. Taylor expanded in t around 0 44.6%

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

      1. cancel-sign-sub-inv 44.6%

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

      2. metadata-eval 44.6%

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

      3. *-lft-identity 44.6%

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

   7. Simplified 44.6%

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

4. Final simplification 57.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.05 \cdot 10^{+27}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq -9 \cdot 10^{-232}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;t \leq 7800000000:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 68.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -6 \cdot 10^{+121} \lor \neg \left(b \leq 1.75 \cdot 10^{+56}\right):\\ \;\;\;\;x - b \cdot \left(2 - \left(y + t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x - \left(y \cdot z + t \cdot a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -6e+121) (not (<= b 1.75e+56)))
   (- x (* b (- 2.0 (+ y t))))
   (- x (+ (* y z) (* t a)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -6e+121) || !(b <= 1.75e+56)) {
		tmp = x - (b * (2.0 - (y + t)));
	} else {
		tmp = x - ((y * z) + (t * a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-6d+121)) .or. (.not. (b <= 1.75d+56))) then
        tmp = x - (b * (2.0d0 - (y + t)))
    else
        tmp = x - ((y * z) + (t * a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -6e+121) || !(b <= 1.75e+56)) {
		tmp = x - (b * (2.0 - (y + t)));
	} else {
		tmp = x - ((y * z) + (t * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -6e+121) or not (b <= 1.75e+56):
		tmp = x - (b * (2.0 - (y + t)))
	else:
		tmp = x - ((y * z) + (t * a))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -6e+121) || !(b <= 1.75e+56))
		tmp = Float64(x - Float64(b * Float64(2.0 - Float64(y + t))));
	else
		tmp = Float64(x - Float64(Float64(y * z) + Float64(t * a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -6e+121) || ~((b <= 1.75e+56)))
		tmp = x - (b * (2.0 - (y + t)));
	else
		tmp = x - ((y * z) + (t * a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -6e+121], N[Not[LessEqual[b, 1.75e+56]], $MachinePrecision]], N[(x - N[(b * N[(2.0 - N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(y * z), $MachinePrecision] + N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -6.0000000000000005e121 or 1.75e56 < b

   1. Initial program 85.4%

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

   3. Taylor expanded in z around 0 88.8%

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

   4. Taylor expanded in a around 0 86.4%

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

   if -6.0000000000000005e121 < b < 1.75e56

   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 89.7%

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

   4. Taylor expanded in y around inf 80.1%

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

      1. *-commutative 80.1%

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

   6. Simplified 80.1%

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

   7. Taylor expanded in t around inf 65.6%

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

4. Final simplification 72.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -6 \cdot 10^{+121} \lor \neg \left(b \leq 1.75 \cdot 10^{+56}\right):\\ \;\;\;\;x - b \cdot \left(2 - \left(y + t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x - \left(y \cdot z + t \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 37.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(-a\right)\\ \mathbf{if}\;t \leq -3.8 \cdot 10^{+26}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 290000000000:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq 4.4 \cdot 10^{+134}:\\ \;\;\;\;t \cdot b\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (- a))))
   (if (<= t -3.8e+26)
     t_1
     (if (<= t 290000000000.0) (+ x a) (if (<= t 4.4e+134) (* t b) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * -a;
	double tmp;
	if (t <= -3.8e+26) {
		tmp = t_1;
	} else if (t <= 290000000000.0) {
		tmp = x + a;
	} else if (t <= 4.4e+134) {
		tmp = t * b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * -a
    if (t <= (-3.8d+26)) then
        tmp = t_1
    else if (t <= 290000000000.0d0) then
        tmp = x + a
    else if (t <= 4.4d+134) then
        tmp = t * b
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * -a;
	double tmp;
	if (t <= -3.8e+26) {
		tmp = t_1;
	} else if (t <= 290000000000.0) {
		tmp = x + a;
	} else if (t <= 4.4e+134) {
		tmp = t * b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t * -a
	tmp = 0
	if t <= -3.8e+26:
		tmp = t_1
	elif t <= 290000000000.0:
		tmp = x + a
	elif t <= 4.4e+134:
		tmp = t * b
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t * Float64(-a))
	tmp = 0.0
	if (t <= -3.8e+26)
		tmp = t_1;
	elseif (t <= 290000000000.0)
		tmp = Float64(x + a);
	elseif (t <= 4.4e+134)
		tmp = Float64(t * b);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t * -a;
	tmp = 0.0;
	if (t <= -3.8e+26)
		tmp = t_1;
	elseif (t <= 290000000000.0)
		tmp = x + a;
	elseif (t <= 4.4e+134)
		tmp = t * b;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t * (-a)), $MachinePrecision]}, If[LessEqual[t, -3.8e+26], t$95$1, If[LessEqual[t, 290000000000.0], N[(x + a), $MachinePrecision], If[LessEqual[t, 4.4e+134], N[(t * b), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.8000000000000002e26 or 4.4e134 < t

