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

Percentage Accurate: 94.9% → 98.7%

Time: 11.7s

Alternatives: 21

Speedup: 0.5×

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

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 94.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.7% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 100.0%

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

      1. associate-+l- 100.0%

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

      2. sub-neg 100.0%

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

      3. metadata-eval 100.0%

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

      4. *-commutative 100.0%

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

      5. sub-neg 100.0%

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

      6. metadata-eval 100.0%

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

      7. sub-neg 100.0%

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

      8. metadata-eval 100.0%

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

      9. associate-+r+ 100.0%

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

      10. +-commutative 100.0%

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

      11. associate-+l+ 100.0%

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

   4. Applied egg-rr 100.0%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in y around inf 17.6%

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

      1. mul-1-neg 17.6%

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

      2. *-commutative 17.6%

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

      3. distribute-rgt-neg-in 17.6%

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

   5. Simplified 17.6%

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

   6. Taylor expanded in y around inf 64.7%

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

      1. associate-+r+ 64.7%

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

      2. mul-1-neg 64.7%

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

      3. sub-neg 64.7%

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

      4. sub-neg 64.7%

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

      5. metadata-eval 64.7%

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

      6. associate-/l* 70.6%

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

   8. Simplified 70.6%

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

4. Final simplification 98.0%

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

Alternative 2: 98.7% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 100.0%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in y around inf 17.6%

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

      1. mul-1-neg 17.6%

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

      2. *-commutative 17.6%

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

      3. distribute-rgt-neg-in 17.6%

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

   5. Simplified 17.6%

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

   6. Taylor expanded in y around inf 64.7%

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

      1. associate-+r+ 64.7%

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

      2. mul-1-neg 64.7%

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

      3. sub-neg 64.7%

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

      4. sub-neg 64.7%

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

      5. metadata-eval 64.7%

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

      6. associate-/l* 70.6%

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

   8. Simplified 70.6%

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

4. Final simplification 98.0%

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

Alternative 3: 84.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(1 - t\right)\\ \mathbf{if}\;b \leq -8.2 \cdot 10^{+145}:\\ \;\;\;\;\left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{elif}\;b \leq -4100000:\\ \;\;\;\;\left(x + z \cdot \left(1 - y\right)\right) - t \cdot \left(a - b\right)\\ \mathbf{elif}\;b \leq 3.6 \cdot 10^{+122}:\\ \;\;\;\;x - \left(\left(y + -1\right) \cdot z - t\_1\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(b \cdot \left(t + \left(y + -2\right)\right) + t\_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (- 1.0 t))))
   (if (<= b -8.2e+145)
     (* (- (+ y t) 2.0) b)
     (if (<= b -4100000.0)
       (- (+ x (* z (- 1.0 y))) (* t (- a b)))
       (if (<= b 3.6e+122)
         (- x (- (* (+ y -1.0) z) t_1))
         (+ x (+ (* b (+ t (+ y -2.0))) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double tmp;
	if (b <= -8.2e+145) {
		tmp = ((y + t) - 2.0) * b;
	} else if (b <= -4100000.0) {
		tmp = (x + (z * (1.0 - y))) - (t * (a - b));
	} else if (b <= 3.6e+122) {
		tmp = x - (((y + -1.0) * z) - t_1);
	} else {
		tmp = x + ((b * (t + (y + -2.0))) + t_1);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (1.0d0 - t)
    if (b <= (-8.2d+145)) then
        tmp = ((y + t) - 2.0d0) * b
    else if (b <= (-4100000.0d0)) then
        tmp = (x + (z * (1.0d0 - y))) - (t * (a - b))
    else if (b <= 3.6d+122) then
        tmp = x - (((y + (-1.0d0)) * z) - t_1)
    else
        tmp = x + ((b * (t + (y + (-2.0d0)))) + t_1)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double tmp;
	if (b <= -8.2e+145) {
		tmp = ((y + t) - 2.0) * b;
	} else if (b <= -4100000.0) {
		tmp = (x + (z * (1.0 - y))) - (t * (a - b));
	} else if (b <= 3.6e+122) {
		tmp = x - (((y + -1.0) * z) - t_1);
	} else {
		tmp = x + ((b * (t + (y + -2.0))) + t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (1.0 - t)
	tmp = 0
	if b <= -8.2e+145:
		tmp = ((y + t) - 2.0) * b
	elif b <= -4100000.0:
		tmp = (x + (z * (1.0 - y))) - (t * (a - b))
	elif b <= 3.6e+122:
		tmp = x - (((y + -1.0) * z) - t_1)
	else:
		tmp = x + ((b * (t + (y + -2.0))) + t_1)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(1.0 - t))
	tmp = 0.0
	if (b <= -8.2e+145)
		tmp = Float64(Float64(Float64(y + t) - 2.0) * b);
	elseif (b <= -4100000.0)
		tmp = Float64(Float64(x + Float64(z * Float64(1.0 - y))) - Float64(t * Float64(a - b)));
	elseif (b <= 3.6e+122)
		tmp = Float64(x - Float64(Float64(Float64(y + -1.0) * z) - t_1));
	else
		tmp = Float64(x + Float64(Float64(b * Float64(t + Float64(y + -2.0))) + t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (1.0 - t);
	tmp = 0.0;
	if (b <= -8.2e+145)
		tmp = ((y + t) - 2.0) * b;
	elseif (b <= -4100000.0)
		tmp = (x + (z * (1.0 - y))) - (t * (a - b));
	elseif (b <= 3.6e+122)
		tmp = x - (((y + -1.0) * z) - t_1);
	else
		tmp = x + ((b * (t + (y + -2.0))) + t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -8.2e+145], N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision], If[LessEqual[b, -4100000.0], N[(N[(x + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(t * N[(a - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.6e+122], N[(x - N[(N[(N[(y + -1.0), $MachinePrecision] * z), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(b * N[(t + N[(y + -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -8.2000000000000003e145

