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

Percentage Accurate: 95.1% → 97.7%

Time: 21.5s

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: 95.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.7% accurate, 0.1× speedup

Math

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

FPCore

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

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x - Float64(Float64(y + -1.0) * z))
	tmp = 0.0
	if (Float64(Float64(t_1 + Float64(a * Float64(1.0 - t))) + Float64(b * Float64(Float64(y + t) - 2.0))) <= Inf)
		tmp = Float64(t_1 - fma(Float64(t + -1.0), a, Float64(b * Float64(Float64(-t) - Float64(y + -2.0)))));
	else
		tmp = Float64(y * Float64(b - z));
	end
	return 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]}, If[LessEqual[N[(N[(t$95$1 + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], Infinity], N[(t$95$1 - N[(N[(t + -1.0), $MachinePrecision] * a + N[(b * N[((-t) - N[(y + -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 100.0%

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

      1. associate-+l- 100.0%

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

      2. sub-neg 100.0%

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

      3. metadata-eval 100.0%

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

      4. *-commutative 100.0%

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

      5. fma-neg 100.0%

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

      6. sub-neg 100.0%

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

      7. metadata-eval 100.0%

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

      8. sub-neg 100.0%

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

      9. metadata-eval 100.0%

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

      10. associate-+r+ 100.0%

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

      11. *-commutative 100.0%

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

      12. associate-+r+ 100.0%

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

      13. +-commutative 100.0%

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

      14. associate-+l+ 100.0%

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

   4. Applied egg-rr 100.0%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in y around inf 71.9%

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

4. Final simplification 99.2%

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

Alternative 2: 97.6% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

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. Step-by-step derivation

   1. +-commutative 97.2%

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

   2. fma-def 98.4%

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

   3. associate--l+ 98.4%

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

   4. sub-neg 98.4%

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

   5. metadata-eval 98.4%

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

   6. sub-neg 98.4%

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

   7. associate-+l- 98.4%

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

   8. fma-neg 98.8%

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

   9. sub-neg 98.8%

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

   10. metadata-eval 98.8%

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

   11. remove-double-neg 98.8%

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

   12. sub-neg 98.8%

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

   13. metadata-eval 98.8%

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

3. Simplified 98.8%

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

5. Final simplification 98.8%

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

Alternative 3: 32.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(1 - t\right)\\ t_2 := z \cdot \left(-y\right)\\ \mathbf{if}\;y \leq -4 \cdot 10^{+73}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -1.4 \cdot 10^{-88}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;y \leq -1.05 \cdot 10^{-214}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -4.7 \cdot 10^{-265}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{-185}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{-130}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{+18}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{+108}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{+133}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (- 1.0 t))) (t_2 (* z (- y))))
   (if (<= y -4e+73)
     t_2
     (if (<= y -1.4e-88)
       (+ x a)
       (if (<= y -1.05e-214)
         t_1
         (if (<= y -4.7e-265)
           (+ x a)
           (if (<= y 5.8e-185)
             (* t b)
             (if (<= y 1.4e-130)
               z
               (if (<= y 3.3e+18)
                 t_1
                 (if (<= y 1.1e+108)
                   t_2
                   (if (<= y 2.2e+133) t_1 (* y b))))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double t_2 = z * -y;
	double tmp;
	if (y <= -4e+73) {
		tmp = t_2;
	} else if (y <= -1.4e-88) {
		tmp = x + a;
	} else if (y <= -1.05e-214) {
		tmp = t_1;
	} else if (y <= -4.7e-265) {
		tmp = x + a;
	} else if (y <= 5.8e-185) {
		tmp = t * b;
	} else if (y <= 1.4e-130) {
		tmp = z;
	} else if (y <= 3.3e+18) {
		tmp = t_1;
	} else if (y <= 1.1e+108) {
		tmp = t_2;
	} else if (y <= 2.2e+133) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a * (1.0d0 - t)
    t_2 = z * -y
    if (y <= (-4d+73)) then
        tmp = t_2
    else if (y <= (-1.4d-88)) then
        tmp = x + a
    else if (y <= (-1.05d-214)) then
        tmp = t_1
    else if (y <= (-4.7d-265)) then
        tmp = x + a
    else if (y <= 5.8d-185) then
        tmp = t * b
    else if (y <= 1.4d-130) then
        tmp = z
    else if (y <= 3.3d+18) then
        tmp = t_1
    else if (y <= 1.1d+108) then
        tmp = t_2
    else if (y <= 2.2d+133) then
        tmp = t_1
    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 t_1 = a * (1.0 - t);
	double t_2 = z * -y;
	double tmp;
	if (y <= -4e+73) {
		tmp = t_2;
	} else if (y <= -1.4e-88) {
		tmp = x + a;
	} else if (y <= -1.05e-214) {
		tmp = t_1;
	} else if (y <= -4.7e-265) {
		tmp = x + a;
	} else if (y <= 5.8e-185) {
		tmp = t * b;
	} else if (y <= 1.4e-130) {
		tmp = z;
	} else if (y <= 3.3e+18) {
		tmp = t_1;
	} else if (y <= 1.1e+108) {
		tmp = t_2;
	} else if (y <= 2.2e+133) {
		tmp = t_1;
	} else {
		tmp = y * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (1.0 - t)
	t_2 = z * -y
	tmp = 0
	if y <= -4e+73:
		tmp = t_2
	elif y <= -1.4e-88:
		tmp = x + a
	elif y <= -1.05e-214:
		tmp = t_1
	elif y <= -4.7e-265:
		tmp = x + a
	elif y <= 5.8e-185:
		tmp = t * b
	elif y <= 1.4e-130:
		tmp = z
	elif y <= 3.3e+18:
		tmp = t_1
	elif y <= 1.1e+108:
		tmp = t_2
	elif y <= 2.2e+133:
		tmp = t_1
	else:
		tmp = y * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(1.0 - t))
	t_2 = Float64(z * Float64(-y))
	tmp = 0.0
	if (y <= -4e+73)
		tmp = t_2;
	elseif (y <= -1.4e-88)
		tmp = Float64(x + a);
	elseif (y <= -1.05e-214)
		tmp = t_1;
	elseif (y <= -4.7e-265)
		tmp = Float64(x + a);
	elseif (y <= 5.8e-185)
		tmp = Float64(t * b);
	elseif (y <= 1.4e-130)
		tmp = z;
	elseif (y <= 3.3e+18)
		tmp = t_1;
	elseif (y <= 1.1e+108)
		tmp = t_2;
	elseif (y <= 2.2e+133)
		tmp = t_1;
	else
		tmp = Float64(y * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (1.0 - t);
	t_2 = z * -y;
	tmp = 0.0;
	if (y <= -4e+73)
		tmp = t_2;
	elseif (y <= -1.4e-88)
		tmp = x + a;
	elseif (y <= -1.05e-214)
		tmp = t_1;
	elseif (y <= -4.7e-265)
		tmp = x + a;
	elseif (y <= 5.8e-185)
		tmp = t * b;
	elseif (y <= 1.4e-130)
		tmp = z;
	elseif (y <= 3.3e+18)
		tmp = t_1;
	elseif (y <= 1.1e+108)
		tmp = t_2;
	elseif (y <= 2.2e+133)
		tmp = t_1;
	else
		tmp = y * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * (-y)), $MachinePrecision]}, If[LessEqual[y, -4e+73], t$95$2, If[LessEqual[y, -1.4e-88], N[(x + a), $MachinePrecision], If[LessEqual[y, -1.05e-214], t$95$1, If[LessEqual[y, -4.7e-265], N[(x + a), $MachinePrecision], If[LessEqual[y, 5.8e-185], N[(t * b), $MachinePrecision], If[LessEqual[y, 1.4e-130], z, If[LessEqual[y, 3.3e+18], t$95$1, If[LessEqual[y, 1.1e+108], t$95$2, If[LessEqual[y, 2.2e+133], t$95$1, N[(y * b), $MachinePrecision]]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if y < -3.99999999999999993e73 or 3.3e18 < y < 1.1000000000000001e108

