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

Percentage Accurate: 95.5% → 98.6%

Time: 19.4s

Alternatives: 27

Speedup: 0.5×

• 36.4% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 95.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.6% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. fma-define 100.0%

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

      3. associate--l+ 100.0%

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

      4. sub-neg 100.0%

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

      5. metadata-eval 100.0%

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

      6. sub-neg 100.0%

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

      7. associate-+l- 100.0%

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

      8. fma-neg 100.0%

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

      9. sub-neg 100.0%

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

      10. metadata-eval 100.0%

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

      11. remove-double-neg 100.0%

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

      12. sub-neg 100.0%

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

      13. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in z around inf 23.1%

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

      1. associate--l+ 23.1%

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

      2. sub-neg 23.1%

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

      3. metadata-eval 23.1%

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

      4. associate-+r+ 23.1%

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

      5. associate-/l* 61.5%

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

      6. sub-neg 61.5%

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

      7. metadata-eval 61.5%

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

      8. associate-/l* 84.6%

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

   5. Simplified 84.6%

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

4. Final simplification 99.2%

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

Alternative 2: 47.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(y - 2\right)\\ t_2 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -15500000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -1.4 \cdot 10^{-39}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -6.5 \cdot 10^{-55}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq -3.25 \cdot 10^{-131}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -5.5 \cdot 10^{-172}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq -5.1 \cdot 10^{-241}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -4 \cdot 10^{-249}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;t \leq 8 \cdot 10^{-292}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq 3.3 \cdot 10^{-260}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{-260}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{-80}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 9.2 \cdot 10^{-12}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- y 2.0))) (t_2 (* t (- b a))))
   (if (<= t -15500000.0)
     t_2
     (if (<= t -1.4e-39)
       t_1
       (if (<= t -6.5e-55)
         (+ x a)
         (if (<= t -3.25e-131)
           t_1
           (if (<= t -5.5e-172)
             (+ x a)
             (if (<= t -5.1e-241)
               t_1
               (if (<= t -4e-249)
                 (* y (- z))
                 (if (<= t 8e-292)
                   (+ x a)
                   (if (<= t 3.3e-260)
                     t_1
                     (if (<= t 3.5e-260)
                       x
                       (if (<= t 1.5e-80)
                         t_1
                         (if (<= t 9.2e-12) (+ x z) 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 <= -15500000.0) {
		tmp = t_2;
	} else if (t <= -1.4e-39) {
		tmp = t_1;
	} else if (t <= -6.5e-55) {
		tmp = x + a;
	} else if (t <= -3.25e-131) {
		tmp = t_1;
	} else if (t <= -5.5e-172) {
		tmp = x + a;
	} else if (t <= -5.1e-241) {
		tmp = t_1;
	} else if (t <= -4e-249) {
		tmp = y * -z;
	} else if (t <= 8e-292) {
		tmp = x + a;
	} else if (t <= 3.3e-260) {
		tmp = t_1;
	} else if (t <= 3.5e-260) {
		tmp = x;
	} else if (t <= 1.5e-80) {
		tmp = t_1;
	} else if (t <= 9.2e-12) {
		tmp = x + z;
	} 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 <= (-15500000.0d0)) then
        tmp = t_2
    else if (t <= (-1.4d-39)) then
        tmp = t_1
    else if (t <= (-6.5d-55)) then
        tmp = x + a
    else if (t <= (-3.25d-131)) then
        tmp = t_1
    else if (t <= (-5.5d-172)) then
        tmp = x + a
    else if (t <= (-5.1d-241)) then
        tmp = t_1
    else if (t <= (-4d-249)) then
        tmp = y * -z
    else if (t <= 8d-292) then
        tmp = x + a
    else if (t <= 3.3d-260) then
        tmp = t_1
    else if (t <= 3.5d-260) then
        tmp = x
    else if (t <= 1.5d-80) then
        tmp = t_1
    else if (t <= 9.2d-12) then
        tmp = x + z
    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 <= -15500000.0) {
		tmp = t_2;
	} else if (t <= -1.4e-39) {
		tmp = t_1;
	} else if (t <= -6.5e-55) {
		tmp = x + a;
	} else if (t <= -3.25e-131) {
		tmp = t_1;
	} else if (t <= -5.5e-172) {
		tmp = x + a;
	} else if (t <= -5.1e-241) {
		tmp = t_1;
	} else if (t <= -4e-249) {
		tmp = y * -z;
	} else if (t <= 8e-292) {
		tmp = x + a;
	} else if (t <= 3.3e-260) {
		tmp = t_1;
	} else if (t <= 3.5e-260) {
		tmp = x;
	} else if (t <= 1.5e-80) {
		tmp = t_1;
	} else if (t <= 9.2e-12) {
		tmp = x + z;
	} 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 <= -15500000.0:
		tmp = t_2
	elif t <= -1.4e-39:
		tmp = t_1
	elif t <= -6.5e-55:
		tmp = x + a
	elif t <= -3.25e-131:
		tmp = t_1
	elif t <= -5.5e-172:
		tmp = x + a
	elif t <= -5.1e-241:
		tmp = t_1
	elif t <= -4e-249:
		tmp = y * -z
	elif t <= 8e-292:
		tmp = x + a
	elif t <= 3.3e-260:
		tmp = t_1
	elif t <= 3.5e-260:
		tmp = x
	elif t <= 1.5e-80:
		tmp = t_1
	elif t <= 9.2e-12:
		tmp = x + z
	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 <= -15500000.0)
		tmp = t_2;
	elseif (t <= -1.4e-39)
		tmp = t_1;
	elseif (t <= -6.5e-55)
		tmp = Float64(x + a);
	elseif (t <= -3.25e-131)
		tmp = t_1;
	elseif (t <= -5.5e-172)
		tmp = Float64(x + a);
	elseif (t <= -5.1e-241)
		tmp = t_1;
	elseif (t <= -4e-249)
		tmp = Float64(y * Float64(-z));
	elseif (t <= 8e-292)
		tmp = Float64(x + a);
	elseif (t <= 3.3e-260)
		tmp = t_1;
	elseif (t <= 3.5e-260)
		tmp = x;
	elseif (t <= 1.5e-80)
		tmp = t_1;
	elseif (t <= 9.2e-12)
		tmp = Float64(x + z);
	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 <= -15500000.0)
		tmp = t_2;
	elseif (t <= -1.4e-39)
		tmp = t_1;
	elseif (t <= -6.5e-55)
		tmp = x + a;
	elseif (t <= -3.25e-131)
		tmp = t_1;
	elseif (t <= -5.5e-172)
		tmp = x + a;
	elseif (t <= -5.1e-241)
		tmp = t_1;
	elseif (t <= -4e-249)
		tmp = y * -z;
	elseif (t <= 8e-292)
		tmp = x + a;
	elseif (t <= 3.3e-260)
		tmp = t_1;
	elseif (t <= 3.5e-260)
		tmp = x;
	elseif (t <= 1.5e-80)
		tmp = t_1;
	elseif (t <= 9.2e-12)
		tmp = x + z;
	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, -15500000.0], t$95$2, If[LessEqual[t, -1.4e-39], t$95$1, If[LessEqual[t, -6.5e-55], N[(x + a), $MachinePrecision], If[LessEqual[t, -3.25e-131], t$95$1, If[LessEqual[t, -5.5e-172], N[(x + a), $MachinePrecision], If[LessEqual[t, -5.1e-241], t$95$1, If[LessEqual[t, -4e-249], N[(y * (-z)), $MachinePrecision], If[LessEqual[t, 8e-292], N[(x + a), $MachinePrecision], If[LessEqual[t, 3.3e-260], t$95$1, If[LessEqual[t, 3.5e-260], x, If[LessEqual[t, 1.5e-80], t$95$1, If[LessEqual[t, 9.2e-12], N[(x + z), $MachinePrecision], t$95$2]]]]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if t < -1.55e7 or 9.19999999999999957e-12 < t

   1. Initial program 90.1%

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

   3. Taylor expanded in t around inf 77.6%

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

   if -1.55e7 < t < -1.4000000000000001e-39 or -6.50000000000000006e-55 < t < -3.2500000000000001e-131 or -5.5000000000000004e-172 < t < -5.0999999999999998e-241 or 8.0000000000000004e-292 < t < 3.2999999999999997e-260 or 3.5e-260 < t < 1.50000000000000004e-80

   1. Initial program 98.6%

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

   3. Taylor expanded in y around inf 65.2%

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

      1. mul-1-neg 65.2%

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

      2. *-commutative 65.2%

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

      3. distribute-rgt-neg-in 65.2%

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

   5. Simplified 65.2%

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

   6. Taylor expanded in t around 0 64.0%

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

   7. Taylor expanded in z around 0 46.8%

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

   if -1.4000000000000001e-39 < t < -6.50000000000000006e-55 or -3.2500000000000001e-131 < t < -5.5000000000000004e-172 or -4.00000000000000022e-249 < t < 8.0000000000000004e-292

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 79.5%

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

   4. Taylor expanded in t around 0 79.5%

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

      1. associate--l+ 79.5%

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

      2. sub-neg 79.5%

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

      3. metadata-eval 79.5%

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

      4. neg-mul-1 79.5%

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

   6. Simplified 79.5%

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

      1. sub-neg 79.5%

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

      2. remove-double-neg 79.5%

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

   8. Applied egg-rr 79.5%

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

   9. Taylor expanded in b around 0 53.8%

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

   if -5.0999999999999998e-241 < t < -4.00000000000000022e-249

   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 68.5%

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

   4. Taylor expanded in y around inf 68.5%

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

      1. mul-1-neg 68.5%

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

      2. distribute-lft-neg-out 68.5%

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

      3. *-commutative 68.5%

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

   6. Simplified 68.5%

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

   if 3.2999999999999997e-260 < t < 3.5e-260

   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 100.0%

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

   if 1.50000000000000004e-80 < t < 9.19999999999999957e-12

   1. Initial program 100.0%

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

   3. Taylor expanded in a around 0 82.2%

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

   4. Taylor expanded in y around 0 55.1%

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

      1. sub-neg 55.1%

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

      2. metadata-eval 55.1%

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

      3. neg-mul-1 55.1%

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

   6. Simplified 55.1%

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

   7. Taylor expanded in x around inf 52.9%

      \[\leadsto \color{blue}{x} - \left(-z\right) \]
3. Recombined 6 regimes into one program.

4. Final simplification 63.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -15500000:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq -1.4 \cdot 10^{-39}:\\ \;\;\;\;b \cdot \left(y - 2\right)\\ \mathbf{elif}\;t \leq -6.5 \cdot 10^{-55}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq -3.25 \cdot 10^{-131}:\\ \;\;\;\;b \cdot \left(y - 2\right)\\ \mathbf{elif}\;t \leq -5.5 \cdot 10^{-172}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq -5.1 \cdot 10^{-241}:\\ \;\;\;\;b \cdot \left(y - 2\right)\\ \mathbf{elif}\;t \leq -4 \cdot 10^{-249}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;t \leq 8 \cdot 10^{-292}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq 3.3 \cdot 10^{-260}:\\ \;\;\;\;b \cdot \left(y - 2\right)\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{-260}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{-80}:\\ \;\;\;\;b \cdot \left(y - 2\right)\\ \mathbf{elif}\;t \leq 9.2 \cdot 10^{-12}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 98.6% accurate, 0.4× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 100.0%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in z around inf 23.1%

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

      1. associate--l+ 23.1%

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

      2. sub-neg 23.1%

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

      3. metadata-eval 23.1%

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

      4. associate-+r+ 23.1%

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

      5. associate-/l* 61.5%

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

      6. sub-neg 61.5%

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

      7. metadata-eval 61.5%

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

      8. associate-/l* 84.6%

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

   5. Simplified 84.6%

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

4. Final simplification 99.2%

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

Alternative 4: 48.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(y - 2\right)\\ t_2 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -68000000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -9 \cdot 10^{-39}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -3.8 \cdot 10^{-59}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq -1.6 \cdot 10^{-131}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -2.1 \cdot 10^{-173}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq -5.1 \cdot 10^{-241}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -2.3 \cdot 10^{-249}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{-286}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{-33}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- y 2.0))) (t_2 (* t (- b a))))
   (if (<= t -68000000.0)
     t_2
     (if (<= t -9e-39)
       t_1
       (if (<= t -3.8e-59)
         (+ x a)
         (if (<= t -1.6e-131)
           t_1
           (if (<= t -2.1e-173)
             (+ x a)
             (if (<= t -5.1e-241)
               t_1
               (if (<= t -2.3e-249)
                 (* y (- z))
                 (if (<= t 5.8e-286)
                   (+ x a)
                   (if (<= t 4.6e-33) (* y (- b z)) 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 <= -68000000.0) {
		tmp = t_2;
	} else if (t <= -9e-39) {
		tmp = t_1;
	} else if (t <= -3.8e-59) {
		tmp = x + a;
	} else if (t <= -1.6e-131) {
		tmp = t_1;
	} else if (t <= -2.1e-173) {
		tmp = x + a;
	} else if (t <= -5.1e-241) {
		tmp = t_1;
	} else if (t <= -2.3e-249) {
		tmp = y * -z;
	} else if (t <= 5.8e-286) {
		tmp = x + a;
	} else if (t <= 4.6e-33) {
		tmp = y * (b - z);
	} 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 <= (-68000000.0d0)) then
        tmp = t_2
    else if (t <= (-9d-39)) then
        tmp = t_1
    else if (t <= (-3.8d-59)) then
        tmp = x + a
    else if (t <= (-1.6d-131)) then
        tmp = t_1
    else if (t <= (-2.1d-173)) then
        tmp = x + a
    else if (t <= (-5.1d-241)) then
        tmp = t_1
    else if (t <= (-2.3d-249)) then
        tmp = y * -z
    else if (t <= 5.8d-286) then
        tmp = x + a
    else if (t <= 4.6d-33) then
        tmp = y * (b - z)
    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 <= -68000000.0) {
		tmp = t_2;
	} else if (t <= -9e-39) {
		tmp = t_1;
	} else if (t <= -3.8e-59) {
		tmp = x + a;
	} else if (t <= -1.6e-131) {
		tmp = t_1;
	} else if (t <= -2.1e-173) {
		tmp = x + a;
	} else if (t <= -5.1e-241) {
		tmp = t_1;
	} else if (t <= -2.3e-249) {
		tmp = y * -z;
	} else if (t <= 5.8e-286) {
		tmp = x + a;
	} else if (t <= 4.6e-33) {
		tmp = y * (b - z);
	} 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 <= -68000000.0:
		tmp = t_2
	elif t <= -9e-39:
		tmp = t_1
	elif t <= -3.8e-59:
		tmp = x + a
	elif t <= -1.6e-131:
		tmp = t_1
	elif t <= -2.1e-173:
		tmp = x + a
	elif t <= -5.1e-241:
		tmp = t_1
	elif t <= -2.3e-249:
		tmp = y * -z
	elif t <= 5.8e-286:
		tmp = x + a
	elif t <= 4.6e-33:
		tmp = y * (b - z)
	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 <= -68000000.0)
		tmp = t_2;
	elseif (t <= -9e-39)
		tmp = t_1;
	elseif (t <= -3.8e-59)
		tmp = Float64(x + a);
	elseif (t <= -1.6e-131)
		tmp = t_1;
	elseif (t <= -2.1e-173)
		tmp = Float64(x + a);
	elseif (t <= -5.1e-241)
		tmp = t_1;
	elseif (t <= -2.3e-249)
		tmp = Float64(y * Float64(-z));
	elseif (t <= 5.8e-286)
		tmp = Float64(x + a);
	elseif (t <= 4.6e-33)
		tmp = Float64(y * Float64(b - z));
	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 <= -68000000.0)
		tmp = t_2;
	elseif (t <= -9e-39)
		tmp = t_1;
	elseif (t <= -3.8e-59)
		tmp = x + a;
	elseif (t <= -1.6e-131)
		tmp = t_1;
	elseif (t <= -2.1e-173)
		tmp = x + a;
	elseif (t <= -5.1e-241)
		tmp = t_1;
	elseif (t <= -2.3e-249)
		tmp = y * -z;
	elseif (t <= 5.8e-286)
		tmp = x + a;
	elseif (t <= 4.6e-33)
		tmp = y * (b - z);
	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, -68000000.0], t$95$2, If[LessEqual[t, -9e-39], t$95$1, If[LessEqual[t, -3.8e-59], N[(x + a), $MachinePrecision], If[LessEqual[t, -1.6e-131], t$95$1, If[LessEqual[t, -2.1e-173], N[(x + a), $MachinePrecision], If[LessEqual[t, -5.1e-241], t$95$1, If[LessEqual[t, -2.3e-249], N[(y * (-z)), $MachinePrecision], If[LessEqual[t, 5.8e-286], N[(x + a), $MachinePrecision], If[LessEqual[t, 4.6e-33], N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -6.8e7 or 4.59999999999999971e-33 < t

