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

Percentage Accurate: 95.4% → 97.9%

Time: 11.1s

Alternatives: 21

Speedup: 0.5×

• 35.8% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 95.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.9% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. fma-define 100.0%

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

      3. associate--l+ 100.0%

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

      4. sub-neg 100.0%

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

      5. metadata-eval 100.0%

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

      6. sub-neg 100.0%

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

      7. associate-+l- 100.0%

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

      8. fmm-def 100.0%

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

      9. sub-neg 100.0%

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

      10. metadata-eval 100.0%

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

      11. remove-double-neg 100.0%

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

      12. sub-neg 100.0%

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

      13. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in t around inf 90.9%

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

4. Final simplification 99.6%

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

Alternative 2: 97.9% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(x + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(t + -1.0), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[(t * N[(b - a), $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 t around inf 90.9%

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

4. Final simplification 99.6%

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

Alternative 3: 87.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(1 - y\right)\\ \mathbf{if}\;b \leq -1.7 \cdot 10^{+14} \lor \neg \left(b \leq 1.35 \cdot 10^{+67}\right):\\ \;\;\;\;b \cdot \left(\left(t + \left(y + \left(\frac{x}{b} + \frac{t\_1}{b}\right)\right)\right) - 2\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(t\_1 - \left(t + -1\right) \cdot a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (- 1.0 y))))
   (if (or (<= b -1.7e+14) (not (<= b 1.35e+67)))
     (* b (- (+ t (+ y (+ (/ x b) (/ t_1 b)))) 2.0))
     (+ x (- t_1 (* (+ t -1.0) a))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (1.0 - y);
	double tmp;
	if ((b <= -1.7e+14) || !(b <= 1.35e+67)) {
		tmp = b * ((t + (y + ((x / b) + (t_1 / b)))) - 2.0);
	} else {
		tmp = x + (t_1 - ((t + -1.0) * a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z * (1.0d0 - y)
    if ((b <= (-1.7d+14)) .or. (.not. (b <= 1.35d+67))) then
        tmp = b * ((t + (y + ((x / b) + (t_1 / b)))) - 2.0d0)
    else
        tmp = x + (t_1 - ((t + (-1.0d0)) * a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (1.0 - y);
	double tmp;
	if ((b <= -1.7e+14) || !(b <= 1.35e+67)) {
		tmp = b * ((t + (y + ((x / b) + (t_1 / b)))) - 2.0);
	} else {
		tmp = x + (t_1 - ((t + -1.0) * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * (1.0 - y)
	tmp = 0
	if (b <= -1.7e+14) or not (b <= 1.35e+67):
		tmp = b * ((t + (y + ((x / b) + (t_1 / b)))) - 2.0)
	else:
		tmp = x + (t_1 - ((t + -1.0) * a))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(1.0 - y))
	tmp = 0.0
	if ((b <= -1.7e+14) || !(b <= 1.35e+67))
		tmp = Float64(b * Float64(Float64(t + Float64(y + Float64(Float64(x / b) + Float64(t_1 / b)))) - 2.0));
	else
		tmp = Float64(x + Float64(t_1 - Float64(Float64(t + -1.0) * a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * (1.0 - y);
	tmp = 0.0;
	if ((b <= -1.7e+14) || ~((b <= 1.35e+67)))
		tmp = b * ((t + (y + ((x / b) + (t_1 / b)))) - 2.0);
	else
		tmp = x + (t_1 - ((t + -1.0) * a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[b, -1.7e+14], N[Not[LessEqual[b, 1.35e+67]], $MachinePrecision]], N[(b * N[(N[(t + N[(y + N[(N[(x / b), $MachinePrecision] + N[(t$95$1 / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision], N[(x + N[(t$95$1 - N[(N[(t + -1.0), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if b < -1.7e14 or 1.35e67 < b