   1. Initial program 93.7%

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

   3. Taylor expanded in z around inf 48.0%

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

   4. Taylor expanded in y around inf 48.0%

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

      1. mul-1-neg 48.0%

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

      2. *-commutative 48.0%

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

      3. distribute-rgt-neg-in 48.0%

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

   6. Simplified 48.0%

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

   if -3.99999999999999993e73 < y < -1.39999999999999988e-88 or -1.04999999999999996e-214 < y < -4.69999999999999986e-265

   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 88.4%

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

   4. Taylor expanded in b around 0 60.8%

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

   5. Taylor expanded in t around 0 43.8%

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

      1. cancel-sign-sub-inv 43.8%

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

      2. metadata-eval 43.8%

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

      3. *-lft-identity 43.8%

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

      4. +-commutative 43.8%

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

   7. Simplified 43.8%

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

   if -1.39999999999999988e-88 < y < -1.04999999999999996e-214 or 1.40000000000000008e-130 < y < 3.3e18 or 1.1000000000000001e108 < y < 2.2e133

   1. Initial program 96.9%

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

   3. Taylor expanded in a around inf 47.9%

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

   if -4.69999999999999986e-265 < y < 5.79999999999999989e-185

   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-def 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

   5. Taylor expanded in t around 0 90.8%

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

   6. Taylor expanded in t around inf 42.6%

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

   if 5.79999999999999989e-185 < y < 1.40000000000000008e-130

   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 58.3%

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

   4. Taylor expanded in y around 0 58.3%

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

   if 2.2e133 < y

   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 58.8%

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

   4. Taylor expanded in y around inf 50.3%

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

4. Final simplification 47.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{+73}:\\ \;\;\;\;z \cdot \left(-y\right)\\ \mathbf{elif}\;y \leq -1.4 \cdot 10^{-88}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;y \leq -1.05 \cdot 10^{-214}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;y \leq -4.7 \cdot 10^{-265}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{-185}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{-130}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{+18}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{+108}:\\ \;\;\;\;z \cdot \left(-y\right)\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{+133}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 97.7% accurate, 0.5× speedup

Math

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

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1
         (+ (+ (- x (* (+ y -1.0) z)) (* a (- 1.0 t))) (* b (- (+ y t) 2.0)))))
   (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))) + (b * ((y + t) - 2.0));
	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))) + (b * ((y + t) - 2.0));
	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))) + (b * ((y + t) - 2.0))
	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(b * Float64(Float64(y + t) - 2.0)))
	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))) + (b * ((y + t) - 2.0));
	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[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 100.0%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in y around inf 71.9%

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

4. Final simplification 99.2%

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

Alternative 5: 34.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(1 - t\right)\\ t_2 := z \cdot \left(-y\right)\\ \mathbf{if}\;y \leq -4.35 \cdot 10^{+71}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -3 \cdot 10^{-164}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{-179}:\\ \;\;\;\;b \cdot \left(t - 2\right)\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{-133}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq 1.28 \cdot 10^{+17}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 3.7 \cdot 10^{+107}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 4 \cdot 10^{+133}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (- 1.0 t))) (t_2 (* z (- y))))
   (if (<= y -4.35e+71)
     t_2
     (if (<= y -3e-164)
       (+ x a)
       (if (<= y 4.5e-179)
         (* b (- t 2.0))
         (if (<= y 1.25e-133)
           z
           (if (<= y 1.28e+17)
             t_1
             (if (<= y 3.7e+107) t_2 (if (<= y 4e+133) t_1 (* y b))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double t_2 = z * -y;
	double tmp;
	if (y <= -4.35e+71) {
		tmp = t_2;
	} else if (y <= -3e-164) {
		tmp = x + a;
	} else if (y <= 4.5e-179) {
		tmp = b * (t - 2.0);
	} else if (y <= 1.25e-133) {
		tmp = z;
	} else if (y <= 1.28e+17) {
		tmp = t_1;
	} else if (y <= 3.7e+107) {
		tmp = t_2;
	} else if (y <= 4e+133) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a * (1.0d0 - t)
    t_2 = z * -y
    if (y <= (-4.35d+71)) then
        tmp = t_2
    else if (y <= (-3d-164)) then
        tmp = x + a
    else if (y <= 4.5d-179) then
        tmp = b * (t - 2.0d0)
    else if (y <= 1.25d-133) then
        tmp = z
    else if (y <= 1.28d+17) then
        tmp = t_1
    else if (y <= 3.7d+107) then
        tmp = t_2
    else if (y <= 4d+133) then
        tmp = t_1
    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 t_1 = a * (1.0 - t);
	double t_2 = z * -y;
	double tmp;
	if (y <= -4.35e+71) {
		tmp = t_2;
	} else if (y <= -3e-164) {
		tmp = x + a;
	} else if (y <= 4.5e-179) {
		tmp = b * (t - 2.0);
	} else if (y <= 1.25e-133) {
		tmp = z;
	} else if (y <= 1.28e+17) {
		tmp = t_1;
	} else if (y <= 3.7e+107) {
		tmp = t_2;
	} else if (y <= 4e+133) {
		tmp = t_1;
	} else {
		tmp = y * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (1.0 - t)
	t_2 = z * -y
	tmp = 0
	if y <= -4.35e+71:
		tmp = t_2
	elif y <= -3e-164:
		tmp = x + a
	elif y <= 4.5e-179:
		tmp = b * (t - 2.0)
	elif y <= 1.25e-133:
		tmp = z
	elif y <= 1.28e+17:
		tmp = t_1
	elif y <= 3.7e+107:
		tmp = t_2
	elif y <= 4e+133:
		tmp = t_1
	else:
		tmp = y * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(1.0 - t))
	t_2 = Float64(z * Float64(-y))
	tmp = 0.0
	if (y <= -4.35e+71)
		tmp = t_2;
	elseif (y <= -3e-164)
		tmp = Float64(x + a);
	elseif (y <= 4.5e-179)
		tmp = Float64(b * Float64(t - 2.0));
	elseif (y <= 1.25e-133)
		tmp = z;
	elseif (y <= 1.28e+17)
		tmp = t_1;
	elseif (y <= 3.7e+107)
		tmp = t_2;
	elseif (y <= 4e+133)
		tmp = t_1;
	else
		tmp = Float64(y * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (1.0 - t);
	t_2 = z * -y;
	tmp = 0.0;
	if (y <= -4.35e+71)
		tmp = t_2;
	elseif (y <= -3e-164)
		tmp = x + a;
	elseif (y <= 4.5e-179)
		tmp = b * (t - 2.0);
	elseif (y <= 1.25e-133)
		tmp = z;
	elseif (y <= 1.28e+17)
		tmp = t_1;
	elseif (y <= 3.7e+107)
		tmp = t_2;
	elseif (y <= 4e+133)
		tmp = t_1;
	else
		tmp = y * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * (-y)), $MachinePrecision]}, If[LessEqual[y, -4.35e+71], t$95$2, If[LessEqual[y, -3e-164], N[(x + a), $MachinePrecision], If[LessEqual[y, 4.5e-179], N[(b * N[(t - 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.25e-133], z, If[LessEqual[y, 1.28e+17], t$95$1, If[LessEqual[y, 3.7e+107], t$95$2, If[LessEqual[y, 4e+133], t$95$1, N[(y * b), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if y < -4.3499999999999999e71 or 1.28e17 < y < 3.7e107