   1. Initial program 90.2%

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

   3. Taylor expanded in t around inf 76.3%

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

   if -6.8e7 < t < -9.0000000000000002e-39 or -3.79999999999999983e-59 < t < -1.6e-131 or -2.10000000000000001e-173 < t < -5.0999999999999998e-241

   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 66.1%

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

      1. mul-1-neg 66.1%

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

      2. *-commutative 66.1%

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

      3. distribute-rgt-neg-in 66.1%

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

   5. Simplified 66.1%

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

   6. Taylor expanded in t around 0 63.0%

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

   7. Taylor expanded in z around 0 48.9%

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

   if -9.0000000000000002e-39 < t < -3.79999999999999983e-59 or -1.6e-131 < t < -2.10000000000000001e-173 or -2.2999999999999998e-249 < t < 5.7999999999999996e-286

   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 79.5%

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

   4. Taylor expanded in t around 0 79.5%

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

      1. associate--l+ 79.5%

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

      2. sub-neg 79.5%

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

      3. metadata-eval 79.5%

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

      4. neg-mul-1 79.5%

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

   6. Simplified 79.5%

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

      1. sub-neg 79.5%

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

      2. remove-double-neg 79.5%

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

   8. Applied egg-rr 79.5%

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

   9. Taylor expanded in b around 0 53.8%

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

   if -5.0999999999999998e-241 < t < -2.2999999999999998e-249

   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 68.5%

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

   4. Taylor expanded in y around inf 68.5%

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

      1. mul-1-neg 68.5%

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

      2. distribute-lft-neg-out 68.5%

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

      3. *-commutative 68.5%

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

   6. Simplified 68.5%

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

   if 5.7999999999999996e-286 < t < 4.59999999999999971e-33

   1. Initial program 98.2%

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

   3. Taylor expanded in y around inf 44.6%

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

4. Final simplification 62.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -68000000:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq -9 \cdot 10^{-39}:\\ \;\;\;\;b \cdot \left(y - 2\right)\\ \mathbf{elif}\;t \leq -3.8 \cdot 10^{-59}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq -1.6 \cdot 10^{-131}:\\ \;\;\;\;b \cdot \left(y - 2\right)\\ \mathbf{elif}\;t \leq -2.1 \cdot 10^{-173}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq -5.1 \cdot 10^{-241}:\\ \;\;\;\;b \cdot \left(y - 2\right)\\ \mathbf{elif}\;t \leq -2.3 \cdot 10^{-249}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{-286}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{-33}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 58.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \left(y + -1\right) \cdot z\\ t_2 := \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{if}\;b \leq -7.5 \cdot 10^{+23}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -2.8 \cdot 10^{-70}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;b \leq -9.6 \cdot 10^{-129}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -1.65 \cdot 10^{-202}:\\ \;\;\;\;x + \left(z + a\right)\\ \mathbf{elif}\;b \leq 8.8 \cdot 10^{-166}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 3.6 \cdot 10^{+31} \lor \neg \left(b \leq 5.2 \cdot 10^{+65}\right) \land b \leq 1.1 \cdot 10^{+155}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- x (* (+ y -1.0) z))) (t_2 (* (- (+ y t) 2.0) b)))
   (if (<= b -7.5e+23)
     t_2
     (if (<= b -2.8e-70)
       (* t (- b a))
       (if (<= b -9.6e-129)
         t_1
         (if (<= b -1.65e-202)
           (+ x (+ z a))
           (if (<= b 8.8e-166)
             t_1
             (if (or (<= b 3.6e+31) (and (not (<= b 5.2e+65)) (<= b 1.1e+155)))
               (+ x (* a (- 1.0 t)))
               t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x - ((y + -1.0) * z);
	double t_2 = ((y + t) - 2.0) * b;
	double tmp;
	if (b <= -7.5e+23) {
		tmp = t_2;
	} else if (b <= -2.8e-70) {
		tmp = t * (b - a);
	} else if (b <= -9.6e-129) {
		tmp = t_1;
	} else if (b <= -1.65e-202) {
		tmp = x + (z + a);
	} else if (b <= 8.8e-166) {
		tmp = t_1;
	} else if ((b <= 3.6e+31) || (!(b <= 5.2e+65) && (b <= 1.1e+155))) {
		tmp = x + (a * (1.0 - t));
	} 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 + (-1.0d0)) * z)
    t_2 = ((y + t) - 2.0d0) * b
    if (b <= (-7.5d+23)) then
        tmp = t_2
    else if (b <= (-2.8d-70)) then
        tmp = t * (b - a)
    else if (b <= (-9.6d-129)) then
        tmp = t_1
    else if (b <= (-1.65d-202)) then
        tmp = x + (z + a)
    else if (b <= 8.8d-166) then
        tmp = t_1
    else if ((b <= 3.6d+31) .or. (.not. (b <= 5.2d+65)) .and. (b <= 1.1d+155)) then
        tmp = x + (a * (1.0d0 - t))
    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 + -1.0) * z);
	double t_2 = ((y + t) - 2.0) * b;
	double tmp;
	if (b <= -7.5e+23) {
		tmp = t_2;
	} else if (b <= -2.8e-70) {
		tmp = t * (b - a);
	} else if (b <= -9.6e-129) {
		tmp = t_1;
	} else if (b <= -1.65e-202) {
		tmp = x + (z + a);
	} else if (b <= 8.8e-166) {
		tmp = t_1;
	} else if ((b <= 3.6e+31) || (!(b <= 5.2e+65) && (b <= 1.1e+155))) {
		tmp = x + (a * (1.0 - t));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x - ((y + -1.0) * z)
	t_2 = ((y + t) - 2.0) * b
	tmp = 0
	if b <= -7.5e+23:
		tmp = t_2
	elif b <= -2.8e-70:
		tmp = t * (b - a)
	elif b <= -9.6e-129:
		tmp = t_1
	elif b <= -1.65e-202:
		tmp = x + (z + a)
	elif b <= 8.8e-166:
		tmp = t_1
	elif (b <= 3.6e+31) or (not (b <= 5.2e+65) and (b <= 1.1e+155)):
		tmp = x + (a * (1.0 - t))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x - Float64(Float64(y + -1.0) * z))
	t_2 = Float64(Float64(Float64(y + t) - 2.0) * b)
	tmp = 0.0
	if (b <= -7.5e+23)
		tmp = t_2;
	elseif (b <= -2.8e-70)
		tmp = Float64(t * Float64(b - a));
	elseif (b <= -9.6e-129)
		tmp = t_1;
	elseif (b <= -1.65e-202)
		tmp = Float64(x + Float64(z + a));
	elseif (b <= 8.8e-166)
		tmp = t_1;
	elseif ((b <= 3.6e+31) || (!(b <= 5.2e+65) && (b <= 1.1e+155)))
		tmp = Float64(x + Float64(a * Float64(1.0 - t)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x - ((y + -1.0) * z);
	t_2 = ((y + t) - 2.0) * b;
	tmp = 0.0;
	if (b <= -7.5e+23)
		tmp = t_2;
	elseif (b <= -2.8e-70)
		tmp = t * (b - a);
	elseif (b <= -9.6e-129)
		tmp = t_1;
	elseif (b <= -1.65e-202)
		tmp = x + (z + a);
	elseif (b <= 8.8e-166)
		tmp = t_1;
	elseif ((b <= 3.6e+31) || (~((b <= 5.2e+65)) && (b <= 1.1e+155)))
		tmp = x + (a * (1.0 - t));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x - N[(N[(y + -1.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[b, -7.5e+23], t$95$2, If[LessEqual[b, -2.8e-70], N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -9.6e-129], t$95$1, If[LessEqual[b, -1.65e-202], N[(x + N[(z + a), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 8.8e-166], t$95$1, If[Or[LessEqual[b, 3.6e+31], And[N[Not[LessEqual[b, 5.2e+65]], $MachinePrecision], LessEqual[b, 1.1e+155]]], N[(x + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -7.49999999999999987e23 or 3.59999999999999996e31 < b < 5.20000000000000005e65 or 1.1000000000000001e155 < b

   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 b around inf 79.2%

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

   if -7.49999999999999987e23 < b < -2.7999999999999999e-70

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 58.6%

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

   if -2.7999999999999999e-70 < b < -9.59999999999999954e-129 or -1.64999999999999995e-202 < b < 8.8000000000000005e-166

   1. Initial program 97.9%

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

   3. Taylor expanded in a around 0 67.3%

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

   4. Taylor expanded in b around 0 65.3%

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

   if -9.59999999999999954e-129 < b < -1.64999999999999995e-202

   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 t around 0 91.4%

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

      1. +-commutative 91.4%

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

      2. sub-neg 91.4%

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

      3. metadata-eval 91.4%

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

      4. neg-mul-1 91.4%

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

      5. unsub-neg 91.4%

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

   6. Simplified 91.4%

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

   7. Taylor expanded in y around 0 73.7%

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

      1. neg-mul-1 73.7%

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

   9. Simplified 73.7%

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

   if 8.8000000000000005e-166 < b < 3.59999999999999996e31 or 5.20000000000000005e65 < b < 1.1000000000000001e155

   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 z around 0 70.6%

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

   4. Taylor expanded in b around 0 63.7%

      \[\leadsto \color{blue}{x - a \cdot \left(t - 1\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 72.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -7.5 \cdot 10^{+23}:\\ \;\;\;\;\left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{elif}\;b \leq -2.8 \cdot 10^{-70}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;b \leq -9.6 \cdot 10^{-129}:\\ \;\;\;\;x - \left(y + -1\right) \cdot z\\ \mathbf{elif}\;b \leq -1.65 \cdot 10^{-202}:\\ \;\;\;\;x + \left(z + a\right)\\ \mathbf{elif}\;b \leq 8.8 \cdot 10^{-166}:\\ \;\;\;\;x - \left(y + -1\right) \cdot z\\ \mathbf{elif}\;b \leq 3.6 \cdot 10^{+31} \lor \neg \left(b \leq 5.2 \cdot 10^{+65}\right) \land b \leq 1.1 \cdot 10^{+155}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(y + t\right) - 2\right) \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 53.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(z + a\right)\\ t_2 := \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{if}\;b \leq -4.2 \cdot 10^{+27}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -4 \cdot 10^{-64}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;b \leq -4.4 \cdot 10^{-116}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq -3.7 \cdot 10^{-292}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 4.3 \cdot 10^{-190}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 4.2 \cdot 10^{+28}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1.05 \cdot 10^{+75} \lor \neg \left(b \leq 8.6 \cdot 10^{+77}\right):\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (+ z a))) (t_2 (* (- (+ y t) 2.0) b)))
   (if (<= b -4.2e+27)
     t_2
     (if (<= b -4e-64)
       (* t (- b a))
       (if (<= b -4.4e-116)
         (* z (- 1.0 y))
         (if (<= b -3.7e-292)
           t_1
           (if (<= b 4.3e-190)
             (* a (- 1.0 t))
             (if (<= b 4.2e+28)
               t_1
               (if (or (<= b 1.05e+75) (not (<= b 8.6e+77))) t_2 x)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (z + a);
	double t_2 = ((y + t) - 2.0) * b;
	double tmp;
	if (b <= -4.2e+27) {
		tmp = t_2;
	} else if (b <= -4e-64) {
		tmp = t * (b - a);
	} else if (b <= -4.4e-116) {
		tmp = z * (1.0 - y);
	} else if (b <= -3.7e-292) {
		tmp = t_1;
	} else if (b <= 4.3e-190) {
		tmp = a * (1.0 - t);
	} else if (b <= 4.2e+28) {
		tmp = t_1;
	} else if ((b <= 1.05e+75) || !(b <= 8.6e+77)) {
		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 = x + (z + a)
    t_2 = ((y + t) - 2.0d0) * b
    if (b <= (-4.2d+27)) then
        tmp = t_2
    else if (b <= (-4d-64)) then
        tmp = t * (b - a)
    else if (b <= (-4.4d-116)) then
        tmp = z * (1.0d0 - y)
    else if (b <= (-3.7d-292)) then
        tmp = t_1
    else if (b <= 4.3d-190) then
        tmp = a * (1.0d0 - t)
    else if (b <= 4.2d+28) then
        tmp = t_1
    else if ((b <= 1.05d+75) .or. (.not. (b <= 8.6d+77))) 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 = x + (z + a);
	double t_2 = ((y + t) - 2.0) * b;
	double tmp;
	if (b <= -4.2e+27) {
		tmp = t_2;
	} else if (b <= -4e-64) {
		tmp = t * (b - a);
	} else if (b <= -4.4e-116) {
		tmp = z * (1.0 - y);
	} else if (b <= -3.7e-292) {
		tmp = t_1;
	} else if (b <= 4.3e-190) {
		tmp = a * (1.0 - t);
	} else if (b <= 4.2e+28) {
		tmp = t_1;
	} else if ((b <= 1.05e+75) || !(b <= 8.6e+77)) {
		tmp = t_2;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (z + a)
	t_2 = ((y + t) - 2.0) * b
	tmp = 0
	if b <= -4.2e+27:
		tmp = t_2
	elif b <= -4e-64:
		tmp = t * (b - a)
	elif b <= -4.4e-116:
		tmp = z * (1.0 - y)
	elif b <= -3.7e-292:
		tmp = t_1
	elif b <= 4.3e-190:
		tmp = a * (1.0 - t)
	elif b <= 4.2e+28:
		tmp = t_1
	elif (b <= 1.05e+75) or not (b <= 8.6e+77):
		tmp = t_2
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(z + a))
	t_2 = Float64(Float64(Float64(y + t) - 2.0) * b)
	tmp = 0.0
	if (b <= -4.2e+27)
		tmp = t_2;
	elseif (b <= -4e-64)
		tmp = Float64(t * Float64(b - a));
	elseif (b <= -4.4e-116)
		tmp = Float64(z * Float64(1.0 - y));
	elseif (b <= -3.7e-292)
		tmp = t_1;
	elseif (b <= 4.3e-190)
		tmp = Float64(a * Float64(1.0 - t));
	elseif (b <= 4.2e+28)
		tmp = t_1;
	elseif ((b <= 1.05e+75) || !(b <= 8.6e+77))
		tmp = t_2;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (z + a);
	t_2 = ((y + t) - 2.0) * b;
	tmp = 0.0;
	if (b <= -4.2e+27)
		tmp = t_2;
	elseif (b <= -4e-64)
		tmp = t * (b - a);
	elseif (b <= -4.4e-116)
		tmp = z * (1.0 - y);
	elseif (b <= -3.7e-292)
		tmp = t_1;
	elseif (b <= 4.3e-190)
		tmp = a * (1.0 - t);
	elseif (b <= 4.2e+28)
		tmp = t_1;
	elseif ((b <= 1.05e+75) || ~((b <= 8.6e+77)))
		tmp = t_2;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(z + a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[b, -4.2e+27], t$95$2, If[LessEqual[b, -4e-64], N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -4.4e-116], N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -3.7e-292], t$95$1, If[LessEqual[b, 4.3e-190], N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 4.2e+28], t$95$1, If[Or[LessEqual[b, 1.05e+75], N[Not[LessEqual[b, 8.6e+77]], $MachinePrecision]], t$95$2, x]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if b < -4.19999999999999989e27 or 4.19999999999999978e28 < b < 1.04999999999999999e75 or 8.59999999999999983e77 < b

