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

Percentage Accurate: 94.8% → 97.2%

Time: 17.9s

Alternatives: 25

Speedup: 0.5×

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

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 94.8% 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: 97.2% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 1.62 \cdot 10^{+212}:\\ \;\;\;\;\mathsf{fma}\left(y + \left(t + -2\right), b, x - \mathsf{fma}\left(y + -1, z, a \cdot \left(t + -1\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b 1.62e+212)
   (fma (+ y (+ t -2.0)) b (- x (fma (+ y -1.0) z (* a (+ t -1.0)))))
   (* b (- (+ y t) 2.0))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 1.62e+212) {
		tmp = fma((y + (t + -2.0)), b, (x - fma((y + -1.0), z, (a * (t + -1.0)))));
	} else {
		tmp = b * ((y + t) - 2.0);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= 1.62e+212)
		tmp = fma(Float64(y + Float64(t + -2.0)), b, Float64(x - fma(Float64(y + -1.0), z, Float64(a * Float64(t + -1.0)))));
	else
		tmp = Float64(b * Float64(Float64(y + t) - 2.0));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, 1.62e+212], N[(N[(y + N[(t + -2.0), $MachinePrecision]), $MachinePrecision] * b + N[(x - N[(N[(y + -1.0), $MachinePrecision] * z + N[(a * N[(t + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < 1.61999999999999994e212

   1. Initial program 95.2%

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

      1. +-commutative 95.2%

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

      2. fma-define 97.8%

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

      3. associate--l+ 97.8%

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

      4. sub-neg 97.8%

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

      5. metadata-eval 97.8%

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

      6. sub-neg 97.8%

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

      7. associate-+l- 97.8%

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

      8. fma-neg 98.2%

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

      9. sub-neg 98.2%

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

      10. metadata-eval 98.2%

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

      11. remove-double-neg 98.2%

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

      12. sub-neg 98.2%

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

      13. metadata-eval 98.2%

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

   3. Simplified 98.2%

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

   if 1.61999999999999994e212 < b

   1. Initial program 81.5%

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

   3. Taylor expanded in b around inf 96.5%

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

4. Final simplification 98.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq 1.62 \cdot 10^{+212}:\\ \;\;\;\;\mathsf{fma}\left(y + \left(t + -2\right), b, x - \mathsf{fma}\left(y + -1, z, a \cdot \left(t + -1\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 97.6% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if (+.f64 (-.f64 (-.f64 x (*.f64 (-.f64 y 1) z)) (*.f64 (-.f64 t 1) a)) (*.f64 (-.f64 (+.f64 y t) 2) 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 1) z)) (*.f64 (-.f64 t 1) a)) (*.f64 (-.f64 (+.f64 y t) 2) b))

   1. Initial program 0.0%

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

   3. Taylor expanded in y around inf 57.1%

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

4. Final simplification 97.3%

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

Alternative 3: 49.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(y - 2\right)\\ t_2 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -2.1 \cdot 10^{+35}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -2.2 \cdot 10^{-151}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq -6 \cdot 10^{-262}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 5 \cdot 10^{-229}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq 3.55 \cdot 10^{-71}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{-64}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{-45}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{+16}:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- y 2.0))) (t_2 (* t (- b a))))
   (if (<= t -2.1e+35)
     t_2
     (if (<= t -2.2e-151)
       (+ x a)
       (if (<= t -6e-262)
         t_1
         (if (<= t 5e-229)
           (+ x a)
           (if (<= t 3.55e-71)
             t_1
             (if (<= t 3.5e-64)
               (+ x a)
               (if (<= t 1.25e-45)
                 (* y (- z))
                 (if (<= t 4.8e+16) (+ x a) t_2))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (y - 2.0);
	double t_2 = t * (b - a);
	double tmp;
	if (t <= -2.1e+35) {
		tmp = t_2;
	} else if (t <= -2.2e-151) {
		tmp = x + a;
	} else if (t <= -6e-262) {
		tmp = t_1;
	} else if (t <= 5e-229) {
		tmp = x + a;
	} else if (t <= 3.55e-71) {
		tmp = t_1;
	} else if (t <= 3.5e-64) {
		tmp = x + a;
	} else if (t <= 1.25e-45) {
		tmp = y * -z;
	} else if (t <= 4.8e+16) {
		tmp = x + a;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = b * (y - 2.0d0)
    t_2 = t * (b - a)
    if (t <= (-2.1d+35)) then
        tmp = t_2
    else if (t <= (-2.2d-151)) then
        tmp = x + a
    else if (t <= (-6d-262)) then
        tmp = t_1
    else if (t <= 5d-229) then
        tmp = x + a
    else if (t <= 3.55d-71) then
        tmp = t_1
    else if (t <= 3.5d-64) then
        tmp = x + a
    else if (t <= 1.25d-45) then
        tmp = y * -z
    else if (t <= 4.8d+16) then
        tmp = x + a
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (y - 2.0);
	double t_2 = t * (b - a);
	double tmp;
	if (t <= -2.1e+35) {
		tmp = t_2;
	} else if (t <= -2.2e-151) {
		tmp = x + a;
	} else if (t <= -6e-262) {
		tmp = t_1;
	} else if (t <= 5e-229) {
		tmp = x + a;
	} else if (t <= 3.55e-71) {
		tmp = t_1;
	} else if (t <= 3.5e-64) {
		tmp = x + a;
	} else if (t <= 1.25e-45) {
		tmp = y * -z;
	} else if (t <= 4.8e+16) {
		tmp = x + a;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * (y - 2.0)
	t_2 = t * (b - a)
	tmp = 0
	if t <= -2.1e+35:
		tmp = t_2
	elif t <= -2.2e-151:
		tmp = x + a
	elif t <= -6e-262:
		tmp = t_1
	elif t <= 5e-229:
		tmp = x + a
	elif t <= 3.55e-71:
		tmp = t_1
	elif t <= 3.5e-64:
		tmp = x + a
	elif t <= 1.25e-45:
		tmp = y * -z
	elif t <= 4.8e+16:
		tmp = x + a
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(y - 2.0))
	t_2 = Float64(t * Float64(b - a))
	tmp = 0.0
	if (t <= -2.1e+35)
		tmp = t_2;
	elseif (t <= -2.2e-151)
		tmp = Float64(x + a);
	elseif (t <= -6e-262)
		tmp = t_1;
	elseif (t <= 5e-229)
		tmp = Float64(x + a);
	elseif (t <= 3.55e-71)
		tmp = t_1;
	elseif (t <= 3.5e-64)
		tmp = Float64(x + a);
	elseif (t <= 1.25e-45)
		tmp = Float64(y * Float64(-z));
	elseif (t <= 4.8e+16)
		tmp = Float64(x + a);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * (y - 2.0);
	t_2 = t * (b - a);
	tmp = 0.0;
	if (t <= -2.1e+35)
		tmp = t_2;
	elseif (t <= -2.2e-151)
		tmp = x + a;
	elseif (t <= -6e-262)
		tmp = t_1;
	elseif (t <= 5e-229)
		tmp = x + a;
	elseif (t <= 3.55e-71)
		tmp = t_1;
	elseif (t <= 3.5e-64)
		tmp = x + a;
	elseif (t <= 1.25e-45)
		tmp = y * -z;
	elseif (t <= 4.8e+16)
		tmp = x + a;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(y - 2.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.1e+35], t$95$2, If[LessEqual[t, -2.2e-151], N[(x + a), $MachinePrecision], If[LessEqual[t, -6e-262], t$95$1, If[LessEqual[t, 5e-229], N[(x + a), $MachinePrecision], If[LessEqual[t, 3.55e-71], t$95$1, If[LessEqual[t, 3.5e-64], N[(x + a), $MachinePrecision], If[LessEqual[t, 1.25e-45], N[(y * (-z)), $MachinePrecision], If[LessEqual[t, 4.8e+16], N[(x + a), $MachinePrecision], t$95$2]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -2.0999999999999999e35 or 4.8e16 < 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 71.2%

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

   if -2.0999999999999999e35 < t < -2.1999999999999999e-151 or -6.00000000000000036e-262 < t < 5.00000000000000016e-229 or 3.55000000000000004e-71 < t < 3.5000000000000003e-64 or 1.24999999999999994e-45 < t < 4.8e16

   1. Initial program 97.4%

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

   3. Taylor expanded in z around 0 76.2%

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

   4. Taylor expanded in b around 0 52.9%

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

   5. Taylor expanded in t around 0 48.7%

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

      1. neg-mul-1 48.7%

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

   7. Simplified 48.7%

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

   if -2.1999999999999999e-151 < t < -6.00000000000000036e-262 or 5.00000000000000016e-229 < t < 3.55000000000000004e-71