   1. Initial program 84.8%

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

   3. Taylor expanded in b around inf 94.0%

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

   if -8.2000000000000003e145 < b < -4.1e6

   1. Initial program 90.0%

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

      1. associate-+l- 90.0%

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

      2. sub-neg 90.0%

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

      3. metadata-eval 90.0%

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

      4. *-commutative 90.0%

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

      5. sub-neg 90.0%

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

      6. metadata-eval 90.0%

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

      7. sub-neg 90.0%

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

      8. metadata-eval 90.0%

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

      9. associate-+r+ 90.0%

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

      10. +-commutative 90.0%

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

      11. associate-+l+ 90.0%

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

   4. Applied egg-rr 90.0%

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

   5. Taylor expanded in t around inf 83.7%

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

   if -4.1e6 < b < 3.6000000000000003e122

   1. Initial program 97.4%

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

   3. Taylor expanded in b around 0 90.9%

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

   if 3.6000000000000003e122 < b

   1. Initial program 86.1%

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

      1. associate-+l- 86.1%

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

      2. sub-neg 86.1%

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

      3. metadata-eval 86.1%

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

      4. *-commutative 86.1%

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

      5. sub-neg 86.1%

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

      6. metadata-eval 86.1%

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

      7. sub-neg 86.1%

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

      8. metadata-eval 86.1%

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

      9. associate-+r+ 86.1%

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

      10. +-commutative 86.1%

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

      11. associate-+l+ 86.1%

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

   4. Applied egg-rr 86.1%

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

   5. Taylor expanded in z around 0 97.2%

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

      1. associate--l+ 97.2%

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

      2. sub-neg 97.2%

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

      3. metadata-eval 97.2%

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

      4. associate-+r+ 97.2%

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

      5. sub-neg 97.2%

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

      6. metadata-eval 97.2%

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

      7. +-commutative 97.2%

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

   7. Simplified 97.2%

      \[\leadsto \color{blue}{x + \left(b \cdot \left(t + \left(y + -2\right)\right) - a \cdot \left(-1 + t\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 91.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -8.2 \cdot 10^{+145}:\\ \;\;\;\;\left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{elif}\;b \leq -4100000:\\ \;\;\;\;\left(x + z \cdot \left(1 - y\right)\right) - t \cdot \left(a - b\right)\\ \mathbf{elif}\;b \leq 3.6 \cdot 10^{+122}:\\ \;\;\;\;x - \left(\left(y + -1\right) \cdot z - a \cdot \left(1 - t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(b \cdot \left(t + \left(y + -2\right)\right) + a \cdot \left(1 - t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 36.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(-a\right)\\ \mathbf{if}\;t \leq -6.8 \cdot 10^{+101}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -0.00044:\\ \;\;\;\;z \cdot \left(-y\right)\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{+37}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq 2.65 \cdot 10^{+97} \lor \neg \left(t \leq 1.52 \cdot 10^{+196}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (- a))))
   (if (<= t -6.8e+101)
     t_1
     (if (<= t -0.00044)
       (* z (- y))
       (if (<= t 6.2e+37)
         (+ x a)
         (if (or (<= t 2.65e+97) (not (<= t 1.52e+196))) t_1 (* t b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * -a;
	double tmp;
	if (t <= -6.8e+101) {
		tmp = t_1;
	} else if (t <= -0.00044) {
		tmp = z * -y;
	} else if (t <= 6.2e+37) {
		tmp = x + a;
	} else if ((t <= 2.65e+97) || !(t <= 1.52e+196)) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = t * -a
    if (t <= (-6.8d+101)) then
        tmp = t_1
    else if (t <= (-0.00044d0)) then
        tmp = z * -y
    else if (t <= 6.2d+37) then
        tmp = x + a
    else if ((t <= 2.65d+97) .or. (.not. (t <= 1.52d+196))) then
        tmp = t_1
    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 t_1 = t * -a;
	double tmp;
	if (t <= -6.8e+101) {
		tmp = t_1;
	} else if (t <= -0.00044) {
		tmp = z * -y;
	} else if (t <= 6.2e+37) {
		tmp = x + a;
	} else if ((t <= 2.65e+97) || !(t <= 1.52e+196)) {
		tmp = t_1;
	} else {
		tmp = t * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t * -a
	tmp = 0
	if t <= -6.8e+101:
		tmp = t_1
	elif t <= -0.00044:
		tmp = z * -y
	elif t <= 6.2e+37:
		tmp = x + a
	elif (t <= 2.65e+97) or not (t <= 1.52e+196):
		tmp = t_1
	else:
		tmp = t * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t * Float64(-a))
	tmp = 0.0
	if (t <= -6.8e+101)
		tmp = t_1;
	elseif (t <= -0.00044)
		tmp = Float64(z * Float64(-y));
	elseif (t <= 6.2e+37)
		tmp = Float64(x + a);
	elseif ((t <= 2.65e+97) || !(t <= 1.52e+196))
		tmp = t_1;
	else
		tmp = Float64(t * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t * -a;
	tmp = 0.0;
	if (t <= -6.8e+101)
		tmp = t_1;
	elseif (t <= -0.00044)
		tmp = z * -y;
	elseif (t <= 6.2e+37)
		tmp = x + a;
	elseif ((t <= 2.65e+97) || ~((t <= 1.52e+196)))
		tmp = t_1;
	else
		tmp = t * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t * (-a)), $MachinePrecision]}, If[LessEqual[t, -6.8e+101], t$95$1, If[LessEqual[t, -0.00044], N[(z * (-y)), $MachinePrecision], If[LessEqual[t, 6.2e+37], N[(x + a), $MachinePrecision], If[Or[LessEqual[t, 2.65e+97], N[Not[LessEqual[t, 1.52e+196]], $MachinePrecision]], t$95$1, N[(t * b), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -6.80000000000000034e101 or 6.2000000000000004e37 < t < 2.6500000000000001e97 or 1.52e196 < t

   1. Initial program 87.2%

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

   3. Taylor expanded in t around inf 72.5%

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

   4. Taylor expanded in b around 0 50.6%

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

      1. associate-*r* 50.6%

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

      2. neg-mul-1 50.6%

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

   6. Simplified 50.6%

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

   if -6.80000000000000034e101 < t < -4.40000000000000016e-4

   1. Initial program 76.9%

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

   3. Taylor expanded in z around inf 62.0%

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

   4. Taylor expanded in y around inf 54.9%

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

      1. mul-1-neg 54.9%

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

      2. *-commutative 54.9%

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

      3. distribute-rgt-neg-in 54.9%

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

   6. Simplified 54.9%

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

   if -4.40000000000000016e-4 < t < 6.2000000000000004e37

   1. Initial program 98.6%

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

      1. associate-+l- 98.6%

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

      2. sub-neg 98.6%

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

      3. metadata-eval 98.6%

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

      4. *-commutative 98.6%

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

      5. sub-neg 98.6%

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

      6. metadata-eval 98.6%

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

      7. sub-neg 98.6%

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

      8. metadata-eval 98.6%

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

      9. associate-+r+ 98.6%

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

      10. +-commutative 98.6%

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

      11. associate-+l+ 98.6%

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

   4. Applied egg-rr 98.6%

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

   5. Taylor expanded in z around 0 71.3%

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

      1. associate--l+ 71.3%

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

      2. sub-neg 71.3%

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

      3. metadata-eval 71.3%

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

      4. associate-+r+ 71.3%

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

      5. sub-neg 71.3%

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

      6. metadata-eval 71.3%

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

      7. +-commutative 71.3%

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

   7. Simplified 71.3%

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

   8. Taylor expanded in b around 0 40.9%

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

   9. Taylor expanded in t around 0 39.5%

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

       1. cancel-sign-sub-inv 39.5%

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

       2. metadata-eval 39.5%

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

       3. *-lft-identity 39.5%

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

       4. +-commutative 39.5%

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

   11. Simplified 39.5%

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

   if 2.6500000000000001e97 < t < 1.52e196

   1. Initial program 91.3%

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

   3. Taylor expanded in t around inf 78.7%

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

   4. Taylor expanded in b around inf 61.8%

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

      1. *-commutative 61.8%

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

   6. Simplified 61.8%

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

4. Final simplification 45.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.8 \cdot 10^{+101}:\\ \;\;\;\;t \cdot \left(-a\right)\\ \mathbf{elif}\;t \leq -0.00044:\\ \;\;\;\;z \cdot \left(-y\right)\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{+37}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq 2.65 \cdot 10^{+97} \lor \neg \left(t \leq 1.52 \cdot 10^{+196}\right):\\ \;\;\;\;t \cdot \left(-a\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 83.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{if}\;b \leq -1.3 \cdot 10^{+146}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -5500000000:\\ \;\;\;\;\left(x + z \cdot \left(1 - y\right)\right) - t \cdot \left(a - b\right)\\ \mathbf{elif}\;b \leq 3.7 \cdot 10^{+130}:\\ \;\;\;\;x - \left(\left(y + -1\right) \cdot z - a \cdot \left(1 - t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- (+ y t) 2.0) b)))
   (if (<= b -1.3e+146)
     t_1
     (if (<= b -5500000000.0)
       (- (+ x (* z (- 1.0 y))) (* t (- a b)))
       (if (<= b 3.7e+130) (- x (- (* (+ y -1.0) z) (* a (- 1.0 t)))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((y + t) - 2.0) * b;
	double tmp;
	if (b <= -1.3e+146) {
		tmp = t_1;
	} else if (b <= -5500000000.0) {
		tmp = (x + (z * (1.0 - y))) - (t * (a - b));
	} else if (b <= 3.7e+130) {
		tmp = x - (((y + -1.0) * z) - (a * (1.0 - t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((y + t) - 2.0d0) * b
    if (b <= (-1.3d+146)) then
        tmp = t_1
    else if (b <= (-5500000000.0d0)) then
        tmp = (x + (z * (1.0d0 - y))) - (t * (a - b))
    else if (b <= 3.7d+130) then
        tmp = x - (((y + (-1.0d0)) * z) - (a * (1.0d0 - t)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((y + t) - 2.0) * b;
	double tmp;
	if (b <= -1.3e+146) {
		tmp = t_1;
	} else if (b <= -5500000000.0) {
		tmp = (x + (z * (1.0 - y))) - (t * (a - b));
	} else if (b <= 3.7e+130) {
		tmp = x - (((y + -1.0) * z) - (a * (1.0 - t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((y + t) - 2.0) * b
	tmp = 0
	if b <= -1.3e+146:
		tmp = t_1
	elif b <= -5500000000.0:
		tmp = (x + (z * (1.0 - y))) - (t * (a - b))
	elif b <= 3.7e+130:
		tmp = x - (((y + -1.0) * z) - (a * (1.0 - t)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(y + t) - 2.0) * b)
	tmp = 0.0
	if (b <= -1.3e+146)
		tmp = t_1;
	elseif (b <= -5500000000.0)
		tmp = Float64(Float64(x + Float64(z * Float64(1.0 - y))) - Float64(t * Float64(a - b)));
	elseif (b <= 3.7e+130)
		tmp = Float64(x - Float64(Float64(Float64(y + -1.0) * z) - Float64(a * Float64(1.0 - t))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((y + t) - 2.0) * b;
	tmp = 0.0;
	if (b <= -1.3e+146)
		tmp = t_1;
	elseif (b <= -5500000000.0)
		tmp = (x + (z * (1.0 - y))) - (t * (a - b));
	elseif (b <= 3.7e+130)
		tmp = x - (((y + -1.0) * z) - (a * (1.0 - t)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[b, -1.3e+146], t$95$1, If[LessEqual[b, -5500000000.0], N[(N[(x + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(t * N[(a - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.7e+130], N[(x - N[(N[(N[(y + -1.0), $MachinePrecision] * z), $MachinePrecision] - N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.30000000000000007e146 or 3.7000000000000001e130 < b