   1. Initial program 91.8%

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

   3. Taylor expanded in b around inf 75.1%

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

   if -4.19999999999999989e27 < b < -3.99999999999999986e-64

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 58.6%

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

   if -3.99999999999999986e-64 < b < -4.4000000000000002e-116

   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 56.1%

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

   if -4.4000000000000002e-116 < b < -3.69999999999999997e-292 or 4.3e-190 < b < 4.19999999999999978e28

   1. Initial program 98.5%

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

   3. Taylor expanded in b around 0 94.6%

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

   4. Taylor expanded in t around 0 81.4%

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

      1. +-commutative 81.4%

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

      2. sub-neg 81.4%

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

      3. metadata-eval 81.4%

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

      4. neg-mul-1 81.4%

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

      5. unsub-neg 81.4%

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

   6. Simplified 81.4%

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

   7. Taylor expanded in y around 0 66.3%

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

      1. neg-mul-1 66.3%

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

   9. Simplified 66.3%

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

   if -3.69999999999999997e-292 < b < 4.3e-190

   1. Initial program 100.0%

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

   3. Taylor expanded in a around inf 52.2%

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

   if 1.04999999999999999e75 < b < 8.59999999999999983e77

   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 100.0%

      \[\leadsto \color{blue}{x} \]
3. Recombined 6 regimes into one program.

4. Final simplification 69.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.2 \cdot 10^{+27}:\\ \;\;\;\;\left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{elif}\;b \leq -4 \cdot 10^{-64}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;b \leq -4.4 \cdot 10^{-116}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq -3.7 \cdot 10^{-292}:\\ \;\;\;\;x + \left(z + a\right)\\ \mathbf{elif}\;b \leq 4.3 \cdot 10^{-190}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 4.2 \cdot 10^{+28}:\\ \;\;\;\;x + \left(z + a\right)\\ \mathbf{elif}\;b \leq 1.05 \cdot 10^{+75} \lor \neg \left(b \leq 8.6 \cdot 10^{+77}\right):\\ \;\;\;\;\left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 57.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(z + a\right)\\ t_2 := x + a \cdot \left(1 - t\right)\\ t_3 := z \cdot \left(1 - y\right)\\ t_4 := \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{if}\;b \leq -1.85 \cdot 10^{+19}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;b \leq -1 \cdot 10^{-64}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;b \leq -7 \cdot 10^{-114}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;b \leq -1.45 \cdot 10^{-257}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1.3 \cdot 10^{-179}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 2.2 \cdot 10^{-152}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;b \leq 1.56 \cdot 10^{-75}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1.6 \cdot 10^{+27}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (+ z a)))
        (t_2 (+ x (* a (- 1.0 t))))
        (t_3 (* z (- 1.0 y)))
        (t_4 (* (- (+ y t) 2.0) b)))
   (if (<= b -1.85e+19)
     t_4
     (if (<= b -1e-64)
       (* t (- b a))
       (if (<= b -7e-114)
         t_3
         (if (<= b -1.45e-257)
           t_1
           (if (<= b 1.3e-179)
             t_2
             (if (<= b 2.2e-152)
               t_3
               (if (<= b 1.56e-75) t_1 (if (<= b 1.6e+27) t_2 t_4))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (z + a);
	double t_2 = x + (a * (1.0 - t));
	double t_3 = z * (1.0 - y);
	double t_4 = ((y + t) - 2.0) * b;
	double tmp;
	if (b <= -1.85e+19) {
		tmp = t_4;
	} else if (b <= -1e-64) {
		tmp = t * (b - a);
	} else if (b <= -7e-114) {
		tmp = t_3;
	} else if (b <= -1.45e-257) {
		tmp = t_1;
	} else if (b <= 1.3e-179) {
		tmp = t_2;
	} else if (b <= 2.2e-152) {
		tmp = t_3;
	} else if (b <= 1.56e-75) {
		tmp = t_1;
	} else if (b <= 1.6e+27) {
		tmp = t_2;
	} else {
		tmp = t_4;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = x + (z + a)
    t_2 = x + (a * (1.0d0 - t))
    t_3 = z * (1.0d0 - y)
    t_4 = ((y + t) - 2.0d0) * b
    if (b <= (-1.85d+19)) then
        tmp = t_4
    else if (b <= (-1d-64)) then
        tmp = t * (b - a)
    else if (b <= (-7d-114)) then
        tmp = t_3
    else if (b <= (-1.45d-257)) then
        tmp = t_1
    else if (b <= 1.3d-179) then
        tmp = t_2
    else if (b <= 2.2d-152) then
        tmp = t_3
    else if (b <= 1.56d-75) then
        tmp = t_1
    else if (b <= 1.6d+27) then
        tmp = t_2
    else
        tmp = t_4
    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);
	double t_2 = x + (a * (1.0 - t));
	double t_3 = z * (1.0 - y);
	double t_4 = ((y + t) - 2.0) * b;
	double tmp;
	if (b <= -1.85e+19) {
		tmp = t_4;
	} else if (b <= -1e-64) {
		tmp = t * (b - a);
	} else if (b <= -7e-114) {
		tmp = t_3;
	} else if (b <= -1.45e-257) {
		tmp = t_1;
	} else if (b <= 1.3e-179) {
		tmp = t_2;
	} else if (b <= 2.2e-152) {
		tmp = t_3;
	} else if (b <= 1.56e-75) {
		tmp = t_1;
	} else if (b <= 1.6e+27) {
		tmp = t_2;
	} else {
		tmp = t_4;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (z + a)
	t_2 = x + (a * (1.0 - t))
	t_3 = z * (1.0 - y)
	t_4 = ((y + t) - 2.0) * b
	tmp = 0
	if b <= -1.85e+19:
		tmp = t_4
	elif b <= -1e-64:
		tmp = t * (b - a)
	elif b <= -7e-114:
		tmp = t_3
	elif b <= -1.45e-257:
		tmp = t_1
	elif b <= 1.3e-179:
		tmp = t_2
	elif b <= 2.2e-152:
		tmp = t_3
	elif b <= 1.56e-75:
		tmp = t_1
	elif b <= 1.6e+27:
		tmp = t_2
	else:
		tmp = t_4
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(z + a))
	t_2 = Float64(x + Float64(a * Float64(1.0 - t)))
	t_3 = Float64(z * Float64(1.0 - y))
	t_4 = Float64(Float64(Float64(y + t) - 2.0) * b)
	tmp = 0.0
	if (b <= -1.85e+19)
		tmp = t_4;
	elseif (b <= -1e-64)
		tmp = Float64(t * Float64(b - a));
	elseif (b <= -7e-114)
		tmp = t_3;
	elseif (b <= -1.45e-257)
		tmp = t_1;
	elseif (b <= 1.3e-179)
		tmp = t_2;
	elseif (b <= 2.2e-152)
		tmp = t_3;
	elseif (b <= 1.56e-75)
		tmp = t_1;
	elseif (b <= 1.6e+27)
		tmp = t_2;
	else
		tmp = t_4;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (z + a);
	t_2 = x + (a * (1.0 - t));
	t_3 = z * (1.0 - y);
	t_4 = ((y + t) - 2.0) * b;
	tmp = 0.0;
	if (b <= -1.85e+19)
		tmp = t_4;
	elseif (b <= -1e-64)
		tmp = t * (b - a);
	elseif (b <= -7e-114)
		tmp = t_3;
	elseif (b <= -1.45e-257)
		tmp = t_1;
	elseif (b <= 1.3e-179)
		tmp = t_2;
	elseif (b <= 2.2e-152)
		tmp = t_3;
	elseif (b <= 1.56e-75)
		tmp = t_1;
	elseif (b <= 1.6e+27)
		tmp = t_2;
	else
		tmp = t_4;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(z + a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[b, -1.85e+19], t$95$4, If[LessEqual[b, -1e-64], N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -7e-114], t$95$3, If[LessEqual[b, -1.45e-257], t$95$1, If[LessEqual[b, 1.3e-179], t$95$2, If[LessEqual[b, 2.2e-152], t$95$3, If[LessEqual[b, 1.56e-75], t$95$1, If[LessEqual[b, 1.6e+27], t$95$2, t$95$4]]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -1.85e19 or 1.60000000000000008e27 < b

   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 b around inf 73.7%

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

   if -1.85e19 < b < -9.99999999999999965e-65

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 58.6%

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

   if -9.99999999999999965e-65 < b < -7e-114 or 1.30000000000000003e-179 < b < 2.19999999999999985e-152

   1. Initial program 93.3%

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

   3. Taylor expanded in z around inf 60.5%

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

   if -7e-114 < b < -1.4500000000000001e-257 or 2.19999999999999985e-152 < b < 1.5600000000000001e-75

   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 95.7%

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

   4. Taylor expanded in t around 0 87.5%

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

      1. +-commutative 87.5%

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

      2. sub-neg 87.5%

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

      3. metadata-eval 87.5%

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

      4. neg-mul-1 87.5%

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

      5. unsub-neg 87.5%

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

   6. Simplified 87.5%

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

   7. Taylor expanded in y around 0 71.2%

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

      1. neg-mul-1 71.2%

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

   9. Simplified 71.2%

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

   if -1.4500000000000001e-257 < b < 1.30000000000000003e-179 or 1.5600000000000001e-75 < b < 1.60000000000000008e27

   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 68.4%

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

   4. Taylor expanded in b around 0 65.9%

      \[\leadsto \color{blue}{x - a \cdot \left(t - 1\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 70.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.85 \cdot 10^{+19}:\\ \;\;\;\;\left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{elif}\;b \leq -1 \cdot 10^{-64}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;b \leq -7 \cdot 10^{-114}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq -1.45 \cdot 10^{-257}:\\ \;\;\;\;x + \left(z + a\right)\\ \mathbf{elif}\;b \leq 1.3 \cdot 10^{-179}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 2.2 \cdot 10^{-152}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq 1.56 \cdot 10^{-75}:\\ \;\;\;\;x + \left(z + a\right)\\ \mathbf{elif}\;b \leq 1.6 \cdot 10^{+27}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(y + t\right) - 2\right) \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 98.1% accurate, 0.5× speedup

Math

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

FPCore

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

Python

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

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((x - ((y + -1.0) * z)) + (a * (1.0 - t))) + (((y + t) - 2.0) * b);
	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[(N[(x - N[(N[(y + -1.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 100.0%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in y around inf 70.2%