   1. Initial program 92.3%

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

   3. Taylor expanded in b around inf 44.9%

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

   4. Taylor expanded in t around 0 44.9%

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

   if 3.5000000000000003e-64 < t < 1.24999999999999994e-45

   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 86.0%

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

   4. Taylor expanded in y around inf 86.0%

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

      1. mul-1-neg 86.0%

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

      2. distribute-lft-neg-out 86.0%

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

      3. *-commutative 86.0%

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

   6. Simplified 86.0%

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

4. Final simplification 59.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.1 \cdot 10^{+35}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq -2.2 \cdot 10^{-151}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq -6 \cdot 10^{-262}:\\ \;\;\;\;b \cdot \left(y - 2\right)\\ \mathbf{elif}\;t \leq 5 \cdot 10^{-229}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq 3.55 \cdot 10^{-71}:\\ \;\;\;\;b \cdot \left(y - 2\right)\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{-64}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{-45}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{+16}:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 51.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(b - z\right)\\ t_2 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -1.05 \cdot 10^{+35}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -3.6 \cdot 10^{-151}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq -9 \cdot 10^{-304}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{-246}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq 4.4 \cdot 10^{-35}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{-9}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq 8.8 \cdot 10^{+16}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (- b z))) (t_2 (* t (- b a))))
   (if (<= t -1.05e+35)
     t_2
     (if (<= t -3.6e-151)
       (+ x a)
       (if (<= t -9e-304)
         t_1
         (if (<= t 8.5e-246)
           (+ x a)
           (if (<= t 4.4e-35)
             t_1
             (if (<= t 1.9e-9) (+ x a) (if (<= t 8.8e+16) t_1 t_2)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (b - z);
	double t_2 = t * (b - a);
	double tmp;
	if (t <= -1.05e+35) {
		tmp = t_2;
	} else if (t <= -3.6e-151) {
		tmp = x + a;
	} else if (t <= -9e-304) {
		tmp = t_1;
	} else if (t <= 8.5e-246) {
		tmp = x + a;
	} else if (t <= 4.4e-35) {
		tmp = t_1;
	} else if (t <= 1.9e-9) {
		tmp = x + a;
	} else if (t <= 8.8e+16) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y * (b - z)
    t_2 = t * (b - a)
    if (t <= (-1.05d+35)) then
        tmp = t_2
    else if (t <= (-3.6d-151)) then
        tmp = x + a
    else if (t <= (-9d-304)) then
        tmp = t_1
    else if (t <= 8.5d-246) then
        tmp = x + a
    else if (t <= 4.4d-35) then
        tmp = t_1
    else if (t <= 1.9d-9) then
        tmp = x + a
    else if (t <= 8.8d+16) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (b - z);
	double t_2 = t * (b - a);
	double tmp;
	if (t <= -1.05e+35) {
		tmp = t_2;
	} else if (t <= -3.6e-151) {
		tmp = x + a;
	} else if (t <= -9e-304) {
		tmp = t_1;
	} else if (t <= 8.5e-246) {
		tmp = x + a;
	} else if (t <= 4.4e-35) {
		tmp = t_1;
	} else if (t <= 1.9e-9) {
		tmp = x + a;
	} else if (t <= 8.8e+16) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y * (b - z)
	t_2 = t * (b - a)
	tmp = 0
	if t <= -1.05e+35:
		tmp = t_2
	elif t <= -3.6e-151:
		tmp = x + a
	elif t <= -9e-304:
		tmp = t_1
	elif t <= 8.5e-246:
		tmp = x + a
	elif t <= 4.4e-35:
		tmp = t_1
	elif t <= 1.9e-9:
		tmp = x + a
	elif t <= 8.8e+16:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y * Float64(b - z))
	t_2 = Float64(t * Float64(b - a))
	tmp = 0.0
	if (t <= -1.05e+35)
		tmp = t_2;
	elseif (t <= -3.6e-151)
		tmp = Float64(x + a);
	elseif (t <= -9e-304)
		tmp = t_1;
	elseif (t <= 8.5e-246)
		tmp = Float64(x + a);
	elseif (t <= 4.4e-35)
		tmp = t_1;
	elseif (t <= 1.9e-9)
		tmp = Float64(x + a);
	elseif (t <= 8.8e+16)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y * (b - z);
	t_2 = t * (b - a);
	tmp = 0.0;
	if (t <= -1.05e+35)
		tmp = t_2;
	elseif (t <= -3.6e-151)
		tmp = x + a;
	elseif (t <= -9e-304)
		tmp = t_1;
	elseif (t <= 8.5e-246)
		tmp = x + a;
	elseif (t <= 4.4e-35)
		tmp = t_1;
	elseif (t <= 1.9e-9)
		tmp = x + a;
	elseif (t <= 8.8e+16)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.05e+35], t$95$2, If[LessEqual[t, -3.6e-151], N[(x + a), $MachinePrecision], If[LessEqual[t, -9e-304], t$95$1, If[LessEqual[t, 8.5e-246], N[(x + a), $MachinePrecision], If[LessEqual[t, 4.4e-35], t$95$1, If[LessEqual[t, 1.9e-9], N[(x + a), $MachinePrecision], If[LessEqual[t, 8.8e+16], t$95$1, t$95$2]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.0499999999999999e35 or 8.8e16 < 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 71.2%

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

   if -1.0499999999999999e35 < t < -3.60000000000000032e-151 or -8.9999999999999995e-304 < t < 8.4999999999999998e-246 or 4.39999999999999987e-35 < t < 1.90000000000000006e-9

   1. Initial program 98.1%

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

   3. Taylor expanded in z around 0 77.9%

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

   4. Taylor expanded in b around 0 56.1%

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

   5. Taylor expanded in t around 0 52.7%

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

      1. neg-mul-1 52.7%

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

   7. Simplified 52.7%

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

   if -3.60000000000000032e-151 < t < -8.9999999999999995e-304 or 8.4999999999999998e-246 < t < 4.39999999999999987e-35 or 1.90000000000000006e-9 < t < 8.8e16

   1. Initial program 94.0%

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

   3. Taylor expanded in y around inf 54.6%

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

4. Final simplification 61.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.05 \cdot 10^{+35}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq -3.6 \cdot 10^{-151}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq -9 \cdot 10^{-304}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{-246}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq 4.4 \cdot 10^{-35}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{-9}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq 8.8 \cdot 10^{+16}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 28.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(-z\right)\\ \mathbf{if}\;y \leq -2 \cdot 10^{+38}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{-115}:\\ \;\;\;\;b \cdot t\\ \mathbf{elif}\;y \leq 2.65 \cdot 10^{-36}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 4 \cdot 10^{+29}:\\ \;\;\;\;a\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{+72} \lor \neg \left(y \leq 6 \cdot 10^{+120}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (- z))))
   (if (<= y -2e+38)
     t_1
     (if (<= y 1.9e-115)
       (* b t)
       (if (<= y 2.65e-36)
         x
         (if (<= y 4e+29)
           a
           (if (or (<= y 5.5e+72) (not (<= y 6e+120))) t_1 (* b y))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * -z;
	double tmp;
	if (y <= -2e+38) {
		tmp = t_1;
	} else if (y <= 1.9e-115) {
		tmp = b * t;
	} else if (y <= 2.65e-36) {
		tmp = x;
	} else if (y <= 4e+29) {
		tmp = a;
	} else if ((y <= 5.5e+72) || !(y <= 6e+120)) {
		tmp = t_1;
	} else {
		tmp = b * 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) :: t_1
    real(8) :: tmp
    t_1 = y * -z
    if (y <= (-2d+38)) then
        tmp = t_1
    else if (y <= 1.9d-115) then
        tmp = b * t
    else if (y <= 2.65d-36) then
        tmp = x
    else if (y <= 4d+29) then
        tmp = a
    else if ((y <= 5.5d+72) .or. (.not. (y <= 6d+120))) then
        tmp = t_1
    else
        tmp = b * 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 t_1 = y * -z;
	double tmp;
	if (y <= -2e+38) {
		tmp = t_1;
	} else if (y <= 1.9e-115) {
		tmp = b * t;
	} else if (y <= 2.65e-36) {
		tmp = x;
	} else if (y <= 4e+29) {
		tmp = a;
	} else if ((y <= 5.5e+72) || !(y <= 6e+120)) {
		tmp = t_1;
	} else {
		tmp = b * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y * -z
	tmp = 0
	if y <= -2e+38:
		tmp = t_1
	elif y <= 1.9e-115:
		tmp = b * t
	elif y <= 2.65e-36:
		tmp = x
	elif y <= 4e+29:
		tmp = a
	elif (y <= 5.5e+72) or not (y <= 6e+120):
		tmp = t_1
	else:
		tmp = b * y
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y * Float64(-z))
	tmp = 0.0
	if (y <= -2e+38)
		tmp = t_1;
	elseif (y <= 1.9e-115)
		tmp = Float64(b * t);
	elseif (y <= 2.65e-36)
		tmp = x;
	elseif (y <= 4e+29)
		tmp = a;
	elseif ((y <= 5.5e+72) || !(y <= 6e+120))
		tmp = t_1;
	else
		tmp = Float64(b * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y * -z;
	tmp = 0.0;
	if (y <= -2e+38)
		tmp = t_1;
	elseif (y <= 1.9e-115)
		tmp = b * t;
	elseif (y <= 2.65e-36)
		tmp = x;
	elseif (y <= 4e+29)
		tmp = a;
	elseif ((y <= 5.5e+72) || ~((y <= 6e+120)))
		tmp = t_1;
	else
		tmp = b * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y * (-z)), $MachinePrecision]}, If[LessEqual[y, -2e+38], t$95$1, If[LessEqual[y, 1.9e-115], N[(b * t), $MachinePrecision], If[LessEqual[y, 2.65e-36], x, If[LessEqual[y, 4e+29], a, If[Or[LessEqual[y, 5.5e+72], N[Not[LessEqual[y, 6e+120]], $MachinePrecision]], t$95$1, N[(b * y), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -1.99999999999999995e38 or 3.99999999999999966e29 < y < 5.5e72 or 6e120 < y

   1. Initial program 88.3%

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

   3. Taylor expanded in z around inf 47.2%

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

   4. Taylor expanded in y around inf 47.2%

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

      1. mul-1-neg 47.2%

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

      2. distribute-lft-neg-out 47.2%

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

      3. *-commutative 47.2%

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

   6. Simplified 47.2%

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

   if -1.99999999999999995e38 < y < 1.89999999999999996e-115

   1. Initial program 97.5%

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

   3. Taylor expanded in b around inf 42.7%

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

   4. Taylor expanded in t around inf 29.8%

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

   if 1.89999999999999996e-115 < y < 2.6499999999999999e-36

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 44.9%

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

   if 2.6499999999999999e-36 < y < 3.99999999999999966e29

   1. Initial program 92.2%

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

   3. Taylor expanded in a around inf 40.0%

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

   4. Taylor expanded in t around 0 25.5%

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

   if 5.5e72 < y < 6e120

   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 0 100.0%

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

   4. Taylor expanded in y around inf 63.2%

      \[\leadsto \color{blue}{b \cdot y} \]
3. Recombined 5 regimes into one program.