   1. Initial program 85.3%

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

   3. Taylor expanded in b around inf 93.9%

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

   if -1.30000000000000007e146 < b < -5.5e9

   1. Initial program 90.0%

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

      1. associate-+l- 90.0%

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

      2. sub-neg 90.0%

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

      3. metadata-eval 90.0%

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

      4. *-commutative 90.0%

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

      5. sub-neg 90.0%

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

      6. metadata-eval 90.0%

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

      7. sub-neg 90.0%

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

      8. metadata-eval 90.0%

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

      9. associate-+r+ 90.0%

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

      10. +-commutative 90.0%

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

      11. associate-+l+ 90.0%

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

   4. Applied egg-rr 90.0%

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

   5. Taylor expanded in t around inf 83.7%

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

   if -5.5e9 < b < 3.7000000000000001e130

   1. Initial program 97.4%

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

   3. Taylor expanded in b around 0 90.9%

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

4. Final simplification 90.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.3 \cdot 10^{+146}:\\ \;\;\;\;\left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{elif}\;b \leq -5500000000:\\ \;\;\;\;\left(x + z \cdot \left(1 - y\right)\right) - t \cdot \left(a - b\right)\\ \mathbf{elif}\;b \leq 3.7 \cdot 10^{+130}:\\ \;\;\;\;x - \left(\left(y + -1\right) \cdot z - a \cdot \left(1 - t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(y + t\right) - 2\right) \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 85.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(1 - t\right)\\ \mathbf{if}\;b \leq -1.2 \cdot 10^{-25}:\\ \;\;\;\;\left(x + \left(\left(y + t\right) - 2\right) \cdot b\right) + z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq 3.6 \cdot 10^{+122}:\\ \;\;\;\;x - \left(\left(y + -1\right) \cdot z - t\_1\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(b \cdot \left(t + \left(y + -2\right)\right) + t\_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (- 1.0 t))))
   (if (<= b -1.2e-25)
     (+ (+ x (* (- (+ y t) 2.0) b)) (* z (- 1.0 y)))
     (if (<= b 3.6e+122)
       (- x (- (* (+ y -1.0) z) t_1))
       (+ x (+ (* b (+ t (+ y -2.0))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double tmp;
	if (b <= -1.2e-25) {
		tmp = (x + (((y + t) - 2.0) * b)) + (z * (1.0 - y));
	} else if (b <= 3.6e+122) {
		tmp = x - (((y + -1.0) * z) - t_1);
	} else {
		tmp = x + ((b * (t + (y + -2.0))) + t_1);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (1.0d0 - t)
    if (b <= (-1.2d-25)) then
        tmp = (x + (((y + t) - 2.0d0) * b)) + (z * (1.0d0 - y))
    else if (b <= 3.6d+122) then
        tmp = x - (((y + (-1.0d0)) * z) - t_1)
    else
        tmp = x + ((b * (t + (y + (-2.0d0)))) + t_1)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double tmp;
	if (b <= -1.2e-25) {
		tmp = (x + (((y + t) - 2.0) * b)) + (z * (1.0 - y));
	} else if (b <= 3.6e+122) {
		tmp = x - (((y + -1.0) * z) - t_1);
	} else {
		tmp = x + ((b * (t + (y + -2.0))) + t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (1.0 - t)
	tmp = 0
	if b <= -1.2e-25:
		tmp = (x + (((y + t) - 2.0) * b)) + (z * (1.0 - y))
	elif b <= 3.6e+122:
		tmp = x - (((y + -1.0) * z) - t_1)
	else:
		tmp = x + ((b * (t + (y + -2.0))) + t_1)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(1.0 - t))
	tmp = 0.0
	if (b <= -1.2e-25)
		tmp = Float64(Float64(x + Float64(Float64(Float64(y + t) - 2.0) * b)) + Float64(z * Float64(1.0 - y)));
	elseif (b <= 3.6e+122)
		tmp = Float64(x - Float64(Float64(Float64(y + -1.0) * z) - t_1));
	else
		tmp = Float64(x + Float64(Float64(b * Float64(t + Float64(y + -2.0))) + t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (1.0 - t);
	tmp = 0.0;
	if (b <= -1.2e-25)
		tmp = (x + (((y + t) - 2.0) * b)) + (z * (1.0 - y));
	elseif (b <= 3.6e+122)
		tmp = x - (((y + -1.0) * z) - t_1);
	else
		tmp = x + ((b * (t + (y + -2.0))) + t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.2e-25], N[(N[(x + N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision] + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.6e+122], N[(x - N[(N[(N[(y + -1.0), $MachinePrecision] * z), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(b * N[(t + N[(y + -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.20000000000000005e-25

   1. Initial program 88.1%

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

   3. Taylor expanded in a around 0 83.9%

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

   if -1.20000000000000005e-25 < b < 3.6000000000000003e122

   1. Initial program 97.4%

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

   3. Taylor expanded in b around 0 91.9%

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

   if 3.6000000000000003e122 < b

   1. Initial program 86.1%

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

      1. associate-+l- 86.1%

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

      2. sub-neg 86.1%

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

      3. metadata-eval 86.1%

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

      4. *-commutative 86.1%

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

      5. sub-neg 86.1%

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

      6. metadata-eval 86.1%

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

      7. sub-neg 86.1%

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

      8. metadata-eval 86.1%

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

      9. associate-+r+ 86.1%

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

      10. +-commutative 86.1%

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

      11. associate-+l+ 86.1%

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

   4. Applied egg-rr 86.1%

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

   5. Taylor expanded in z around 0 97.2%

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

      1. associate--l+ 97.2%

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

      2. sub-neg 97.2%

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

      3. metadata-eval 97.2%

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

      4. associate-+r+ 97.2%

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

      5. sub-neg 97.2%

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

      6. metadata-eval 97.2%

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

      7. +-commutative 97.2%

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

   7. Simplified 97.2%

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

4. Final simplification 90.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.2 \cdot 10^{-25}:\\ \;\;\;\;\left(x + \left(\left(y + t\right) - 2\right) \cdot b\right) + z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq 3.6 \cdot 10^{+122}:\\ \;\;\;\;x - \left(\left(y + -1\right) \cdot z - a \cdot \left(1 - t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(b \cdot \left(t + \left(y + -2\right)\right) + a \cdot \left(1 - t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 71.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + z\right) + t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -2 \cdot 10^{+94}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -0.098:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;t \leq 250:\\ \;\;\;\;a + \left(x + b \cdot \left(y - 2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (+ x z) (* t (- b a)))))
   (if (<= t -2e+94)
     t_1
     (if (<= t -0.098)
       (* y (- b z))
       (if (<= t 250.0) (+ a (+ x (* b (- y 2.0)))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + z) + (t * (b - a));
	double tmp;
	if (t <= -2e+94) {
		tmp = t_1;
	} else if (t <= -0.098) {
		tmp = y * (b - z);
	} else if (t <= 250.0) {
		tmp = a + (x + (b * (y - 2.0)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x + z) + (t * (b - a))
    if (t <= (-2d+94)) then
        tmp = t_1
    else if (t <= (-0.098d0)) then
        tmp = y * (b - z)
    else if (t <= 250.0d0) then
        tmp = a + (x + (b * (y - 2.0d0)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + z) + (t * (b - a));
	double tmp;
	if (t <= -2e+94) {
		tmp = t_1;
	} else if (t <= -0.098) {
		tmp = y * (b - z);
	} else if (t <= 250.0) {
		tmp = a + (x + (b * (y - 2.0)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x + z) + (t * (b - a))
	tmp = 0
	if t <= -2e+94:
		tmp = t_1
	elif t <= -0.098:
		tmp = y * (b - z)
	elif t <= 250.0:
		tmp = a + (x + (b * (y - 2.0)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + z) + Float64(t * Float64(b - a)))
	tmp = 0.0
	if (t <= -2e+94)
		tmp = t_1;
	elseif (t <= -0.098)
		tmp = Float64(y * Float64(b - z));
	elseif (t <= 250.0)
		tmp = Float64(a + Float64(x + Float64(b * Float64(y - 2.0))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x + z) + (t * (b - a));
	tmp = 0.0;
	if (t <= -2e+94)
		tmp = t_1;
	elseif (t <= -0.098)
		tmp = y * (b - z);
	elseif (t <= 250.0)
		tmp = a + (x + (b * (y - 2.0)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x + z), $MachinePrecision] + N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2e+94], t$95$1, If[LessEqual[t, -0.098], N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 250.0], N[(a + N[(x + N[(b * N[(y - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2e94 or 250 < t