   1. Initial program 90.1%

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

   3. Taylor expanded in a around 0 88.2%

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

      1. sub-neg 88.2%

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

      2. metadata-eval 88.2%

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

      3. *-commutative 88.2%

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

      4. cancel-sign-sub-inv 88.2%

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

      5. +-commutative 88.2%

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

      6. distribute-neg-in 88.2%

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

      7. metadata-eval 88.2%

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

      8. *-commutative 88.2%

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

      9. sub-neg 88.2%

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

      10. +-commutative 88.2%

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

      11. sub-neg 88.2%

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

      12. fma-define 88.2%

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

      13. sub-neg 88.2%

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

   5. Simplified 88.2%

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

   6. Taylor expanded in b around inf 88.2%

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

   if -1.7e14 < b < 1.35e67

   1. Initial program 99.3%

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

   3. Taylor expanded in b around 0 91.2%

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

4. Final simplification 90.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.7 \cdot 10^{+14} \lor \neg \left(b \leq 1.35 \cdot 10^{+67}\right):\\ \;\;\;\;b \cdot \left(\left(t + \left(y + \left(\frac{x}{b} + \frac{z \cdot \left(1 - y\right)}{b}\right)\right)\right) - 2\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(z \cdot \left(1 - y\right) - \left(t + -1\right) \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 86.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(1 - y\right)\\ \mathbf{if}\;b \leq -2.8 \cdot 10^{+14} \lor \neg \left(b \leq 4.2 \cdot 10^{+68}\right):\\ \;\;\;\;\left(x + \left(\left(y + t\right) - 2\right) \cdot b\right) + t\_1\\ \mathbf{else}:\\ \;\;\;\;x + \left(t\_1 - \left(t + -1\right) \cdot a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (- 1.0 y))))
   (if (or (<= b -2.8e+14) (not (<= b 4.2e+68)))
     (+ (+ x (* (- (+ y t) 2.0) b)) t_1)
     (+ x (- t_1 (* (+ t -1.0) a))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (1.0 - y);
	double tmp;
	if ((b <= -2.8e+14) || !(b <= 4.2e+68)) {
		tmp = (x + (((y + t) - 2.0) * b)) + t_1;
	} else {
		tmp = x + (t_1 - ((t + -1.0) * a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z * (1.0d0 - y)
    if ((b <= (-2.8d+14)) .or. (.not. (b <= 4.2d+68))) then
        tmp = (x + (((y + t) - 2.0d0) * b)) + t_1
    else
        tmp = x + (t_1 - ((t + (-1.0d0)) * a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (1.0 - y);
	double tmp;
	if ((b <= -2.8e+14) || !(b <= 4.2e+68)) {
		tmp = (x + (((y + t) - 2.0) * b)) + t_1;
	} else {
		tmp = x + (t_1 - ((t + -1.0) * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * (1.0 - y)
	tmp = 0
	if (b <= -2.8e+14) or not (b <= 4.2e+68):
		tmp = (x + (((y + t) - 2.0) * b)) + t_1
	else:
		tmp = x + (t_1 - ((t + -1.0) * a))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(1.0 - y))
	tmp = 0.0
	if ((b <= -2.8e+14) || !(b <= 4.2e+68))
		tmp = Float64(Float64(x + Float64(Float64(Float64(y + t) - 2.0) * b)) + t_1);
	else
		tmp = Float64(x + Float64(t_1 - Float64(Float64(t + -1.0) * a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * (1.0 - y);
	tmp = 0.0;
	if ((b <= -2.8e+14) || ~((b <= 4.2e+68)))
		tmp = (x + (((y + t) - 2.0) * b)) + t_1;
	else
		tmp = x + (t_1 - ((t + -1.0) * a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[b, -2.8e+14], N[Not[LessEqual[b, 4.2e+68]], $MachinePrecision]], N[(N[(x + N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], N[(x + N[(t$95$1 - N[(N[(t + -1.0), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if b < -2.8e14 or 4.20000000000000002e68 < b

   1. Initial program 90.1%

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

   3. Taylor expanded in a around 0 88.2%

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

   if -2.8e14 < b < 4.20000000000000002e68

   1. Initial program 99.3%

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

   3. Taylor expanded in b around 0 91.2%

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

4. Final simplification 90.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.8 \cdot 10^{+14} \lor \neg \left(b \leq 4.2 \cdot 10^{+68}\right):\\ \;\;\;\;\left(x + \left(\left(y + t\right) - 2\right) \cdot b\right) + z \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(z \cdot \left(1 - y\right) - \left(t + -1\right) \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 27.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.95 \cdot 10^{-10}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;t \leq -9.2 \cdot 10^{-246}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq 86000000000:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{+177}:\\ \;\;\;\;t \cdot \left(-a\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -1.95e-10)
   (* t b)
   (if (<= t -9.2e-246)
     a
     (if (<= t 86000000000.0) x (if (<= t 1.9e+177) (* t (- a)) (* t b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1.95e-10) {
		tmp = t * b;
	} else if (t <= -9.2e-246) {
		tmp = a;
	} else if (t <= 86000000000.0) {
		tmp = x;
	} else if (t <= 1.9e+177) {
		tmp = t * -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 <= (-1.95d-10)) then
        tmp = t * b
    else if (t <= (-9.2d-246)) then
        tmp = a
    else if (t <= 86000000000.0d0) then
        tmp = x
    else if (t <= 1.9d+177) then
        tmp = t * -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 <= -1.95e-10) {
		tmp = t * b;
	} else if (t <= -9.2e-246) {
		tmp = a;
	} else if (t <= 86000000000.0) {
		tmp = x;
	} else if (t <= 1.9e+177) {
		tmp = t * -a;
	} else {
		tmp = t * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -1.95e-10:
		tmp = t * b
	elif t <= -9.2e-246:
		tmp = a
	elif t <= 86000000000.0:
		tmp = x
	elif t <= 1.9e+177:
		tmp = t * -a
	else:
		tmp = t * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -1.95e-10)
		tmp = Float64(t * b);
	elseif (t <= -9.2e-246)
		tmp = a;
	elseif (t <= 86000000000.0)
		tmp = x;
	elseif (t <= 1.9e+177)
		tmp = Float64(t * Float64(-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 <= -1.95e-10)
		tmp = t * b;
	elseif (t <= -9.2e-246)
		tmp = a;
	elseif (t <= 86000000000.0)
		tmp = x;
	elseif (t <= 1.9e+177)
		tmp = t * -a;
	else
		tmp = t * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -1.95e-10], N[(t * b), $MachinePrecision], If[LessEqual[t, -9.2e-246], a, If[LessEqual[t, 86000000000.0], x, If[LessEqual[t, 1.9e+177], N[(t * (-a)), $MachinePrecision], N[(t * b), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.95e-10 or 1.8999999999999999e177 < t