4. Final simplification 38.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{+38}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{-115}:\\ \;\;\;\;b \cdot t\\ \mathbf{elif}\;y \leq 2.65 \cdot 10^{-36}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 4 \cdot 10^{+29}:\\ \;\;\;\;a\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{+72} \lor \neg \left(y \leq 6 \cdot 10^{+120}\right):\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 25.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(-z\right)\\ t_2 := t \cdot \left(-a\right)\\ \mathbf{if}\;x \leq -2.4 \cdot 10^{+166}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -1.8 \cdot 10^{-61}:\\ \;\;\;\;b \cdot t\\ \mathbf{elif}\;x \leq 7.8 \cdot 10^{-185}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 5.6 \cdot 10^{-92}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 98:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 9.4 \cdot 10^{+139}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (- z))) (t_2 (* t (- a))))
   (if (<= x -2.4e+166)
     x
     (if (<= x -1.8e-61)
       (* b t)
       (if (<= x 7.8e-185)
         t_1
         (if (<= x 5.6e-92)
           t_2
           (if (<= x 98.0) t_1 (if (<= x 9.4e+139) t_2 x))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * -z;
	double t_2 = t * -a;
	double tmp;
	if (x <= -2.4e+166) {
		tmp = x;
	} else if (x <= -1.8e-61) {
		tmp = b * t;
	} else if (x <= 7.8e-185) {
		tmp = t_1;
	} else if (x <= 5.6e-92) {
		tmp = t_2;
	} else if (x <= 98.0) {
		tmp = t_1;
	} else if (x <= 9.4e+139) {
		tmp = t_2;
	} 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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y * -z
    t_2 = t * -a
    if (x <= (-2.4d+166)) then
        tmp = x
    else if (x <= (-1.8d-61)) then
        tmp = b * t
    else if (x <= 7.8d-185) then
        tmp = t_1
    else if (x <= 5.6d-92) then
        tmp = t_2
    else if (x <= 98.0d0) then
        tmp = t_1
    else if (x <= 9.4d+139) then
        tmp = t_2
    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 t_1 = y * -z;
	double t_2 = t * -a;
	double tmp;
	if (x <= -2.4e+166) {
		tmp = x;
	} else if (x <= -1.8e-61) {
		tmp = b * t;
	} else if (x <= 7.8e-185) {
		tmp = t_1;
	} else if (x <= 5.6e-92) {
		tmp = t_2;
	} else if (x <= 98.0) {
		tmp = t_1;
	} else if (x <= 9.4e+139) {
		tmp = t_2;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y * -z
	t_2 = t * -a
	tmp = 0
	if x <= -2.4e+166:
		tmp = x
	elif x <= -1.8e-61:
		tmp = b * t
	elif x <= 7.8e-185:
		tmp = t_1
	elif x <= 5.6e-92:
		tmp = t_2
	elif x <= 98.0:
		tmp = t_1
	elif x <= 9.4e+139:
		tmp = t_2
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y * Float64(-z))
	t_2 = Float64(t * Float64(-a))
	tmp = 0.0
	if (x <= -2.4e+166)
		tmp = x;
	elseif (x <= -1.8e-61)
		tmp = Float64(b * t);
	elseif (x <= 7.8e-185)
		tmp = t_1;
	elseif (x <= 5.6e-92)
		tmp = t_2;
	elseif (x <= 98.0)
		tmp = t_1;
	elseif (x <= 9.4e+139)
		tmp = t_2;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y * -z;
	t_2 = t * -a;
	tmp = 0.0;
	if (x <= -2.4e+166)
		tmp = x;
	elseif (x <= -1.8e-61)
		tmp = b * t;
	elseif (x <= 7.8e-185)
		tmp = t_1;
	elseif (x <= 5.6e-92)
		tmp = t_2;
	elseif (x <= 98.0)
		tmp = t_1;
	elseif (x <= 9.4e+139)
		tmp = t_2;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y * (-z)), $MachinePrecision]}, Block[{t$95$2 = N[(t * (-a)), $MachinePrecision]}, If[LessEqual[x, -2.4e+166], x, If[LessEqual[x, -1.8e-61], N[(b * t), $MachinePrecision], If[LessEqual[x, 7.8e-185], t$95$1, If[LessEqual[x, 5.6e-92], t$95$2, If[LessEqual[x, 98.0], t$95$1, If[LessEqual[x, 9.4e+139], t$95$2, x]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -2.39999999999999992e166 or 9.4000000000000002e139 < x

   1. Initial program 97.2%

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

   3. Taylor expanded in x around inf 54.7%

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

   if -2.39999999999999992e166 < x < -1.80000000000000007e-61

   1. Initial program 95.1%

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

   3. Taylor expanded in b around inf 47.6%

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

   4. Taylor expanded in t around inf 28.7%

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

   if -1.80000000000000007e-61 < x < 7.7999999999999999e-185 or 5.6e-92 < x < 98

   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 z around inf 38.4%

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

   4. Taylor expanded in y around inf 33.4%

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

      1. mul-1-neg 33.4%

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

      2. distribute-lft-neg-out 33.4%

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

      3. *-commutative 33.4%

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

   6. Simplified 33.4%

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

   if 7.7999999999999999e-185 < x < 5.6e-92 or 98 < x < 9.4000000000000002e139

   1. Initial program 94.2%

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

   3. Taylor expanded in b around 0 70.3%

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

   4. Taylor expanded in t around inf 36.8%

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

      1. associate-*r* 36.8%

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

      2. neg-mul-1 36.8%

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

   6. Simplified 36.8%

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

4. Final simplification 39.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.4 \cdot 10^{+166}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -1.8 \cdot 10^{-61}:\\ \;\;\;\;b \cdot t\\ \mathbf{elif}\;x \leq 7.8 \cdot 10^{-185}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;x \leq 5.6 \cdot 10^{-92}:\\ \;\;\;\;t \cdot \left(-a\right)\\ \mathbf{elif}\;x \leq 98:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;x \leq 9.4 \cdot 10^{+139}:\\ \;\;\;\;t \cdot \left(-a\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 57.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -5 \cdot 10^{+35}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 5.6 \cdot 10^{-64}:\\ \;\;\;\;x + b \cdot \left(y - 2\right)\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{-35}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;t \leq 16000:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{+17}:\\ \;\;\;\;z \cdot \left(\frac{x}{z} - y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (- b a))))
   (if (<= t -5e+35)
     t_1
     (if (<= t 5.6e-64)
       (+ x (* b (- y 2.0)))
       (if (<= t 1.8e-35)
         (* y (- b z))
         (if (<= t 16000.0)
           (+ x (* a (- 1.0 t)))
           (if (<= t 1.8e+17) (* z (- (/ x z) y)) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (b - a);
	double tmp;
	if (t <= -5e+35) {
		tmp = t_1;
	} else if (t <= 5.6e-64) {
		tmp = x + (b * (y - 2.0));
	} else if (t <= 1.8e-35) {
		tmp = y * (b - z);
	} else if (t <= 16000.0) {
		tmp = x + (a * (1.0 - t));
	} else if (t <= 1.8e+17) {
		tmp = z * ((x / z) - 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 = t * (b - a)
    if (t <= (-5d+35)) then
        tmp = t_1
    else if (t <= 5.6d-64) then
        tmp = x + (b * (y - 2.0d0))
    else if (t <= 1.8d-35) then
        tmp = y * (b - z)
    else if (t <= 16000.0d0) then
        tmp = x + (a * (1.0d0 - t))
    else if (t <= 1.8d+17) then
        tmp = z * ((x / z) - 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 = t * (b - a);
	double tmp;
	if (t <= -5e+35) {
		tmp = t_1;
	} else if (t <= 5.6e-64) {
		tmp = x + (b * (y - 2.0));
	} else if (t <= 1.8e-35) {
		tmp = y * (b - z);
	} else if (t <= 16000.0) {
		tmp = x + (a * (1.0 - t));
	} else if (t <= 1.8e+17) {
		tmp = z * ((x / z) - y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t * (b - a)
	tmp = 0
	if t <= -5e+35:
		tmp = t_1
	elif t <= 5.6e-64:
		tmp = x + (b * (y - 2.0))
	elif t <= 1.8e-35:
		tmp = y * (b - z)
	elif t <= 16000.0:
		tmp = x + (a * (1.0 - t))
	elif t <= 1.8e+17:
		tmp = z * ((x / z) - y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t * Float64(b - a))
	tmp = 0.0
	if (t <= -5e+35)
		tmp = t_1;
	elseif (t <= 5.6e-64)
		tmp = Float64(x + Float64(b * Float64(y - 2.0)));
	elseif (t <= 1.8e-35)
		tmp = Float64(y * Float64(b - z));
	elseif (t <= 16000.0)
		tmp = Float64(x + Float64(a * Float64(1.0 - t)));
	elseif (t <= 1.8e+17)
		tmp = Float64(z * Float64(Float64(x / z) - y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t * (b - a);
	tmp = 0.0;
	if (t <= -5e+35)
		tmp = t_1;
	elseif (t <= 5.6e-64)
		tmp = x + (b * (y - 2.0));
	elseif (t <= 1.8e-35)
		tmp = y * (b - z);
	elseif (t <= 16000.0)
		tmp = x + (a * (1.0 - t));
	elseif (t <= 1.8e+17)
		tmp = z * ((x / z) - y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -5e+35], t$95$1, If[LessEqual[t, 5.6e-64], N[(x + N[(b * N[(y - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.8e-35], N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 16000.0], N[(x + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.8e+17], N[(z * N[(N[(x / z), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -5.00000000000000021e35 or 1.8e17 < 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 71.2%

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

   if -5.00000000000000021e35 < t < 5.60000000000000008e-64

   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 0 73.9%

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

   4. Taylor expanded in a around 0 59.5%

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

   5. Taylor expanded in t around 0 59.5%

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

   if 5.60000000000000008e-64 < t < 1.80000000000000009e-35

   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 73.2%

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

   if 1.80000000000000009e-35 < t < 16000

   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 0 82.1%

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

   4. Taylor expanded in b around 0 63.3%

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

   if 16000 < t < 1.8e17

   1. Initial program 100.0%

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

   3. Taylor expanded in b around 0 100.0%

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

   4. Taylor expanded in y around inf 76.5%

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

   5. Taylor expanded in z around inf 76.5%

      \[\leadsto \color{blue}{z \cdot \left(\frac{x}{z} - y\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 66.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5 \cdot 10^{+35}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq 5.6 \cdot 10^{-64}:\\ \;\;\;\;x + b \cdot \left(y - 2\right)\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{-35}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;t \leq 16000:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{+17}:\\ \;\;\;\;z \cdot \left(\frac{x}{z} - y\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 32.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(-a\right)\\ t_2 := y \cdot \left(-z\right)\\ \mathbf{if}\;z \leq -6.5 \cdot 10^{+96}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-99}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{+62}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 10^{+152}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+156}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (- a))) (t_2 (* y (- z))))
   (if (<= z -6.5e+96)
     t_2
     (if (<= z 5.8e-99)
       (+ x a)
       (if (<= z 5.6e+62)
         t_1
         (if (<= z 1e+152) (+ x a) (if (<= z 1.4e+156) t_1 t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * -a;
	double t_2 = y * -z;
	double tmp;
	if (z <= -6.5e+96) {
		tmp = t_2;
	} else if (z <= 5.8e-99) {
		tmp = x + a;
	} else if (z <= 5.6e+62) {
		tmp = t_1;
	} else if (z <= 1e+152) {
		tmp = x + a;
	} else if (z <= 1.4e+156) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t * -a
    t_2 = y * -z
    if (z <= (-6.5d+96)) then
        tmp = t_2
    else if (z <= 5.8d-99) then
        tmp = x + a
    else if (z <= 5.6d+62) then
        tmp = t_1
    else if (z <= 1d+152) then
        tmp = x + a
    else if (z <= 1.4d+156) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * -a;
	double t_2 = y * -z;
	double tmp;
	if (z <= -6.5e+96) {
		tmp = t_2;
	} else if (z <= 5.8e-99) {
		tmp = x + a;
	} else if (z <= 5.6e+62) {
		tmp = t_1;
	} else if (z <= 1e+152) {
		tmp = x + a;
	} else if (z <= 1.4e+156) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t * -a
	t_2 = y * -z
	tmp = 0
	if z <= -6.5e+96:
		tmp = t_2
	elif z <= 5.8e-99:
		tmp = x + a
	elif z <= 5.6e+62:
		tmp = t_1
	elif z <= 1e+152:
		tmp = x + a
	elif z <= 1.4e+156:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t * Float64(-a))
	t_2 = Float64(y * Float64(-z))
	tmp = 0.0
	if (z <= -6.5e+96)
		tmp = t_2;
	elseif (z <= 5.8e-99)
		tmp = Float64(x + a);
	elseif (z <= 5.6e+62)
		tmp = t_1;
	elseif (z <= 1e+152)
		tmp = Float64(x + a);
	elseif (z <= 1.4e+156)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t * -a;
	t_2 = y * -z;
	tmp = 0.0;
	if (z <= -6.5e+96)
		tmp = t_2;
	elseif (z <= 5.8e-99)
		tmp = x + a;
	elseif (z <= 5.6e+62)
		tmp = t_1;
	elseif (z <= 1e+152)
		tmp = x + a;
	elseif (z <= 1.4e+156)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t * (-a)), $MachinePrecision]}, Block[{t$95$2 = N[(y * (-z)), $MachinePrecision]}, If[LessEqual[z, -6.5e+96], t$95$2, If[LessEqual[z, 5.8e-99], N[(x + a), $MachinePrecision], If[LessEqual[z, 5.6e+62], t$95$1, If[LessEqual[z, 1e+152], N[(x + a), $MachinePrecision], If[LessEqual[z, 1.4e+156], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.5e96 or 1.39999999999999994e156 < z