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

4. Final simplification 98.5%

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

Alternative 9: 51.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(1 - y\right)\\ t_2 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -750000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -2.8 \cdot 10^{-34}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.06 \cdot 10^{-281}:\\ \;\;\;\;x + \left(z + a\right)\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{-236}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{-221}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 10^{-181}:\\ \;\;\;\;b \cdot \left(y - 2\right)\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{-33}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (- 1.0 y))) (t_2 (* t (- b a))))
   (if (<= t -750000.0)
     t_2
     (if (<= t -2.8e-34)
       t_1
       (if (<= t 1.06e-281)
         (+ x (+ z a))
         (if (<= t 1.6e-236)
           (* y (- b z))
           (if (<= t 8.5e-221)
             t_1
             (if (<= t 1e-181)
               (* b (- y 2.0))
               (if (<= t 4.6e-33) t_1 t_2)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (1.0 - y);
	double t_2 = t * (b - a);
	double tmp;
	if (t <= -750000.0) {
		tmp = t_2;
	} else if (t <= -2.8e-34) {
		tmp = t_1;
	} else if (t <= 1.06e-281) {
		tmp = x + (z + a);
	} else if (t <= 1.6e-236) {
		tmp = y * (b - z);
	} else if (t <= 8.5e-221) {
		tmp = t_1;
	} else if (t <= 1e-181) {
		tmp = b * (y - 2.0);
	} else if (t <= 4.6e-33) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = z * (1.0d0 - y)
    t_2 = t * (b - a)
    if (t <= (-750000.0d0)) then
        tmp = t_2
    else if (t <= (-2.8d-34)) then
        tmp = t_1
    else if (t <= 1.06d-281) then
        tmp = x + (z + a)
    else if (t <= 1.6d-236) then
        tmp = y * (b - z)
    else if (t <= 8.5d-221) then
        tmp = t_1
    else if (t <= 1d-181) then
        tmp = b * (y - 2.0d0)
    else if (t <= 4.6d-33) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (1.0 - y);
	double t_2 = t * (b - a);
	double tmp;
	if (t <= -750000.0) {
		tmp = t_2;
	} else if (t <= -2.8e-34) {
		tmp = t_1;
	} else if (t <= 1.06e-281) {
		tmp = x + (z + a);
	} else if (t <= 1.6e-236) {
		tmp = y * (b - z);
	} else if (t <= 8.5e-221) {
		tmp = t_1;
	} else if (t <= 1e-181) {
		tmp = b * (y - 2.0);
	} else if (t <= 4.6e-33) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * (1.0 - y)
	t_2 = t * (b - a)
	tmp = 0
	if t <= -750000.0:
		tmp = t_2
	elif t <= -2.8e-34:
		tmp = t_1
	elif t <= 1.06e-281:
		tmp = x + (z + a)
	elif t <= 1.6e-236:
		tmp = y * (b - z)
	elif t <= 8.5e-221:
		tmp = t_1
	elif t <= 1e-181:
		tmp = b * (y - 2.0)
	elif t <= 4.6e-33:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(1.0 - y))
	t_2 = Float64(t * Float64(b - a))
	tmp = 0.0
	if (t <= -750000.0)
		tmp = t_2;
	elseif (t <= -2.8e-34)
		tmp = t_1;
	elseif (t <= 1.06e-281)
		tmp = Float64(x + Float64(z + a));
	elseif (t <= 1.6e-236)
		tmp = Float64(y * Float64(b - z));
	elseif (t <= 8.5e-221)
		tmp = t_1;
	elseif (t <= 1e-181)
		tmp = Float64(b * Float64(y - 2.0));
	elseif (t <= 4.6e-33)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * (1.0 - y);
	t_2 = t * (b - a);
	tmp = 0.0;
	if (t <= -750000.0)
		tmp = t_2;
	elseif (t <= -2.8e-34)
		tmp = t_1;
	elseif (t <= 1.06e-281)
		tmp = x + (z + a);
	elseif (t <= 1.6e-236)
		tmp = y * (b - z);
	elseif (t <= 8.5e-221)
		tmp = t_1;
	elseif (t <= 1e-181)
		tmp = b * (y - 2.0);
	elseif (t <= 4.6e-33)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -750000.0], t$95$2, If[LessEqual[t, -2.8e-34], t$95$1, If[LessEqual[t, 1.06e-281], N[(x + N[(z + a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.6e-236], N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 8.5e-221], t$95$1, If[LessEqual[t, 1e-181], N[(b * N[(y - 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.6e-33], t$95$1, t$95$2]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -7.5e5 or 4.59999999999999971e-33 < t

   1. Initial program 90.3%

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

   3. Taylor expanded in t around inf 76.1%

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

   if -7.5e5 < t < -2.79999999999999997e-34 or 1.6e-236 < t < 8.49999999999999984e-221 or 1.00000000000000005e-181 < t < 4.59999999999999971e-33

   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 54.1%

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

   if -2.79999999999999997e-34 < t < 1.06e-281

   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 69.2%

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

   4. Taylor expanded in t around 0 69.2%

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

      1. +-commutative 69.2%

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

      2. sub-neg 69.2%

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

      3. metadata-eval 69.2%

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

      4. neg-mul-1 69.2%

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

      5. unsub-neg 69.2%

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

   6. Simplified 69.2%

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

   7. Taylor expanded in y around 0 55.9%

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

      1. neg-mul-1 55.9%

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

   9. Simplified 55.9%

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

   if 1.06e-281 < t < 1.6e-236

   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 y around inf 49.0%

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

   if 8.49999999999999984e-221 < t < 1.00000000000000005e-181

   1. Initial program 99.8%

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

   3. Taylor expanded in y around inf 72.1%

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

      1. mul-1-neg 72.1%

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

      2. *-commutative 72.1%

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

      3. distribute-rgt-neg-in 72.1%

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

   5. Simplified 72.1%

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

   6. Taylor expanded in t around 0 72.1%

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

   7. Taylor expanded in z around 0 72.1%

      \[\leadsto \color{blue}{b \cdot \left(y - 2\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 65.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -750000:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq -2.8 \cdot 10^{-34}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{elif}\;t \leq 1.06 \cdot 10^{-281}:\\ \;\;\;\;x + \left(z + a\right)\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{-236}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{-221}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{elif}\;t \leq 10^{-181}:\\ \;\;\;\;b \cdot \left(y - 2\right)\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{-33}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 47.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(1 - y\right)\\ t_2 := t \cdot \left(b - a\right)\\ t_3 := b \cdot \left(y - 2\right)\\ \mathbf{if}\;t \leq -180000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -1.12 \cdot 10^{-36}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{-304}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{-238}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{-223}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{-155}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{-43}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (- 1.0 y))) (t_2 (* t (- b a))) (t_3 (* b (- y 2.0))))
   (if (<= t -180000.0)
     t_2
     (if (<= t -1.12e-36)
       t_1
       (if (<= t 2.9e-304)
         (+ x a)
         (if (<= t 2.6e-238)
           t_3
           (if (<= t 4.2e-223)
             t_1
             (if (<= t 2.1e-155) t_3 (if (<= t 5.8e-43) t_1 t_2)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (1.0 - y);
	double t_2 = t * (b - a);
	double t_3 = b * (y - 2.0);
	double tmp;
	if (t <= -180000.0) {
		tmp = t_2;
	} else if (t <= -1.12e-36) {
		tmp = t_1;
	} else if (t <= 2.9e-304) {
		tmp = x + a;
	} else if (t <= 2.6e-238) {
		tmp = t_3;
	} else if (t <= 4.2e-223) {
		tmp = t_1;
	} else if (t <= 2.1e-155) {
		tmp = t_3;
	} else if (t <= 5.8e-43) {
		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) :: t_3
    real(8) :: tmp
    t_1 = z * (1.0d0 - y)
    t_2 = t * (b - a)
    t_3 = b * (y - 2.0d0)
    if (t <= (-180000.0d0)) then
        tmp = t_2
    else if (t <= (-1.12d-36)) then
        tmp = t_1
    else if (t <= 2.9d-304) then
        tmp = x + a
    else if (t <= 2.6d-238) then
        tmp = t_3
    else if (t <= 4.2d-223) then
        tmp = t_1
    else if (t <= 2.1d-155) then
        tmp = t_3
    else if (t <= 5.8d-43) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (1.0 - y);
	double t_2 = t * (b - a);
	double t_3 = b * (y - 2.0);
	double tmp;
	if (t <= -180000.0) {
		tmp = t_2;
	} else if (t <= -1.12e-36) {
		tmp = t_1;
	} else if (t <= 2.9e-304) {
		tmp = x + a;
	} else if (t <= 2.6e-238) {
		tmp = t_3;
	} else if (t <= 4.2e-223) {
		tmp = t_1;
	} else if (t <= 2.1e-155) {
		tmp = t_3;
	} else if (t <= 5.8e-43) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * (1.0 - y)
	t_2 = t * (b - a)
	t_3 = b * (y - 2.0)
	tmp = 0
	if t <= -180000.0:
		tmp = t_2
	elif t <= -1.12e-36:
		tmp = t_1
	elif t <= 2.9e-304:
		tmp = x + a
	elif t <= 2.6e-238:
		tmp = t_3
	elif t <= 4.2e-223:
		tmp = t_1
	elif t <= 2.1e-155:
		tmp = t_3
	elif t <= 5.8e-43:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(1.0 - y))
	t_2 = Float64(t * Float64(b - a))
	t_3 = Float64(b * Float64(y - 2.0))
	tmp = 0.0
	if (t <= -180000.0)
		tmp = t_2;
	elseif (t <= -1.12e-36)
		tmp = t_1;
	elseif (t <= 2.9e-304)
		tmp = Float64(x + a);
	elseif (t <= 2.6e-238)
		tmp = t_3;
	elseif (t <= 4.2e-223)
		tmp = t_1;
	elseif (t <= 2.1e-155)
		tmp = t_3;
	elseif (t <= 5.8e-43)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * (1.0 - y);
	t_2 = t * (b - a);
	t_3 = b * (y - 2.0);
	tmp = 0.0;
	if (t <= -180000.0)
		tmp = t_2;
	elseif (t <= -1.12e-36)
		tmp = t_1;
	elseif (t <= 2.9e-304)
		tmp = x + a;
	elseif (t <= 2.6e-238)
		tmp = t_3;
	elseif (t <= 4.2e-223)
		tmp = t_1;
	elseif (t <= 2.1e-155)
		tmp = t_3;
	elseif (t <= 5.8e-43)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(b * N[(y - 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -180000.0], t$95$2, If[LessEqual[t, -1.12e-36], t$95$1, If[LessEqual[t, 2.9e-304], N[(x + a), $MachinePrecision], If[LessEqual[t, 2.6e-238], t$95$3, If[LessEqual[t, 4.2e-223], t$95$1, If[LessEqual[t, 2.1e-155], t$95$3, If[LessEqual[t, 5.8e-43], t$95$1, t$95$2]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.8e5 or 5.8000000000000003e-43 < t

   1. Initial program 90.4%

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

   3. Taylor expanded in t around inf 75.5%

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

   if -1.8e5 < t < -1.12e-36 or 2.6000000000000001e-238 < t < 4.19999999999999965e-223 or 2.1000000000000002e-155 < t < 5.8000000000000003e-43

   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 58.0%

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

   if -1.12e-36 < t < 2.9e-304

   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 75.3%

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

   4. Taylor expanded in t around 0 75.3%

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

      1. associate--l+ 75.3%

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

      2. sub-neg 75.3%

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

      3. metadata-eval 75.3%

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

      4. neg-mul-1 75.3%

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

   6. Simplified 75.3%

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

      1. sub-neg 75.3%

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

      2. remove-double-neg 75.3%

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

   8. Applied egg-rr 75.3%

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

   9. Taylor expanded in b around 0 43.8%

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

   if 2.9e-304 < t < 2.6000000000000001e-238 or 4.19999999999999965e-223 < t < 2.1000000000000002e-155

   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 y around inf 61.6%

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

      1. mul-1-neg 61.6%

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

      2. *-commutative 61.6%

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

      3. distribute-rgt-neg-in 61.6%

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

   5. Simplified 61.6%

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

   6. Taylor expanded in t around 0 61.6%

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

   7. Taylor expanded in z around 0 53.7%

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

Alternative 11: 37.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(1 - t\right)\\ \mathbf{if}\;a \leq -6.4 \cdot 10^{+40}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -1.9 \cdot 10^{-49}:\\ \;\;\;\;b \cdot -2\\ \mathbf{elif}\;a \leq -8 \cdot 10^{-144}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;a \leq 1.85 \cdot 10^{-268}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;a \leq 1.45 \cdot 10^{-233}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;a \leq 1.06 \cdot 10^{-207}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;a \leq 5.6 \cdot 10^{+29}:\\ \;\;\;\;t \cdot b\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (- 1.0 t))))
   (if (<= a -6.4e+40)
     t_1
     (if (<= a -1.9e-49)
       (* b -2.0)
       (if (<= a -8e-144)
         (* t b)
         (if (<= a 1.85e-268)
           (+ x z)
           (if (<= a 1.45e-233)
             (* t b)
             (if (<= a 1.06e-207)
               (+ x z)
               (if (<= a 5.6e+29) (* t b) t_1)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double tmp;
	if (a <= -6.4e+40) {
		tmp = t_1;
	} else if (a <= -1.9e-49) {
		tmp = b * -2.0;
	} else if (a <= -8e-144) {
		tmp = t * b;
	} else if (a <= 1.85e-268) {
		tmp = x + z;
	} else if (a <= 1.45e-233) {
		tmp = t * b;
	} else if (a <= 1.06e-207) {
		tmp = x + z;
	} else if (a <= 5.6e+29) {
		tmp = t * b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (1.0d0 - t)
    if (a <= (-6.4d+40)) then
        tmp = t_1
    else if (a <= (-1.9d-49)) then
        tmp = b * (-2.0d0)
    else if (a <= (-8d-144)) then
        tmp = t * b
    else if (a <= 1.85d-268) then
        tmp = x + z
    else if (a <= 1.45d-233) then
        tmp = t * b
    else if (a <= 1.06d-207) then
        tmp = x + z
    else if (a <= 5.6d+29) then
        tmp = t * b
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double tmp;
	if (a <= -6.4e+40) {
		tmp = t_1;
	} else if (a <= -1.9e-49) {
		tmp = b * -2.0;
	} else if (a <= -8e-144) {
		tmp = t * b;
	} else if (a <= 1.85e-268) {
		tmp = x + z;
	} else if (a <= 1.45e-233) {
		tmp = t * b;
	} else if (a <= 1.06e-207) {
		tmp = x + z;
	} else if (a <= 5.6e+29) {
		tmp = t * b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (1.0 - t)
	tmp = 0
	if a <= -6.4e+40:
		tmp = t_1
	elif a <= -1.9e-49:
		tmp = b * -2.0
	elif a <= -8e-144:
		tmp = t * b
	elif a <= 1.85e-268:
		tmp = x + z
	elif a <= 1.45e-233:
		tmp = t * b
	elif a <= 1.06e-207:
		tmp = x + z
	elif a <= 5.6e+29:
		tmp = t * b
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(1.0 - t))
	tmp = 0.0
	if (a <= -6.4e+40)
		tmp = t_1;
	elseif (a <= -1.9e-49)
		tmp = Float64(b * -2.0);
	elseif (a <= -8e-144)
		tmp = Float64(t * b);
	elseif (a <= 1.85e-268)
		tmp = Float64(x + z);
	elseif (a <= 1.45e-233)
		tmp = Float64(t * b);
	elseif (a <= 1.06e-207)
		tmp = Float64(x + z);
	elseif (a <= 5.6e+29)
		tmp = Float64(t * b);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (1.0 - t);
	tmp = 0.0;
	if (a <= -6.4e+40)
		tmp = t_1;
	elseif (a <= -1.9e-49)
		tmp = b * -2.0;
	elseif (a <= -8e-144)
		tmp = t * b;
	elseif (a <= 1.85e-268)
		tmp = x + z;
	elseif (a <= 1.45e-233)
		tmp = t * b;
	elseif (a <= 1.06e-207)
		tmp = x + z;
	elseif (a <= 5.6e+29)
		tmp = t * b;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -6.4e+40], t$95$1, If[LessEqual[a, -1.9e-49], N[(b * -2.0), $MachinePrecision], If[LessEqual[a, -8e-144], N[(t * b), $MachinePrecision], If[LessEqual[a, 1.85e-268], N[(x + z), $MachinePrecision], If[LessEqual[a, 1.45e-233], N[(t * b), $MachinePrecision], If[LessEqual[a, 1.06e-207], N[(x + z), $MachinePrecision], If[LessEqual[a, 5.6e+29], N[(t * b), $MachinePrecision], t$95$1]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -6.39999999999999961e40 or 5.5999999999999999e29 < a