   1. Initial program 89.6%

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

      1. associate-+l- 89.6%

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

      2. sub-neg 89.6%

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

      3. metadata-eval 89.6%

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

      4. *-commutative 89.6%

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

      5. sub-neg 89.6%

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

      6. metadata-eval 89.6%

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

      7. sub-neg 89.6%

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

      8. metadata-eval 89.6%

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

      9. associate-+r+ 89.6%

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

      10. +-commutative 89.6%

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

      11. associate-+l+ 89.6%

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

   4. Applied egg-rr 89.6%

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

   5. Taylor expanded in t around inf 90.1%

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

   6. Taylor expanded in y around 0 84.1%

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

      1. mul-1-neg 84.1%

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

   8. Simplified 84.1%

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

   if -2e94 < t < -0.098000000000000004

   1. Initial program 72.7%

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

   3. Taylor expanded in y around inf 82.6%

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

   if -0.098000000000000004 < t < 250

   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. Step-by-step derivation

      1. associate-+l- 98.4%

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

      2. sub-neg 98.4%

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

      3. metadata-eval 98.4%

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

      4. *-commutative 98.4%

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

      5. sub-neg 98.4%

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

      6. metadata-eval 98.4%

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

      7. sub-neg 98.4%

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

      8. metadata-eval 98.4%

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

      9. associate-+r+ 98.4%

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

      10. +-commutative 98.4%

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

      11. associate-+l+ 98.4%

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

   4. Applied egg-rr 98.4%

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

   5. Taylor expanded in z around 0 73.1%

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

      1. associate--l+ 73.1%

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

      2. sub-neg 73.1%

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

      3. metadata-eval 73.1%

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

      4. associate-+r+ 73.1%

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

      5. sub-neg 73.1%

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

      6. metadata-eval 73.1%

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

      7. +-commutative 73.1%

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

   7. Simplified 73.1%

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

   8. Taylor expanded in t around 0 72.2%

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

      1. sub-neg 72.2%

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

      2. metadata-eval 72.2%

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

      3. neg-mul-1 72.2%

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

   10. Simplified 72.2%

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

   11. Taylor expanded in x around 0 72.2%

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

4. Final simplification 78.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2 \cdot 10^{+94}:\\ \;\;\;\;\left(x + z\right) + t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq -0.098:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;t \leq 250:\\ \;\;\;\;a + \left(x + b \cdot \left(y - 2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + z\right) + t \cdot \left(b - a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 69.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -2 \cdot 10^{+94}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -0.054:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;t \leq 270:\\ \;\;\;\;a + \left(x + b \cdot \left(y - 2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* t (- b a)))))
   (if (<= t -2e+94)
     t_1
     (if (<= t -0.054)
       (* y (- b z))
       (if (<= t 270.0) (+ a (+ x (* b (- y 2.0)))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (t * (b - a));
	double tmp;
	if (t <= -2e+94) {
		tmp = t_1;
	} else if (t <= -0.054) {
		tmp = y * (b - z);
	} else if (t <= 270.0) {
		tmp = a + (x + (b * (y - 2.0)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (t * (b - a))
    if (t <= (-2d+94)) then
        tmp = t_1
    else if (t <= (-0.054d0)) then
        tmp = y * (b - z)
    else if (t <= 270.0d0) then
        tmp = a + (x + (b * (y - 2.0d0)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (t * (b - a));
	double tmp;
	if (t <= -2e+94) {
		tmp = t_1;
	} else if (t <= -0.054) {
		tmp = y * (b - z);
	} else if (t <= 270.0) {
		tmp = a + (x + (b * (y - 2.0)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (t * (b - a))
	tmp = 0
	if t <= -2e+94:
		tmp = t_1
	elif t <= -0.054:
		tmp = y * (b - z)
	elif t <= 270.0:
		tmp = a + (x + (b * (y - 2.0)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(t * Float64(b - a)))
	tmp = 0.0
	if (t <= -2e+94)
		tmp = t_1;
	elseif (t <= -0.054)
		tmp = Float64(y * Float64(b - z));
	elseif (t <= 270.0)
		tmp = Float64(a + Float64(x + Float64(b * Float64(y - 2.0))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (t * (b - a));
	tmp = 0.0;
	if (t <= -2e+94)
		tmp = t_1;
	elseif (t <= -0.054)
		tmp = y * (b - z);
	elseif (t <= 270.0)
		tmp = a + (x + (b * (y - 2.0)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2e+94], t$95$1, If[LessEqual[t, -0.054], N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 270.0], N[(a + N[(x + N[(b * N[(y - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2e94 or 270 < t