   1. Initial program 88.2%

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

   3. Taylor expanded in z around inf 65.2%

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

   4. Taylor expanded in y around inf 50.5%

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

      1. mul-1-neg 50.5%

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

      2. distribute-lft-neg-out 50.5%

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

      3. *-commutative 50.5%

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

   6. Simplified 50.5%

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

   if -6.5e96 < z < 5.79999999999999971e-99 or 5.60000000000000029e62 < z < 1e152

   1. Initial program 95.2%

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

   3. Taylor expanded in z around 0 91.1%

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

   4. Taylor expanded in b around 0 55.9%

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

   5. Taylor expanded in t around 0 37.8%

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

      1. neg-mul-1 37.8%

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

   7. Simplified 37.8%

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

   if 5.79999999999999971e-99 < z < 5.60000000000000029e62 or 1e152 < z < 1.39999999999999994e156

   1. Initial program 100.0%

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

   3. Taylor expanded in b around 0 68.5%

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

   4. Taylor expanded in t around inf 38.7%

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

      1. associate-*r* 38.7%

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

      2. neg-mul-1 38.7%

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

   6. Simplified 38.7%

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

4. Final simplification 41.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{+96}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-99}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{+62}:\\ \;\;\;\;t \cdot \left(-a\right)\\ \mathbf{elif}\;z \leq 10^{+152}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+156}:\\ \;\;\;\;t \cdot \left(-a\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 60.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + b \cdot \left(\left(y + t\right) - 2\right)\\ t_2 := x + a \cdot \left(1 - t\right)\\ \mathbf{if}\;a \leq -1.16 \cdot 10^{+128}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -1.05 \cdot 10^{-60}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -7.5 \cdot 10^{-125}:\\ \;\;\;\;z \cdot \left(\frac{x}{z} - y\right)\\ \mathbf{elif}\;a \leq 7.8 \cdot 10^{+147}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* b (- (+ y t) 2.0)))) (t_2 (+ x (* a (- 1.0 t)))))
   (if (<= a -1.16e+128)
     t_2
     (if (<= a -1.05e-60)
       t_1
       (if (<= a -7.5e-125)
         (* z (- (/ x z) y))
         (if (<= a 7.8e+147) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (b * ((y + t) - 2.0));
	double t_2 = x + (a * (1.0 - t));
	double tmp;
	if (a <= -1.16e+128) {
		tmp = t_2;
	} else if (a <= -1.05e-60) {
		tmp = t_1;
	} else if (a <= -7.5e-125) {
		tmp = z * ((x / z) - y);
	} else if (a <= 7.8e+147) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + (b * ((y + t) - 2.0d0))
    t_2 = x + (a * (1.0d0 - t))
    if (a <= (-1.16d+128)) then
        tmp = t_2
    else if (a <= (-1.05d-60)) then
        tmp = t_1
    else if (a <= (-7.5d-125)) then
        tmp = z * ((x / z) - y)
    else if (a <= 7.8d+147) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (b * ((y + t) - 2.0));
	double t_2 = x + (a * (1.0 - t));
	double tmp;
	if (a <= -1.16e+128) {
		tmp = t_2;
	} else if (a <= -1.05e-60) {
		tmp = t_1;
	} else if (a <= -7.5e-125) {
		tmp = z * ((x / z) - y);
	} else if (a <= 7.8e+147) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (b * ((y + t) - 2.0))
	t_2 = x + (a * (1.0 - t))
	tmp = 0
	if a <= -1.16e+128:
		tmp = t_2
	elif a <= -1.05e-60:
		tmp = t_1
	elif a <= -7.5e-125:
		tmp = z * ((x / z) - y)
	elif a <= 7.8e+147:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(b * Float64(Float64(y + t) - 2.0)))
	t_2 = Float64(x + Float64(a * Float64(1.0 - t)))
	tmp = 0.0
	if (a <= -1.16e+128)
		tmp = t_2;
	elseif (a <= -1.05e-60)
		tmp = t_1;
	elseif (a <= -7.5e-125)
		tmp = Float64(z * Float64(Float64(x / z) - y));
	elseif (a <= 7.8e+147)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (b * ((y + t) - 2.0));
	t_2 = x + (a * (1.0 - t));
	tmp = 0.0;
	if (a <= -1.16e+128)
		tmp = t_2;
	elseif (a <= -1.05e-60)
		tmp = t_1;
	elseif (a <= -7.5e-125)
		tmp = z * ((x / z) - y);
	elseif (a <= 7.8e+147)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.16e+128], t$95$2, If[LessEqual[a, -1.05e-60], t$95$1, If[LessEqual[a, -7.5e-125], N[(z * N[(N[(x / z), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 7.8e+147], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.1600000000000001e128 or 7.80000000000000033e147 < a

   1. Initial program 92.2%

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

   3. Taylor expanded in z around 0 77.4%

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

   4. Taylor expanded in b around 0 70.1%

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

   if -1.1600000000000001e128 < a < -1.04999999999999996e-60 or -7.5e-125 < a < 7.80000000000000033e147

   1. Initial program 95.1%

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

   3. Taylor expanded in z around 0 76.7%

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

   4. Taylor expanded in a around 0 70.0%

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

   if -1.04999999999999996e-60 < a < -7.5e-125

   1. Initial program 87.5%

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

   3. Taylor expanded in b around 0 87.5%

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

   4. Taylor expanded in y around inf 54.5%

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

   5. Taylor expanded in z around inf 60.3%

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

4. Final simplification 69.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.16 \cdot 10^{+128}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;a \leq -1.05 \cdot 10^{-60}:\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{elif}\;a \leq -7.5 \cdot 10^{-125}:\\ \;\;\;\;z \cdot \left(\frac{x}{z} - y\right)\\ \mathbf{elif}\;a \leq 7.8 \cdot 10^{+147}:\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 71.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(z + a \cdot \left(1 - t\right)\right)\\ t_2 := x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{if}\;b \leq -9 \cdot 10^{-15}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -2 \cdot 10^{-297}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 8.5 \cdot 10^{-294}:\\ \;\;\;\;x - y \cdot z\\ \mathbf{elif}\;b \leq 3.7 \cdot 10^{-25}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (+ z (* a (- 1.0 t))))) (t_2 (+ x (* b (- (+ y t) 2.0)))))
   (if (<= b -9e-15)
     t_2
     (if (<= b -2e-297)
       t_1
       (if (<= b 8.5e-294) (- x (* y z)) (if (<= b 3.7e-25) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (z + (a * (1.0 - t)));
	double t_2 = x + (b * ((y + t) - 2.0));
	double tmp;
	if (b <= -9e-15) {
		tmp = t_2;
	} else if (b <= -2e-297) {
		tmp = t_1;
	} else if (b <= 8.5e-294) {
		tmp = x - (y * z);
	} else if (b <= 3.7e-25) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + (z + (a * (1.0d0 - t)))
    t_2 = x + (b * ((y + t) - 2.0d0))
    if (b <= (-9d-15)) then
        tmp = t_2
    else if (b <= (-2d-297)) then
        tmp = t_1
    else if (b <= 8.5d-294) then
        tmp = x - (y * z)
    else if (b <= 3.7d-25) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (z + (a * (1.0 - t)));
	double t_2 = x + (b * ((y + t) - 2.0));
	double tmp;
	if (b <= -9e-15) {
		tmp = t_2;
	} else if (b <= -2e-297) {
		tmp = t_1;
	} else if (b <= 8.5e-294) {
		tmp = x - (y * z);
	} else if (b <= 3.7e-25) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (z + (a * (1.0 - t)))
	t_2 = x + (b * ((y + t) - 2.0))
	tmp = 0
	if b <= -9e-15:
		tmp = t_2
	elif b <= -2e-297:
		tmp = t_1
	elif b <= 8.5e-294:
		tmp = x - (y * z)
	elif b <= 3.7e-25:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(z + Float64(a * Float64(1.0 - t))))
	t_2 = Float64(x + Float64(b * Float64(Float64(y + t) - 2.0)))
	tmp = 0.0
	if (b <= -9e-15)
		tmp = t_2;
	elseif (b <= -2e-297)
		tmp = t_1;
	elseif (b <= 8.5e-294)
		tmp = Float64(x - Float64(y * z));
	elseif (b <= 3.7e-25)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (z + (a * (1.0 - t)));
	t_2 = x + (b * ((y + t) - 2.0));
	tmp = 0.0;
	if (b <= -9e-15)
		tmp = t_2;
	elseif (b <= -2e-297)
		tmp = t_1;
	elseif (b <= 8.5e-294)
		tmp = x - (y * z);
	elseif (b <= 3.7e-25)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(z + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -9e-15], t$95$2, If[LessEqual[b, -2e-297], t$95$1, If[LessEqual[b, 8.5e-294], N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.7e-25], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -8.9999999999999995e-15 or 3.70000000000000009e-25 < b

   1. Initial program 87.4%

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

   3. Taylor expanded in z around 0 85.3%

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

   4. Taylor expanded in a around 0 76.2%

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

   if -8.9999999999999995e-15 < b < -2.00000000000000008e-297 or 8.4999999999999999e-294 < b < 3.70000000000000009e-25