   1. Initial program 92.8%

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

   3. Taylor expanded in a around inf 53.8%

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

   if -6.39999999999999961e40 < a < -1.8999999999999999e-49

   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 75.5%

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

      1. mul-1-neg 75.5%

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

      2. *-commutative 75.5%

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

      3. distribute-rgt-neg-in 75.5%

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

   5. Simplified 75.5%

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

   6. Taylor expanded in t around 0 51.6%

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

   7. Taylor expanded in y around 0 33.5%

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

      1. *-commutative 33.5%

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

   9. Simplified 33.5%

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

   if -1.8999999999999999e-49 < a < -7.9999999999999996e-144 or 1.85000000000000009e-268 < a < 1.44999999999999991e-233 or 1.05999999999999997e-207 < a < 5.5999999999999999e29

   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 b around inf 62.8%

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

   4. Taylor expanded in t around inf 38.3%

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

   if -7.9999999999999996e-144 < a < 1.85000000000000009e-268 or 1.44999999999999991e-233 < a < 1.05999999999999997e-207

   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 a around 0 95.2%

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

   4. Taylor expanded in y around 0 73.2%

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

      1. sub-neg 73.2%

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

      2. metadata-eval 73.2%

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

      3. neg-mul-1 73.2%

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

   6. Simplified 73.2%

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

   7. Taylor expanded in x around inf 37.6%

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

4. Final simplification 45.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6.4 \cdot 10^{+40}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;a \leq -1.9 \cdot 10^{-49}:\\ \;\;\;\;b \cdot -2\\ \mathbf{elif}\;a \leq -8 \cdot 10^{-144}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;a \leq 1.85 \cdot 10^{-268}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;a \leq 1.45 \cdot 10^{-233}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;a \leq 1.06 \cdot 10^{-207}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;a \leq 5.6 \cdot 10^{+29}:\\ \;\;\;\;t \cdot b\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 63.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(\left(y + t\right) - 2\right) \cdot b\\ t_2 := x - \left(y + -1\right) \cdot z\\ \mathbf{if}\;b \leq -3.1 \cdot 10^{+19}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -9.5 \cdot 10^{-70}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;b \leq -1.05 \cdot 10^{-120}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -7 \cdot 10^{-201}:\\ \;\;\;\;x + \left(z + a\right)\\ \mathbf{elif}\;b \leq 1.25 \cdot 10^{-205}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 6.5 \cdot 10^{+30}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* (- (+ y t) 2.0) b))) (t_2 (- x (* (+ y -1.0) z))))
   (if (<= b -3.1e+19)
     t_1
     (if (<= b -9.5e-70)
       (* t (- b a))
       (if (<= b -1.05e-120)
         t_2
         (if (<= b -7e-201)
           (+ x (+ z a))
           (if (<= b 1.25e-205)
             t_2
             (if (<= b 6.5e+30) (+ x (* a (- 1.0 t))) t_1))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (((y + t) - 2.0) * b);
	double t_2 = x - ((y + -1.0) * z);
	double tmp;
	if (b <= -3.1e+19) {
		tmp = t_1;
	} else if (b <= -9.5e-70) {
		tmp = t * (b - a);
	} else if (b <= -1.05e-120) {
		tmp = t_2;
	} else if (b <= -7e-201) {
		tmp = x + (z + a);
	} else if (b <= 1.25e-205) {
		tmp = t_2;
	} else if (b <= 6.5e+30) {
		tmp = x + (a * (1.0 - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + (((y + t) - 2.0d0) * b)
    t_2 = x - ((y + (-1.0d0)) * z)
    if (b <= (-3.1d+19)) then
        tmp = t_1
    else if (b <= (-9.5d-70)) then
        tmp = t * (b - a)
    else if (b <= (-1.05d-120)) then
        tmp = t_2
    else if (b <= (-7d-201)) then
        tmp = x + (z + a)
    else if (b <= 1.25d-205) then
        tmp = t_2
    else if (b <= 6.5d+30) then
        tmp = x + (a * (1.0d0 - t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (((y + t) - 2.0) * b);
	double t_2 = x - ((y + -1.0) * z);
	double tmp;
	if (b <= -3.1e+19) {
		tmp = t_1;
	} else if (b <= -9.5e-70) {
		tmp = t * (b - a);
	} else if (b <= -1.05e-120) {
		tmp = t_2;
	} else if (b <= -7e-201) {
		tmp = x + (z + a);
	} else if (b <= 1.25e-205) {
		tmp = t_2;
	} else if (b <= 6.5e+30) {
		tmp = x + (a * (1.0 - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (((y + t) - 2.0) * b)
	t_2 = x - ((y + -1.0) * z)
	tmp = 0
	if b <= -3.1e+19:
		tmp = t_1
	elif b <= -9.5e-70:
		tmp = t * (b - a)
	elif b <= -1.05e-120:
		tmp = t_2
	elif b <= -7e-201:
		tmp = x + (z + a)
	elif b <= 1.25e-205:
		tmp = t_2
	elif b <= 6.5e+30:
		tmp = x + (a * (1.0 - t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(Float64(Float64(y + t) - 2.0) * b))
	t_2 = Float64(x - Float64(Float64(y + -1.0) * z))
	tmp = 0.0
	if (b <= -3.1e+19)
		tmp = t_1;
	elseif (b <= -9.5e-70)
		tmp = Float64(t * Float64(b - a));
	elseif (b <= -1.05e-120)
		tmp = t_2;
	elseif (b <= -7e-201)
		tmp = Float64(x + Float64(z + a));
	elseif (b <= 1.25e-205)
		tmp = t_2;
	elseif (b <= 6.5e+30)
		tmp = Float64(x + Float64(a * Float64(1.0 - t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (((y + t) - 2.0) * b);
	t_2 = x - ((y + -1.0) * z);
	tmp = 0.0;
	if (b <= -3.1e+19)
		tmp = t_1;
	elseif (b <= -9.5e-70)
		tmp = t * (b - a);
	elseif (b <= -1.05e-120)
		tmp = t_2;
	elseif (b <= -7e-201)
		tmp = x + (z + a);
	elseif (b <= 1.25e-205)
		tmp = t_2;
	elseif (b <= 6.5e+30)
		tmp = x + (a * (1.0 - t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x - N[(N[(y + -1.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -3.1e+19], t$95$1, If[LessEqual[b, -9.5e-70], N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -1.05e-120], t$95$2, If[LessEqual[b, -7e-201], N[(x + N[(z + a), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.25e-205], t$95$2, If[LessEqual[b, 6.5e+30], N[(x + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -3.1e19 or 6.5e30 < b

   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 a around 0 85.8%

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

   4. Taylor expanded in z around 0 81.0%

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

   if -3.1e19 < b < -9.4999999999999994e-70

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 58.6%

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

   if -9.4999999999999994e-70 < b < -1.05e-120 or -7.00000000000000016e-201 < b < 1.25e-205

   1. Initial program 100.0%

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

   3. Taylor expanded in a around 0 69.0%

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

   4. Taylor expanded in b around 0 66.6%

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

   if -1.05e-120 < b < -7.00000000000000016e-201

   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 t around 0 91.4%

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

      1. +-commutative 91.4%

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

      2. sub-neg 91.4%

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

      3. metadata-eval 91.4%

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

      4. neg-mul-1 91.4%

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

      5. unsub-neg 91.4%

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

   6. Simplified 91.4%

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

   7. Taylor expanded in y around 0 73.7%

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

      1. neg-mul-1 73.7%

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

   9. Simplified 73.7%

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

   if 1.25e-205 < b < 6.5e30

   1. Initial program 97.7%

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

   3. Taylor expanded in z around 0 70.5%

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

   4. Taylor expanded in b around 0 64.5%

      \[\leadsto \color{blue}{x - a \cdot \left(t - 1\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 74.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.1 \cdot 10^{+19}:\\ \;\;\;\;x + \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{elif}\;b \leq -9.5 \cdot 10^{-70}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;b \leq -1.05 \cdot 10^{-120}:\\ \;\;\;\;x - \left(y + -1\right) \cdot z\\ \mathbf{elif}\;b \leq -7 \cdot 10^{-201}:\\ \;\;\;\;x + \left(z + a\right)\\ \mathbf{elif}\;b \leq 1.25 \cdot 10^{-205}:\\ \;\;\;\;x - \left(y + -1\right) \cdot z\\ \mathbf{elif}\;b \leq 6.5 \cdot 10^{+30}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(\left(y + t\right) - 2\right) \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 83.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(a \cdot \left(1 - t\right) - \left(y + -1\right) \cdot z\right)\\ t_2 := x + \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{if}\;b \leq -3 \cdot 10^{+31}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 2.15 \cdot 10^{+27}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 2.9 \cdot 10^{+73}:\\ \;\;\;\;z \cdot \left(\left(1 + \left(t + \left(y + -2\right)\right) \cdot \frac{b}{z}\right) - y\right)\\ \mathbf{elif}\;b \leq 2.9 \cdot 10^{+100}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (- (* a (- 1.0 t)) (* (+ y -1.0) z))))
        (t_2 (+ x (* (- (+ y t) 2.0) b))))
   (if (<= b -3e+31)
     t_2
     (if (<= b 2.15e+27)
       t_1
       (if (<= b 2.9e+73)
         (* z (- (+ 1.0 (* (+ t (+ y -2.0)) (/ b z))) y))
         (if (<= b 2.9e+100) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + ((a * (1.0 - t)) - ((y + -1.0) * z));
	double t_2 = x + (((y + t) - 2.0) * b);
	double tmp;
	if (b <= -3e+31) {
		tmp = t_2;
	} else if (b <= 2.15e+27) {
		tmp = t_1;
	} else if (b <= 2.9e+73) {
		tmp = z * ((1.0 + ((t + (y + -2.0)) * (b / z))) - y);
	} else if (b <= 2.9e+100) {
		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 + ((a * (1.0d0 - t)) - ((y + (-1.0d0)) * z))
    t_2 = x + (((y + t) - 2.0d0) * b)
    if (b <= (-3d+31)) then
        tmp = t_2
    else if (b <= 2.15d+27) then
        tmp = t_1
    else if (b <= 2.9d+73) then
        tmp = z * ((1.0d0 + ((t + (y + (-2.0d0))) * (b / z))) - y)
    else if (b <= 2.9d+100) 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 + ((a * (1.0 - t)) - ((y + -1.0) * z));
	double t_2 = x + (((y + t) - 2.0) * b);
	double tmp;
	if (b <= -3e+31) {
		tmp = t_2;
	} else if (b <= 2.15e+27) {
		tmp = t_1;
	} else if (b <= 2.9e+73) {
		tmp = z * ((1.0 + ((t + (y + -2.0)) * (b / z))) - y);
	} else if (b <= 2.9e+100) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + ((a * (1.0 - t)) - ((y + -1.0) * z))
	t_2 = x + (((y + t) - 2.0) * b)
	tmp = 0
	if b <= -3e+31:
		tmp = t_2
	elif b <= 2.15e+27:
		tmp = t_1
	elif b <= 2.9e+73:
		tmp = z * ((1.0 + ((t + (y + -2.0)) * (b / z))) - y)
	elif b <= 2.9e+100:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(Float64(a * Float64(1.0 - t)) - Float64(Float64(y + -1.0) * z)))
	t_2 = Float64(x + Float64(Float64(Float64(y + t) - 2.0) * b))
	tmp = 0.0
	if (b <= -3e+31)
		tmp = t_2;
	elseif (b <= 2.15e+27)
		tmp = t_1;
	elseif (b <= 2.9e+73)
		tmp = Float64(z * Float64(Float64(1.0 + Float64(Float64(t + Float64(y + -2.0)) * Float64(b / z))) - y));
	elseif (b <= 2.9e+100)
		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 + ((a * (1.0 - t)) - ((y + -1.0) * z));
	t_2 = x + (((y + t) - 2.0) * b);
	tmp = 0.0;
	if (b <= -3e+31)
		tmp = t_2;
	elseif (b <= 2.15e+27)
		tmp = t_1;
	elseif (b <= 2.9e+73)
		tmp = z * ((1.0 + ((t + (y + -2.0)) * (b / z))) - y);
	elseif (b <= 2.9e+100)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision] - N[(N[(y + -1.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -3e+31], t$95$2, If[LessEqual[b, 2.15e+27], t$95$1, If[LessEqual[b, 2.9e+73], N[(z * N[(N[(1.0 + N[(N[(t + N[(y + -2.0), $MachinePrecision]), $MachinePrecision] * N[(b / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.9e+100], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -2.99999999999999989e31 or 2.9e100 < b

   1. Initial program 91.4%

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

   3. Taylor expanded in a around 0 85.8%

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

   4. Taylor expanded in z around 0 84.2%

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

   if -2.99999999999999989e31 < b < 2.15000000000000004e27 or 2.9000000000000002e73 < b < 2.9e100