   1. Initial program 92.1%

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

   3. Taylor expanded in t around inf 69.6%

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

   4. Taylor expanded in b around inf 42.4%

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

   if -1.95e-10 < t < -9.199999999999999e-246

   1. Initial program 100.0%

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

   3. Taylor expanded in a around inf 34.4%

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

   4. Taylor expanded in t around 0 34.4%

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

   if -9.199999999999999e-246 < t < 8.6e10

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 26.0%

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

   if 8.6e10 < t < 1.8999999999999999e177

   1. Initial program 89.9%

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

   3. Taylor expanded in t around inf 52.0%

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

   4. Taylor expanded in b around 0 34.3%

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

      1. mul-1-neg 34.3%

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

      2. *-commutative 34.3%

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

      3. distribute-rgt-neg-in 34.3%

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

   6. Simplified 34.3%

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

Alternative 6: 60.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot b + z \cdot \left(1 - y\right)\\ \mathbf{if}\;z \leq -9 \cdot 10^{+39}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{-308}:\\ \;\;\;\;x - \left(t + -1\right) \cdot a\\ \mathbf{elif}\;z \leq 2150000000000:\\ \;\;\;\;x + \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (* t b) (* z (- 1.0 y)))))
   (if (<= z -9e+39)
     t_1
     (if (<= z -7.5e-308)
       (- x (* (+ t -1.0) a))
       (if (<= z 2150000000000.0) (+ x (* (- (+ y t) 2.0) b)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t * b) + (z * (1.0 - y));
	double tmp;
	if (z <= -9e+39) {
		tmp = t_1;
	} else if (z <= -7.5e-308) {
		tmp = x - ((t + -1.0) * a);
	} else if (z <= 2150000000000.0) {
		tmp = x + (((y + t) - 2.0) * b);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (t * b) + (z * (1.0d0 - y))
    if (z <= (-9d+39)) then
        tmp = t_1
    else if (z <= (-7.5d-308)) then
        tmp = x - ((t + (-1.0d0)) * a)
    else if (z <= 2150000000000.0d0) then
        tmp = x + (((y + t) - 2.0d0) * b)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t * b) + (z * (1.0 - y));
	double tmp;
	if (z <= -9e+39) {
		tmp = t_1;
	} else if (z <= -7.5e-308) {
		tmp = x - ((t + -1.0) * a);
	} else if (z <= 2150000000000.0) {
		tmp = x + (((y + t) - 2.0) * b);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (t * b) + (z * (1.0 - y))
	tmp = 0
	if z <= -9e+39:
		tmp = t_1
	elif z <= -7.5e-308:
		tmp = x - ((t + -1.0) * a)
	elif z <= 2150000000000.0:
		tmp = x + (((y + t) - 2.0) * b)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t * b) + Float64(z * Float64(1.0 - y)))
	tmp = 0.0
	if (z <= -9e+39)
		tmp = t_1;
	elseif (z <= -7.5e-308)
		tmp = Float64(x - Float64(Float64(t + -1.0) * a));
	elseif (z <= 2150000000000.0)
		tmp = Float64(x + Float64(Float64(Float64(y + t) - 2.0) * b));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (t * b) + (z * (1.0 - y));
	tmp = 0.0;
	if (z <= -9e+39)
		tmp = t_1;
	elseif (z <= -7.5e-308)
		tmp = x - ((t + -1.0) * a);
	elseif (z <= 2150000000000.0)
		tmp = x + (((y + t) - 2.0) * b);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t * b), $MachinePrecision] + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -9e+39], t$95$1, If[LessEqual[z, -7.5e-308], N[(x - N[(N[(t + -1.0), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2150000000000.0], N[(x + N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.99999999999999991e39 or 2.15e12 < z

   1. Initial program 93.8%

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

   3. Taylor expanded in a around 0 82.2%

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

      1. sub-neg 82.2%

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

      2. metadata-eval 82.2%

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

      3. *-commutative 82.2%

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

      4. cancel-sign-sub-inv 82.2%

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

      5. +-commutative 82.2%

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

      6. distribute-neg-in 82.2%

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

      7. metadata-eval 82.2%

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

      8. *-commutative 82.2%

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

      9. sub-neg 82.2%

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

      10. +-commutative 82.2%

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

      11. sub-neg 82.2%

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

      12. fma-define 82.2%

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

      13. sub-neg 82.2%

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

   5. Simplified 82.2%

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

   6. Taylor expanded in z around inf 76.7%

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

   7. Taylor expanded in t around inf 75.5%

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

   if -8.99999999999999991e39 < z < -7.4999999999999998e-308

   1. Initial program 94.8%

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

   3. Taylor expanded in b around 0 67.7%

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

   4. Taylor expanded in a around inf 61.8%

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

   if -7.4999999999999998e-308 < z < 2.15e12

   1. Initial program 100.0%

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

   3. Taylor expanded in a around 0 74.2%

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

      1. sub-neg 74.2%

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

      2. metadata-eval 74.2%

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

      3. *-commutative 74.2%

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

      4. cancel-sign-sub-inv 74.2%

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

      5. +-commutative 74.2%

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

      6. distribute-neg-in 74.2%

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

      7. metadata-eval 74.2%

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

      8. *-commutative 74.2%

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

      9. sub-neg 74.2%

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

      10. +-commutative 74.2%

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

      11. sub-neg 74.2%

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

      12. fma-define 74.2%

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

      13. sub-neg 74.2%

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

   5. Simplified 74.2%

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

   6. Taylor expanded in z around 0 61.1%

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

4. Final simplification 67.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{+39}:\\ \;\;\;\;t \cdot b + z \cdot \left(1 - y\right)\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{-308}:\\ \;\;\;\;x - \left(t + -1\right) \cdot a\\ \mathbf{elif}\;z \leq 2150000000000:\\ \;\;\;\;x + \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;t \cdot b + z \cdot \left(1 - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 83.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(1 - y\right)\\ \mathbf{if}\;b \leq -9.5 \cdot 10^{+107} \lor \neg \left(b \leq 1.35 \cdot 10^{+67}\right):\\ \;\;\;\;\left(\left(y + t\right) - 2\right) \cdot b + t\_1\\ \mathbf{else}:\\ \;\;\;\;x + \left(t\_1 - \left(t + -1\right) \cdot a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (- 1.0 y))))
   (if (or (<= b -9.5e+107) (not (<= b 1.35e+67)))
     (+ (* (- (+ y t) 2.0) b) t_1)
     (+ x (- t_1 (* (+ t -1.0) a))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (1.0 - y);
	double tmp;
	if ((b <= -9.5e+107) || !(b <= 1.35e+67)) {
		tmp = (((y + t) - 2.0) * b) + t_1;
	} else {
		tmp = x + (t_1 - ((t + -1.0) * a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z * (1.0d0 - y)
    if ((b <= (-9.5d+107)) .or. (.not. (b <= 1.35d+67))) then
        tmp = (((y + t) - 2.0d0) * b) + t_1
    else
        tmp = x + (t_1 - ((t + (-1.0d0)) * a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (1.0 - y);
	double tmp;
	if ((b <= -9.5e+107) || !(b <= 1.35e+67)) {
		tmp = (((y + t) - 2.0) * b) + t_1;
	} else {
		tmp = x + (t_1 - ((t + -1.0) * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * (1.0 - y)
	tmp = 0
	if (b <= -9.5e+107) or not (b <= 1.35e+67):
		tmp = (((y + t) - 2.0) * b) + t_1
	else:
		tmp = x + (t_1 - ((t + -1.0) * a))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(1.0 - y))
	tmp = 0.0
	if ((b <= -9.5e+107) || !(b <= 1.35e+67))
		tmp = Float64(Float64(Float64(Float64(y + t) - 2.0) * b) + t_1);
	else
		tmp = Float64(x + Float64(t_1 - Float64(Float64(t + -1.0) * a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * (1.0 - y);
	tmp = 0.0;
	if ((b <= -9.5e+107) || ~((b <= 1.35e+67)))
		tmp = (((y + t) - 2.0) * b) + t_1;
	else
		tmp = x + (t_1 - ((t + -1.0) * a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[b, -9.5e+107], N[Not[LessEqual[b, 1.35e+67]], $MachinePrecision]], N[(N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision] + t$95$1), $MachinePrecision], N[(x + N[(t$95$1 - N[(N[(t + -1.0), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if b < -9.50000000000000019e107 or 1.35e67 < b