   1. Initial program 92.4%

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

   3. Taylor expanded in t around inf 78.4%

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

   4. Taylor expanded in b around 0 53.7%

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

      1. associate-*r* 53.7%

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

      2. neg-mul-1 53.7%

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

   6. Simplified 53.7%

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

   if -3.8000000000000002e26 < t < 2.9e11

   1. Initial program 96.4%

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

   3. Taylor expanded in b around 0 72.0%

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

   4. Taylor expanded in z around 0 38.2%

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

   5. Taylor expanded in t around 0 38.2%

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

      1. cancel-sign-sub-inv 38.2%

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

      2. metadata-eval 38.2%

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

      3. *-lft-identity 38.2%

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

   7. Simplified 38.2%

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

   if 2.9e11 < t < 4.4e134

   1. Initial program 84.0%

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

   3. Taylor expanded in t around inf 53.7%

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

   4. Taylor expanded in b around inf 41.2%

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

      1. *-commutative 41.2%

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

   6. Simplified 41.2%

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

4. Final simplification 44.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.8 \cdot 10^{+26}:\\ \;\;\;\;t \cdot \left(-a\right)\\ \mathbf{elif}\;t \leq 290000000000:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq 4.4 \cdot 10^{+134}:\\ \;\;\;\;t \cdot b\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 26.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -9.5 \cdot 10^{+59}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;t \leq -1.35 \cdot 10^{-81}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.56:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -9.5e+59)
   (* t b)
   (if (<= t -1.35e-81) x (if (<= t 1.56) a (* t b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -9.5e+59) {
		tmp = t * b;
	} else if (t <= -1.35e-81) {
		tmp = x;
	} else if (t <= 1.56) {
		tmp = a;
	} else {
		tmp = t * b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-9.5d+59)) then
        tmp = t * b
    else if (t <= (-1.35d-81)) then
        tmp = x
    else if (t <= 1.56d0) then
        tmp = a
    else
        tmp = t * b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -9.5e+59) {
		tmp = t * b;
	} else if (t <= -1.35e-81) {
		tmp = x;
	} else if (t <= 1.56) {
		tmp = a;
	} else {
		tmp = t * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -9.5e+59:
		tmp = t * b
	elif t <= -1.35e-81:
		tmp = x
	elif t <= 1.56:
		tmp = a
	else:
		tmp = t * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -9.5e+59)
		tmp = Float64(t * b);
	elseif (t <= -1.35e-81)
		tmp = x;
	elseif (t <= 1.56)
		tmp = a;
	else
		tmp = Float64(t * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -9.5e+59)
		tmp = t * b;
	elseif (t <= -1.35e-81)
		tmp = x;
	elseif (t <= 1.56)
		tmp = a;
	else
		tmp = t * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -9.5e+59], N[(t * b), $MachinePrecision], If[LessEqual[t, -1.35e-81], x, If[LessEqual[t, 1.56], a, N[(t * b), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -9.50000000000000023e59 or 1.5600000000000001 < t

   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 t around inf 72.2%

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

   4. Taylor expanded in b around inf 38.4%

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

      1. *-commutative 38.4%

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

   6. Simplified 38.4%

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

   if -9.50000000000000023e59 < t < -1.34999999999999995e-81

   1. Initial program 96.8%

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

   3. Taylor expanded in x around inf 24.2%

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

   if -1.34999999999999995e-81 < t < 1.5600000000000001

   1. Initial program 96.5%

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

   3. Taylor expanded in a around inf 25.2%

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

   4. Taylor expanded in t around 0 25.2%

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

Alternative 17: 42.9% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.7 \cdot 10^{+75} \lor \neg \left(a \leq 1.12 \cdot 10^{+76}\right):\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -2.7e+75) (not (<= a 1.12e+76))) (* a (- 1.0 t)) (+ x z)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -2.7e+75) || !(a <= 1.12e+76)) {
		tmp = a * (1.0 - t);
	} else {
		tmp = x + z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((a <= (-2.7d+75)) .or. (.not. (a <= 1.12d+76))) then
        tmp = a * (1.0d0 - t)
    else
        tmp = x + z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -2.7e+75) || !(a <= 1.12e+76)) {
		tmp = a * (1.0 - t);
	} else {
		tmp = x + z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (a <= -2.7e+75) or not (a <= 1.12e+76):
		tmp = a * (1.0 - t)
	else:
		tmp = x + z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((a <= -2.7e+75) || !(a <= 1.12e+76))
		tmp = Float64(a * Float64(1.0 - t));
	else
		tmp = Float64(x + z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((a <= -2.7e+75) || ~((a <= 1.12e+76)))
		tmp = a * (1.0 - t);
	else
		tmp = x + z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[a, -2.7e+75], N[Not[LessEqual[a, 1.12e+76]], $MachinePrecision]], N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision], N[(x + z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -2.69999999999999998e75 or 1.12000000000000005e76 < a