   1. Initial program 89.6%

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

      1. associate-+l- 89.6%

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

      2. sub-neg 89.6%

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

      3. metadata-eval 89.6%

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

      4. *-commutative 89.6%

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

      5. sub-neg 89.6%

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

      6. metadata-eval 89.6%

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

      7. sub-neg 89.6%

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

      8. metadata-eval 89.6%

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

      9. associate-+r+ 89.6%

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

      10. +-commutative 89.6%

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

      11. associate-+l+ 89.6%

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

   4. Applied egg-rr 89.6%

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

   5. Taylor expanded in t around inf 90.1%

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

   6. Taylor expanded in z around 0 76.3%

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

   if -2e94 < t < -0.0539999999999999994

   1. Initial program 72.7%

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

   3. Taylor expanded in y around inf 82.6%

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

   if -0.0539999999999999994 < t < 270

   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. Step-by-step derivation

      1. associate-+l- 98.4%

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

      2. sub-neg 98.4%

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

      3. metadata-eval 98.4%

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

      4. *-commutative 98.4%

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

      5. sub-neg 98.4%

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

      6. metadata-eval 98.4%

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

      7. sub-neg 98.4%

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

      8. metadata-eval 98.4%

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

      9. associate-+r+ 98.4%

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

      10. +-commutative 98.4%

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

      11. associate-+l+ 98.4%

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

   4. Applied egg-rr 98.4%

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

   5. Taylor expanded in z around 0 73.1%

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

      1. associate--l+ 73.1%

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

      2. sub-neg 73.1%

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

      3. metadata-eval 73.1%

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

      4. associate-+r+ 73.1%

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

      5. sub-neg 73.1%

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

      6. metadata-eval 73.1%

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

      7. +-commutative 73.1%

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

   7. Simplified 73.1%

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

   8. Taylor expanded in t around 0 72.2%

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

      1. sub-neg 72.2%

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

      2. metadata-eval 72.2%

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

      3. neg-mul-1 72.2%

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

   10. Simplified 72.2%

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

   11. Taylor expanded in x around 0 72.2%

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

4. Final simplification 74.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2 \cdot 10^{+94}:\\ \;\;\;\;x + t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq -0.054:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;t \leq 270:\\ \;\;\;\;a + \left(x + b \cdot \left(y - 2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \left(b - a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 81.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -4.2 \cdot 10^{+81} \lor \neg \left(b \leq 2.8 \cdot 10^{+126}\right):\\ \;\;\;\;\left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;x - \left(\left(y + -1\right) \cdot z - a \cdot \left(1 - t\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -4.2e+81) (not (<= b 2.8e+126)))
   (* (- (+ y t) 2.0) b)
   (- x (- (* (+ y -1.0) z) (* a (- 1.0 t))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -4.2e+81) || !(b <= 2.8e+126)) {
		tmp = ((y + t) - 2.0) * b;
	} else {
		tmp = x - (((y + -1.0) * z) - (a * (1.0 - t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-4.2d+81)) .or. (.not. (b <= 2.8d+126))) then
        tmp = ((y + t) - 2.0d0) * b
    else
        tmp = x - (((y + (-1.0d0)) * z) - (a * (1.0d0 - t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -4.2e+81) || !(b <= 2.8e+126)) {
		tmp = ((y + t) - 2.0) * b;
	} else {
		tmp = x - (((y + -1.0) * z) - (a * (1.0 - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -4.2e+81) or not (b <= 2.8e+126):
		tmp = ((y + t) - 2.0) * b
	else:
		tmp = x - (((y + -1.0) * z) - (a * (1.0 - t)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -4.2e+81) || !(b <= 2.8e+126))
		tmp = Float64(Float64(Float64(y + t) - 2.0) * b);
	else
		tmp = Float64(x - Float64(Float64(Float64(y + -1.0) * z) - Float64(a * Float64(1.0 - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -4.2e+81) || ~((b <= 2.8e+126)))
		tmp = ((y + t) - 2.0) * b;
	else
		tmp = x - (((y + -1.0) * z) - (a * (1.0 - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -4.2e+81], N[Not[LessEqual[b, 2.8e+126]], $MachinePrecision]], N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision], N[(x - N[(N[(N[(y + -1.0), $MachinePrecision] * z), $MachinePrecision] - N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -4.1999999999999997e81 or 2.80000000000000009e126 < b

   1. Initial program 84.1%

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

   3. Taylor expanded in b around inf 87.7%

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

   if -4.1999999999999997e81 < b < 2.80000000000000009e126

   1. Initial program 97.7%

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

   3. Taylor expanded in b around 0 89.2%

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

4. Final simplification 88.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.2 \cdot 10^{+81} \lor \neg \left(b \leq 2.8 \cdot 10^{+126}\right):\\ \;\;\;\;\left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;x - \left(\left(y + -1\right) \cdot z - a \cdot \left(1 - t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 60.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{if}\;b \leq -1 \cdot 10^{+80}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -1.8 \cdot 10^{-191}:\\ \;\;\;\;x + z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq 3 \cdot 10^{+126}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- (+ y t) 2.0) b)))
   (if (<= b -1e+80)
     t_1
     (if (<= b -1.8e-191)
       (+ x (* z (- 1.0 y)))
       (if (<= b 3e+126) (+ x (* a (- 1.0 t))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((y + t) - 2.0) * b;
	double tmp;
	if (b <= -1e+80) {
		tmp = t_1;
	} else if (b <= -1.8e-191) {
		tmp = x + (z * (1.0 - y));
	} else if (b <= 3e+126) {
		tmp = x + (a * (1.0 - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((y + t) - 2.0d0) * b
    if (b <= (-1d+80)) then
        tmp = t_1
    else if (b <= (-1.8d-191)) then
        tmp = x + (z * (1.0d0 - y))
    else if (b <= 3d+126) then
        tmp = x + (a * (1.0d0 - t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((y + t) - 2.0) * b;
	double tmp;
	if (b <= -1e+80) {
		tmp = t_1;
	} else if (b <= -1.8e-191) {
		tmp = x + (z * (1.0 - y));
	} else if (b <= 3e+126) {
		tmp = x + (a * (1.0 - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((y + t) - 2.0) * b
	tmp = 0
	if b <= -1e+80:
		tmp = t_1
	elif b <= -1.8e-191:
		tmp = x + (z * (1.0 - y))
	elif b <= 3e+126:
		tmp = x + (a * (1.0 - t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(y + t) - 2.0) * b)
	tmp = 0.0
	if (b <= -1e+80)
		tmp = t_1;
	elseif (b <= -1.8e-191)
		tmp = Float64(x + Float64(z * Float64(1.0 - y)));
	elseif (b <= 3e+126)
		tmp = Float64(x + Float64(a * Float64(1.0 - t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((y + t) - 2.0) * b;
	tmp = 0.0;
	if (b <= -1e+80)
		tmp = t_1;
	elseif (b <= -1.8e-191)
		tmp = x + (z * (1.0 - y));
	elseif (b <= 3e+126)
		tmp = x + (a * (1.0 - t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[b, -1e+80], t$95$1, If[LessEqual[b, -1.8e-191], N[(x + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3e+126], N[(x + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -1e80 or 3.0000000000000002e126 < b

   1. Initial program 84.1%

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

   3. Taylor expanded in b around inf 87.7%

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

   if -1e80 < b < -1.8000000000000001e-191

   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. Step-by-step derivation

      1. associate-+l- 98.2%

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

      2. sub-neg 98.2%

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

      3. metadata-eval 98.2%

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

      4. *-commutative 98.2%

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

      5. sub-neg 98.2%

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

      6. metadata-eval 98.2%

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

      7. sub-neg 98.2%

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

      8. metadata-eval 98.2%

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

      9. associate-+r+ 98.2%

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

      10. +-commutative 98.2%

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

      11. associate-+l+ 98.2%

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

   4. Applied egg-rr 98.2%

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

   5. Taylor expanded in t around inf 77.2%

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

   6. Taylor expanded in t around 0 55.7%

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

   if -1.8000000000000001e-191 < b < 3.0000000000000002e126

   1. Initial program 97.4%

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

      1. associate-+l- 97.4%

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

      2. sub-neg 97.4%

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

      3. metadata-eval 97.4%

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

      4. *-commutative 97.4%

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

      5. sub-neg 97.4%

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

      6. metadata-eval 97.4%

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

      7. sub-neg 97.4%

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

      8. metadata-eval 97.4%

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

      9. associate-+r+ 97.4%

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

      10. +-commutative 97.4%

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

      11. associate-+l+ 97.4%

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

   4. Applied egg-rr 97.4%

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

   5. Taylor expanded in z around 0 66.4%

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

      1. associate--l+ 66.5%

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

      2. sub-neg 66.5%

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

      3. metadata-eval 66.5%

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

      4. associate-+r+ 66.5%

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

      5. sub-neg 66.5%

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

      6. metadata-eval 66.5%

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

      7. +-commutative 66.5%

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

   7. Simplified 66.5%

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

   8. Taylor expanded in b around 0 62.5%

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

4. Final simplification 69.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1 \cdot 10^{+80}:\\ \;\;\;\;\left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{elif}\;b \leq -1.8 \cdot 10^{-191}:\\ \;\;\;\;x + z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq 3 \cdot 10^{+126}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(y + t\right) - 2\right) \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 56.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -2 \cdot 10^{+94}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -0.045:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;t \leq 500:\\ \;\;\;\;a + b \cdot \left(y - 2\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (- b a))))
   (if (<= t -2e+94)
     t_1
     (if (<= t -0.045)
       (* y (- b z))
       (if (<= t 500.0) (+ a (* b (- y 2.0))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (b - a);
	double tmp;
	if (t <= -2e+94) {
		tmp = t_1;
	} else if (t <= -0.045) {
		tmp = y * (b - z);
	} else if (t <= 500.0) {
		tmp = a + (b * (y - 2.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (b - a)
    if (t <= (-2d+94)) then
        tmp = t_1
    else if (t <= (-0.045d0)) then
        tmp = y * (b - z)
    else if (t <= 500.0d0) then
        tmp = a + (b * (y - 2.0d0))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (b - a);
	double tmp;
	if (t <= -2e+94) {
		tmp = t_1;
	} else if (t <= -0.045) {
		tmp = y * (b - z);
	} else if (t <= 500.0) {
		tmp = a + (b * (y - 2.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t * (b - a)
	tmp = 0
	if t <= -2e+94:
		tmp = t_1
	elif t <= -0.045:
		tmp = y * (b - z)
	elif t <= 500.0:
		tmp = a + (b * (y - 2.0))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t * Float64(b - a))
	tmp = 0.0
	if (t <= -2e+94)
		tmp = t_1;
	elseif (t <= -0.045)
		tmp = Float64(y * Float64(b - z));
	elseif (t <= 500.0)
		tmp = Float64(a + Float64(b * Float64(y - 2.0)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t * (b - a);
	tmp = 0.0;
	if (t <= -2e+94)
		tmp = t_1;
	elseif (t <= -0.045)
		tmp = y * (b - z);
	elseif (t <= 500.0)
		tmp = a + (b * (y - 2.0));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2e+94], t$95$1, If[LessEqual[t, -0.045], N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 500.0], N[(a + N[(b * N[(y - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2e94 or 500 < t