   1. Initial program 93.7%

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

   3. Taylor expanded in z around inf 48.0%

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

   4. Taylor expanded in y around inf 48.0%

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

      1. mul-1-neg 48.0%

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

      2. *-commutative 48.0%

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

      3. distribute-rgt-neg-in 48.0%

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

   6. Simplified 48.0%

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

   if -4.3499999999999999e71 < y < -3.0000000000000001e-164

   1. Initial program 98.0%

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

   3. Taylor expanded in z around 0 88.7%

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

   4. Taylor expanded in b around 0 66.1%

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

   5. Taylor expanded in t around 0 39.2%

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

      1. cancel-sign-sub-inv 39.2%

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

      2. metadata-eval 39.2%

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

      3. *-lft-identity 39.2%

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

      4. +-commutative 39.2%

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

   7. Simplified 39.2%

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

   if -3.0000000000000001e-164 < y < 4.49999999999999992e-179

   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 inf 60.1%

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

   4. Taylor expanded in y around 0 60.1%

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

   if 4.49999999999999992e-179 < y < 1.25e-133

   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 66.1%

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

   4. Taylor expanded in y around 0 66.1%

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

   if 1.25e-133 < y < 1.28e17 or 3.7e107 < y < 4.0000000000000001e133

   1. Initial program 97.5%

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

   3. Taylor expanded in a around inf 49.7%

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

   if 4.0000000000000001e133 < y

   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 58.8%

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

   4. Taylor expanded in y around inf 50.3%

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

4. Final simplification 50.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.35 \cdot 10^{+71}:\\ \;\;\;\;z \cdot \left(-y\right)\\ \mathbf{elif}\;y \leq -3 \cdot 10^{-164}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{-179}:\\ \;\;\;\;b \cdot \left(t - 2\right)\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{-133}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq 1.28 \cdot 10^{+17}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;y \leq 3.7 \cdot 10^{+107}:\\ \;\;\;\;z \cdot \left(-y\right)\\ \mathbf{elif}\;y \leq 4 \cdot 10^{+133}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 52.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - t \cdot a\\ t_2 := y \cdot \left(b - z\right)\\ t_3 := x + \left(z + a\right)\\ \mathbf{if}\;y \leq -7.5 \cdot 10^{+72}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -2 \cdot 10^{+52}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -125000000:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;y \leq -1.45 \cdot 10^{-90}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -4 \cdot 10^{-265}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{-186}:\\ \;\;\;\;b \cdot \left(t - 2\right)\\ \mathbf{elif}\;y \leq 500000000:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- x (* t a))) (t_2 (* y (- b z))) (t_3 (+ x (+ z a))))
   (if (<= y -7.5e+72)
     t_2
     (if (<= y -2e+52)
       t_1
       (if (<= y -125000000.0)
         (* t (- b a))
         (if (<= y -1.45e-90)
           t_3
           (if (<= y -4e-265)
             t_1
             (if (<= y 1.8e-186)
               (* b (- t 2.0))
               (if (<= y 500000000.0) t_3 t_2)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x - (t * a);
	double t_2 = y * (b - z);
	double t_3 = x + (z + a);
	double tmp;
	if (y <= -7.5e+72) {
		tmp = t_2;
	} else if (y <= -2e+52) {
		tmp = t_1;
	} else if (y <= -125000000.0) {
		tmp = t * (b - a);
	} else if (y <= -1.45e-90) {
		tmp = t_3;
	} else if (y <= -4e-265) {
		tmp = t_1;
	} else if (y <= 1.8e-186) {
		tmp = b * (t - 2.0);
	} else if (y <= 500000000.0) {
		tmp = t_3;
	} 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 = x - (t * a)
    t_2 = y * (b - z)
    t_3 = x + (z + a)
    if (y <= (-7.5d+72)) then
        tmp = t_2
    else if (y <= (-2d+52)) then
        tmp = t_1
    else if (y <= (-125000000.0d0)) then
        tmp = t * (b - a)
    else if (y <= (-1.45d-90)) then
        tmp = t_3
    else if (y <= (-4d-265)) then
        tmp = t_1
    else if (y <= 1.8d-186) then
        tmp = b * (t - 2.0d0)
    else if (y <= 500000000.0d0) then
        tmp = t_3
    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 - (t * a);
	double t_2 = y * (b - z);
	double t_3 = x + (z + a);
	double tmp;
	if (y <= -7.5e+72) {
		tmp = t_2;
	} else if (y <= -2e+52) {
		tmp = t_1;
	} else if (y <= -125000000.0) {
		tmp = t * (b - a);
	} else if (y <= -1.45e-90) {
		tmp = t_3;
	} else if (y <= -4e-265) {
		tmp = t_1;
	} else if (y <= 1.8e-186) {
		tmp = b * (t - 2.0);
	} else if (y <= 500000000.0) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x - (t * a)
	t_2 = y * (b - z)
	t_3 = x + (z + a)
	tmp = 0
	if y <= -7.5e+72:
		tmp = t_2
	elif y <= -2e+52:
		tmp = t_1
	elif y <= -125000000.0:
		tmp = t * (b - a)
	elif y <= -1.45e-90:
		tmp = t_3
	elif y <= -4e-265:
		tmp = t_1
	elif y <= 1.8e-186:
		tmp = b * (t - 2.0)
	elif y <= 500000000.0:
		tmp = t_3
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x - Float64(t * a))
	t_2 = Float64(y * Float64(b - z))
	t_3 = Float64(x + Float64(z + a))
	tmp = 0.0
	if (y <= -7.5e+72)
		tmp = t_2;
	elseif (y <= -2e+52)
		tmp = t_1;
	elseif (y <= -125000000.0)
		tmp = Float64(t * Float64(b - a));
	elseif (y <= -1.45e-90)
		tmp = t_3;
	elseif (y <= -4e-265)
		tmp = t_1;
	elseif (y <= 1.8e-186)
		tmp = Float64(b * Float64(t - 2.0));
	elseif (y <= 500000000.0)
		tmp = t_3;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x - (t * a);
	t_2 = y * (b - z);
	t_3 = x + (z + a);
	tmp = 0.0;
	if (y <= -7.5e+72)
		tmp = t_2;
	elseif (y <= -2e+52)
		tmp = t_1;
	elseif (y <= -125000000.0)
		tmp = t * (b - a);
	elseif (y <= -1.45e-90)
		tmp = t_3;
	elseif (y <= -4e-265)
		tmp = t_1;
	elseif (y <= 1.8e-186)
		tmp = b * (t - 2.0);
	elseif (y <= 500000000.0)
		tmp = t_3;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x - N[(t * a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x + N[(z + a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -7.5e+72], t$95$2, If[LessEqual[y, -2e+52], t$95$1, If[LessEqual[y, -125000000.0], N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.45e-90], t$95$3, If[LessEqual[y, -4e-265], t$95$1, If[LessEqual[y, 1.8e-186], N[(b * N[(t - 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 500000000.0], t$95$3, t$95$2]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -7.50000000000000027e72 or 5e8 < y