   1. Initial program 90.6%

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

   3. Taylor expanded in a around 0 90.7%

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

      1. sub-neg 90.7%

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

      2. metadata-eval 90.7%

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

      3. *-commutative 90.7%

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

      4. cancel-sign-sub-inv 90.7%

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

      5. +-commutative 90.7%

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

      6. distribute-neg-in 90.7%

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

      7. metadata-eval 90.7%

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

      8. *-commutative 90.7%

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

      9. sub-neg 90.7%

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

      10. +-commutative 90.7%

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

      11. sub-neg 90.7%

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

      12. fma-define 90.7%

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

      13. sub-neg 90.7%

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

   5. Simplified 90.7%

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

   6. Taylor expanded in z around inf 86.4%

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

   if -9.50000000000000019e107 < b < 1.35e67

   1. Initial program 98.2%

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

   3. Taylor expanded in b around 0 88.6%

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

4. Final simplification 87.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -9.5 \cdot 10^{+107} \lor \neg \left(b \leq 1.35 \cdot 10^{+67}\right):\\ \;\;\;\;\left(\left(y + t\right) - 2\right) \cdot b + z \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(z \cdot \left(1 - y\right) - \left(t + -1\right) \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 76.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(1 - y\right)\\ \mathbf{if}\;b \leq -3800 \lor \neg \left(b \leq 2.6 \cdot 10^{+46}\right):\\ \;\;\;\;\left(\left(y + t\right) - 2\right) \cdot b + t\_1\\ \mathbf{else}:\\ \;\;\;\;x + \left(t\_1 - t \cdot a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (- 1.0 y))))
   (if (or (<= b -3800.0) (not (<= b 2.6e+46)))
     (+ (* (- (+ y t) 2.0) b) t_1)
     (+ x (- t_1 (* t a))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (1.0 - y);
	double tmp;
	if ((b <= -3800.0) || !(b <= 2.6e+46)) {
		tmp = (((y + t) - 2.0) * b) + t_1;
	} else {
		tmp = x + (t_1 - (t * a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z * (1.0d0 - y)
    if ((b <= (-3800.0d0)) .or. (.not. (b <= 2.6d+46))) then
        tmp = (((y + t) - 2.0d0) * b) + t_1
    else
        tmp = x + (t_1 - (t * a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (1.0 - y);
	double tmp;
	if ((b <= -3800.0) || !(b <= 2.6e+46)) {
		tmp = (((y + t) - 2.0) * b) + t_1;
	} else {
		tmp = x + (t_1 - (t * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * (1.0 - y)
	tmp = 0
	if (b <= -3800.0) or not (b <= 2.6e+46):
		tmp = (((y + t) - 2.0) * b) + t_1
	else:
		tmp = x + (t_1 - (t * a))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(1.0 - y))
	tmp = 0.0
	if ((b <= -3800.0) || !(b <= 2.6e+46))
		tmp = Float64(Float64(Float64(Float64(y + t) - 2.0) * b) + t_1);
	else
		tmp = Float64(x + Float64(t_1 - Float64(t * a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * (1.0 - y);
	tmp = 0.0;
	if ((b <= -3800.0) || ~((b <= 2.6e+46)))
		tmp = (((y + t) - 2.0) * b) + t_1;
	else
		tmp = x + (t_1 - (t * a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[b, -3800.0], N[Not[LessEqual[b, 2.6e+46]], $MachinePrecision]], N[(N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision] + t$95$1), $MachinePrecision], N[(x + N[(t$95$1 - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if b < -3800 or 2.60000000000000013e46 < b