   1. Initial program 100.0%

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

   3. Taylor expanded in b around 0 92.5%

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

   4. Taylor expanded in y around 0 70.4%

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

      1. +-commutative 70.4%

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

      2. sub-neg 70.4%

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

      3. metadata-eval 70.4%

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

      4. neg-mul-1 70.4%

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

      5. unsub-neg 70.4%

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

   6. Simplified 70.4%

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

   if -2.00000000000000008e-297 < b < 8.4999999999999999e-294

   1. Initial program 100.0%

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

   3. Taylor expanded in b around 0 100.0%

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

   4. Taylor expanded in y around inf 97.7%

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

4. Final simplification 73.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -9 \cdot 10^{-15}:\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{elif}\;b \leq -2 \cdot 10^{-297}:\\ \;\;\;\;x + \left(z + a \cdot \left(1 - t\right)\right)\\ \mathbf{elif}\;b \leq 8.5 \cdot 10^{-294}:\\ \;\;\;\;x - y \cdot z\\ \mathbf{elif}\;b \leq 3.7 \cdot 10^{-25}:\\ \;\;\;\;x + \left(z + a \cdot \left(1 - t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 69.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(z + a \cdot \left(1 - t\right)\right)\\ t_2 := x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{if}\;b \leq -8 \cdot 10^{-15}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -1.5 \cdot 10^{-207}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 9.6 \cdot 10^{-294}:\\ \;\;\;\;z \cdot \left(1 - y\right) - t \cdot a\\ \mathbf{elif}\;b \leq 8 \cdot 10^{-25}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (+ z (* a (- 1.0 t))))) (t_2 (+ x (* b (- (+ y t) 2.0)))))
   (if (<= b -8e-15)
     t_2
     (if (<= b -1.5e-207)
       t_1
       (if (<= b 9.6e-294)
         (- (* z (- 1.0 y)) (* t a))
         (if (<= b 8e-25) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (z + (a * (1.0 - t)));
	double t_2 = x + (b * ((y + t) - 2.0));
	double tmp;
	if (b <= -8e-15) {
		tmp = t_2;
	} else if (b <= -1.5e-207) {
		tmp = t_1;
	} else if (b <= 9.6e-294) {
		tmp = (z * (1.0 - y)) - (t * a);
	} else if (b <= 8e-25) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + (z + (a * (1.0d0 - t)))
    t_2 = x + (b * ((y + t) - 2.0d0))
    if (b <= (-8d-15)) then
        tmp = t_2
    else if (b <= (-1.5d-207)) then
        tmp = t_1
    else if (b <= 9.6d-294) then
        tmp = (z * (1.0d0 - y)) - (t * a)
    else if (b <= 8d-25) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (z + (a * (1.0 - t)));
	double t_2 = x + (b * ((y + t) - 2.0));
	double tmp;
	if (b <= -8e-15) {
		tmp = t_2;
	} else if (b <= -1.5e-207) {
		tmp = t_1;
	} else if (b <= 9.6e-294) {
		tmp = (z * (1.0 - y)) - (t * a);
	} else if (b <= 8e-25) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (z + (a * (1.0 - t)))
	t_2 = x + (b * ((y + t) - 2.0))
	tmp = 0
	if b <= -8e-15:
		tmp = t_2
	elif b <= -1.5e-207:
		tmp = t_1
	elif b <= 9.6e-294:
		tmp = (z * (1.0 - y)) - (t * a)
	elif b <= 8e-25:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(z + Float64(a * Float64(1.0 - t))))
	t_2 = Float64(x + Float64(b * Float64(Float64(y + t) - 2.0)))
	tmp = 0.0
	if (b <= -8e-15)
		tmp = t_2;
	elseif (b <= -1.5e-207)
		tmp = t_1;
	elseif (b <= 9.6e-294)
		tmp = Float64(Float64(z * Float64(1.0 - y)) - Float64(t * a));
	elseif (b <= 8e-25)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (z + (a * (1.0 - t)));
	t_2 = x + (b * ((y + t) - 2.0));
	tmp = 0.0;
	if (b <= -8e-15)
		tmp = t_2;
	elseif (b <= -1.5e-207)
		tmp = t_1;
	elseif (b <= 9.6e-294)
		tmp = (z * (1.0 - y)) - (t * a);
	elseif (b <= 8e-25)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(z + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -8e-15], t$95$2, If[LessEqual[b, -1.5e-207], t$95$1, If[LessEqual[b, 9.6e-294], N[(N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 8e-25], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -8.0000000000000006e-15 or 8.00000000000000031e-25 < b

   1. Initial program 87.4%

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

   3. Taylor expanded in z around 0 85.3%

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

   4. Taylor expanded in a around 0 76.2%

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

   if -8.0000000000000006e-15 < b < -1.5e-207 or 9.59999999999999988e-294 < b < 8.00000000000000031e-25

   1. Initial program 100.0%

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

   3. Taylor expanded in b around 0 92.4%

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

   4. Taylor expanded in y around 0 71.1%

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

      1. +-commutative 71.1%

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

      2. sub-neg 71.1%

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

      3. metadata-eval 71.1%

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

      4. neg-mul-1 71.1%

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

      5. unsub-neg 71.1%

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

   6. Simplified 71.1%

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

   if -1.5e-207 < b < 9.59999999999999988e-294

   1. Initial program 100.0%

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

   3. Taylor expanded in b around 0 95.1%

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

   4. Taylor expanded in t around inf 85.4%

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

      1. *-commutative 25.5%

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

   6. Simplified 85.4%

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

   7. Taylor expanded in x around 0 80.4%

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

      1. mul-1-neg 80.4%

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

      2. +-commutative 80.4%

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

      3. sub-neg 80.4%

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

      4. metadata-eval 80.4%

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

      5. *-commutative 80.4%

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

      6. distribute-neg-in 80.4%

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

      7. sub-neg 80.4%

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

      8. distribute-rgt-neg-in 80.4%

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

      9. +-commutative 80.4%

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

      10. distribute-neg-in 80.4%

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

      11. metadata-eval 80.4%

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

      12. sub-neg 80.4%

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

      13. *-commutative 80.4%

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

   9. Simplified 80.4%

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

4. Final simplification 74.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -8 \cdot 10^{-15}:\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{elif}\;b \leq -1.5 \cdot 10^{-207}:\\ \;\;\;\;x + \left(z + a \cdot \left(1 - t\right)\right)\\ \mathbf{elif}\;b \leq 9.6 \cdot 10^{-294}:\\ \;\;\;\;z \cdot \left(1 - y\right) - t \cdot a\\ \mathbf{elif}\;b \leq 8 \cdot 10^{-25}:\\ \;\;\;\;x + \left(z + a \cdot \left(1 - t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 49.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(b - z\right)\\ \mathbf{if}\;y \leq -2.6 \cdot 10^{+126}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -6.2 \cdot 10^{+57}:\\ \;\;\;\;x - t \cdot a\\ \mathbf{elif}\;y \leq -1.6 \cdot 10^{+37} \lor \neg \left(y \leq 1.6 \cdot 10^{+32}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x + b \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (- b z))))
   (if (<= y -2.6e+126)
     t_1
     (if (<= y -6.2e+57)
       (- x (* t a))
       (if (or (<= y -1.6e+37) (not (<= y 1.6e+32))) t_1 (+ x (* b t)))))))

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 <= -2.6e+126) {
		tmp = t_1;
	} else if (y <= -6.2e+57) {
		tmp = x - (t * a);
	} else if ((y <= -1.6e+37) || !(y <= 1.6e+32)) {
		tmp = t_1;
	} else {
		tmp = x + (b * 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) :: t_1
    real(8) :: tmp
    t_1 = y * (b - z)
    if (y <= (-2.6d+126)) then
        tmp = t_1
    else if (y <= (-6.2d+57)) then
        tmp = x - (t * a)
    else if ((y <= (-1.6d+37)) .or. (.not. (y <= 1.6d+32))) then
        tmp = t_1
    else
        tmp = x + (b * 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 t_1 = y * (b - z);
	double tmp;
	if (y <= -2.6e+126) {
		tmp = t_1;
	} else if (y <= -6.2e+57) {
		tmp = x - (t * a);
	} else if ((y <= -1.6e+37) || !(y <= 1.6e+32)) {
		tmp = t_1;
	} else {
		tmp = x + (b * t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y * (b - z)
	tmp = 0
	if y <= -2.6e+126:
		tmp = t_1
	elif y <= -6.2e+57:
		tmp = x - (t * a)
	elif (y <= -1.6e+37) or not (y <= 1.6e+32):
		tmp = t_1
	else:
		tmp = x + (b * t)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y * Float64(b - z))
	tmp = 0.0
	if (y <= -2.6e+126)
		tmp = t_1;
	elseif (y <= -6.2e+57)
		tmp = Float64(x - Float64(t * a));
	elseif ((y <= -1.6e+37) || !(y <= 1.6e+32))
		tmp = t_1;
	else
		tmp = Float64(x + Float64(b * t));
	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 <= -2.6e+126)
		tmp = t_1;
	elseif (y <= -6.2e+57)
		tmp = x - (t * a);
	elseif ((y <= -1.6e+37) || ~((y <= 1.6e+32)))
		tmp = t_1;
	else
		tmp = x + (b * t);
	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, -2.6e+126], t$95$1, If[LessEqual[y, -6.2e+57], N[(x - N[(t * a), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, -1.6e+37], N[Not[LessEqual[y, 1.6e+32]], $MachinePrecision]], t$95$1, N[(x + N[(b * t), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.6e126 or -6.20000000000000026e57 < y < -1.60000000000000007e37 or 1.5999999999999999e32 < y

   1. Initial program 88.7%

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

   3. Taylor expanded in y around inf 75.0%

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

   if -2.6e126 < y < -6.20000000000000026e57

   1. Initial program 92.9%

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

   3. Taylor expanded in z around 0 86.1%

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

   4. Taylor expanded in b around 0 71.4%

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

   5. Taylor expanded in t around inf 58.4%

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

      1. *-commutative 58.4%

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

   7. Simplified 58.4%

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

   if -1.60000000000000007e37 < y < 1.5999999999999999e32

   1. Initial program 97.2%

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

   3. Taylor expanded in z around 0 85.6%

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

   4. Taylor expanded in a around 0 61.5%

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

   5. Taylor expanded in t around inf 48.7%

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

4. Final simplification 59.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{+126}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;y \leq -6.2 \cdot 10^{+57}:\\ \;\;\;\;x - t \cdot a\\ \mathbf{elif}\;y \leq -1.6 \cdot 10^{+37} \lor \neg \left(y \leq 1.6 \cdot 10^{+32}\right):\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{else}:\\ \;\;\;\;x + b \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 35.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(1 - t\right)\\ t_2 := y \cdot \left(-z\right)\\ \mathbf{if}\;z \leq -8 \cdot 10^{+101}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -5.3 \cdot 10^{-191}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{-99}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{+159}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (- 1.0 t))) (t_2 (* y (- z))))
   (if (<= z -8e+101)
     t_2
     (if (<= z -5.3e-191)
       t_1
       (if (<= z 1.65e-99) (+ x a) (if (<= z 5.8e+159) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double t_2 = y * -z;
	double tmp;
	if (z <= -8e+101) {
		tmp = t_2;
	} else if (z <= -5.3e-191) {
		tmp = t_1;
	} else if (z <= 1.65e-99) {
		tmp = x + a;
	} else if (z <= 5.8e+159) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a * (1.0d0 - t)
    t_2 = y * -z
    if (z <= (-8d+101)) then
        tmp = t_2
    else if (z <= (-5.3d-191)) then
        tmp = t_1
    else if (z <= 1.65d-99) then
        tmp = x + a
    else if (z <= 5.8d+159) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double t_2 = y * -z;
	double tmp;
	if (z <= -8e+101) {
		tmp = t_2;
	} else if (z <= -5.3e-191) {
		tmp = t_1;
	} else if (z <= 1.65e-99) {
		tmp = x + a;
	} else if (z <= 5.8e+159) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (1.0 - t)
	t_2 = y * -z
	tmp = 0
	if z <= -8e+101:
		tmp = t_2
	elif z <= -5.3e-191:
		tmp = t_1
	elif z <= 1.65e-99:
		tmp = x + a
	elif z <= 5.8e+159:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(1.0 - t))
	t_2 = Float64(y * Float64(-z))
	tmp = 0.0
	if (z <= -8e+101)
		tmp = t_2;
	elseif (z <= -5.3e-191)
		tmp = t_1;
	elseif (z <= 1.65e-99)
		tmp = Float64(x + a);
	elseif (z <= 5.8e+159)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (1.0 - t);
	t_2 = y * -z;
	tmp = 0.0;
	if (z <= -8e+101)
		tmp = t_2;
	elseif (z <= -5.3e-191)
		tmp = t_1;
	elseif (z <= 1.65e-99)
		tmp = x + a;
	elseif (z <= 5.8e+159)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * (-z)), $MachinePrecision]}, If[LessEqual[z, -8e+101], t$95$2, If[LessEqual[z, -5.3e-191], t$95$1, If[LessEqual[z, 1.65e-99], N[(x + a), $MachinePrecision], If[LessEqual[z, 5.8e+159], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.9999999999999998e101 or 5.80000000000000029e159 < z