   1. Initial program 94.5%

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

   3. Taylor expanded in y around inf 71.2%

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

   if -7.50000000000000027e72 < y < -2e52 or -1.44999999999999992e-90 < y < -3.99999999999999994e-265

   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 z around 0 86.6%

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

   4. Taylor expanded in b around 0 64.8%

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

   5. Taylor expanded in t around inf 61.1%

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

      1. *-commutative 61.1%

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

   7. Simplified 61.1%

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

   if -2e52 < y < -1.25e8

   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 57.1%

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

   if -1.25e8 < y < -1.44999999999999992e-90 or 1.7999999999999999e-186 < y < 5e8

   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. Step-by-step derivation

      1. +-commutative 99.9%

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

      2. fma-def 99.9%

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

      3. associate--l+ 99.9%

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

      4. sub-neg 99.9%

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

      5. metadata-eval 99.9%

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

      6. sub-neg 99.9%

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

      7. associate-+l- 99.9%

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

      8. fma-neg 99.9%

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

      9. sub-neg 99.9%

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

      10. metadata-eval 99.9%

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

      11. remove-double-neg 99.9%

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

      12. sub-neg 99.9%

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

      13. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in t around 0 89.9%

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

   6. Taylor expanded in b around 0 71.5%

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

      1. associate--r+ 71.5%

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

      2. sub-neg 71.5%

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

      3. mul-1-neg 71.5%

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

      4. remove-double-neg 71.5%

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

      5. sub-neg 71.5%

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

      6. metadata-eval 71.5%

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

      7. +-commutative 71.5%

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

   8. Simplified 71.5%

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

   9. Taylor expanded in y around 0 69.0%

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

       1. cancel-sign-sub-inv 69.0%

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

       2. metadata-eval 69.0%

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

       3. *-lft-identity 69.0%

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

       4. +-commutative 69.0%

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

       5. associate-+l+ 69.0%

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

   11. Simplified 69.0%

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

   if -3.99999999999999994e-265 < y < 1.7999999999999999e-186

   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 inf 72.7%

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

   4. Taylor expanded in y around 0 72.7%

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

4. Final simplification 68.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{+72}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;y \leq -2 \cdot 10^{+52}:\\ \;\;\;\;x - t \cdot a\\ \mathbf{elif}\;y \leq -125000000:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;y \leq -1.45 \cdot 10^{-90}:\\ \;\;\;\;x + \left(z + a\right)\\ \mathbf{elif}\;y \leq -4 \cdot 10^{-265}:\\ \;\;\;\;x - t \cdot a\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{-186}:\\ \;\;\;\;b \cdot \left(t - 2\right)\\ \mathbf{elif}\;y \leq 500000000:\\ \;\;\;\;x + \left(z + a\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 69.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + z\right) - a \cdot \left(t + -1\right)\\ t_2 := x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{if}\;b \leq -1.9 \cdot 10^{+35}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -2.5 \cdot 10^{-6}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -2.3 \cdot 10^{-45}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;b \leq -2.9 \cdot 10^{-112}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -3.1 \cdot 10^{-165}:\\ \;\;\;\;a + z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq 2 \cdot 10^{+47}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ x z) (* a (+ t -1.0)))) (t_2 (+ x (* b (- (+ y t) 2.0)))))
   (if (<= b -1.9e+35)
     t_2
     (if (<= b -2.5e-6)
       t_1
       (if (<= b -2.3e-45)
         (* y (- b z))
         (if (<= b -2.9e-112)
           t_1
           (if (<= b -3.1e-165)
             (+ a (* z (- 1.0 y)))
             (if (<= b 2e+47) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + z) - (a * (t + -1.0));
	double t_2 = x + (b * ((y + t) - 2.0));
	double tmp;
	if (b <= -1.9e+35) {
		tmp = t_2;
	} else if (b <= -2.5e-6) {
		tmp = t_1;
	} else if (b <= -2.3e-45) {
		tmp = y * (b - z);
	} else if (b <= -2.9e-112) {
		tmp = t_1;
	} else if (b <= -3.1e-165) {
		tmp = a + (z * (1.0 - y));
	} else if (b <= 2e+47) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x + z) - (a * (t + (-1.0d0)))
    t_2 = x + (b * ((y + t) - 2.0d0))
    if (b <= (-1.9d+35)) then
        tmp = t_2
    else if (b <= (-2.5d-6)) then
        tmp = t_1
    else if (b <= (-2.3d-45)) then
        tmp = y * (b - z)
    else if (b <= (-2.9d-112)) then
        tmp = t_1
    else if (b <= (-3.1d-165)) then
        tmp = a + (z * (1.0d0 - y))
    else if (b <= 2d+47) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + z) - (a * (t + -1.0));
	double t_2 = x + (b * ((y + t) - 2.0));
	double tmp;
	if (b <= -1.9e+35) {
		tmp = t_2;
	} else if (b <= -2.5e-6) {
		tmp = t_1;
	} else if (b <= -2.3e-45) {
		tmp = y * (b - z);
	} else if (b <= -2.9e-112) {
		tmp = t_1;
	} else if (b <= -3.1e-165) {
		tmp = a + (z * (1.0 - y));
	} else if (b <= 2e+47) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x + z) - (a * (t + -1.0))
	t_2 = x + (b * ((y + t) - 2.0))
	tmp = 0
	if b <= -1.9e+35:
		tmp = t_2
	elif b <= -2.5e-6:
		tmp = t_1
	elif b <= -2.3e-45:
		tmp = y * (b - z)
	elif b <= -2.9e-112:
		tmp = t_1
	elif b <= -3.1e-165:
		tmp = a + (z * (1.0 - y))
	elif b <= 2e+47:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + z) - Float64(a * Float64(t + -1.0)))
	t_2 = Float64(x + Float64(b * Float64(Float64(y + t) - 2.0)))
	tmp = 0.0
	if (b <= -1.9e+35)
		tmp = t_2;
	elseif (b <= -2.5e-6)
		tmp = t_1;
	elseif (b <= -2.3e-45)
		tmp = Float64(y * Float64(b - z));
	elseif (b <= -2.9e-112)
		tmp = t_1;
	elseif (b <= -3.1e-165)
		tmp = Float64(a + Float64(z * Float64(1.0 - y)));
	elseif (b <= 2e+47)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x + z) - (a * (t + -1.0));
	t_2 = x + (b * ((y + t) - 2.0));
	tmp = 0.0;
	if (b <= -1.9e+35)
		tmp = t_2;
	elseif (b <= -2.5e-6)
		tmp = t_1;
	elseif (b <= -2.3e-45)
		tmp = y * (b - z);
	elseif (b <= -2.9e-112)
		tmp = t_1;
	elseif (b <= -3.1e-165)
		tmp = a + (z * (1.0 - y));
	elseif (b <= 2e+47)
		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[(N[(x + z), $MachinePrecision] - N[(a * N[(t + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.9e+35], t$95$2, If[LessEqual[b, -2.5e-6], t$95$1, If[LessEqual[b, -2.3e-45], N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -2.9e-112], t$95$1, If[LessEqual[b, -3.1e-165], N[(a + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2e+47], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -1.9e35 or 2.0000000000000001e47 < b