   1. Initial program 98.2%

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

   3. Taylor expanded in b around 0 92.5%

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

   if 2.15000000000000004e27 < b < 2.9000000000000002e73

   1. Initial program 100.0%

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

   3. Taylor expanded in a around 0 89.2%

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

   4. Taylor expanded in z around inf 74.3%

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

      1. associate-+r- 74.3%

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

      2. associate-/l* 74.2%

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

      3. sub-neg 74.2%

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

      4. metadata-eval 74.2%

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

   6. Simplified 74.2%

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

   7. Taylor expanded in x around 0 80.9%

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

      1. sub-neg 80.9%

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

      2. metadata-eval 80.9%

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

      3. associate-+r+ 80.9%

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

      4. associate-*l/ 80.9%

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

   9. Simplified 80.9%

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

4. Final simplification 87.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3 \cdot 10^{+31}:\\ \;\;\;\;x + \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{elif}\;b \leq 2.15 \cdot 10^{+27}:\\ \;\;\;\;x + \left(a \cdot \left(1 - t\right) - \left(y + -1\right) \cdot z\right)\\ \mathbf{elif}\;b \leq 2.9 \cdot 10^{+73}:\\ \;\;\;\;z \cdot \left(\left(1 + \left(t + \left(y + -2\right)\right) \cdot \frac{b}{z}\right) - y\right)\\ \mathbf{elif}\;b \leq 2.9 \cdot 10^{+100}:\\ \;\;\;\;x + \left(a \cdot \left(1 - t\right) - \left(y + -1\right) \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(\left(y + t\right) - 2\right) \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 83.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(a \cdot \left(1 - t\right) - \left(y + -1\right) \cdot z\right)\\ t_2 := \left(\left(y + t\right) - 2\right) \cdot b\\ t_3 := x + t\_2\\ \mathbf{if}\;b \leq -2.7 \cdot 10^{+31}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;b \leq 4.6 \cdot 10^{+32}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 8.2 \cdot 10^{+67}:\\ \;\;\;\;t\_2 - y \cdot z\\ \mathbf{elif}\;b \leq 2.8 \cdot 10^{+99}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (- (* a (- 1.0 t)) (* (+ y -1.0) z))))
        (t_2 (* (- (+ y t) 2.0) b))
        (t_3 (+ x t_2)))
   (if (<= b -2.7e+31)
     t_3
     (if (<= b 4.6e+32)
       t_1
       (if (<= b 8.2e+67) (- t_2 (* y z)) (if (<= b 2.8e+99) t_1 t_3))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + ((a * (1.0 - t)) - ((y + -1.0) * z));
	double t_2 = ((y + t) - 2.0) * b;
	double t_3 = x + t_2;
	double tmp;
	if (b <= -2.7e+31) {
		tmp = t_3;
	} else if (b <= 4.6e+32) {
		tmp = t_1;
	} else if (b <= 8.2e+67) {
		tmp = t_2 - (y * z);
	} else if (b <= 2.8e+99) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = x + ((a * (1.0d0 - t)) - ((y + (-1.0d0)) * z))
    t_2 = ((y + t) - 2.0d0) * b
    t_3 = x + t_2
    if (b <= (-2.7d+31)) then
        tmp = t_3
    else if (b <= 4.6d+32) then
        tmp = t_1
    else if (b <= 8.2d+67) then
        tmp = t_2 - (y * z)
    else if (b <= 2.8d+99) then
        tmp = t_1
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + ((a * (1.0 - t)) - ((y + -1.0) * z));
	double t_2 = ((y + t) - 2.0) * b;
	double t_3 = x + t_2;
	double tmp;
	if (b <= -2.7e+31) {
		tmp = t_3;
	} else if (b <= 4.6e+32) {
		tmp = t_1;
	} else if (b <= 8.2e+67) {
		tmp = t_2 - (y * z);
	} else if (b <= 2.8e+99) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + ((a * (1.0 - t)) - ((y + -1.0) * z))
	t_2 = ((y + t) - 2.0) * b
	t_3 = x + t_2
	tmp = 0
	if b <= -2.7e+31:
		tmp = t_3
	elif b <= 4.6e+32:
		tmp = t_1
	elif b <= 8.2e+67:
		tmp = t_2 - (y * z)
	elif b <= 2.8e+99:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(Float64(a * Float64(1.0 - t)) - Float64(Float64(y + -1.0) * z)))
	t_2 = Float64(Float64(Float64(y + t) - 2.0) * b)
	t_3 = Float64(x + t_2)
	tmp = 0.0
	if (b <= -2.7e+31)
		tmp = t_3;
	elseif (b <= 4.6e+32)
		tmp = t_1;
	elseif (b <= 8.2e+67)
		tmp = Float64(t_2 - Float64(y * z));
	elseif (b <= 2.8e+99)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + ((a * (1.0 - t)) - ((y + -1.0) * z));
	t_2 = ((y + t) - 2.0) * b;
	t_3 = x + t_2;
	tmp = 0.0;
	if (b <= -2.7e+31)
		tmp = t_3;
	elseif (b <= 4.6e+32)
		tmp = t_1;
	elseif (b <= 8.2e+67)
		tmp = t_2 - (y * z);
	elseif (b <= 2.8e+99)
		tmp = t_1;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision] - N[(N[(y + -1.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]}, Block[{t$95$3 = N[(x + t$95$2), $MachinePrecision]}, If[LessEqual[b, -2.7e+31], t$95$3, If[LessEqual[b, 4.6e+32], t$95$1, If[LessEqual[b, 8.2e+67], N[(t$95$2 - N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.8e+99], t$95$1, t$95$3]]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -2.69999999999999986e31 or 2.8e99 < b

   1. Initial program 91.4%

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

   3. Taylor expanded in a around 0 85.8%

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

   4. Taylor expanded in z around 0 84.2%

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

   if -2.69999999999999986e31 < b < 4.5999999999999999e32 or 8.19999999999999959e67 < b < 2.8e99

   1. Initial program 98.2%

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

   3. Taylor expanded in b around 0 92.7%

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

   if 4.5999999999999999e32 < b < 8.19999999999999959e67

   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 71.7%

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

      1. mul-1-neg 71.7%

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

      2. *-commutative 71.7%

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

      3. distribute-rgt-neg-in 71.7%

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

   5. Simplified 71.7%

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

4. Final simplification 87.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.7 \cdot 10^{+31}:\\ \;\;\;\;x + \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{elif}\;b \leq 4.6 \cdot 10^{+32}:\\ \;\;\;\;x + \left(a \cdot \left(1 - t\right) - \left(y + -1\right) \cdot z\right)\\ \mathbf{elif}\;b \leq 8.2 \cdot 10^{+67}:\\ \;\;\;\;\left(\left(y + t\right) - 2\right) \cdot b - y \cdot z\\ \mathbf{elif}\;b \leq 2.8 \cdot 10^{+99}:\\ \;\;\;\;x + \left(a \cdot \left(1 - t\right) - \left(y + -1\right) \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(\left(y + t\right) - 2\right) \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 69.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{if}\;b \leq -1.26 \cdot 10^{-34}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 100000000000:\\ \;\;\;\;x + \left(a - \left(y + -1\right) \cdot z\right)\\ \mathbf{elif}\;b \leq 3.6 \cdot 10^{+88}:\\ \;\;\;\;z + \left(x + b \cdot \left(t + -2\right)\right)\\ \mathbf{elif}\;b \leq 8 \cdot 10^{+97}:\\ \;\;\;\;x - t \cdot a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* (- (+ y t) 2.0) b))))
   (if (<= b -1.26e-34)
     t_1
     (if (<= b 100000000000.0)
       (+ x (- a (* (+ y -1.0) z)))
       (if (<= b 3.6e+88)
         (+ z (+ x (* b (+ t -2.0))))
         (if (<= b 8e+97) (- x (* t a)) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (((y + t) - 2.0) * b);
	double tmp;
	if (b <= -1.26e-34) {
		tmp = t_1;
	} else if (b <= 100000000000.0) {
		tmp = x + (a - ((y + -1.0) * z));
	} else if (b <= 3.6e+88) {
		tmp = z + (x + (b * (t + -2.0)));
	} else if (b <= 8e+97) {
		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 = x + (((y + t) - 2.0d0) * b)
    if (b <= (-1.26d-34)) then
        tmp = t_1
    else if (b <= 100000000000.0d0) then
        tmp = x + (a - ((y + (-1.0d0)) * z))
    else if (b <= 3.6d+88) then
        tmp = z + (x + (b * (t + (-2.0d0))))
    else if (b <= 8d+97) 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 = x + (((y + t) - 2.0) * b);
	double tmp;
	if (b <= -1.26e-34) {
		tmp = t_1;
	} else if (b <= 100000000000.0) {
		tmp = x + (a - ((y + -1.0) * z));
	} else if (b <= 3.6e+88) {
		tmp = z + (x + (b * (t + -2.0)));
	} else if (b <= 8e+97) {
		tmp = x - (t * a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (((y + t) - 2.0) * b)
	tmp = 0
	if b <= -1.26e-34:
		tmp = t_1
	elif b <= 100000000000.0:
		tmp = x + (a - ((y + -1.0) * z))
	elif b <= 3.6e+88:
		tmp = z + (x + (b * (t + -2.0)))
	elif b <= 8e+97:
		tmp = x - (t * a)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(Float64(Float64(y + t) - 2.0) * b))
	tmp = 0.0
	if (b <= -1.26e-34)
		tmp = t_1;
	elseif (b <= 100000000000.0)
		tmp = Float64(x + Float64(a - Float64(Float64(y + -1.0) * z)));
	elseif (b <= 3.6e+88)
		tmp = Float64(z + Float64(x + Float64(b * Float64(t + -2.0))));
	elseif (b <= 8e+97)
		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 = x + (((y + t) - 2.0) * b);
	tmp = 0.0;
	if (b <= -1.26e-34)
		tmp = t_1;
	elseif (b <= 100000000000.0)
		tmp = x + (a - ((y + -1.0) * z));
	elseif (b <= 3.6e+88)
		tmp = z + (x + (b * (t + -2.0)));
	elseif (b <= 8e+97)
		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[(x + N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.26e-34], t$95$1, If[LessEqual[b, 100000000000.0], N[(x + N[(a - N[(N[(y + -1.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.6e+88], N[(z + N[(x + N[(b * N[(t + -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 8e+97], N[(x - N[(t * a), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -1.26000000000000009e-34 or 8.0000000000000006e97 < b

   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 a around 0 83.8%

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

   4. Taylor expanded in z around 0 81.6%

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

   if -1.26000000000000009e-34 < b < 1e11

   1. Initial program 99.0%

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

   3. Taylor expanded in b around 0 94.3%

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

   4. Taylor expanded in t around 0 78.2%

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

      1. +-commutative 78.2%

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

      2. sub-neg 78.2%

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

      3. metadata-eval 78.2%

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

      4. neg-mul-1 78.2%

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

      5. unsub-neg 78.2%

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

   6. Simplified 78.2%

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

   if 1e11 < b < 3.6000000000000002e88

   1. Initial program 100.0%

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

   3. Taylor expanded in a around 0 88.0%

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

   4. Taylor expanded in y around 0 69.0%

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

      1. sub-neg 69.0%

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

      2. metadata-eval 69.0%

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

      3. neg-mul-1 69.0%

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

   6. Simplified 69.0%

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

   if 3.6000000000000002e88 < b < 8.0000000000000006e97

   1. Initial program 50.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   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 t around inf 52.3%

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

      1. *-commutative 52.3%

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

   6. Simplified 52.3%

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

4. Final simplification 79.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.26 \cdot 10^{-34}:\\ \;\;\;\;x + \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{elif}\;b \leq 100000000000:\\ \;\;\;\;x + \left(a - \left(y + -1\right) \cdot z\right)\\ \mathbf{elif}\;b \leq 3.6 \cdot 10^{+88}:\\ \;\;\;\;z + \left(x + b \cdot \left(t + -2\right)\right)\\ \mathbf{elif}\;b \leq 8 \cdot 10^{+97}:\\ \;\;\;\;x - t \cdot a\\ \mathbf{else}:\\ \;\;\;\;x + \left(\left(y + t\right) - 2\right) \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 70.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(y + t\right) - 2\right) \cdot b\\ t_2 := x + t\_1\\ \mathbf{if}\;b \leq -1.26 \cdot 10^{-34}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 1.26 \cdot 10^{+29}:\\ \;\;\;\;x + \left(a - \left(y + -1\right) \cdot z\right)\\ \mathbf{elif}\;b \leq 2.45 \cdot 10^{+69}:\\ \;\;\;\;t\_1 - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- (+ y t) 2.0) b)) (t_2 (+ x t_1)))
   (if (<= b -1.26e-34)
     t_2
     (if (<= b 1.26e+29)
       (+ x (- a (* (+ y -1.0) z)))
       (if (<= b 2.45e+69) (- t_1 (* y z)) t_2)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((y + t) - 2.0) * b;
	double t_2 = x + t_1;
	double tmp;
	if (b <= -1.26e-34) {
		tmp = t_2;
	} else if (b <= 1.26e+29) {
		tmp = x + (a - ((y + -1.0) * z));
	} else if (b <= 2.45e+69) {
		tmp = t_1 - (y * z);
	} 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 + t) - 2.0d0) * b
    t_2 = x + t_1
    if (b <= (-1.26d-34)) then
        tmp = t_2
    else if (b <= 1.26d+29) then
        tmp = x + (a - ((y + (-1.0d0)) * z))
    else if (b <= 2.45d+69) then
        tmp = t_1 - (y * z)
    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 + t) - 2.0) * b;
	double t_2 = x + t_1;
	double tmp;
	if (b <= -1.26e-34) {
		tmp = t_2;
	} else if (b <= 1.26e+29) {
		tmp = x + (a - ((y + -1.0) * z));
	} else if (b <= 2.45e+69) {
		tmp = t_1 - (y * z);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((y + t) - 2.0) * b
	t_2 = x + t_1
	tmp = 0
	if b <= -1.26e-34:
		tmp = t_2
	elif b <= 1.26e+29:
		tmp = x + (a - ((y + -1.0) * z))
	elif b <= 2.45e+69:
		tmp = t_1 - (y * z)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(y + t) - 2.0) * b)
	t_2 = Float64(x + t_1)
	tmp = 0.0
	if (b <= -1.26e-34)
		tmp = t_2;
	elseif (b <= 1.26e+29)
		tmp = Float64(x + Float64(a - Float64(Float64(y + -1.0) * z)));
	elseif (b <= 2.45e+69)
		tmp = Float64(t_1 - Float64(y * z));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((y + t) - 2.0) * b;
	t_2 = x + t_1;
	tmp = 0.0;
	if (b <= -1.26e-34)
		tmp = t_2;
	elseif (b <= 1.26e+29)
		tmp = x + (a - ((y + -1.0) * z));
	elseif (b <= 2.45e+69)
		tmp = t_1 - (y * z);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]}, Block[{t$95$2 = N[(x + t$95$1), $MachinePrecision]}, If[LessEqual[b, -1.26e-34], t$95$2, If[LessEqual[b, 1.26e+29], N[(x + N[(a - N[(N[(y + -1.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.45e+69], N[(t$95$1 - N[(y * z), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.26000000000000009e-34 or 2.45e69 < b