   1. Initial program 89.6%

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

   3. Taylor expanded in t around inf 68.5%

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

   if -2e94 < t < -0.044999999999999998

   1. Initial program 72.7%

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

   3. Taylor expanded in y around inf 82.6%

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

   if -0.044999999999999998 < t < 500

   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. Step-by-step derivation

      1. associate-+l- 98.4%

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

      2. sub-neg 98.4%

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

      3. metadata-eval 98.4%

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

      4. *-commutative 98.4%

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

      5. sub-neg 98.4%

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

      6. metadata-eval 98.4%

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

      7. sub-neg 98.4%

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

      8. metadata-eval 98.4%

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

      9. associate-+r+ 98.4%

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

      10. +-commutative 98.4%

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

      11. associate-+l+ 98.4%

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

   4. Applied egg-rr 98.4%

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

   5. Taylor expanded in z around 0 73.1%

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

      1. associate--l+ 73.1%

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

      2. sub-neg 73.1%

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

      3. metadata-eval 73.1%

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

      4. associate-+r+ 73.1%

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

      5. sub-neg 73.1%

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

      6. metadata-eval 73.1%

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

      7. +-commutative 73.1%

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

   7. Simplified 73.1%

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

   8. Taylor expanded in t around 0 72.2%

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

      1. sub-neg 72.2%

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

      2. metadata-eval 72.2%

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

      3. neg-mul-1 72.2%

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

   10. Simplified 72.2%

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

   11. Taylor expanded in x around 0 56.9%

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

Alternative 12: 50.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -1.65 \cdot 10^{+96}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.1 \cdot 10^{-73}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;t \leq 4100000000:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (- b a))))
   (if (<= t -1.65e+96)
     t_1
     (if (<= t -1.1e-73) (* y (- b z)) (if (<= t 4100000000.0) (+ 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 <= -1.65e+96) {
		tmp = t_1;
	} else if (t <= -1.1e-73) {
		tmp = y * (b - z);
	} else if (t <= 4100000000.0) {
		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 <= (-1.65d+96)) then
        tmp = t_1
    else if (t <= (-1.1d-73)) then
        tmp = y * (b - z)
    else if (t <= 4100000000.0d0) 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 <= -1.65e+96) {
		tmp = t_1;
	} else if (t <= -1.1e-73) {
		tmp = y * (b - z);
	} else if (t <= 4100000000.0) {
		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 <= -1.65e+96:
		tmp = t_1
	elif t <= -1.1e-73:
		tmp = y * (b - z)
	elif t <= 4100000000.0:
		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 <= -1.65e+96)
		tmp = t_1;
	elseif (t <= -1.1e-73)
		tmp = Float64(y * Float64(b - z));
	elseif (t <= 4100000000.0)
		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 <= -1.65e+96)
		tmp = t_1;
	elseif (t <= -1.1e-73)
		tmp = y * (b - z);
	elseif (t <= 4100000000.0)
		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, -1.65e+96], t$95$1, If[LessEqual[t, -1.1e-73], N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4100000000.0], N[(x + a), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.64999999999999992e96 or 4.1e9 < t

   1. Initial program 89.4%

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

   3. Taylor expanded in t around inf 69.5%

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

   if -1.64999999999999992e96 < t < -1.1e-73

   1. Initial program 87.1%

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

   3. Taylor expanded in y around inf 56.9%

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

   if -1.1e-73 < t < 4.1e9

   1. Initial program 99.1%

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

      1. associate-+l- 99.1%

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

      2. sub-neg 99.1%

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

      3. metadata-eval 99.1%

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

      4. *-commutative 99.1%

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

      5. sub-neg 99.1%

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

      6. metadata-eval 99.1%

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

      7. sub-neg 99.1%

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

      8. metadata-eval 99.1%

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

      9. associate-+r+ 99.1%

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

      10. +-commutative 99.1%

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

      11. associate-+l+ 99.1%

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

   4. Applied egg-rr 99.1%

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

   5. Taylor expanded in z around 0 73.6%

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

      1. associate--l+ 73.6%

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

      2. sub-neg 73.6%

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

      3. metadata-eval 73.6%

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

      4. associate-+r+ 73.6%

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

      5. sub-neg 73.6%

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

      6. metadata-eval 73.6%

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

      7. +-commutative 73.6%

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

   7. Simplified 73.6%

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

   8. Taylor expanded in b around 0 43.2%

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

   9. Taylor expanded in t around 0 42.7%

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

       1. cancel-sign-sub-inv 42.7%

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

       2. metadata-eval 42.7%

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

       3. *-lft-identity 42.7%

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

       4. +-commutative 42.7%

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

   11. Simplified 42.7%

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

4. Final simplification 56.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.65 \cdot 10^{+96}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq -1.1 \cdot 10^{-73}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;t \leq 4100000000:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 49.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -3.3 \cdot 10^{+90}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -8.5 \cdot 10^{-6}:\\ \;\;\;\;z \cdot \left(-y\right)\\ \mathbf{elif}\;t \leq 85000000:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (- b a))))
   (if (<= t -3.3e+90)
     t_1
     (if (<= t -8.5e-6) (* z (- y)) (if (<= t 85000000.0) (+ 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 <= -3.3e+90) {
		tmp = t_1;
	} else if (t <= -8.5e-6) {
		tmp = z * -y;
	} else if (t <= 85000000.0) {
		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 <= (-3.3d+90)) then
        tmp = t_1
    else if (t <= (-8.5d-6)) then
        tmp = z * -y
    else if (t <= 85000000.0d0) 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 <= -3.3e+90) {
		tmp = t_1;
	} else if (t <= -8.5e-6) {
		tmp = z * -y;
	} else if (t <= 85000000.0) {
		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 <= -3.3e+90:
		tmp = t_1
	elif t <= -8.5e-6:
		tmp = z * -y
	elif t <= 85000000.0:
		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 <= -3.3e+90)
		tmp = t_1;
	elseif (t <= -8.5e-6)
		tmp = Float64(z * Float64(-y));
	elseif (t <= 85000000.0)
		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 <= -3.3e+90)
		tmp = t_1;
	elseif (t <= -8.5e-6)
		tmp = z * -y;
	elseif (t <= 85000000.0)
		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, -3.3e+90], t$95$1, If[LessEqual[t, -8.5e-6], N[(z * (-y)), $MachinePrecision], If[LessEqual[t, 85000000.0], N[(x + a), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.30000000000000008e90 or 8.5e7 < t