   1. Initial program 90.5%

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

   3. Taylor expanded in a around 0 86.8%

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

      1. sub-neg 86.8%

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

      2. metadata-eval 86.8%

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

      3. *-commutative 86.8%

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

      4. cancel-sign-sub-inv 86.8%

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

      5. +-commutative 86.8%

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

      6. distribute-neg-in 86.8%

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

      7. metadata-eval 86.8%

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

      8. *-commutative 86.8%

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

      9. sub-neg 86.8%

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

      10. +-commutative 86.8%

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

      11. sub-neg 86.8%

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

      12. fma-define 86.8%

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

      13. sub-neg 86.8%

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

   5. Simplified 86.8%

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

   6. Taylor expanded in z around inf 81.5%

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

   if -3800 < b < 2.60000000000000013e46

   1. Initial program 99.3%

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

   3. Taylor expanded in b around 0 91.0%

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

   4. Taylor expanded in t around inf 76.8%

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

4. Final simplification 78.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3800 \lor \neg \left(b \leq 2.6 \cdot 10^{+46}\right):\\ \;\;\;\;\left(\left(y + t\right) - 2\right) \cdot b + z \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(z \cdot \left(1 - y\right) - t \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 60.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{if}\;b \leq -9.5 \cdot 10^{+107}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 4.6 \cdot 10^{-20}:\\ \;\;\;\;x - \left(t + -1\right) \cdot a\\ \mathbf{elif}\;b \leq 5 \cdot 10^{+73}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- (+ y t) 2.0) b)))
   (if (<= b -9.5e+107)
     t_1
     (if (<= b 4.6e-20)
       (- x (* (+ t -1.0) a))
       (if (<= b 5e+73) (* z (- 1.0 y)) 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 <= -9.5e+107) {
		tmp = t_1;
	} else if (b <= 4.6e-20) {
		tmp = x - ((t + -1.0) * a);
	} else if (b <= 5e+73) {
		tmp = z * (1.0 - y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((y + t) - 2.0d0) * b
    if (b <= (-9.5d+107)) then
        tmp = t_1
    else if (b <= 4.6d-20) then
        tmp = x - ((t + (-1.0d0)) * a)
    else if (b <= 5d+73) then
        tmp = z * (1.0d0 - y)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((y + t) - 2.0) * b;
	double tmp;
	if (b <= -9.5e+107) {
		tmp = t_1;
	} else if (b <= 4.6e-20) {
		tmp = x - ((t + -1.0) * a);
	} else if (b <= 5e+73) {
		tmp = z * (1.0 - y);
	} 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 <= -9.5e+107:
		tmp = t_1
	elif b <= 4.6e-20:
		tmp = x - ((t + -1.0) * a)
	elif b <= 5e+73:
		tmp = z * (1.0 - y)
	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 <= -9.5e+107)
		tmp = t_1;
	elseif (b <= 4.6e-20)
		tmp = Float64(x - Float64(Float64(t + -1.0) * a));
	elseif (b <= 5e+73)
		tmp = Float64(z * Float64(1.0 - y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((y + t) - 2.0) * b;
	tmp = 0.0;
	if (b <= -9.5e+107)
		tmp = t_1;
	elseif (b <= 4.6e-20)
		tmp = x - ((t + -1.0) * a);
	elseif (b <= 5e+73)
		tmp = z * (1.0 - y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[b, -9.5e+107], t$95$1, If[LessEqual[b, 4.6e-20], N[(x - N[(N[(t + -1.0), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 5e+73], N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -9.50000000000000019e107 or 4.99999999999999976e73 < b

   1. Initial program 90.5%

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

   3. Taylor expanded in b around inf 78.3%

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

   if -9.50000000000000019e107 < b < 4.5999999999999998e-20

   1. Initial program 98.6%

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

   3. Taylor expanded in b around 0 89.5%

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

   4. Taylor expanded in a around inf 56.3%

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

   if 4.5999999999999998e-20 < b < 4.99999999999999976e73

   1. Initial program 95.7%

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

   3. Taylor expanded in z around inf 51.8%

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

4. Final simplification 63.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -9.5 \cdot 10^{+107}:\\ \;\;\;\;\left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{elif}\;b \leq 4.6 \cdot 10^{-20}:\\ \;\;\;\;x - \left(t + -1\right) \cdot a\\ \mathbf{elif}\;b \leq 5 \cdot 10^{+73}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(y + t\right) - 2\right) \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 56.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(b - z\right)\\ \mathbf{if}\;y \leq -125000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{-50}:\\ \;\;\;\;z + b \cdot \left(t - 2\right)\\ \mathbf{elif}\;y \leq 600000:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (- b z))))
   (if (<= y -125000000000.0)
     t_1
     (if (<= y 2.8e-50)
       (+ z (* b (- t 2.0)))
       (if (<= y 600000.0) (* 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 * (b - z);
	double tmp;
	if (y <= -125000000000.0) {
		tmp = t_1;
	} else if (y <= 2.8e-50) {
		tmp = z + (b * (t - 2.0));
	} else if (y <= 600000.0) {
		tmp = a * (1.0 - t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (b - z)
    if (y <= (-125000000000.0d0)) then
        tmp = t_1
    else if (y <= 2.8d-50) then
        tmp = z + (b * (t - 2.0d0))
    else if (y <= 600000.0d0) then
        tmp = a * (1.0d0 - t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (b - z);
	double tmp;
	if (y <= -125000000000.0) {
		tmp = t_1;
	} else if (y <= 2.8e-50) {
		tmp = z + (b * (t - 2.0));
	} else if (y <= 600000.0) {
		tmp = a * (1.0 - t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y * (b - z)
	tmp = 0
	if y <= -125000000000.0:
		tmp = t_1
	elif y <= 2.8e-50:
		tmp = z + (b * (t - 2.0))
	elif y <= 600000.0:
		tmp = a * (1.0 - t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y * Float64(b - z))
	tmp = 0.0
	if (y <= -125000000000.0)
		tmp = t_1;
	elseif (y <= 2.8e-50)
		tmp = Float64(z + Float64(b * Float64(t - 2.0)));
	elseif (y <= 600000.0)
		tmp = Float64(a * Float64(1.0 - t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y * (b - z);
	tmp = 0.0;
	if (y <= -125000000000.0)
		tmp = t_1;
	elseif (y <= 2.8e-50)
		tmp = z + (b * (t - 2.0));
	elseif (y <= 600000.0)
		tmp = a * (1.0 - t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -125000000000.0], t$95$1, If[LessEqual[y, 2.8e-50], N[(z + N[(b * N[(t - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 600000.0], N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.25e11 or 6e5 < y