   1. Initial program 93.0%

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

   3. Taylor expanded in z around 0 90.1%

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

   4. Taylor expanded in a around 0 82.3%

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

   if -1.9e35 < b < -2.5000000000000002e-6 or -2.29999999999999992e-45 < b < -2.89999999999999992e-112 or -3.09999999999999996e-165 < b < 2.0000000000000001e47

   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 0 78.4%

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

   4. Taylor expanded in b around 0 74.9%

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

      1. associate--r+ 74.9%

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

      2. sub-neg 74.9%

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

      3. metadata-eval 74.9%

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

      4. +-commutative 74.9%

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

      5. *-commutative 74.9%

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

      6. cancel-sign-sub-inv 74.9%

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

      7. cancel-sign-sub-inv 74.9%

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

      8. metadata-eval 74.9%

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

      9. *-lft-identity 74.9%

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

      10. distribute-neg-in 74.9%

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

      11. metadata-eval 74.9%

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

      12. sub-neg 74.9%

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

      13. *-commutative 74.9%

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

   6. Simplified 74.9%

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

   if -2.5000000000000002e-6 < b < -2.29999999999999992e-45

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 80.3%

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

   if -2.89999999999999992e-112 < b < -3.09999999999999996e-165

   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. Step-by-step derivation

      1. +-commutative 99.9%

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

      2. fma-def 99.9%

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

      3. associate--l+ 99.9%

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

      4. sub-neg 99.9%

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

      5. metadata-eval 99.9%

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

      6. sub-neg 99.9%

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

      7. associate-+l- 99.9%

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

      8. fma-neg 99.9%

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

      9. sub-neg 99.9%

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

      10. metadata-eval 99.9%

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

      11. remove-double-neg 99.9%

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

      12. sub-neg 99.9%

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

      13. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in t around 0 99.9%

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

   6. Taylor expanded in b around 0 86.8%

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

      1. associate--r+ 86.8%

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

      2. sub-neg 86.8%

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

      3. mul-1-neg 86.8%

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

      4. remove-double-neg 86.8%

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

      5. sub-neg 86.8%

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

      6. metadata-eval 86.8%

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

      7. +-commutative 86.8%

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

   8. Simplified 86.8%

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

   9. Taylor expanded in x around 0 70.2%

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

4. Final simplification 77.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.9 \cdot 10^{+35}:\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{elif}\;b \leq -2.5 \cdot 10^{-6}:\\ \;\;\;\;\left(x + z\right) - a \cdot \left(t + -1\right)\\ \mathbf{elif}\;b \leq -2.3 \cdot 10^{-45}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;b \leq -2.9 \cdot 10^{-112}:\\ \;\;\;\;\left(x + z\right) - a \cdot \left(t + -1\right)\\ \mathbf{elif}\;b \leq -3.1 \cdot 10^{-165}:\\ \;\;\;\;a + z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq 2 \cdot 10^{+47}:\\ \;\;\;\;\left(x + z\right) - a \cdot \left(t + -1\right)\\ \mathbf{else}:\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 70.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + a\right) - \left(y + -1\right) \cdot z\\ t_2 := \left(x + z\right) - a \cdot \left(t + -1\right)\\ t_3 := x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{if}\;b \leq -1.9 \cdot 10^{+35}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq -3.8 \cdot 10^{-8}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -9.8 \cdot 10^{-53}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;b \leq -3.8 \cdot 10^{-167}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 5.3 \cdot 10^{-179}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 2.25 \cdot 10^{+17}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ x a) (* (+ y -1.0) z)))
        (t_2 (- (+ x z) (* a (+ t -1.0))))
        (t_3 (+ x (* b (- (+ y t) 2.0)))))
   (if (<= b -1.9e+35)
     t_3
     (if (<= b -3.8e-8)
       t_2
       (if (<= b -9.8e-53)
         (* y (- b z))
         (if (<= b -3.8e-167)
           t_1
           (if (<= b 5.3e-179) t_2 (if (<= b 2.25e+17) t_1 t_3))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + a) - ((y + -1.0) * z);
	double t_2 = (x + z) - (a * (t + -1.0));
	double t_3 = x + (b * ((y + t) - 2.0));
	double tmp;
	if (b <= -1.9e+35) {
		tmp = t_3;
	} else if (b <= -3.8e-8) {
		tmp = t_2;
	} else if (b <= -9.8e-53) {
		tmp = y * (b - z);
	} else if (b <= -3.8e-167) {
		tmp = t_1;
	} else if (b <= 5.3e-179) {
		tmp = t_2;
	} else if (b <= 2.25e+17) {
		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) - ((y + (-1.0d0)) * z)
    t_2 = (x + z) - (a * (t + (-1.0d0)))
    t_3 = x + (b * ((y + t) - 2.0d0))
    if (b <= (-1.9d+35)) then
        tmp = t_3
    else if (b <= (-3.8d-8)) then
        tmp = t_2
    else if (b <= (-9.8d-53)) then
        tmp = y * (b - z)
    else if (b <= (-3.8d-167)) then
        tmp = t_1
    else if (b <= 5.3d-179) then
        tmp = t_2
    else if (b <= 2.25d+17) 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) - ((y + -1.0) * z);
	double t_2 = (x + z) - (a * (t + -1.0));
	double t_3 = x + (b * ((y + t) - 2.0));
	double tmp;
	if (b <= -1.9e+35) {
		tmp = t_3;
	} else if (b <= -3.8e-8) {
		tmp = t_2;
	} else if (b <= -9.8e-53) {
		tmp = y * (b - z);
	} else if (b <= -3.8e-167) {
		tmp = t_1;
	} else if (b <= 5.3e-179) {
		tmp = t_2;
	} else if (b <= 2.25e+17) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x + a) - ((y + -1.0) * z)
	t_2 = (x + z) - (a * (t + -1.0))
	t_3 = x + (b * ((y + t) - 2.0))
	tmp = 0
	if b <= -1.9e+35:
		tmp = t_3
	elif b <= -3.8e-8:
		tmp = t_2
	elif b <= -9.8e-53:
		tmp = y * (b - z)
	elif b <= -3.8e-167:
		tmp = t_1
	elif b <= 5.3e-179:
		tmp = t_2
	elif b <= 2.25e+17:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + a) - Float64(Float64(y + -1.0) * z))
	t_2 = Float64(Float64(x + z) - Float64(a * Float64(t + -1.0)))
	t_3 = Float64(x + Float64(b * Float64(Float64(y + t) - 2.0)))
	tmp = 0.0
	if (b <= -1.9e+35)
		tmp = t_3;
	elseif (b <= -3.8e-8)
		tmp = t_2;
	elseif (b <= -9.8e-53)
		tmp = Float64(y * Float64(b - z));
	elseif (b <= -3.8e-167)
		tmp = t_1;
	elseif (b <= 5.3e-179)
		tmp = t_2;
	elseif (b <= 2.25e+17)
		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) - ((y + -1.0) * z);
	t_2 = (x + z) - (a * (t + -1.0));
	t_3 = x + (b * ((y + t) - 2.0));
	tmp = 0.0;
	if (b <= -1.9e+35)
		tmp = t_3;
	elseif (b <= -3.8e-8)
		tmp = t_2;
	elseif (b <= -9.8e-53)
		tmp = y * (b - z);
	elseif (b <= -3.8e-167)
		tmp = t_1;
	elseif (b <= 5.3e-179)
		tmp = t_2;
	elseif (b <= 2.25e+17)
		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[(N[(x + a), $MachinePrecision] - N[(N[(y + -1.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x + z), $MachinePrecision] - N[(a * N[(t + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x + N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.9e+35], t$95$3, If[LessEqual[b, -3.8e-8], t$95$2, If[LessEqual[b, -9.8e-53], N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -3.8e-167], t$95$1, If[LessEqual[b, 5.3e-179], t$95$2, If[LessEqual[b, 2.25e+17], t$95$1, t$95$3]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -1.9e35 or 2.25e17 < b