   1. Initial program 91.5%

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

   3. Taylor expanded in a around 0 83.0%

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

   4. Taylor expanded in z around 0 80.8%

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

   if -1.26000000000000009e-34 < b < 1.26e29

   1. Initial program 99.0%

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

   3. Taylor expanded in b around 0 94.5%

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

   4. Taylor expanded in t around 0 78.1%

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

      1. +-commutative 78.1%

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

      2. sub-neg 78.1%

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

      3. metadata-eval 78.1%

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

      4. neg-mul-1 78.1%

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

      5. unsub-neg 78.1%

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

   6. Simplified 78.1%

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

   if 1.26e29 < b < 2.45e69

   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 67.4%

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

      1. mul-1-neg 67.4%

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

      2. *-commutative 67.4%

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

      3. distribute-rgt-neg-in 67.4%

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

   5. Simplified 67.4%

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

4. Final simplification 79.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.26 \cdot 10^{-34}:\\ \;\;\;\;x + \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{elif}\;b \leq 1.26 \cdot 10^{+29}:\\ \;\;\;\;x + \left(a - \left(y + -1\right) \cdot z\right)\\ \mathbf{elif}\;b \leq 2.45 \cdot 10^{+69}:\\ \;\;\;\;\left(\left(y + t\right) - 2\right) \cdot b - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + \left(\left(y + t\right) - 2\right) \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 39.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t - 2\right)\\ t_2 := a \cdot \left(1 - t\right)\\ \mathbf{if}\;a \leq -1.65 \cdot 10^{+121}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq 5.1 \cdot 10^{-191}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 7.6 \cdot 10^{-137}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;a \leq 4.9 \cdot 10^{+33}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- t 2.0))) (t_2 (* a (- 1.0 t))))
   (if (<= a -1.65e+121)
     t_2
     (if (<= a 5.1e-191)
       t_1
       (if (<= a 7.6e-137) (+ x z) (if (<= a 4.9e+33) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (t - 2.0);
	double t_2 = a * (1.0 - t);
	double tmp;
	if (a <= -1.65e+121) {
		tmp = t_2;
	} else if (a <= 5.1e-191) {
		tmp = t_1;
	} else if (a <= 7.6e-137) {
		tmp = x + z;
	} else if (a <= 4.9e+33) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = b * (t - 2.0d0)
    t_2 = a * (1.0d0 - t)
    if (a <= (-1.65d+121)) then
        tmp = t_2
    else if (a <= 5.1d-191) then
        tmp = t_1
    else if (a <= 7.6d-137) then
        tmp = x + z
    else if (a <= 4.9d+33) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (t - 2.0);
	double t_2 = a * (1.0 - t);
	double tmp;
	if (a <= -1.65e+121) {
		tmp = t_2;
	} else if (a <= 5.1e-191) {
		tmp = t_1;
	} else if (a <= 7.6e-137) {
		tmp = x + z;
	} else if (a <= 4.9e+33) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * (t - 2.0)
	t_2 = a * (1.0 - t)
	tmp = 0
	if a <= -1.65e+121:
		tmp = t_2
	elif a <= 5.1e-191:
		tmp = t_1
	elif a <= 7.6e-137:
		tmp = x + z
	elif a <= 4.9e+33:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(t - 2.0))
	t_2 = Float64(a * Float64(1.0 - t))
	tmp = 0.0
	if (a <= -1.65e+121)
		tmp = t_2;
	elseif (a <= 5.1e-191)
		tmp = t_1;
	elseif (a <= 7.6e-137)
		tmp = Float64(x + z);
	elseif (a <= 4.9e+33)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * (t - 2.0);
	t_2 = a * (1.0 - t);
	tmp = 0.0;
	if (a <= -1.65e+121)
		tmp = t_2;
	elseif (a <= 5.1e-191)
		tmp = t_1;
	elseif (a <= 7.6e-137)
		tmp = x + z;
	elseif (a <= 4.9e+33)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(t - 2.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.65e+121], t$95$2, If[LessEqual[a, 5.1e-191], t$95$1, If[LessEqual[a, 7.6e-137], N[(x + z), $MachinePrecision], If[LessEqual[a, 4.9e+33], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.6499999999999999e121 or 4.90000000000000014e33 < a

   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 a around inf 56.1%

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

   if -1.6499999999999999e121 < a < 5.1000000000000002e-191 or 7.59999999999999997e-137 < a < 4.90000000000000014e33

   1. Initial program 97.1%

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

   3. Taylor expanded in b around inf 59.4%

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

   4. Taylor expanded in y around 0 48.1%

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

   if 5.1000000000000002e-191 < a < 7.59999999999999997e-137

   1. Initial program 99.8%

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

   3. Taylor expanded in a around 0 99.8%

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

   4. Taylor expanded in y around 0 64.7%

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

      1. sub-neg 64.7%

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

      2. metadata-eval 64.7%

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

      3. neg-mul-1 64.7%

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

   6. Simplified 64.7%

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

   7. Taylor expanded in x around inf 55.7%

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

4. Final simplification 51.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.65 \cdot 10^{+121}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;a \leq 5.1 \cdot 10^{-191}:\\ \;\;\;\;b \cdot \left(t - 2\right)\\ \mathbf{elif}\;a \leq 7.6 \cdot 10^{-137}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;a \leq 4.9 \cdot 10^{+33}:\\ \;\;\;\;b \cdot \left(t - 2\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 86.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(1 - t\right)\\ \mathbf{if}\;b \leq -2.2 \cdot 10^{-35} \lor \neg \left(b \leq 6.6 \cdot 10^{-44}\right):\\ \;\;\;\;\left(x + \left(\left(y + t\right) - 2\right) \cdot b\right) + t\_1\\ \mathbf{else}:\\ \;\;\;\;x + \left(t\_1 - \left(y + -1\right) \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (- 1.0 t))))
   (if (or (<= b -2.2e-35) (not (<= b 6.6e-44)))
     (+ (+ x (* (- (+ y t) 2.0) b)) t_1)
     (+ x (- t_1 (* (+ y -1.0) z))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double tmp;
	if ((b <= -2.2e-35) || !(b <= 6.6e-44)) {
		tmp = (x + (((y + t) - 2.0) * b)) + t_1;
	} else {
		tmp = x + (t_1 - ((y + -1.0) * z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (1.0d0 - t)
    if ((b <= (-2.2d-35)) .or. (.not. (b <= 6.6d-44))) then
        tmp = (x + (((y + t) - 2.0d0) * b)) + t_1
    else
        tmp = x + (t_1 - ((y + (-1.0d0)) * z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double tmp;
	if ((b <= -2.2e-35) || !(b <= 6.6e-44)) {
		tmp = (x + (((y + t) - 2.0) * b)) + t_1;
	} else {
		tmp = x + (t_1 - ((y + -1.0) * z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (1.0 - t)
	tmp = 0
	if (b <= -2.2e-35) or not (b <= 6.6e-44):
		tmp = (x + (((y + t) - 2.0) * b)) + t_1
	else:
		tmp = x + (t_1 - ((y + -1.0) * z))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(1.0 - t))
	tmp = 0.0
	if ((b <= -2.2e-35) || !(b <= 6.6e-44))
		tmp = Float64(Float64(x + Float64(Float64(Float64(y + t) - 2.0) * b)) + t_1);
	else
		tmp = Float64(x + Float64(t_1 - Float64(Float64(y + -1.0) * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (1.0 - t);
	tmp = 0.0;
	if ((b <= -2.2e-35) || ~((b <= 6.6e-44)))
		tmp = (x + (((y + t) - 2.0) * b)) + t_1;
	else
		tmp = x + (t_1 - ((y + -1.0) * z));
	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[Or[LessEqual[b, -2.2e-35], N[Not[LessEqual[b, 6.6e-44]], $MachinePrecision]], N[(N[(x + N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], N[(x + N[(t$95$1 - N[(N[(y + -1.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if b < -2.19999999999999994e-35 or 6.60000000000000011e-44 < b

   1. Initial program 92.7%

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

   3. Taylor expanded in z around 0 86.7%

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

   if -2.19999999999999994e-35 < b < 6.60000000000000011e-44

   1. Initial program 98.9%

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

   3. Taylor expanded in b around 0 95.0%

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

4. Final simplification 89.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.2 \cdot 10^{-35} \lor \neg \left(b \leq 6.6 \cdot 10^{-44}\right):\\ \;\;\;\;\left(x + \left(\left(y + t\right) - 2\right) \cdot b\right) + a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(a \cdot \left(1 - t\right) - \left(y + -1\right) \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 87.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(1 - t\right)\\ \mathbf{if}\;z \leq -320000000000:\\ \;\;\;\;z \cdot \left(\left(1 + \left(\frac{x}{z} + b \cdot \frac{t + \left(y + -2\right)}{z}\right)\right) - y\right)\\ \mathbf{elif}\;z \leq 6.3 \cdot 10^{+81}:\\ \;\;\;\;\left(x + \left(\left(y + t\right) - 2\right) \cdot b\right) + t\_1\\ \mathbf{else}:\\ \;\;\;\;x + \left(t\_1 - \left(y + -1\right) \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (- 1.0 t))))
   (if (<= z -320000000000.0)
     (* z (- (+ 1.0 (+ (/ x z) (* b (/ (+ t (+ y -2.0)) z)))) y))
     (if (<= z 6.3e+81)
       (+ (+ x (* (- (+ y t) 2.0) b)) t_1)
       (+ x (- t_1 (* (+ y -1.0) z)))))))

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 (z <= -320000000000.0) {
		tmp = z * ((1.0 + ((x / z) + (b * ((t + (y + -2.0)) / z)))) - y);
	} else if (z <= 6.3e+81) {
		tmp = (x + (((y + t) - 2.0) * b)) + t_1;
	} else {
		tmp = x + (t_1 - ((y + -1.0) * z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (1.0d0 - t)
    if (z <= (-320000000000.0d0)) then
        tmp = z * ((1.0d0 + ((x / z) + (b * ((t + (y + (-2.0d0))) / z)))) - y)
    else if (z <= 6.3d+81) then
        tmp = (x + (((y + t) - 2.0d0) * b)) + t_1
    else
        tmp = x + (t_1 - ((y + (-1.0d0)) * z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double tmp;
	if (z <= -320000000000.0) {
		tmp = z * ((1.0 + ((x / z) + (b * ((t + (y + -2.0)) / z)))) - y);
	} else if (z <= 6.3e+81) {
		tmp = (x + (((y + t) - 2.0) * b)) + t_1;
	} else {
		tmp = x + (t_1 - ((y + -1.0) * z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (1.0 - t)
	tmp = 0
	if z <= -320000000000.0:
		tmp = z * ((1.0 + ((x / z) + (b * ((t + (y + -2.0)) / z)))) - y)
	elif z <= 6.3e+81:
		tmp = (x + (((y + t) - 2.0) * b)) + t_1
	else:
		tmp = x + (t_1 - ((y + -1.0) * z))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(1.0 - t))
	tmp = 0.0
	if (z <= -320000000000.0)
		tmp = Float64(z * Float64(Float64(1.0 + Float64(Float64(x / z) + Float64(b * Float64(Float64(t + Float64(y + -2.0)) / z)))) - y));
	elseif (z <= 6.3e+81)
		tmp = Float64(Float64(x + Float64(Float64(Float64(y + t) - 2.0) * b)) + t_1);
	else
		tmp = Float64(x + Float64(t_1 - Float64(Float64(y + -1.0) * z)));
	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 (z <= -320000000000.0)
		tmp = z * ((1.0 + ((x / z) + (b * ((t + (y + -2.0)) / z)))) - y);
	elseif (z <= 6.3e+81)
		tmp = (x + (((y + t) - 2.0) * b)) + t_1;
	else
		tmp = x + (t_1 - ((y + -1.0) * z));
	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[z, -320000000000.0], N[(z * N[(N[(1.0 + N[(N[(x / z), $MachinePrecision] + N[(b * N[(N[(t + N[(y + -2.0), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.3e+81], N[(N[(x + N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], N[(x + N[(t$95$1 - N[(N[(y + -1.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.2e11

   1. Initial program 83.3%

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

   3. Taylor expanded in a around 0 82.1%

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

   4. Taylor expanded in z around inf 85.7%

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

      1. associate-+r- 85.7%

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

      2. associate-/l* 87.6%

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

      3. sub-neg 87.6%

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

      4. metadata-eval 87.6%

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

   6. Simplified 87.6%

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

   if -3.2e11 < z < 6.3000000000000004e81

   1. Initial program 99.3%

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

   3. Taylor expanded in z around 0 95.9%

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

   if 6.3000000000000004e81 < z

   1. Initial program 95.0%

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

   3. Taylor expanded in b around 0 83.8%

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

4. Final simplification 91.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -320000000000:\\ \;\;\;\;z \cdot \left(\left(1 + \left(\frac{x}{z} + b \cdot \frac{t + \left(y + -2\right)}{z}\right)\right) - y\right)\\ \mathbf{elif}\;z \leq 6.3 \cdot 10^{+81}:\\ \;\;\;\;\left(x + \left(\left(y + t\right) - 2\right) \cdot b\right) + a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(a \cdot \left(1 - t\right) - \left(y + -1\right) \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 86.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(\left(y + t\right) - 2\right) \cdot b\\ t_2 := a \cdot \left(1 - t\right)\\ \mathbf{if}\;z \leq -1.4 \cdot 10^{+34}:\\ \;\;\;\;t\_1 + z \cdot \left(1 - y\right)\\ \mathbf{elif}\;z \leq 7.4 \cdot 10^{+81}:\\ \;\;\;\;t\_1 + t\_2\\ \mathbf{else}:\\ \;\;\;\;x + \left(t\_2 - \left(y + -1\right) \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* (- (+ y t) 2.0) b))) (t_2 (* a (- 1.0 t))))
   (if (<= z -1.4e+34)
     (+ t_1 (* z (- 1.0 y)))
     (if (<= z 7.4e+81) (+ t_1 t_2) (+ x (- t_2 (* (+ y -1.0) z)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (((y + t) - 2.0) * b);
	double t_2 = a * (1.0 - t);
	double tmp;
	if (z <= -1.4e+34) {
		tmp = t_1 + (z * (1.0 - y));
	} else if (z <= 7.4e+81) {
		tmp = t_1 + t_2;
	} else {
		tmp = x + (t_2 - ((y + -1.0) * z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + (((y + t) - 2.0d0) * b)
    t_2 = a * (1.0d0 - t)
    if (z <= (-1.4d+34)) then
        tmp = t_1 + (z * (1.0d0 - y))
    else if (z <= 7.4d+81) then
        tmp = t_1 + t_2
    else
        tmp = x + (t_2 - ((y + (-1.0d0)) * z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (((y + t) - 2.0) * b);
	double t_2 = a * (1.0 - t);
	double tmp;
	if (z <= -1.4e+34) {
		tmp = t_1 + (z * (1.0 - y));
	} else if (z <= 7.4e+81) {
		tmp = t_1 + t_2;
	} else {
		tmp = x + (t_2 - ((y + -1.0) * z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (((y + t) - 2.0) * b)
	t_2 = a * (1.0 - t)
	tmp = 0
	if z <= -1.4e+34:
		tmp = t_1 + (z * (1.0 - y))
	elif z <= 7.4e+81:
		tmp = t_1 + t_2
	else:
		tmp = x + (t_2 - ((y + -1.0) * z))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(Float64(Float64(y + t) - 2.0) * b))
	t_2 = Float64(a * Float64(1.0 - t))
	tmp = 0.0
	if (z <= -1.4e+34)
		tmp = Float64(t_1 + Float64(z * Float64(1.0 - y)));
	elseif (z <= 7.4e+81)
		tmp = Float64(t_1 + t_2);
	else
		tmp = Float64(x + Float64(t_2 - Float64(Float64(y + -1.0) * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (((y + t) - 2.0) * b);
	t_2 = a * (1.0 - t);
	tmp = 0.0;
	if (z <= -1.4e+34)
		tmp = t_1 + (z * (1.0 - y));
	elseif (z <= 7.4e+81)
		tmp = t_1 + t_2;
	else
		tmp = x + (t_2 - ((y + -1.0) * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.4e+34], N[(t$95$1 + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.4e+81], N[(t$95$1 + t$95$2), $MachinePrecision], N[(x + N[(t$95$2 - N[(N[(y + -1.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.40000000000000004e34