   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 a around inf 61.7%

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

   if -2.69999999999999998e75 < a < 1.12000000000000005e76

   1. Initial program 95.1%

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

   3. Taylor expanded in b around 0 60.9%

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

   4. Taylor expanded in a around 0 54.5%

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

   5. Taylor expanded in y around 0 29.9%

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

      1. cancel-sign-sub-inv 29.9%

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

      2. metadata-eval 29.9%

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

      3. *-lft-identity 29.9%

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

   7. Simplified 29.9%

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

4. Final simplification 44.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.7 \cdot 10^{+75} \lor \neg \left(a \leq 1.12 \cdot 10^{+76}\right):\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + z\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 35.9% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -9 \cdot 10^{+59} \lor \neg \left(t \leq 1.4 \cdot 10^{+14}\right):\\ \;\;\;\;t \cdot b\\ \mathbf{else}:\\ \;\;\;\;x + a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -9e+59) (not (<= t 1.4e+14))) (* t b) (+ x a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -9e+59) || !(t <= 1.4e+14)) {
		tmp = t * b;
	} else {
		tmp = x + a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-9d+59)) .or. (.not. (t <= 1.4d+14))) then
        tmp = t * b
    else
        tmp = x + a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -9e+59) || !(t <= 1.4e+14)) {
		tmp = t * b;
	} else {
		tmp = x + a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -9e+59) or not (t <= 1.4e+14):
		tmp = t * b
	else:
		tmp = x + a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -9e+59) || !(t <= 1.4e+14))
		tmp = Float64(t * b);
	else
		tmp = Float64(x + a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -9e+59) || ~((t <= 1.4e+14)))
		tmp = t * b;
	else
		tmp = x + a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -9e+59], N[Not[LessEqual[t, 1.4e+14]], $MachinePrecision]], N[(t * b), $MachinePrecision], N[(x + a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -8.99999999999999919e59 or 1.4e14 < t

   1. Initial program 89.9%

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

   3. Taylor expanded in t around inf 73.1%

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

   4. Taylor expanded in b around inf 38.6%

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

      1. *-commutative 38.6%

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

   6. Simplified 38.6%

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

   if -8.99999999999999919e59 < t < 1.4e14

   1. Initial program 96.6%

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

   3. Taylor expanded in b around 0 72.8%

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

   4. Taylor expanded in z around 0 40.8%

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

   5. Taylor expanded in t around 0 37.8%

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

      1. cancel-sign-sub-inv 37.8%

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

      2. metadata-eval 37.8%

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

      3. *-lft-identity 37.8%

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

   7. Simplified 37.8%

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

4. Final simplification 38.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9 \cdot 10^{+59} \lor \neg \left(t \leq 1.4 \cdot 10^{+14}\right):\\ \;\;\;\;t \cdot b\\ \mathbf{else}:\\ \;\;\;\;x + a\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 19.3% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7.4 \cdot 10^{+52}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{+240}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -7.4e+52) x (if (<= x 2.8e+240) a x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -7.4e+52) {
		tmp = x;
	} else if (x <= 2.8e+240) {
		tmp = a;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= (-7.4d+52)) then
        tmp = x
    else if (x <= 2.8d+240) then
        tmp = a
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -7.4e+52) {
		tmp = x;
	} else if (x <= 2.8e+240) {
		tmp = a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -7.4e+52:
		tmp = x
	elif x <= 2.8e+240:
		tmp = a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -7.4e+52)
		tmp = x;
	elseif (x <= 2.8e+240)
		tmp = a;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -7.4e+52)
		tmp = x;
	elseif (x <= 2.8e+240)
		tmp = a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -7.4e+52], x, If[LessEqual[x, 2.8e+240], a, x]]

Derivation

1. Split input into 2 regimes

2. if x < -7.3999999999999999e52 or 2.8000000000000001e240 < x

   1. Initial program 91.9%

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

   3. Taylor expanded in x around inf 39.9%

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

   if -7.3999999999999999e52 < x < 2.8000000000000001e240

   1. Initial program 94.5%

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

   3. Taylor expanded in a around inf 37.3%

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

   4. Taylor expanded in t around 0 15.9%

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

Alternative 20: 11.3% 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 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 a around inf 32.5%

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

4. Taylor expanded in t around 0 13.0%

   \[\leadsto \color{blue}{a} \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024157 
(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)))