   1. Initial program 88.6%

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

   3. Taylor expanded in t around inf 69.0%

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

   if -3.30000000000000008e90 < t < -8.4999999999999999e-6

   1. Initial program 81.8%

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

   3. Taylor expanded in z around inf 73.1%

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

   4. Taylor expanded in y around inf 64.7%

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

      1. mul-1-neg 64.7%

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

      2. *-commutative 64.7%

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

      3. distribute-rgt-neg-in 64.7%

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

   6. Simplified 64.7%

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

   if -8.4999999999999999e-6 < t < 8.5e7

   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. Step-by-step derivation

      1. associate-+l- 98.5%

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

      2. sub-neg 98.5%

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

      3. metadata-eval 98.5%

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

      4. *-commutative 98.5%

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

      5. sub-neg 98.5%

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

      6. metadata-eval 98.5%

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

      7. sub-neg 98.5%

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

      8. metadata-eval 98.5%

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

      9. associate-+r+ 98.5%

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

      10. +-commutative 98.5%

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

      11. associate-+l+ 98.5%

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

   4. Applied egg-rr 98.5%

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

   5. Taylor expanded in z around 0 73.3%

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

      1. associate--l+ 73.3%

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

      2. sub-neg 73.3%

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

      3. metadata-eval 73.3%

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

      4. associate-+r+ 73.3%

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

      5. sub-neg 73.3%

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

      6. metadata-eval 73.3%

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

      7. +-commutative 73.3%

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

   7. Simplified 73.3%

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

   8. Taylor expanded in b around 0 42.6%

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

   9. Taylor expanded in t around 0 41.8%

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

       1. cancel-sign-sub-inv 41.8%

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

       2. metadata-eval 41.8%

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

       3. *-lft-identity 41.8%

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

       4. +-commutative 41.8%

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

   11. Simplified 41.8%

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

4. Final simplification 54.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.3 \cdot 10^{+90}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq -8.5 \cdot 10^{-6}:\\ \;\;\;\;z \cdot \left(-y\right)\\ \mathbf{elif}\;t \leq 85000000:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 36.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.2 \cdot 10^{+90}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;t \leq -0.0036:\\ \;\;\;\;z \cdot \left(-y\right)\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{+14}:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -4.2e+90)
   (* t b)
   (if (<= t -0.0036) (* z (- y)) (if (<= t 3.5e+14) (+ x a) (* t b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -4.2e+90) {
		tmp = t * b;
	} else if (t <= -0.0036) {
		tmp = z * -y;
	} else if (t <= 3.5e+14) {
		tmp = x + 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 <= (-4.2d+90)) then
        tmp = t * b
    else if (t <= (-0.0036d0)) then
        tmp = z * -y
    else if (t <= 3.5d+14) then
        tmp = x + 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 <= -4.2e+90) {
		tmp = t * b;
	} else if (t <= -0.0036) {
		tmp = z * -y;
	} else if (t <= 3.5e+14) {
		tmp = x + a;
	} else {
		tmp = t * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -4.2e+90:
		tmp = t * b
	elif t <= -0.0036:
		tmp = z * -y
	elif t <= 3.5e+14:
		tmp = x + a
	else:
		tmp = t * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -4.2e+90)
		tmp = Float64(t * b);
	elseif (t <= -0.0036)
		tmp = Float64(z * Float64(-y));
	elseif (t <= 3.5e+14)
		tmp = Float64(x + 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 <= -4.2e+90)
		tmp = t * b;
	elseif (t <= -0.0036)
		tmp = z * -y;
	elseif (t <= 3.5e+14)
		tmp = x + a;
	else
		tmp = t * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -4.2e+90], N[(t * b), $MachinePrecision], If[LessEqual[t, -0.0036], N[(z * (-y)), $MachinePrecision], If[LessEqual[t, 3.5e+14], N[(x + a), $MachinePrecision], N[(t * b), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.19999999999999961e90 or 3.5e14 < t

   1. Initial program 88.4%

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

   3. Taylor expanded in t around inf 69.6%

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

   4. Taylor expanded in b around inf 35.6%

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

      1. *-commutative 35.6%

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

   6. Simplified 35.6%

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

   if -4.19999999999999961e90 < t < -0.0035999999999999999

   1. Initial program 81.8%

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

   3. Taylor expanded in z around inf 73.1%

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

   4. Taylor expanded in y around inf 64.7%

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

      1. mul-1-neg 64.7%

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

      2. *-commutative 64.7%

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

      3. distribute-rgt-neg-in 64.7%

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

   6. Simplified 64.7%

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

   if -0.0035999999999999999 < t < 3.5e14

   1. Initial program 98.5%

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

      1. associate-+l- 98.5%

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

      2. sub-neg 98.5%

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

      3. metadata-eval 98.5%

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

      4. *-commutative 98.5%

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

      5. sub-neg 98.5%

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

      6. metadata-eval 98.5%

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

      7. sub-neg 98.5%

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

      8. metadata-eval 98.5%

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

      9. associate-+r+ 98.5%

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

      10. +-commutative 98.5%

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

      11. associate-+l+ 98.5%

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

   4. Applied egg-rr 98.5%

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

   5. Taylor expanded in z around 0 73.0%

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

      1. associate--l+ 73.0%

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

      2. sub-neg 73.0%

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

      3. metadata-eval 73.0%

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

      4. associate-+r+ 73.0%

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

      5. sub-neg 73.0%

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

      6. metadata-eval 73.0%

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

      7. +-commutative 73.0%

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

   7. Simplified 73.0%

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

   8. Taylor expanded in b around 0 42.8%

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

   9. Taylor expanded in t around 0 41.3%

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

       1. cancel-sign-sub-inv 41.3%

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

       2. metadata-eval 41.3%

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

       3. *-lft-identity 41.3%

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

       4. +-commutative 41.3%

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

   11. Simplified 41.3%

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

4. Final simplification 39.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.2 \cdot 10^{+90}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;t \leq -0.0036:\\ \;\;\;\;z \cdot \left(-y\right)\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{+14}:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 60.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2.22 \cdot 10^{+80} \lor \neg \left(b \leq 3.1 \cdot 10^{+126}\right):\\ \;\;\;\;\left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -2.22e+80) (not (<= b 3.1e+126)))
   (* (- (+ y t) 2.0) b)
   (+ x (* a (- 1.0 t)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -2.22e+80) || !(b <= 3.1e+126)) {
		tmp = ((y + t) - 2.0) * b;
	} else {
		tmp = x + (a * (1.0 - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-2.22d+80)) .or. (.not. (b <= 3.1d+126))) then
        tmp = ((y + t) - 2.0d0) * b
    else
        tmp = x + (a * (1.0d0 - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -2.22e+80) || !(b <= 3.1e+126)) {
		tmp = ((y + t) - 2.0) * b;
	} else {
		tmp = x + (a * (1.0 - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -2.22e+80) or not (b <= 3.1e+126):
		tmp = ((y + t) - 2.0) * b
	else:
		tmp = x + (a * (1.0 - t))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -2.22e+80) || !(b <= 3.1e+126))
		tmp = Float64(Float64(Float64(y + t) - 2.0) * b);
	else
		tmp = Float64(x + Float64(a * Float64(1.0 - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -2.22e+80) || ~((b <= 3.1e+126)))
		tmp = ((y + t) - 2.0) * b;
	else
		tmp = x + (a * (1.0 - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -2.22e+80], N[Not[LessEqual[b, 3.1e+126]], $MachinePrecision]], N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision], N[(x + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -2.21999999999999992e80 or 3.1e126 < b

   1. Initial program 84.1%

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

   3. Taylor expanded in b around inf 87.7%

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

   if -2.21999999999999992e80 < b < 3.1e126

   1. Initial program 97.7%

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

      1. associate-+l- 97.7%

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

      2. sub-neg 97.7%

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

      3. metadata-eval 97.7%

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

      4. *-commutative 97.7%

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

      5. sub-neg 97.7%

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

      6. metadata-eval 97.7%

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

      7. sub-neg 97.7%

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

      8. metadata-eval 97.7%

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

      9. associate-+r+ 97.7%

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

      10. +-commutative 97.7%

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

      11. associate-+l+ 97.7%

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

   4. Applied egg-rr 97.7%

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

   5. Taylor expanded in z around 0 65.4%

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

      1. associate--l+ 65.4%

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

      2. sub-neg 65.4%

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

      3. metadata-eval 65.4%

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

      4. associate-+r+ 65.4%

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

      5. sub-neg 65.4%

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

      6. metadata-eval 65.4%

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

      7. +-commutative 65.4%

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

   7. Simplified 65.4%

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

   8. Taylor expanded in b around 0 57.8%

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

4. Final simplification 67.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.22 \cdot 10^{+80} \lor \neg \left(b \leq 3.1 \cdot 10^{+126}\right):\\ \;\;\;\;\left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 49.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -4.4 \cdot 10^{-28} \lor \neg \left(b \leq 2.8 \cdot 10^{+126}\right):\\ \;\;\;\;\left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;a - t \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -4.4e-28) (not (<= b 2.8e+126)))
   (* (- (+ y t) 2.0) b)
   (- a (* t a))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -4.4e-28) || !(b <= 2.8e+126)) {
		tmp = ((y + t) - 2.0) * b;
	} else {
		tmp = a - (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 <= (-4.4d-28)) .or. (.not. (b <= 2.8d+126))) then
        tmp = ((y + t) - 2.0d0) * b
    else
        tmp = a - (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 <= -4.4e-28) || !(b <= 2.8e+126)) {
		tmp = ((y + t) - 2.0) * b;
	} else {
		tmp = a - (t * a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -4.4e-28) or not (b <= 2.8e+126):
		tmp = ((y + t) - 2.0) * b
	else:
		tmp = a - (t * a)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -4.4e-28) || !(b <= 2.8e+126))
		tmp = Float64(Float64(Float64(y + t) - 2.0) * b);
	else
		tmp = Float64(a - Float64(t * a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -4.4e-28) || ~((b <= 2.8e+126)))
		tmp = ((y + t) - 2.0) * b;
	else
		tmp = a - (t * a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -4.4e-28], N[Not[LessEqual[b, 2.8e+126]], $MachinePrecision]], N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision], N[(a - N[(t * a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -4.39999999999999992e-28 or 2.80000000000000009e126 < b