   1. Initial program 88.2%

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

   3. Taylor expanded in z around inf 65.2%

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

   4. Taylor expanded in y around inf 50.5%

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

      1. mul-1-neg 50.5%

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

      2. distribute-lft-neg-out 50.5%

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

      3. *-commutative 50.5%

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

   6. Simplified 50.5%

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

   if -7.9999999999999998e101 < z < -5.29999999999999985e-191 or 1.64999999999999993e-99 < z < 5.80000000000000029e159

   1. Initial program 96.4%

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

   3. Taylor expanded in a around inf 41.2%

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

   if -5.29999999999999985e-191 < z < 1.64999999999999993e-99

   1. Initial program 95.5%

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

   3. Taylor expanded in z around 0 95.5%

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

   4. Taylor expanded in b around 0 49.9%

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

   5. Taylor expanded in t around 0 38.1%

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

      1. neg-mul-1 38.1%

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

   7. Simplified 38.1%

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

4. Final simplification 43.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{+101}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;z \leq -5.3 \cdot 10^{-191}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{-99}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{+159}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 34.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(1 - t\right)\\ \mathbf{if}\;x \leq -7 \cdot 10^{+158}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;x \leq -1.8 \cdot 10^{-71}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.4 \cdot 10^{-299}:\\ \;\;\;\;b \cdot \left(y - 2\right)\\ \mathbf{elif}\;x \leq 3.9 \cdot 10^{+139}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x + a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (- 1.0 t))))
   (if (<= x -7e+158)
     (+ x a)
     (if (<= x -1.8e-71)
       t_1
       (if (<= x 1.4e-299)
         (* b (- y 2.0))
         (if (<= x 3.9e+139) t_1 (+ x a)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double tmp;
	if (x <= -7e+158) {
		tmp = x + a;
	} else if (x <= -1.8e-71) {
		tmp = t_1;
	} else if (x <= 1.4e-299) {
		tmp = b * (y - 2.0);
	} else if (x <= 3.9e+139) {
		tmp = t_1;
	} else {
		tmp = x + a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (1.0d0 - t)
    if (x <= (-7d+158)) then
        tmp = x + a
    else if (x <= (-1.8d-71)) then
        tmp = t_1
    else if (x <= 1.4d-299) then
        tmp = b * (y - 2.0d0)
    else if (x <= 3.9d+139) then
        tmp = t_1
    else
        tmp = x + a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double tmp;
	if (x <= -7e+158) {
		tmp = x + a;
	} else if (x <= -1.8e-71) {
		tmp = t_1;
	} else if (x <= 1.4e-299) {
		tmp = b * (y - 2.0);
	} else if (x <= 3.9e+139) {
		tmp = t_1;
	} else {
		tmp = x + a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (1.0 - t)
	tmp = 0
	if x <= -7e+158:
		tmp = x + a
	elif x <= -1.8e-71:
		tmp = t_1
	elif x <= 1.4e-299:
		tmp = b * (y - 2.0)
	elif x <= 3.9e+139:
		tmp = t_1
	else:
		tmp = x + a
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(1.0 - t))
	tmp = 0.0
	if (x <= -7e+158)
		tmp = Float64(x + a);
	elseif (x <= -1.8e-71)
		tmp = t_1;
	elseif (x <= 1.4e-299)
		tmp = Float64(b * Float64(y - 2.0));
	elseif (x <= 3.9e+139)
		tmp = t_1;
	else
		tmp = Float64(x + a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (1.0 - t);
	tmp = 0.0;
	if (x <= -7e+158)
		tmp = x + a;
	elseif (x <= -1.8e-71)
		tmp = t_1;
	elseif (x <= 1.4e-299)
		tmp = b * (y - 2.0);
	elseif (x <= 3.9e+139)
		tmp = t_1;
	else
		tmp = x + a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -7e+158], N[(x + a), $MachinePrecision], If[LessEqual[x, -1.8e-71], t$95$1, If[LessEqual[x, 1.4e-299], N[(b * N[(y - 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.9e+139], t$95$1, N[(x + a), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -7.0000000000000003e158 or 3.90000000000000006e139 < x

   1. Initial program 97.3%

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

   3. Taylor expanded in z around 0 87.9%

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

   4. Taylor expanded in b around 0 62.8%

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

   5. Taylor expanded in t around 0 55.6%

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

      1. neg-mul-1 55.6%

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

   7. Simplified 55.6%

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

   if -7.0000000000000003e158 < x < -1.8e-71 or 1.4000000000000001e-299 < x < 3.90000000000000006e139

   1. Initial program 92.0%

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

   3. Taylor expanded in a around inf 41.8%

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

   if -1.8e-71 < x < 1.4000000000000001e-299

   1. Initial program 93.5%

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

   3. Taylor expanded in b around inf 58.9%

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

   4. Taylor expanded in t around 0 42.0%

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

4. Final simplification 45.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7 \cdot 10^{+158}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;x \leq -1.8 \cdot 10^{-71}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;x \leq 1.4 \cdot 10^{-299}:\\ \;\;\;\;b \cdot \left(y - 2\right)\\ \mathbf{elif}\;x \leq 3.9 \cdot 10^{+139}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + a\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 51.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - y \cdot z\\ t_2 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -10200:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 4 \cdot 10^{-229}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 7.8 \cdot 10^{-132}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;t \leq 1.08 \cdot 10^{+21}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- x (* y z))) (t_2 (* t (- b a))))
   (if (<= t -10200.0)
     t_2
     (if (<= t 4e-229)
       t_1
       (if (<= t 7.8e-132) (* y (- b z)) (if (<= t 1.08e+21) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x - (y * z);
	double t_2 = t * (b - a);
	double tmp;
	if (t <= -10200.0) {
		tmp = t_2;
	} else if (t <= 4e-229) {
		tmp = t_1;
	} else if (t <= 7.8e-132) {
		tmp = y * (b - z);
	} else if (t <= 1.08e+21) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x - (y * z)
    t_2 = t * (b - a)
    if (t <= (-10200.0d0)) then
        tmp = t_2
    else if (t <= 4d-229) then
        tmp = t_1
    else if (t <= 7.8d-132) then
        tmp = y * (b - z)
    else if (t <= 1.08d+21) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x - (y * z);
	double t_2 = t * (b - a);
	double tmp;
	if (t <= -10200.0) {
		tmp = t_2;
	} else if (t <= 4e-229) {
		tmp = t_1;
	} else if (t <= 7.8e-132) {
		tmp = y * (b - z);
	} else if (t <= 1.08e+21) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x - (y * z)
	t_2 = t * (b - a)
	tmp = 0
	if t <= -10200.0:
		tmp = t_2
	elif t <= 4e-229:
		tmp = t_1
	elif t <= 7.8e-132:
		tmp = y * (b - z)
	elif t <= 1.08e+21:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x - Float64(y * z))
	t_2 = Float64(t * Float64(b - a))
	tmp = 0.0
	if (t <= -10200.0)
		tmp = t_2;
	elseif (t <= 4e-229)
		tmp = t_1;
	elseif (t <= 7.8e-132)
		tmp = Float64(y * Float64(b - z));
	elseif (t <= 1.08e+21)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x - (y * z);
	t_2 = t * (b - a);
	tmp = 0.0;
	if (t <= -10200.0)
		tmp = t_2;
	elseif (t <= 4e-229)
		tmp = t_1;
	elseif (t <= 7.8e-132)
		tmp = y * (b - z);
	elseif (t <= 1.08e+21)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -10200.0], t$95$2, If[LessEqual[t, 4e-229], t$95$1, If[LessEqual[t, 7.8e-132], N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.08e+21], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -10200 or 1.08e21 < t

   1. Initial program 91.9%

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

   3. Taylor expanded in t around inf 69.3%

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

   if -10200 < t < 4.00000000000000028e-229 or 7.79999999999999964e-132 < t < 1.08e21

   1. Initial program 95.7%

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

   3. Taylor expanded in b around 0 74.0%

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

   4. Taylor expanded in y around inf 50.9%

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

   if 4.00000000000000028e-229 < t < 7.79999999999999964e-132

   1. Initial program 92.9%

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

   3. Taylor expanded in y around inf 64.4%

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

4. Final simplification 60.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -10200:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq 4 \cdot 10^{-229}:\\ \;\;\;\;x - y \cdot z\\ \mathbf{elif}\;t \leq 7.8 \cdot 10^{-132}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;t \leq 1.08 \cdot 10^{+21}:\\ \;\;\;\;x - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 86.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -6.8 \cdot 10^{-15} \lor \neg \left(b \leq 1.05 \cdot 10^{-51}\right):\\ \;\;\;\;\left(x + b \cdot \left(\left(y + t\right) - 2\right)\right) + a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;x - \left(a \cdot \left(t + -1\right) + z \cdot \left(y + -1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -6.8e-15) (not (<= b 1.05e-51)))
   (+ (+ x (* b (- (+ y t) 2.0))) (* a (- 1.0 t)))
   (- x (+ (* a (+ t -1.0)) (* z (+ y -1.0))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -6.8e-15) || !(b <= 1.05e-51)) {
		tmp = (x + (b * ((y + t) - 2.0))) + (a * (1.0 - t));
	} else {
		tmp = x - ((a * (t + -1.0)) + (z * (y + -1.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-6.8d-15)) .or. (.not. (b <= 1.05d-51))) then
        tmp = (x + (b * ((y + t) - 2.0d0))) + (a * (1.0d0 - t))
    else
        tmp = x - ((a * (t + (-1.0d0))) + (z * (y + (-1.0d0))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -6.8e-15) || !(b <= 1.05e-51)) {
		tmp = (x + (b * ((y + t) - 2.0))) + (a * (1.0 - t));
	} else {
		tmp = x - ((a * (t + -1.0)) + (z * (y + -1.0)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -6.8e-15) or not (b <= 1.05e-51):
		tmp = (x + (b * ((y + t) - 2.0))) + (a * (1.0 - t))
	else:
		tmp = x - ((a * (t + -1.0)) + (z * (y + -1.0)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -6.8e-15) || !(b <= 1.05e-51))
		tmp = Float64(Float64(x + Float64(b * Float64(Float64(y + t) - 2.0))) + Float64(a * Float64(1.0 - t)));
	else
		tmp = Float64(x - Float64(Float64(a * Float64(t + -1.0)) + Float64(z * Float64(y + -1.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -6.8e-15) || ~((b <= 1.05e-51)))
		tmp = (x + (b * ((y + t) - 2.0))) + (a * (1.0 - t));
	else
		tmp = x - ((a * (t + -1.0)) + (z * (y + -1.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -6.8e-15], N[Not[LessEqual[b, 1.05e-51]], $MachinePrecision]], N[(N[(x + N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(a * N[(t + -1.0), $MachinePrecision]), $MachinePrecision] + N[(z * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -6.8000000000000001e-15 or 1.05000000000000001e-51 < b