   1. Initial program 92.7%

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

   3. Taylor expanded in y around inf 60.6%

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

   if -1.25e11 < y < 2.7999999999999998e-50

   1. Initial program 99.0%

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

   3. Taylor expanded in a around 0 70.7%

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

      1. sub-neg 70.7%

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

      2. metadata-eval 70.7%

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

      3. *-commutative 70.7%

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

      4. cancel-sign-sub-inv 70.7%

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

      5. +-commutative 70.7%

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

      6. distribute-neg-in 70.7%

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

      7. metadata-eval 70.7%

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

      8. *-commutative 70.7%

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

      9. sub-neg 70.7%

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

      10. +-commutative 70.7%

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

      11. sub-neg 70.7%

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

      12. fma-define 70.7%

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

      13. sub-neg 70.7%

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

   5. Simplified 70.7%

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

   6. Taylor expanded in z around inf 57.7%

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

   7. Taylor expanded in y around 0 57.7%

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

   if 2.7999999999999998e-50 < y < 6e5

   1. Initial program 99.9%

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

   3. Taylor expanded in a around inf 50.7%

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

Alternative 11: 66.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6.2 \cdot 10^{+62} \lor \neg \left(t \leq 2.3 \cdot 10^{+95}\right):\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + a\right) + z \cdot \left(1 - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -6.2e+62) (not (<= t 2.3e+95)))
   (* t (- b a))
   (+ (+ x a) (* z (- 1.0 y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -6.2e+62) || !(t <= 2.3e+95)) {
		tmp = t * (b - a);
	} else {
		tmp = (x + a) + (z * (1.0 - y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-6.2d+62)) .or. (.not. (t <= 2.3d+95))) then
        tmp = t * (b - a)
    else
        tmp = (x + a) + (z * (1.0d0 - y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -6.2e+62) || !(t <= 2.3e+95)) {
		tmp = t * (b - a);
	} else {
		tmp = (x + a) + (z * (1.0 - y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -6.2e+62) or not (t <= 2.3e+95):
		tmp = t * (b - a)
	else:
		tmp = (x + a) + (z * (1.0 - y))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -6.2e+62) || !(t <= 2.3e+95))
		tmp = Float64(t * Float64(b - a));
	else
		tmp = Float64(Float64(x + a) + Float64(z * Float64(1.0 - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -6.2e+62) || ~((t <= 2.3e+95)))
		tmp = t * (b - a);
	else
		tmp = (x + a) + (z * (1.0 - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -6.2e+62], N[Not[LessEqual[t, 2.3e+95]], $MachinePrecision]], N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision], N[(N[(x + a), $MachinePrecision] + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -6.20000000000000029e62 or 2.29999999999999997e95 < t

   1. Initial program 89.8%

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

   3. Taylor expanded in t around inf 78.2%

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

   if -6.20000000000000029e62 < t < 2.29999999999999997e95

   1. Initial program 99.3%

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

   3. Taylor expanded in b around 0 79.7%

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

   4. Taylor expanded in t around 0 77.1%

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

      1. associate--r+ 77.1%

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

      2. sub-neg 77.1%

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

      3. metadata-eval 77.1%

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

      4. sub-neg 77.1%

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

      5. sub-neg 77.1%

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

      6. mul-1-neg 77.1%

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

      7. remove-double-neg 77.1%

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

      8. distribute-rgt-neg-in 77.1%

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

      9. +-commutative 77.1%

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

      10. distribute-neg-in 77.1%

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

      11. metadata-eval 77.1%

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

      12. sub-neg 77.1%

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

   6. Simplified 77.1%

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

4. Final simplification 77.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.2 \cdot 10^{+62} \lor \neg \left(t \leq 2.3 \cdot 10^{+95}\right):\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + a\right) + z \cdot \left(1 - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 26.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.95 \cdot 10^{-10}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;t \leq -8.2 \cdot 10^{-258}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq 14000000000000:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -1.95e-10)
   (* t b)
   (if (<= t -8.2e-258) a (if (<= t 14000000000000.0) x (* t b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1.95e-10) {
		tmp = t * b;
	} else if (t <= -8.2e-258) {
		tmp = a;
	} else if (t <= 14000000000000.0) {
		tmp = x;
	} 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 <= (-1.95d-10)) then
        tmp = t * b
    else if (t <= (-8.2d-258)) then
        tmp = a
    else if (t <= 14000000000000.0d0) then
        tmp = x
    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 <= -1.95e-10) {
		tmp = t * b;
	} else if (t <= -8.2e-258) {
		tmp = a;
	} else if (t <= 14000000000000.0) {
		tmp = x;
	} else {
		tmp = t * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -1.95e-10:
		tmp = t * b
	elif t <= -8.2e-258:
		tmp = a
	elif t <= 14000000000000.0:
		tmp = x
	else:
		tmp = t * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -1.95e-10)
		tmp = Float64(t * b);
	elseif (t <= -8.2e-258)
		tmp = a;
	elseif (t <= 14000000000000.0)
		tmp = x;
	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 <= -1.95e-10)
		tmp = t * b;
	elseif (t <= -8.2e-258)
		tmp = a;
	elseif (t <= 14000000000000.0)
		tmp = x;
	else
		tmp = t * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -1.95e-10], N[(t * b), $MachinePrecision], If[LessEqual[t, -8.2e-258], a, If[LessEqual[t, 14000000000000.0], x, N[(t * b), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.95e-10 or 1.4e13 < t

   1. Initial program 91.6%

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

   3. Taylor expanded in t around inf 65.6%

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

   4. Taylor expanded in b around inf 37.2%

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

   if -1.95e-10 < t < -8.2000000000000001e-258

   1. Initial program 100.0%

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

   3. Taylor expanded in a around inf 34.4%

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

   4. Taylor expanded in t around 0 34.4%

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

   if -8.2000000000000001e-258 < t < 1.4e13

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 26.0%

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

Alternative 13: 57.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.15 \cdot 10^{+64} \lor \neg \left(t \leq 2.5 \cdot 10^{+95}\right):\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(1 - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -2.15e+64) (not (<= t 2.5e+95)))
   (* t (- b a))
   (+ x (* z (- 1.0 y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -2.15e+64) || !(t <= 2.5e+95)) {
		tmp = t * (b - a);
	} else {
		tmp = x + (z * (1.0 - y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-2.15d+64)) .or. (.not. (t <= 2.5d+95))) then
        tmp = t * (b - a)
    else
        tmp = x + (z * (1.0d0 - y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -2.15e+64) || !(t <= 2.5e+95)) {
		tmp = t * (b - a);
	} else {
		tmp = x + (z * (1.0 - y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -2.15e+64) or not (t <= 2.5e+95):
		tmp = t * (b - a)
	else:
		tmp = x + (z * (1.0 - y))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -2.15e+64) || !(t <= 2.5e+95))
		tmp = Float64(t * Float64(b - a));
	else
		tmp = Float64(x + Float64(z * Float64(1.0 - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -2.15e+64) || ~((t <= 2.5e+95)))
		tmp = t * (b - a);
	else
		tmp = x + (z * (1.0 - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -2.15e+64], N[Not[LessEqual[t, 2.5e+95]], $MachinePrecision]], N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.1499999999999999e64 or 2.50000000000000012e95 < t