   1. Initial program 82.0%

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

   3. Taylor expanded in a around 0 80.7%

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

   if -1.40000000000000004e34 < z < 7.4000000000000001e81

   1. Initial program 99.3%

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

   3. Taylor expanded in z around 0 95.3%

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

   if 7.4000000000000001e81 < z

   1. Initial program 95.0%

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

   3. Taylor expanded in b around 0 83.8%

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

4. Final simplification 89.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{+34}:\\ \;\;\;\;\left(x + \left(\left(y + t\right) - 2\right) \cdot b\right) + z \cdot \left(1 - y\right)\\ \mathbf{elif}\;z \leq 7.4 \cdot 10^{+81}:\\ \;\;\;\;\left(x + \left(\left(y + t\right) - 2\right) \cdot b\right) + a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(a \cdot \left(1 - t\right) - \left(y + -1\right) \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 31.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -60000000000:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{-270}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq 4.4 \cdot 10^{-183}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{-27}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -60000000000.0)
   (* t b)
   (if (<= t 4.2e-270)
     (+ x a)
     (if (<= t 4.4e-183) (* y b) (if (<= t 5.8e-27) (* y (- z)) (* t b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -60000000000.0) {
		tmp = t * b;
	} else if (t <= 4.2e-270) {
		tmp = x + a;
	} else if (t <= 4.4e-183) {
		tmp = y * b;
	} else if (t <= 5.8e-27) {
		tmp = y * -z;
	} else {
		tmp = t * b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-60000000000.0d0)) then
        tmp = t * b
    else if (t <= 4.2d-270) then
        tmp = x + a
    else if (t <= 4.4d-183) then
        tmp = y * b
    else if (t <= 5.8d-27) then
        tmp = y * -z
    else
        tmp = t * b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -60000000000.0) {
		tmp = t * b;
	} else if (t <= 4.2e-270) {
		tmp = x + a;
	} else if (t <= 4.4e-183) {
		tmp = y * b;
	} else if (t <= 5.8e-27) {
		tmp = y * -z;
	} else {
		tmp = t * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -60000000000.0:
		tmp = t * b
	elif t <= 4.2e-270:
		tmp = x + a
	elif t <= 4.4e-183:
		tmp = y * b
	elif t <= 5.8e-27:
		tmp = y * -z
	else:
		tmp = t * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -60000000000.0)
		tmp = Float64(t * b);
	elseif (t <= 4.2e-270)
		tmp = Float64(x + a);
	elseif (t <= 4.4e-183)
		tmp = Float64(y * b);
	elseif (t <= 5.8e-27)
		tmp = Float64(y * Float64(-z));
	else
		tmp = Float64(t * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -60000000000.0)
		tmp = t * b;
	elseif (t <= 4.2e-270)
		tmp = x + a;
	elseif (t <= 4.4e-183)
		tmp = y * b;
	elseif (t <= 5.8e-27)
		tmp = y * -z;
	else
		tmp = t * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -60000000000.0], N[(t * b), $MachinePrecision], If[LessEqual[t, 4.2e-270], N[(x + a), $MachinePrecision], If[LessEqual[t, 4.4e-183], N[(y * b), $MachinePrecision], If[LessEqual[t, 5.8e-27], N[(y * (-z)), $MachinePrecision], N[(t * b), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -6e10 or 5.80000000000000008e-27 < t

   1. Initial program 90.2%

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

   3. Taylor expanded in b around inf 56.9%

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

   4. Taylor expanded in t around inf 49.1%

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

   if -6e10 < t < 4.19999999999999992e-270

   1. Initial program 98.8%

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

   3. Taylor expanded in z around 0 75.3%

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

   4. Taylor expanded in t around 0 73.1%

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

      1. associate--l+ 73.1%

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

      2. sub-neg 73.1%

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

      3. metadata-eval 73.1%

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

      4. neg-mul-1 73.1%

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

   6. Simplified 73.1%

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

      1. sub-neg 73.1%

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

      2. remove-double-neg 73.1%

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

   8. Applied egg-rr 73.1%

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

   9. Taylor expanded in b around 0 38.7%

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

   if 4.19999999999999992e-270 < t < 4.3999999999999999e-183

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 54.0%

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

   4. Taylor expanded in b around inf 33.4%

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

   if 4.3999999999999999e-183 < t < 5.80000000000000008e-27

   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 45.6%

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

   4. Taylor expanded in y around inf 31.7%

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

      1. mul-1-neg 31.7%

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

      2. distribute-lft-neg-out 31.7%

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

      3. *-commutative 31.7%

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

   6. Simplified 31.7%

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

4. Final simplification 42.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -60000000000:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{-270}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq 4.4 \cdot 10^{-183}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{-27}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 32.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -24500000:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{-270}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq 3.9 \cdot 10^{-191}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{-27}:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -24500000.0)
   (* t b)
   (if (<= t 2.4e-270)
     (+ x a)
     (if (<= t 3.9e-191) (* y b) (if (<= t 5.8e-27) (+ x a) (* t b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -24500000.0) {
		tmp = t * b;
	} else if (t <= 2.4e-270) {
		tmp = x + a;
	} else if (t <= 3.9e-191) {
		tmp = y * b;
	} else if (t <= 5.8e-27) {
		tmp = x + a;
	} else {
		tmp = t * b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-24500000.0d0)) then
        tmp = t * b
    else if (t <= 2.4d-270) then
        tmp = x + a
    else if (t <= 3.9d-191) then
        tmp = y * b
    else if (t <= 5.8d-27) then
        tmp = x + a
    else
        tmp = t * b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -24500000.0) {
		tmp = t * b;
	} else if (t <= 2.4e-270) {
		tmp = x + a;
	} else if (t <= 3.9e-191) {
		tmp = y * b;
	} else if (t <= 5.8e-27) {
		tmp = x + a;
	} else {
		tmp = t * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -24500000.0:
		tmp = t * b
	elif t <= 2.4e-270:
		tmp = x + a
	elif t <= 3.9e-191:
		tmp = y * b
	elif t <= 5.8e-27:
		tmp = x + a
	else:
		tmp = t * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -24500000.0)
		tmp = Float64(t * b);
	elseif (t <= 2.4e-270)
		tmp = Float64(x + a);
	elseif (t <= 3.9e-191)
		tmp = Float64(y * b);
	elseif (t <= 5.8e-27)
		tmp = Float64(x + a);
	else
		tmp = Float64(t * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -24500000.0)
		tmp = t * b;
	elseif (t <= 2.4e-270)
		tmp = x + a;
	elseif (t <= 3.9e-191)
		tmp = y * b;
	elseif (t <= 5.8e-27)
		tmp = x + a;
	else
		tmp = t * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -24500000.0], N[(t * b), $MachinePrecision], If[LessEqual[t, 2.4e-270], N[(x + a), $MachinePrecision], If[LessEqual[t, 3.9e-191], N[(y * b), $MachinePrecision], If[LessEqual[t, 5.8e-27], N[(x + a), $MachinePrecision], N[(t * b), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.45e7 or 5.80000000000000008e-27 < t

   1. Initial program 90.2%

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

   3. Taylor expanded in b around inf 56.9%

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

   4. Taylor expanded in t around inf 49.1%

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

   if -2.45e7 < t < 2.40000000000000002e-270 or 3.8999999999999999e-191 < t < 5.80000000000000008e-27

   1. Initial program 99.1%

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

   3. Taylor expanded in z around 0 71.6%

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

   4. Taylor expanded in t around 0 69.9%

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

      1. associate--l+ 69.9%

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

      2. sub-neg 69.9%

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

      3. metadata-eval 69.9%

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

      4. neg-mul-1 69.9%

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

   6. Simplified 69.9%

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

      1. sub-neg 69.9%

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

      2. remove-double-neg 69.9%

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

   8. Applied egg-rr 69.9%

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

   9. Taylor expanded in b around 0 36.2%

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

   if 2.40000000000000002e-270 < t < 3.8999999999999999e-191

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 54.0%

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

   4. Taylor expanded in b around inf 33.4%

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

4. Final simplification 42.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -24500000:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{-270}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq 3.9 \cdot 10^{-191}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{-27}:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 70.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.26 \cdot 10^{-34} \lor \neg \left(b \leq 4.8 \cdot 10^{-29}\right):\\ \;\;\;\;x + \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;x + \left(a - \left(y + -1\right) \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -1.26e-34) (not (<= b 4.8e-29)))
   (+ x (* (- (+ y t) 2.0) b))
   (+ x (- a (* (+ y -1.0) z)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -1.26e-34) || !(b <= 4.8e-29)) {
		tmp = x + (((y + t) - 2.0) * b);
	} else {
		tmp = x + (a - ((y + -1.0) * z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-1.26d-34)) .or. (.not. (b <= 4.8d-29))) then
        tmp = x + (((y + t) - 2.0d0) * b)
    else
        tmp = x + (a - ((y + (-1.0d0)) * z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -1.26e-34) || !(b <= 4.8e-29)) {
		tmp = x + (((y + t) - 2.0) * b);
	} else {
		tmp = x + (a - ((y + -1.0) * z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -1.26e-34) or not (b <= 4.8e-29):
		tmp = x + (((y + t) - 2.0) * b)
	else:
		tmp = x + (a - ((y + -1.0) * z))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -1.26e-34) || !(b <= 4.8e-29))
		tmp = Float64(x + Float64(Float64(Float64(y + t) - 2.0) * b));
	else
		tmp = Float64(x + Float64(a - Float64(Float64(y + -1.0) * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -1.26e-34) || ~((b <= 4.8e-29)))
		tmp = x + (((y + t) - 2.0) * b);
	else
		tmp = x + (a - ((y + -1.0) * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -1.26e-34], N[Not[LessEqual[b, 4.8e-29]], $MachinePrecision]], N[(x + N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision], N[(x + N[(a - N[(N[(y + -1.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.26000000000000009e-34 or 4.79999999999999984e-29 < b

   1. Initial program 92.7%

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

   3. Taylor expanded in a around 0 81.9%

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

   4. Taylor expanded in z around 0 76.5%

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

   if -1.26000000000000009e-34 < b < 4.79999999999999984e-29

   1. Initial program 98.9%

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

   3. Taylor expanded in b around 0 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 0 79.2%

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

      1. +-commutative 79.2%

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

      2. sub-neg 79.2%

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

      3. metadata-eval 79.2%

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

      4. neg-mul-1 79.2%

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

      5. unsub-neg 79.2%

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

   6. Simplified 79.2%

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

4. Final simplification 77.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.26 \cdot 10^{-34} \lor \neg \left(b \leq 4.8 \cdot 10^{-29}\right):\\ \;\;\;\;x + \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;x + \left(a - \left(y + -1\right) \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 26.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.3 \cdot 10^{+111}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;y \leq -1.7 \cdot 10^{-34}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 8 \cdot 10^{+102}:\\ \;\;\;\;t \cdot b\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -2.3e+111)
   (* y b)
   (if (<= y -1.7e-34) x (if (<= y 8e+102) (* t b) (* y b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -2.3e+111) {
		tmp = y * b;
	} else if (y <= -1.7e-34) {
		tmp = x;
	} else if (y <= 8e+102) {
		tmp = t * b;
	} else {
		tmp = y * b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-2.3d+111)) then
        tmp = y * b
    else if (y <= (-1.7d-34)) then
        tmp = x
    else if (y <= 8d+102) then
        tmp = t * b
    else
        tmp = y * b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -2.3e+111) {
		tmp = y * b;
	} else if (y <= -1.7e-34) {
		tmp = x;
	} else if (y <= 8e+102) {
		tmp = t * b;
	} else {
		tmp = y * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -2.3e+111:
		tmp = y * b
	elif y <= -1.7e-34:
		tmp = x
	elif y <= 8e+102:
		tmp = t * b
	else:
		tmp = y * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -2.3e+111)
		tmp = Float64(y * b);
	elseif (y <= -1.7e-34)
		tmp = x;
	elseif (y <= 8e+102)
		tmp = Float64(t * b);
	else
		tmp = Float64(y * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -2.3e+111)
		tmp = y * b;
	elseif (y <= -1.7e-34)
		tmp = x;
	elseif (y <= 8e+102)
		tmp = t * b;
	else
		tmp = y * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -2.3e+111], N[(y * b), $MachinePrecision], If[LessEqual[y, -1.7e-34], x, If[LessEqual[y, 8e+102], N[(t * b), $MachinePrecision], N[(y * b), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.30000000000000002e111 or 7.99999999999999982e102 < y

   1. Initial program 88.5%

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

   3. Taylor expanded in y around inf 81.6%

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

   4. Taylor expanded in b around inf 51.4%

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

   if -2.30000000000000002e111 < y < -1.7e-34

   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 28.7%

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

   if -1.7e-34 < y < 7.99999999999999982e102

   1. Initial program 97.4%

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

   3. Taylor expanded in b around inf 45.7%

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

   4. Taylor expanded in t around inf 31.1%

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

4. Final simplification 37.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.3 \cdot 10^{+111}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;y \leq -1.7 \cdot 10^{-34}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 8 \cdot 10^{+102}:\\ \;\;\;\;t \cdot b\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 25: 18.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -4.1 \cdot 10^{+121}:\\ \;\;\;\;a\\ \mathbf{elif}\;a \leq 2 \cdot 10^{-134}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -4.1e+121) a (if (<= a 2e-134) x a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -4.1e+121) {
		tmp = a;
	} else if (a <= 2e-134) {
		tmp = x;
	} else {
		tmp = a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (a <= (-4.1d+121)) then
        tmp = a
    else if (a <= 2d-134) then
        tmp = x
    else
        tmp = a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -4.1e+121) {
		tmp = a;
	} else if (a <= 2e-134) {
		tmp = x;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -4.1e+121:
		tmp = a
	elif a <= 2e-134:
		tmp = x
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -4.1e+121)
		tmp = a;
	elseif (a <= 2e-134)
		tmp = x;
	else
		tmp = a;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= -4.1e+121)
		tmp = a;
	elseif (a <= 2e-134)
		tmp = x;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -4.1e+121], a, If[LessEqual[a, 2e-134], x, a]]

Derivation

1. Split input into 2 regimes

2. if a < -4.1e121 or 2.00000000000000008e-134 < a

   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 a around inf 44.3%

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

   4. Taylor expanded in t around 0 17.1%

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

   if -4.1e121 < a < 2.00000000000000008e-134

   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 x around inf 20.8%

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

Alternative 26: 17.3% accurate, 7.0× speedup

Math

\[\begin{array}{l} \\ t \cdot b \end{array} \]

FPCore

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

C

double code(double x, double y, double z, double t, double a, double b) {
	return t * 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 = t * b
end function

Java

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

Python

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

Julia

function code(x, y, z, t, a, b)
	return Float64(t * b)
end

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(t * b), $MachinePrecision]

Derivation

1. Initial program 94.9%

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

3. Taylor expanded in b around inf 46.5%

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

4. Taylor expanded in t around inf 24.7%

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

5. Final simplification 24.7%

   \[\leadsto t \cdot b \]
6. Add Preprocessing

Alternative 27: 11.0% 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 94.9%

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

3. Taylor expanded in a around inf 28.3%

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

4. Taylor expanded in t around 0 10.5%

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

Reproduce

herbie shell --seed 2024107 
(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)))