   1. Initial program 88.2%

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

   3. Taylor expanded in z around 0 86.2%

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

   if -6.8000000000000001e-15 < b < 1.05000000000000001e-51

   1. Initial program 100.0%

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

   3. Taylor expanded in b around 0 93.1%

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

4. Final simplification 89.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -6.8 \cdot 10^{-15} \lor \neg \left(b \leq 1.05 \cdot 10^{-51}\right):\\ \;\;\;\;\left(x + b \cdot \left(\left(y + t\right) - 2\right)\right) + a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;x - \left(a \cdot \left(t + -1\right) + z \cdot \left(y + -1\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 26.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6.4 \cdot 10^{+44}:\\ \;\;\;\;b \cdot t\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{-231}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 2.25 \cdot 10^{-132}:\\ \;\;\;\;b \cdot y\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{+19}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;b \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -6.4e+44)
   (* b t)
   (if (<= t 7.5e-231)
     x
     (if (<= t 2.25e-132) (* b y) (if (<= t 1.35e+19) x (* b t))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -6.4e+44) {
		tmp = b * t;
	} else if (t <= 7.5e-231) {
		tmp = x;
	} else if (t <= 2.25e-132) {
		tmp = b * y;
	} else if (t <= 1.35e+19) {
		tmp = x;
	} else {
		tmp = b * 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 (t <= (-6.4d+44)) then
        tmp = b * t
    else if (t <= 7.5d-231) then
        tmp = x
    else if (t <= 2.25d-132) then
        tmp = b * y
    else if (t <= 1.35d+19) then
        tmp = x
    else
        tmp = b * 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 (t <= -6.4e+44) {
		tmp = b * t;
	} else if (t <= 7.5e-231) {
		tmp = x;
	} else if (t <= 2.25e-132) {
		tmp = b * y;
	} else if (t <= 1.35e+19) {
		tmp = x;
	} else {
		tmp = b * t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -6.4e+44:
		tmp = b * t
	elif t <= 7.5e-231:
		tmp = x
	elif t <= 2.25e-132:
		tmp = b * y
	elif t <= 1.35e+19:
		tmp = x
	else:
		tmp = b * t
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -6.4e+44)
		tmp = Float64(b * t);
	elseif (t <= 7.5e-231)
		tmp = x;
	elseif (t <= 2.25e-132)
		tmp = Float64(b * y);
	elseif (t <= 1.35e+19)
		tmp = x;
	else
		tmp = Float64(b * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -6.4e+44)
		tmp = b * t;
	elseif (t <= 7.5e-231)
		tmp = x;
	elseif (t <= 2.25e-132)
		tmp = b * y;
	elseif (t <= 1.35e+19)
		tmp = x;
	else
		tmp = b * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -6.4e+44], N[(b * t), $MachinePrecision], If[LessEqual[t, 7.5e-231], x, If[LessEqual[t, 2.25e-132], N[(b * y), $MachinePrecision], If[LessEqual[t, 1.35e+19], x, N[(b * t), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -6.40000000000000009e44 or 1.35e19 < t

   1. Initial program 91.1%

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

   3. Taylor expanded in b around inf 47.2%

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

   4. Taylor expanded in t around inf 41.3%

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

   if -6.40000000000000009e44 < t < 7.5000000000000001e-231 or 2.25e-132 < t < 1.35e19

   1. Initial program 96.1%

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

   3. Taylor expanded in x around inf 27.2%

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

   if 7.5000000000000001e-231 < t < 2.25e-132

   1. Initial program 92.9%

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

   3. Taylor expanded in z around 0 72.8%

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

   4. Taylor expanded in y around inf 43.1%

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

4. Final simplification 34.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.4 \cdot 10^{+44}:\\ \;\;\;\;b \cdot t\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{-231}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 2.25 \cdot 10^{-132}:\\ \;\;\;\;b \cdot y\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{+19}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;b \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 82.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{if}\;b \leq -9 \cdot 10^{-15}:\\ \;\;\;\;x + t\_1\\ \mathbf{elif}\;b \leq 4 \cdot 10^{+145}:\\ \;\;\;\;x - \left(a \cdot \left(t + -1\right) + z \cdot \left(y + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- (+ y t) 2.0))))
   (if (<= b -9e-15)
     (+ x t_1)
     (if (<= b 4e+145) (- x (+ (* a (+ t -1.0)) (* z (+ y -1.0)))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * ((y + t) - 2.0);
	double tmp;
	if (b <= -9e-15) {
		tmp = x + t_1;
	} else if (b <= 4e+145) {
		tmp = x - ((a * (t + -1.0)) + (z * (y + -1.0)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * ((y + t) - 2.0d0)
    if (b <= (-9d-15)) then
        tmp = x + t_1
    else if (b <= 4d+145) then
        tmp = x - ((a * (t + (-1.0d0))) + (z * (y + (-1.0d0))))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * ((y + t) - 2.0);
	double tmp;
	if (b <= -9e-15) {
		tmp = x + t_1;
	} else if (b <= 4e+145) {
		tmp = x - ((a * (t + -1.0)) + (z * (y + -1.0)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * ((y + t) - 2.0)
	tmp = 0
	if b <= -9e-15:
		tmp = x + t_1
	elif b <= 4e+145:
		tmp = x - ((a * (t + -1.0)) + (z * (y + -1.0)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(Float64(y + t) - 2.0))
	tmp = 0.0
	if (b <= -9e-15)
		tmp = Float64(x + t_1);
	elseif (b <= 4e+145)
		tmp = Float64(x - Float64(Float64(a * Float64(t + -1.0)) + Float64(z * Float64(y + -1.0))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * ((y + t) - 2.0);
	tmp = 0.0;
	if (b <= -9e-15)
		tmp = x + t_1;
	elseif (b <= 4e+145)
		tmp = x - ((a * (t + -1.0)) + (z * (y + -1.0)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -9e-15], N[(x + t$95$1), $MachinePrecision], If[LessEqual[b, 4e+145], N[(x - N[(N[(a * N[(t + -1.0), $MachinePrecision]), $MachinePrecision] + N[(z * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 3 regimes

2. if b < -8.9999999999999995e-15

   1. Initial program 87.7%

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

   3. Taylor expanded in z around 0 88.0%

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

   4. Taylor expanded in a around 0 76.1%

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

   if -8.9999999999999995e-15 < b < 4e145

   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 88.2%

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

   if 4e145 < b

   1. Initial program 82.1%

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

   3. Taylor expanded in b around inf 88.8%

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

4. Final simplification 85.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -9 \cdot 10^{-15}:\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{elif}\;b \leq 4 \cdot 10^{+145}:\\ \;\;\;\;x - \left(a \cdot \left(t + -1\right) + z \cdot \left(y + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 55.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{if}\;b \leq -2000000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 7.5 \cdot 10^{-235}:\\ \;\;\;\;x - y \cdot z\\ \mathbf{elif}\;b \leq 2 \cdot 10^{+40}:\\ \;\;\;\;x - t \cdot a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- (+ y t) 2.0))))
   (if (<= b -2000000000000.0)
     t_1
     (if (<= b 7.5e-235) (- x (* y z)) (if (<= b 2e+40) (- x (* t a)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * ((y + t) - 2.0);
	double tmp;
	if (b <= -2000000000000.0) {
		tmp = t_1;
	} else if (b <= 7.5e-235) {
		tmp = x - (y * z);
	} else if (b <= 2e+40) {
		tmp = x - (t * a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * ((y + t) - 2.0d0)
    if (b <= (-2000000000000.0d0)) then
        tmp = t_1
    else if (b <= 7.5d-235) then
        tmp = x - (y * z)
    else if (b <= 2d+40) then
        tmp = x - (t * a)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * ((y + t) - 2.0);
	double tmp;
	if (b <= -2000000000000.0) {
		tmp = t_1;
	} else if (b <= 7.5e-235) {
		tmp = x - (y * z);
	} else if (b <= 2e+40) {
		tmp = x - (t * a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * ((y + t) - 2.0)
	tmp = 0
	if b <= -2000000000000.0:
		tmp = t_1
	elif b <= 7.5e-235:
		tmp = x - (y * z)
	elif b <= 2e+40:
		tmp = x - (t * a)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(Float64(y + t) - 2.0))
	tmp = 0.0
	if (b <= -2000000000000.0)
		tmp = t_1;
	elseif (b <= 7.5e-235)
		tmp = Float64(x - Float64(y * z));
	elseif (b <= 2e+40)
		tmp = Float64(x - Float64(t * a));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * ((y + t) - 2.0);
	tmp = 0.0;
	if (b <= -2000000000000.0)
		tmp = t_1;
	elseif (b <= 7.5e-235)
		tmp = x - (y * z);
	elseif (b <= 2e+40)
		tmp = x - (t * a);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2000000000000.0], t$95$1, If[LessEqual[b, 7.5e-235], N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2e+40], N[(x - N[(t * a), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -2e12 or 2.00000000000000006e40 < b