   1. Initial program 89.8%

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

   3. Taylor expanded in t around inf 78.2%

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

   if -2.1499999999999999e64 < t < 2.50000000000000012e95

   1. Initial program 99.3%

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

   3. Taylor expanded in b around 0 79.7%

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

   4. Taylor expanded in a around 0 58.2%

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

4. Final simplification 65.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.15 \cdot 10^{+64} \lor \neg \left(t \leq 2.5 \cdot 10^{+95}\right):\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(1 - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 46.8% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.45 \cdot 10^{+60} \lor \neg \left(t \leq 1.8 \cdot 10^{+95}\right):\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{else}:\\ \;\;\;\;z - y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -2.45e+60) (not (<= t 1.8e+95))) (* t (- b a)) (- z (* y z))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -2.45e+60) || !(t <= 1.8e+95)) {
		tmp = t * (b - a);
	} else {
		tmp = z - (y * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-2.45d+60)) .or. (.not. (t <= 1.8d+95))) then
        tmp = t * (b - a)
    else
        tmp = z - (y * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -2.45e+60) || !(t <= 1.8e+95)) {
		tmp = t * (b - a);
	} else {
		tmp = z - (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -2.45e+60) or not (t <= 1.8e+95):
		tmp = t * (b - a)
	else:
		tmp = z - (y * z)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -2.45e+60) || !(t <= 1.8e+95))
		tmp = Float64(t * Float64(b - a));
	else
		tmp = Float64(z - Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -2.45e+60) || ~((t <= 1.8e+95)))
		tmp = t * (b - a);
	else
		tmp = z - (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -2.45e+60], N[Not[LessEqual[t, 1.8e+95]], $MachinePrecision]], N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision], N[(z - N[(y * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.4500000000000001e60 or 1.79999999999999989e95 < t

   1. Initial program 89.8%

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

   3. Taylor expanded in t around inf 78.2%

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

   if -2.4500000000000001e60 < t < 1.79999999999999989e95

   1. Initial program 99.3%

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

   3. Taylor expanded in z around inf 42.8%

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

      1. sub-neg 42.8%

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

      2. distribute-rgt-in 42.8%

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

      3. *-un-lft-identity 42.8%

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

   5. Applied egg-rr 42.8%

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

4. Final simplification 56.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.45 \cdot 10^{+60} \lor \neg \left(t \leq 1.8 \cdot 10^{+95}\right):\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{else}:\\ \;\;\;\;z - y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 46.8% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.55 \cdot 10^{+63} \lor \neg \left(t \leq 1.65 \cdot 10^{+95}\right):\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -1.55e+63) (not (<= t 1.65e+95)))
   (* t (- b a))
   (* z (- 1.0 y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -1.55e+63) || !(t <= 1.65e+95)) {
		tmp = t * (b - a);
	} else {
		tmp = z * (1.0 - y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-1.55d+63)) .or. (.not. (t <= 1.65d+95))) then
        tmp = t * (b - a)
    else
        tmp = z * (1.0d0 - y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -1.55e+63) || !(t <= 1.65e+95)) {
		tmp = t * (b - a);
	} else {
		tmp = z * (1.0 - y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -1.55e+63) or not (t <= 1.65e+95):
		tmp = t * (b - a)
	else:
		tmp = z * (1.0 - y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -1.55e+63) || !(t <= 1.65e+95))
		tmp = Float64(t * Float64(b - a));
	else
		tmp = Float64(z * Float64(1.0 - y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -1.55e+63) || ~((t <= 1.65e+95)))
		tmp = t * (b - a);
	else
		tmp = z * (1.0 - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -1.55e+63], N[Not[LessEqual[t, 1.65e+95]], $MachinePrecision]], N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision], N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.55e63 or 1.6499999999999999e95 < t

   1. Initial program 89.8%

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

   3. Taylor expanded in t around inf 78.2%

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

   if -1.55e63 < t < 1.6499999999999999e95

   1. Initial program 99.3%

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

   3. Taylor expanded in z around inf 42.8%

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

4. Final simplification 56.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.55 \cdot 10^{+63} \lor \neg \left(t \leq 1.65 \cdot 10^{+95}\right):\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 50.9% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.85 \cdot 10^{+40} \lor \neg \left(t \leq 2.7 \cdot 10^{+50}\right):\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -1.85e+40) (not (<= t 2.7e+50))) (* t (- b a)) (* y (- b z))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -1.85e+40) || !(t <= 2.7e+50)) {
		tmp = t * (b - a);
	} else {
		tmp = y * (b - z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-1.85d+40)) .or. (.not. (t <= 2.7d+50))) then
        tmp = t * (b - a)
    else
        tmp = y * (b - z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -1.85e+40) || !(t <= 2.7e+50)) {
		tmp = t * (b - a);
	} else {
		tmp = y * (b - z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -1.85e+40) or not (t <= 2.7e+50):
		tmp = t * (b - a)
	else:
		tmp = y * (b - z)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -1.85e+40) || !(t <= 2.7e+50))
		tmp = Float64(t * Float64(b - a));
	else
		tmp = Float64(y * Float64(b - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -1.85e+40) || ~((t <= 2.7e+50)))
		tmp = t * (b - a);
	else
		tmp = y * (b - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -1.85e+40], N[Not[LessEqual[t, 2.7e+50]], $MachinePrecision]], N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision], N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.85e40 or 2.7e50 < t

   1. Initial program 90.2%

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

   3. Taylor expanded in t around inf 73.3%

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

   if -1.85e40 < t < 2.7e50

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 41.0%

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

4. Final simplification 55.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.85 \cdot 10^{+40} \lor \neg \left(t \leq 2.7 \cdot 10^{+50}\right):\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 41.7% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.8 \cdot 10^{+40} \lor \neg \left(t \leq 4.4 \cdot 10^{+17}\right):\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -1.8e+40) (not (<= t 4.4e+17))) (* t (- b a)) (* z (- y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -1.8e+40) || !(t <= 4.4e+17)) {
		tmp = t * (b - a);
	} else {
		tmp = z * -y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-1.8d+40)) .or. (.not. (t <= 4.4d+17))) then
        tmp = t * (b - a)
    else
        tmp = z * -y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -1.8e+40) || !(t <= 4.4e+17)) {
		tmp = t * (b - a);
	} else {
		tmp = z * -y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -1.8e+40) or not (t <= 4.4e+17):
		tmp = t * (b - a)
	else:
		tmp = z * -y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -1.8e+40) || !(t <= 4.4e+17))
		tmp = Float64(t * Float64(b - a));
	else
		tmp = Float64(z * Float64(-y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -1.8e+40) || ~((t <= 4.4e+17)))
		tmp = t * (b - a);
	else
		tmp = z * -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -1.8e+40], N[Not[LessEqual[t, 4.4e+17]], $MachinePrecision]], N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision], N[(z * (-y)), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.79999999999999998e40 or 4.4e17 < t