   1. Initial program 87.3%

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

   3. Taylor expanded in b around inf 77.0%

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

   if -4.39999999999999992e-28 < b < 2.80000000000000009e126

   1. Initial program 97.4%

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

   3. Taylor expanded in a around inf 45.4%

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

   4. Taylor expanded in t around 0 45.4%

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

      1. associate-*r* 45.4%

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

      2. neg-mul-1 45.4%

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

   6. Simplified 45.4%

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

4. Final simplification 58.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.4 \cdot 10^{-28} \lor \neg \left(b \leq 2.8 \cdot 10^{+126}\right):\\ \;\;\;\;\left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;a - t \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 35.6% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -4.3 \cdot 10^{+53} \lor \neg \left(b \leq 3.6 \cdot 10^{+142}\right):\\ \;\;\;\;t \cdot b\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -4.3e+53) (not (<= b 3.6e+142))) (* t b) (* a (- 1.0 t))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -4.3e+53) || !(b <= 3.6e+142)) {
		tmp = t * b;
	} else {
		tmp = a * (1.0 - t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-4.3d+53)) .or. (.not. (b <= 3.6d+142))) then
        tmp = t * b
    else
        tmp = a * (1.0d0 - t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -4.3e+53) || !(b <= 3.6e+142)) {
		tmp = t * b;
	} else {
		tmp = a * (1.0 - t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -4.3e+53) or not (b <= 3.6e+142):
		tmp = t * b
	else:
		tmp = a * (1.0 - t)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -4.3e+53) || !(b <= 3.6e+142))
		tmp = Float64(t * b);
	else
		tmp = Float64(a * Float64(1.0 - t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -4.3e+53) || ~((b <= 3.6e+142)))
		tmp = t * b;
	else
		tmp = a * (1.0 - t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -4.3e+53], N[Not[LessEqual[b, 3.6e+142]], $MachinePrecision]], N[(t * b), $MachinePrecision], N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -4.2999999999999998e53 or 3.6000000000000001e142 < b

   1. Initial program 84.5%

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

   3. Taylor expanded in t around inf 44.8%

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

   4. Taylor expanded in b around inf 43.6%

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

      1. *-commutative 43.6%

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

   6. Simplified 43.6%

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

   if -4.2999999999999998e53 < b < 3.6000000000000001e142

   1. Initial program 97.7%

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

   3. Taylor expanded in a around inf 43.7%

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

4. Final simplification 43.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.3 \cdot 10^{+53} \lor \neg \left(b \leq 3.6 \cdot 10^{+142}\right):\\ \;\;\;\;t \cdot b\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 33.4% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -3.9 \cdot 10^{+79} \lor \neg \left(b \leq 7.5 \cdot 10^{+122}\right):\\ \;\;\;\;t \cdot b\\ \mathbf{else}:\\ \;\;\;\;x + a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -3.9e+79) (not (<= b 7.5e+122))) (* t b) (+ x a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -3.9e+79) || !(b <= 7.5e+122)) {
		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 ((b <= (-3.9d+79)) .or. (.not. (b <= 7.5d+122))) 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 ((b <= -3.9e+79) || !(b <= 7.5e+122)) {
		tmp = t * b;
	} else {
		tmp = x + a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -3.9e+79) or not (b <= 7.5e+122):
		tmp = t * b
	else:
		tmp = x + a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -3.9e+79) || !(b <= 7.5e+122))
		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 ((b <= -3.9e+79) || ~((b <= 7.5e+122)))
		tmp = t * b;
	else
		tmp = x + a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -3.9e+79], N[Not[LessEqual[b, 7.5e+122]], $MachinePrecision]], N[(t * b), $MachinePrecision], N[(x + a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -3.8999999999999997e79 or 7.5000000000000002e122 < b

   1. Initial program 84.5%

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

   3. Taylor expanded in t around inf 45.9%

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

   4. Taylor expanded in b around inf 42.5%

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

      1. *-commutative 42.5%

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

   6. Simplified 42.5%

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

   if -3.8999999999999997e79 < b < 7.5000000000000002e122

   1. Initial program 97.7%

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

      1. associate-+l- 97.7%

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

      2. sub-neg 97.7%

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

      3. metadata-eval 97.7%

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

      4. *-commutative 97.7%

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

      5. sub-neg 97.7%

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

      6. metadata-eval 97.7%

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

      7. sub-neg 97.7%

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

      8. metadata-eval 97.7%

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

      9. associate-+r+ 97.7%

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

      10. +-commutative 97.7%

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

      11. associate-+l+ 97.7%

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

   4. Applied egg-rr 97.7%

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

   5. Taylor expanded in z around 0 65.6%

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

      1. associate--l+ 65.6%

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

      2. sub-neg 65.6%

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

      3. metadata-eval 65.6%

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

      4. associate-+r+ 65.6%

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

      5. sub-neg 65.6%

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

      6. metadata-eval 65.6%

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

      7. +-commutative 65.6%

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

   7. Simplified 65.6%

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

   8. Taylor expanded in b around 0 57.9%

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

   9. Taylor expanded in t around 0 35.7%

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

       1. cancel-sign-sub-inv 35.7%

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

       2. metadata-eval 35.7%

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

       3. *-lft-identity 35.7%

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

       4. +-commutative 35.7%

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

   11. Simplified 35.7%

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

4. Final simplification 37.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.9 \cdot 10^{+79} \lor \neg \left(b \leq 7.5 \cdot 10^{+122}\right):\\ \;\;\;\;t \cdot b\\ \mathbf{else}:\\ \;\;\;\;x + a\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 27.5% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -0.041 \lor \neg \left(t \leq 1.05\right):\\ \;\;\;\;t \cdot b\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -0.041) (not (<= t 1.05))) (* t b) a))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -0.041) || !(t <= 1.05)) {
		tmp = t * b;
	} else {
		tmp = a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-0.041d0)) .or. (.not. (t <= 1.05d0))) then
        tmp = t * b
    else
        tmp = a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -0.041) || !(t <= 1.05)) {
		tmp = t * b;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -0.041) or not (t <= 1.05):
		tmp = t * b
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -0.041) || !(t <= 1.05))
		tmp = Float64(t * b);
	else
		tmp = a;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -0.041) || ~((t <= 1.05)))
		tmp = t * b;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -0.041], N[Not[LessEqual[t, 1.05]], $MachinePrecision]], N[(t * b), $MachinePrecision], a]

Derivation

1. Split input into 2 regimes

2. if t < -0.0410000000000000017 or 1.05000000000000004 < t

   1. Initial program 88.3%

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

   3. Taylor expanded in t around inf 62.8%

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

   4. Taylor expanded in b around inf 31.8%

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

      1. *-commutative 31.8%

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

   6. Simplified 31.8%

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

   if -0.0410000000000000017 < t < 1.05000000000000004

   1. Initial program 98.4%

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

   3. Taylor expanded in a around inf 27.4%

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

   4. Taylor expanded in t around 0 26.8%

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

4. Final simplification 29.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -0.041 \lor \neg \left(t \leq 1.05\right):\\ \;\;\;\;t \cdot b\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 19.3% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9 \cdot 10^{+196}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 3 \cdot 10^{-25}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -9e+196) x (if (<= x 3e-25) a x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -9e+196) {
		tmp = x;
	} else if (x <= 3e-25) {
		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 <= (-9d+196)) then
        tmp = x
    else if (x <= 3d-25) 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 <= -9e+196) {
		tmp = x;
	} else if (x <= 3e-25) {
		tmp = a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -9e+196:
		tmp = x
	elif x <= 3e-25:
		tmp = a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -9e+196)
		tmp = x;
	elseif (x <= 3e-25)
		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 <= -9e+196)
		tmp = x;
	elseif (x <= 3e-25)
		tmp = a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -9e+196], x, If[LessEqual[x, 3e-25], a, x]]

Derivation

1. Split input into 2 regimes

2. if x < -8.99999999999999956e196 or 2.9999999999999998e-25 < x

   1. Initial program 93.9%

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

   3. Taylor expanded in x around inf 32.4%

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

   if -8.99999999999999956e196 < x < 2.9999999999999998e-25

   1. Initial program 93.1%

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

   3. Taylor expanded in a around inf 36.3%

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

   4. Taylor expanded in t around 0 18.2%

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

Alternative 21: 11.4% accurate, 21.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 93.3%

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

3. Taylor expanded in a around inf 32.3%

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

4. Taylor expanded in t around 0 14.5%

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

Reproduce

herbie shell --seed 2024180 
(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)))