   1. Initial program 86.5%

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

   3. Taylor expanded in b around inf 72.3%

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

   if -2e12 < b < 7.49999999999999968e-235

   1. Initial program 100.0%

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

   3. Taylor expanded in b around 0 90.6%

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

   4. Taylor expanded in y around inf 57.6%

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

   if 7.49999999999999968e-235 < b < 2.00000000000000006e40

   1. Initial program 98.3%

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

   3. Taylor expanded in z around 0 80.3%

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

   4. Taylor expanded in b around 0 69.2%

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

   5. Taylor expanded in t around inf 62.1%

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

      1. *-commutative 62.1%

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

   7. Simplified 62.1%

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

4. Final simplification 65.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2000000000000:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{elif}\;b \leq 7.5 \cdot 10^{-235}:\\ \;\;\;\;x - y \cdot z\\ \mathbf{elif}\;b \leq 2 \cdot 10^{+40}:\\ \;\;\;\;x - t \cdot a\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 74.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{if}\;b \leq -9 \cdot 10^{-15}:\\ \;\;\;\;x + t\_1\\ \mathbf{elif}\;b \leq 4.3 \cdot 10^{+136}:\\ \;\;\;\;x - \left(z \cdot \left(y + -1\right) + t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- (+ y t) 2.0))))
   (if (<= b -9e-15)
     (+ x t_1)
     (if (<= b 4.3e+136) (- x (+ (* z (+ y -1.0)) (* t a))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * ((y + t) - 2.0);
	double tmp;
	if (b <= -9e-15) {
		tmp = x + t_1;
	} else if (b <= 4.3e+136) {
		tmp = x - ((z * (y + -1.0)) + (t * a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * ((y + t) - 2.0d0)
    if (b <= (-9d-15)) then
        tmp = x + t_1
    else if (b <= 4.3d+136) then
        tmp = x - ((z * (y + (-1.0d0))) + (t * a))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * ((y + t) - 2.0);
	double tmp;
	if (b <= -9e-15) {
		tmp = x + t_1;
	} else if (b <= 4.3e+136) {
		tmp = x - ((z * (y + -1.0)) + (t * a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * ((y + t) - 2.0)
	tmp = 0
	if b <= -9e-15:
		tmp = x + t_1
	elif b <= 4.3e+136:
		tmp = x - ((z * (y + -1.0)) + (t * a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(Float64(y + t) - 2.0))
	tmp = 0.0
	if (b <= -9e-15)
		tmp = Float64(x + t_1);
	elseif (b <= 4.3e+136)
		tmp = Float64(x - Float64(Float64(z * Float64(y + -1.0)) + Float64(t * a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * ((y + t) - 2.0);
	tmp = 0.0;
	if (b <= -9e-15)
		tmp = x + t_1;
	elseif (b <= 4.3e+136)
		tmp = x - ((z * (y + -1.0)) + (t * a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -9e-15], N[(x + t$95$1), $MachinePrecision], If[LessEqual[b, 4.3e+136], N[(x - N[(N[(z * N[(y + -1.0), $MachinePrecision]), $MachinePrecision] + N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 3 regimes

2. if b < -8.9999999999999995e-15

   1. Initial program 87.7%

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

   3. Taylor expanded in z around 0 88.0%

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

   4. Taylor expanded in a around 0 76.1%

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

   if -8.9999999999999995e-15 < b < 4.2999999999999999e136

   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 88.2%

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

   4. Taylor expanded in t around inf 78.5%

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

      1. *-commutative 47.4%

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

   6. Simplified 78.5%

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

   if 4.2999999999999999e136 < b

   1. Initial program 82.1%

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

   3. Taylor expanded in b around inf 88.8%

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

4. Final simplification 79.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -9 \cdot 10^{-15}:\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{elif}\;b \leq 4.3 \cdot 10^{+136}:\\ \;\;\;\;x - \left(z \cdot \left(y + -1\right) + t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 57.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -2.1 \cdot 10^{+35}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{-64}:\\ \;\;\;\;x + b \cdot \left(y - 2\right)\\ \mathbf{elif}\;t \leq 1.08 \cdot 10^{+18}:\\ \;\;\;\;x - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (- b a))))
   (if (<= t -2.1e+35)
     t_1
     (if (<= t 1.6e-64)
       (+ x (* b (- y 2.0)))
       (if (<= t 1.08e+18) (- x (* y z)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (b - a);
	double tmp;
	if (t <= -2.1e+35) {
		tmp = t_1;
	} else if (t <= 1.6e-64) {
		tmp = x + (b * (y - 2.0));
	} else if (t <= 1.08e+18) {
		tmp = x - (y * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (b - a)
    if (t <= (-2.1d+35)) then
        tmp = t_1
    else if (t <= 1.6d-64) then
        tmp = x + (b * (y - 2.0d0))
    else if (t <= 1.08d+18) then
        tmp = x - (y * z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (b - a);
	double tmp;
	if (t <= -2.1e+35) {
		tmp = t_1;
	} else if (t <= 1.6e-64) {
		tmp = x + (b * (y - 2.0));
	} else if (t <= 1.08e+18) {
		tmp = x - (y * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t * (b - a)
	tmp = 0
	if t <= -2.1e+35:
		tmp = t_1
	elif t <= 1.6e-64:
		tmp = x + (b * (y - 2.0))
	elif t <= 1.08e+18:
		tmp = x - (y * z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t * Float64(b - a))
	tmp = 0.0
	if (t <= -2.1e+35)
		tmp = t_1;
	elseif (t <= 1.6e-64)
		tmp = Float64(x + Float64(b * Float64(y - 2.0)));
	elseif (t <= 1.08e+18)
		tmp = Float64(x - Float64(y * z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t * (b - a);
	tmp = 0.0;
	if (t <= -2.1e+35)
		tmp = t_1;
	elseif (t <= 1.6e-64)
		tmp = x + (b * (y - 2.0));
	elseif (t <= 1.08e+18)
		tmp = x - (y * z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.1e+35], t$95$1, If[LessEqual[t, 1.6e-64], N[(x + N[(b * N[(y - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.08e+18], N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.0999999999999999e35 or 1.08e18 < 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 71.2%

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

   if -2.0999999999999999e35 < t < 1.59999999999999988e-64

   1. Initial program 94.5%

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

   3. Taylor expanded in z around 0 73.7%

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

   4. Taylor expanded in a around 0 59.2%

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

   5. Taylor expanded in t around 0 59.2%

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

   if 1.59999999999999988e-64 < t < 1.08e18

   1. Initial program 100.0%

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

   3. Taylor expanded in b around 0 88.7%

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

   4. Taylor expanded in y around inf 53.5%

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

4. Final simplification 64.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.1 \cdot 10^{+35}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{-64}:\\ \;\;\;\;x + b \cdot \left(y - 2\right)\\ \mathbf{elif}\;t \leq 1.08 \cdot 10^{+18}:\\ \;\;\;\;x - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 51.1% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{+37} \lor \neg \left(y \leq 7.5 \cdot 10^{+29}\right):\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{else}:\\ \;\;\;\;x + b \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -9.5e+37) (not (<= y 7.5e+29))) (* y (- b z)) (+ x (* b t))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -9.5e+37) || !(y <= 7.5e+29)) {
		tmp = y * (b - z);
	} else {
		tmp = x + (b * 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 ((y <= (-9.5d+37)) .or. (.not. (y <= 7.5d+29))) then
        tmp = y * (b - z)
    else
        tmp = x + (b * 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 ((y <= -9.5e+37) || !(y <= 7.5e+29)) {
		tmp = y * (b - z);
	} else {
		tmp = x + (b * t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -9.5e+37) or not (y <= 7.5e+29):
		tmp = y * (b - z)
	else:
		tmp = x + (b * t)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -9.5e+37) || !(y <= 7.5e+29))
		tmp = Float64(y * Float64(b - z));
	else
		tmp = Float64(x + Float64(b * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -9.5e+37) || ~((y <= 7.5e+29)))
		tmp = y * (b - z);
	else
		tmp = x + (b * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -9.5e+37], N[Not[LessEqual[y, 7.5e+29]], $MachinePrecision]], N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision], N[(x + N[(b * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -9.4999999999999995e37 or 7.49999999999999945e29 < y

   1. Initial program 89.2%

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

   3. Taylor expanded in y around inf 68.4%

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

   if -9.4999999999999995e37 < y < 7.49999999999999945e29

   1. Initial program 97.2%

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

   3. Taylor expanded in z around 0 85.6%

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

   4. Taylor expanded in a around 0 61.5%

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

   5. Taylor expanded in t around inf 48.7%

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

4. Final simplification 57.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{+37} \lor \neg \left(y \leq 7.5 \cdot 10^{+29}\right):\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{else}:\\ \;\;\;\;x + b \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 26.6% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6.4 \cdot 10^{+44} \lor \neg \left(t \leq 8.5 \cdot 10^{+19}\right):\\ \;\;\;\;b \cdot t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -6.4e+44) (not (<= t 8.5e+19))) (* b t) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -6.4e+44) || !(t <= 8.5e+19)) {
		tmp = b * t;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-6.4d+44)) .or. (.not. (t <= 8.5d+19))) then
        tmp = b * t
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -6.4e+44) || !(t <= 8.5e+19)) {
		tmp = b * t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -6.4e+44) or not (t <= 8.5e+19):
		tmp = b * t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -6.4e+44) || !(t <= 8.5e+19))
		tmp = Float64(b * t);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -6.4e+44) || ~((t <= 8.5e+19)))
		tmp = b * t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -6.4e+44], N[Not[LessEqual[t, 8.5e+19]], $MachinePrecision]], N[(b * t), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if t < -6.40000000000000009e44 or 8.5e19 < t

   1. Initial program 91.1%

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

   3. Taylor expanded in b around inf 47.2%

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

   4. Taylor expanded in t around inf 41.3%

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

   if -6.40000000000000009e44 < t < 8.5e19

   1. Initial program 95.8%

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

   3. Taylor expanded in x around inf 24.8%

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

4. Final simplification 32.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.4 \cdot 10^{+44} \lor \neg \left(t \leq 8.5 \cdot 10^{+19}\right):\\ \;\;\;\;b \cdot t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 20.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.22 \cdot 10^{-14}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.9 \cdot 10^{+139}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -1.22e-14) x (if (<= x 1.9e+139) a x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -1.22e-14) {
		tmp = x;
	} else if (x <= 1.9e+139) {
		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 <= (-1.22d-14)) then
        tmp = x
    else if (x <= 1.9d+139) 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 <= -1.22e-14) {
		tmp = x;
	} else if (x <= 1.9e+139) {
		tmp = a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -1.22e-14:
		tmp = x
	elif x <= 1.9e+139:
		tmp = a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -1.22e-14)
		tmp = x;
	elseif (x <= 1.9e+139)
		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 <= -1.22e-14)
		tmp = x;
	elseif (x <= 1.9e+139)
		tmp = a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -1.22e-14], x, If[LessEqual[x, 1.9e+139], a, x]]

Derivation

1. Split input into 2 regimes

2. if x < -1.21999999999999994e-14 or 1.9e139 < x

   1. Initial program 96.1%

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

   3. Taylor expanded in x around inf 41.6%

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

   if -1.21999999999999994e-14 < x < 1.9e139

   1. Initial program 92.2%

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

   3. Taylor expanded in a around inf 36.0%

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

   4. Taylor expanded in t around 0 12.8%

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

4. Final simplification 24.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.22 \cdot 10^{-14}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.9 \cdot 10^{+139}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 25: 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 93.7%

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

3. Taylor expanded in a around inf 28.4%

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

4. Taylor expanded in t around 0 9.9%

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

5. Final simplification 9.9%

   \[\leadsto a \]
6. Add Preprocessing

Reproduce

herbie shell --seed 2024096 
(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)))