   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 0 89.7%

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

   4. Taylor expanded in a around 0 79.6%

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

   if -1.9e35 < b < -3.80000000000000028e-8 or -3.79999999999999967e-167 < b < 5.29999999999999994e-179

   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 0 85.8%

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

   4. Taylor expanded in b around 0 84.4%

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

      1. associate--r+ 84.4%

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

      2. sub-neg 84.4%

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

      3. metadata-eval 84.4%

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

      4. +-commutative 84.4%

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

      5. *-commutative 84.4%

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

      6. cancel-sign-sub-inv 84.4%

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

      7. cancel-sign-sub-inv 84.4%

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

      8. metadata-eval 84.4%

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

      9. *-lft-identity 84.4%

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

      10. distribute-neg-in 84.4%

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

      11. metadata-eval 84.4%

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

      12. sub-neg 84.4%

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

      13. *-commutative 84.4%

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

   6. Simplified 84.4%

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

   if -3.80000000000000028e-8 < b < -9.79999999999999926e-53

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 73.5%

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

   if -9.79999999999999926e-53 < b < -3.79999999999999967e-167 or 5.29999999999999994e-179 < b < 2.25e17

   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. Step-by-step derivation

      1. +-commutative 99.9%

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

      2. fma-def 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

   5. Taylor expanded in t around 0 88.0%

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

   6. Taylor expanded in b around 0 75.6%

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

      1. associate--r+ 75.7%

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

      2. sub-neg 75.7%

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

      3. mul-1-neg 75.7%

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

      4. remove-double-neg 75.7%

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

      5. sub-neg 75.7%

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

      6. metadata-eval 75.7%

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

      7. +-commutative 75.7%

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

   8. Simplified 75.7%

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

4. Final simplification 79.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.9 \cdot 10^{+35}:\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{elif}\;b \leq -3.8 \cdot 10^{-8}:\\ \;\;\;\;\left(x + z\right) - a \cdot \left(t + -1\right)\\ \mathbf{elif}\;b \leq -9.8 \cdot 10^{-53}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;b \leq -3.8 \cdot 10^{-167}:\\ \;\;\;\;\left(x + a\right) - \left(y + -1\right) \cdot z\\ \mathbf{elif}\;b \leq 5.3 \cdot 10^{-179}:\\ \;\;\;\;\left(x + z\right) - a \cdot \left(t + -1\right)\\ \mathbf{elif}\;b \leq 2.25 \cdot 10^{+17}:\\ \;\;\;\;\left(x + a\right) - \left(y + -1\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 52.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(z + a\right)\\ t_2 := y \cdot \left(b - z\right)\\ \mathbf{if}\;y \leq -4.6 \cdot 10^{+71}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -6.8 \cdot 10^{-93}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -7.6 \cdot 10^{-243}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;y \leq -8.5 \cdot 10^{-266}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{-186}:\\ \;\;\;\;b \cdot \left(t - 2\right)\\ \mathbf{elif}\;y \leq 7000000000:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (+ z a))) (t_2 (* y (- b z))))
   (if (<= y -4.6e+71)
     t_2
     (if (<= y -6.8e-93)
       t_1
       (if (<= y -7.6e-243)
         (* t (- b a))
         (if (<= y -8.5e-266)
           t_1
           (if (<= y 1.85e-186)
             (* b (- t 2.0))
             (if (<= y 7000000000.0) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (z + a);
	double t_2 = y * (b - z);
	double tmp;
	if (y <= -4.6e+71) {
		tmp = t_2;
	} else if (y <= -6.8e-93) {
		tmp = t_1;
	} else if (y <= -7.6e-243) {
		tmp = t * (b - a);
	} else if (y <= -8.5e-266) {
		tmp = t_1;
	} else if (y <= 1.85e-186) {
		tmp = b * (t - 2.0);
	} else if (y <= 7000000000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + (z + a)
    t_2 = y * (b - z)
    if (y <= (-4.6d+71)) then
        tmp = t_2
    else if (y <= (-6.8d-93)) then
        tmp = t_1
    else if (y <= (-7.6d-243)) then
        tmp = t * (b - a)
    else if (y <= (-8.5d-266)) then
        tmp = t_1
    else if (y <= 1.85d-186) then
        tmp = b * (t - 2.0d0)
    else if (y <= 7000000000.0d0) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (z + a);
	double t_2 = y * (b - z);
	double tmp;
	if (y <= -4.6e+71) {
		tmp = t_2;
	} else if (y <= -6.8e-93) {
		tmp = t_1;
	} else if (y <= -7.6e-243) {
		tmp = t * (b - a);
	} else if (y <= -8.5e-266) {
		tmp = t_1;
	} else if (y <= 1.85e-186) {
		tmp = b * (t - 2.0);
	} else if (y <= 7000000000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (z + a)
	t_2 = y * (b - z)
	tmp = 0
	if y <= -4.6e+71:
		tmp = t_2
	elif y <= -6.8e-93:
		tmp = t_1
	elif y <= -7.6e-243:
		tmp = t * (b - a)
	elif y <= -8.5e-266:
		tmp = t_1
	elif y <= 1.85e-186:
		tmp = b * (t - 2.0)
	elif y <= 7000000000.0:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(z + a))
	t_2 = Float64(y * Float64(b - z))
	tmp = 0.0
	if (y <= -4.6e+71)
		tmp = t_2;
	elseif (y <= -6.8e-93)
		tmp = t_1;
	elseif (y <= -7.6e-243)
		tmp = Float64(t * Float64(b - a));
	elseif (y <= -8.5e-266)
		tmp = t_1;
	elseif (y <= 1.85e-186)
		tmp = Float64(b * Float64(t - 2.0));
	elseif (y <= 7000000000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (z + a);
	t_2 = y * (b - z);
	tmp = 0.0;
	if (y <= -4.6e+71)
		tmp = t_2;
	elseif (y <= -6.8e-93)
		tmp = t_1;
	elseif (y <= -7.6e-243)
		tmp = t * (b - a);
	elseif (y <= -8.5e-266)
		tmp = t_1;
	elseif (y <= 1.85e-186)
		tmp = b * (t - 2.0);
	elseif (y <= 7000000000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(z + a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.6e+71], t$95$2, If[LessEqual[y, -6.8e-93], t$95$1, If[LessEqual[y, -7.6e-243], N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -8.5e-266], t$95$1, If[LessEqual[y, 1.85e-186], N[(b * N[(t - 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7000000000.0], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -4.6000000000000005e71 or 7e9 < y

   1. Initial program 94.5%

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

   3. Taylor expanded in y around inf 71.2%

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

   if -4.6000000000000005e71 < y < -6.80000000000000002e-93 or -7.5999999999999996e-243 < y < -8.5000000000000002e-266 or 1.8500000000000001e-186 < y < 7e9