   1. Initial program 90.7%

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

   3. Taylor expanded in t around inf 71.4%

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

   if -1.79999999999999998e40 < t < 4.4e17

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 41.6%

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

   4. Taylor expanded in y around inf 29.3%

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

      1. neg-mul-1 29.3%

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

   6. Simplified 29.3%

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

4. Final simplification 48.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.8 \cdot 10^{+40} \lor \neg \left(t \leq 4.4 \cdot 10^{+17}\right):\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 32.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{+81} \lor \neg \left(z \leq 6.1 \cdot 10^{-108}\right):\\ \;\;\;\;z \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -1.15e+81) (not (<= z 6.1e-108))) (* z (- y)) (* a (- 1.0 t))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.15e+81) || !(z <= 6.1e-108)) {
		tmp = z * -y;
	} 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 ((z <= (-1.15d+81)) .or. (.not. (z <= 6.1d-108))) then
        tmp = z * -y
    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 ((z <= -1.15e+81) || !(z <= 6.1e-108)) {
		tmp = z * -y;
	} else {
		tmp = a * (1.0 - t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -1.15e+81) or not (z <= 6.1e-108):
		tmp = z * -y
	else:
		tmp = a * (1.0 - t)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -1.15e+81) || !(z <= 6.1e-108))
		tmp = Float64(z * Float64(-y));
	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 ((z <= -1.15e+81) || ~((z <= 6.1e-108)))
		tmp = z * -y;
	else
		tmp = a * (1.0 - t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -1.15e+81], N[Not[LessEqual[z, 6.1e-108]], $MachinePrecision]], N[(z * (-y)), $MachinePrecision], N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.1499999999999999e81 or 6.10000000000000007e-108 < z

   1. Initial program 94.6%

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

   3. Taylor expanded in z around inf 55.7%

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

   4. Taylor expanded in y around inf 41.1%

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

      1. neg-mul-1 41.1%

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

   6. Simplified 41.1%

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

   if -1.1499999999999999e81 < z < 6.10000000000000007e-108

   1. Initial program 96.8%

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

   3. Taylor expanded in a around inf 44.0%

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

4. Final simplification 42.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{+81} \lor \neg \left(z \leq 6.1 \cdot 10^{-108}\right):\\ \;\;\;\;z \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 27.4% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.7 \cdot 10^{+66} \lor \neg \left(t \leq 2.5 \cdot 10^{+95}\right):\\ \;\;\;\;t \cdot b\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -2.7e+66) (not (<= t 2.5e+95))) (* t b) (* z (- y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -2.7e+66) || !(t <= 2.5e+95)) {
		tmp = t * b;
	} else {
		tmp = z * -y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-2.7d+66)) .or. (.not. (t <= 2.5d+95))) then
        tmp = t * b
    else
        tmp = z * -y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -2.7e+66) || !(t <= 2.5e+95)) {
		tmp = t * b;
	} else {
		tmp = z * -y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -2.7e+66) or not (t <= 2.5e+95):
		tmp = t * b
	else:
		tmp = z * -y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -2.7e+66) || !(t <= 2.5e+95))
		tmp = Float64(t * b);
	else
		tmp = Float64(z * Float64(-y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -2.7e+66) || ~((t <= 2.5e+95)))
		tmp = t * b;
	else
		tmp = z * -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -2.7e+66], N[Not[LessEqual[t, 2.5e+95]], $MachinePrecision]], N[(t * b), $MachinePrecision], N[(z * (-y)), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.7e66 or 2.50000000000000012e95 < t

   1. Initial program 89.8%

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

   3. Taylor expanded in t around inf 78.2%

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

   4. Taylor expanded in b around inf 44.2%

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

   if -2.7e66 < t < 2.50000000000000012e95

   1. Initial program 99.3%

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

   3. Taylor expanded in z around inf 42.8%

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

   4. Taylor expanded in y around inf 30.2%

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

      1. neg-mul-1 30.2%

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

   6. Simplified 30.2%

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

4. Final simplification 35.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.7 \cdot 10^{+66} \lor \neg \left(t \leq 2.5 \cdot 10^{+95}\right):\\ \;\;\;\;t \cdot b\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 21.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.5 \cdot 10^{+24}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{+79}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -4.5e+24) x (if (<= x 1.1e+79) a x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -4.5e+24) {
		tmp = x;
	} else if (x <= 1.1e+79) {
		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 <= (-4.5d+24)) then
        tmp = x
    else if (x <= 1.1d+79) 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 <= -4.5e+24) {
		tmp = x;
	} else if (x <= 1.1e+79) {
		tmp = a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -4.5e+24:
		tmp = x
	elif x <= 1.1e+79:
		tmp = a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -4.5e+24)
		tmp = x;
	elseif (x <= 1.1e+79)
		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 <= -4.5e+24)
		tmp = x;
	elseif (x <= 1.1e+79)
		tmp = a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -4.5e+24], x, If[LessEqual[x, 1.1e+79], a, x]]

Derivation

1. Split input into 2 regimes

2. if x < -4.50000000000000019e24 or 1.0999999999999999e79 < x

   1. Initial program 96.8%

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

   3. Taylor expanded in x around inf 31.6%

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

   if -4.50000000000000019e24 < x < 1.0999999999999999e79

   1. Initial program 95.0%

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

   3. Taylor expanded in a around inf 37.3%

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

   4. Taylor expanded in t around 0 17.9%

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

Alternative 21: 11.1% accurate, 21.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 95.7%

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

3. Taylor expanded in a around inf 29.8%

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

4. Taylor expanded in t around 0 13.8%

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

Reproduce

herbie shell --seed 2024163 
(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)))