   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. Step-by-step derivation

      1. +-commutative 99.9%

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

      2. fma-def 99.9%

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

      3. associate--l+ 99.9%

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

      4. sub-neg 99.9%

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

      5. metadata-eval 99.9%

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

      6. sub-neg 99.9%

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

      7. associate-+l- 99.9%

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

      8. fma-neg 99.9%

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

      9. sub-neg 99.9%

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

      10. metadata-eval 99.9%

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

      11. remove-double-neg 99.9%

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

      12. sub-neg 99.9%

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

      13. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in t around 0 87.6%

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

   6. Taylor expanded in b around 0 67.4%

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

      1. associate--r+ 67.4%

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

      2. sub-neg 67.4%

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

      3. mul-1-neg 67.4%

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

      4. remove-double-neg 67.4%

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

      5. sub-neg 67.4%

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

      6. metadata-eval 67.4%

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

      7. +-commutative 67.4%

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

   8. Simplified 67.4%

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

   9. Taylor expanded in y around 0 64.4%

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

       1. cancel-sign-sub-inv 64.4%

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

       2. metadata-eval 64.4%

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

       3. *-lft-identity 64.4%

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

       4. +-commutative 64.4%

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

       5. associate-+l+ 64.4%

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

   11. Simplified 64.4%

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

   if -6.80000000000000002e-93 < y < -7.5999999999999996e-243

   1. Initial program 96.2%

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

   3. Taylor expanded in t around inf 55.1%

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

   if -8.5000000000000002e-266 < y < 1.8500000000000001e-186

   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 inf 74.8%

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

   4. Taylor expanded in y around 0 74.8%

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

4. Final simplification 67.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.6 \cdot 10^{+71}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;y \leq -6.8 \cdot 10^{-93}:\\ \;\;\;\;x + \left(z + a\right)\\ \mathbf{elif}\;y \leq -7.6 \cdot 10^{-243}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;y \leq -8.5 \cdot 10^{-266}:\\ \;\;\;\;x + \left(z + a\right)\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{-186}:\\ \;\;\;\;b \cdot \left(t - 2\right)\\ \mathbf{elif}\;y \leq 7000000000:\\ \;\;\;\;x + \left(z + a\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 49.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(b - z\right)\\ \mathbf{if}\;y \leq -2.7 \cdot 10^{+49}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -3.2 \cdot 10^{-165}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;y \leq 6 \cdot 10^{-180}:\\ \;\;\;\;b \cdot \left(t - 2\right)\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{-130}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{+15}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (- b z))))
   (if (<= y -2.7e+49)
     t_1
     (if (<= y -3.2e-165)
       (* t (- b a))
       (if (<= y 6e-180)
         (* b (- t 2.0))
         (if (<= y 2.6e-130) z (if (<= y 6.8e+15) (* a (- 1.0 t)) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (b - z);
	double tmp;
	if (y <= -2.7e+49) {
		tmp = t_1;
	} else if (y <= -3.2e-165) {
		tmp = t * (b - a);
	} else if (y <= 6e-180) {
		tmp = b * (t - 2.0);
	} else if (y <= 2.6e-130) {
		tmp = z;
	} else if (y <= 6.8e+15) {
		tmp = a * (1.0 - t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (b - z)
    if (y <= (-2.7d+49)) then
        tmp = t_1
    else if (y <= (-3.2d-165)) then
        tmp = t * (b - a)
    else if (y <= 6d-180) then
        tmp = b * (t - 2.0d0)
    else if (y <= 2.6d-130) then
        tmp = z
    else if (y <= 6.8d+15) then
        tmp = a * (1.0d0 - t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (b - z);
	double tmp;
	if (y <= -2.7e+49) {
		tmp = t_1;
	} else if (y <= -3.2e-165) {
		tmp = t * (b - a);
	} else if (y <= 6e-180) {
		tmp = b * (t - 2.0);
	} else if (y <= 2.6e-130) {
		tmp = z;
	} else if (y <= 6.8e+15) {
		tmp = a * (1.0 - t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y * (b - z)
	tmp = 0
	if y <= -2.7e+49:
		tmp = t_1
	elif y <= -3.2e-165:
		tmp = t * (b - a)
	elif y <= 6e-180:
		tmp = b * (t - 2.0)
	elif y <= 2.6e-130:
		tmp = z
	elif y <= 6.8e+15:
		tmp = a * (1.0 - t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y * Float64(b - z))
	tmp = 0.0
	if (y <= -2.7e+49)
		tmp = t_1;
	elseif (y <= -3.2e-165)
		tmp = Float64(t * Float64(b - a));
	elseif (y <= 6e-180)
		tmp = Float64(b * Float64(t - 2.0));
	elseif (y <= 2.6e-130)
		tmp = z;
	elseif (y <= 6.8e+15)
		tmp = Float64(a * Float64(1.0 - t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y * (b - z);
	tmp = 0.0;
	if (y <= -2.7e+49)
		tmp = t_1;
	elseif (y <= -3.2e-165)
		tmp = t * (b - a);
	elseif (y <= 6e-180)
		tmp = b * (t - 2.0);
	elseif (y <= 2.6e-130)
		tmp = z;
	elseif (y <= 6.8e+15)
		tmp = a * (1.0 - t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.7e+49], t$95$1, If[LessEqual[y, -3.2e-165], N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6e-180], N[(b * N[(t - 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.6e-130], z, If[LessEqual[y, 6.8e+15], N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -2.7000000000000001e49 or 6.8e15 < y

   1. Initial program 94.7%

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

   3. Taylor expanded in y around inf 69.4%

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

   if -2.7000000000000001e49 < y < -3.20000000000000013e-165

   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 t around inf 47.1%

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

   if -3.20000000000000013e-165 < y < 6.0000000000000001e-180

   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 inf 60.1%

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

   4. Taylor expanded in y around 0 60.1%

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

   if 6.0000000000000001e-180 < y < 2.6000000000000001e-130

   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 66.1%

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

   4. Taylor expanded in y around 0 66.1%

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

   if 2.6000000000000001e-130 < y < 6.8e15

   1. Initial program 99.9%

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

   3. Taylor expanded in a around inf 46.4%

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

4. Final simplification 60.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{+49}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;y \leq -3.2 \cdot 10^{-165}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;y \leq 6 \cdot 10^{-180}:\\ \;\;\;\;b \cdot \left(t - 2\right)\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{-130}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{+15}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 33.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(-y\right)\\ \mathbf{if}\;y \leq -1.4 \cdot 10^{+72}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.32 \cdot 10^{-264}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{-185}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{+15}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;y \leq 2.45 \cdot 10^{+117}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (- y))))
   (if (<= y -1.4e+72)
     t_1
     (if (<= y -1.32e-264)
       (+ x a)
       (if (<= y 5.8e-185)
         (* t b)
         (if (<= y 3.6e+15) (+ x a) (if (<= y 2.45e+117) t_1 (* y b))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * -y;
	double tmp;
	if (y <= -1.4e+72) {
		tmp = t_1;
	} else if (y <= -1.32e-264) {
		tmp = x + a;
	} else if (y <= 5.8e-185) {
		tmp = t * b;
	} else if (y <= 3.6e+15) {
		tmp = x + a;
	} else if (y <= 2.45e+117) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = z * -y
    if (y <= (-1.4d+72)) then
        tmp = t_1
    else if (y <= (-1.32d-264)) then
        tmp = x + a
    else if (y <= 5.8d-185) then
        tmp = t * b
    else if (y <= 3.6d+15) then
        tmp = x + a
    else if (y <= 2.45d+117) then
        tmp = t_1
    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 t_1 = z * -y;
	double tmp;
	if (y <= -1.4e+72) {
		tmp = t_1;
	} else if (y <= -1.32e-264) {
		tmp = x + a;
	} else if (y <= 5.8e-185) {
		tmp = t * b;
	} else if (y <= 3.6e+15) {
		tmp = x + a;
	} else if (y <= 2.45e+117) {
		tmp = t_1;
	} else {
		tmp = y * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * -y
	tmp = 0
	if y <= -1.4e+72:
		tmp = t_1
	elif y <= -1.32e-264:
		tmp = x + a
	elif y <= 5.8e-185:
		tmp = t * b
	elif y <= 3.6e+15:
		tmp = x + a
	elif y <= 2.45e+117:
		tmp = t_1
	else:
		tmp = y * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(-y))
	tmp = 0.0
	if (y <= -1.4e+72)
		tmp = t_1;
	elseif (y <= -1.32e-264)
		tmp = Float64(x + a);
	elseif (y <= 5.8e-185)
		tmp = Float64(t * b);
	elseif (y <= 3.6e+15)
		tmp = Float64(x + a);
	elseif (y <= 2.45e+117)
		tmp = t_1;
	else
		tmp = Float64(y * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * -y;
	tmp = 0.0;
	if (y <= -1.4e+72)
		tmp = t_1;
	elseif (y <= -1.32e-264)
		tmp = x + a;
	elseif (y <= 5.8e-185)
		tmp = t * b;
	elseif (y <= 3.6e+15)
		tmp = x + a;
	elseif (y <= 2.45e+117)
		tmp = t_1;
	else
		tmp = y * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z * (-y)), $MachinePrecision]}, If[LessEqual[y, -1.4e+72], t$95$1, If[LessEqual[y, -1.32e-264], N[(x + a), $MachinePrecision], If[LessEqual[y, 5.8e-185], N[(t * b), $MachinePrecision], If[LessEqual[y, 3.6e+15], N[(x + a), $MachinePrecision], If[LessEqual[y, 2.45e+117], t$95$1, N[(y * b), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.4e72 or 3.6e15 < y < 2.45e117

   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 inf 46.2%

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

   4. Taylor expanded in y around inf 46.2%

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

      1. mul-1-neg 46.2%

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

      2. *-commutative 46.2%

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

      3. distribute-rgt-neg-in 46.2%

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

   6. Simplified 46.2%

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

   if -1.4e72 < y < -1.32000000000000001e-264 or 5.79999999999999989e-185 < y < 3.6e15

   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 77.8%

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

   4. Taylor expanded in b around 0 56.6%

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

   5. Taylor expanded in t around 0 37.6%

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

      1. cancel-sign-sub-inv 37.6%

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

      2. metadata-eval 37.6%

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

      3. *-lft-identity 37.6%

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

      4. +-commutative 37.6%

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

   7. Simplified 37.6%

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

   if -1.32000000000000001e-264 < y < 5.79999999999999989e-185

   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-def 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

   5. Taylor expanded in t around 0 90.8%

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

   6. Taylor expanded in t around inf 42.6%

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

   if 2.45e117 < y

   1. Initial program 97.5%

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

   3. Taylor expanded in b around inf 55.8%

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

   4. Taylor expanded in y around inf 48.0%

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

4. Final simplification 42.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{+72}:\\ \;\;\;\;z \cdot \left(-y\right)\\ \mathbf{elif}\;y \leq -1.32 \cdot 10^{-264}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{-185}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{+15}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;y \leq 2.45 \cdot 10^{+117}:\\ \;\;\;\;z \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 67.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + z\right) - a \cdot \left(t + -1\right)\\ t_2 := y \cdot \left(b - z\right)\\ \mathbf{if}\;y \leq -3.95 \cdot 10^{+73}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -3.5 \cdot 10^{-189}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{-122}:\\ \;\;\;\;z + \left(x + b \cdot \left(t - 2\right)\right)\\ \mathbf{elif}\;y \leq 1.08 \cdot 10^{+17}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ x z) (* a (+ t -1.0)))) (t_2 (* y (- b z))))
   (if (<= y -3.95e+73)
     t_2
     (if (<= y -3.5e-189)
       t_1
       (if (<= y 1.1e-122)
         (+ z (+ x (* b (- t 2.0))))
         (if (<= y 1.08e+17) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + z) - (a * (t + -1.0));
	double t_2 = y * (b - z);
	double tmp;
	if (y <= -3.95e+73) {
		tmp = t_2;
	} else if (y <= -3.5e-189) {
		tmp = t_1;
	} else if (y <= 1.1e-122) {
		tmp = z + (x + (b * (t - 2.0)));
	} else if (y <= 1.08e+17) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x + z) - (a * (t + (-1.0d0)))
    t_2 = y * (b - z)
    if (y <= (-3.95d+73)) then
        tmp = t_2
    else if (y <= (-3.5d-189)) then
        tmp = t_1
    else if (y <= 1.1d-122) then
        tmp = z + (x + (b * (t - 2.0d0)))
    else if (y <= 1.08d+17) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + z) - (a * (t + -1.0));
	double t_2 = y * (b - z);
	double tmp;
	if (y <= -3.95e+73) {
		tmp = t_2;
	} else if (y <= -3.5e-189) {
		tmp = t_1;
	} else if (y <= 1.1e-122) {
		tmp = z + (x + (b * (t - 2.0)));
	} else if (y <= 1.08e+17) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x + z) - (a * (t + -1.0))
	t_2 = y * (b - z)
	tmp = 0
	if y <= -3.95e+73:
		tmp = t_2
	elif y <= -3.5e-189:
		tmp = t_1
	elif y <= 1.1e-122:
		tmp = z + (x + (b * (t - 2.0)))
	elif y <= 1.08e+17:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + z) - Float64(a * Float64(t + -1.0)))
	t_2 = Float64(y * Float64(b - z))
	tmp = 0.0
	if (y <= -3.95e+73)
		tmp = t_2;
	elseif (y <= -3.5e-189)
		tmp = t_1;
	elseif (y <= 1.1e-122)
		tmp = Float64(z + Float64(x + Float64(b * Float64(t - 2.0))));
	elseif (y <= 1.08e+17)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x + z) - (a * (t + -1.0));
	t_2 = y * (b - z);
	tmp = 0.0;
	if (y <= -3.95e+73)
		tmp = t_2;
	elseif (y <= -3.5e-189)
		tmp = t_1;
	elseif (y <= 1.1e-122)
		tmp = z + (x + (b * (t - 2.0)));
	elseif (y <= 1.08e+17)
		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[(N[(x + z), $MachinePrecision] - N[(a * N[(t + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.95e+73], t$95$2, If[LessEqual[y, -3.5e-189], t$95$1, If[LessEqual[y, 1.1e-122], N[(z + N[(x + N[(b * N[(t - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.08e+17], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.9499999999999997e73 or 1.08e17 < y

   1. Initial program 94.4%

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

   3. Taylor expanded in y around inf 71.9%

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

   if -3.9499999999999997e73 < y < -3.5000000000000001e-189 or 1.1e-122 < y < 1.08e17

   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 y around 0 91.5%

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

   4. Taylor expanded in b around 0 75.3%

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

      1. associate--r+ 75.3%

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

      2. sub-neg 75.3%

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

      3. metadata-eval 75.3%

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

      4. +-commutative 75.3%

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

      5. *-commutative 75.3%

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

      6. cancel-sign-sub-inv 75.3%

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

      7. cancel-sign-sub-inv 75.3%

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

      8. metadata-eval 75.3%

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

      9. *-lft-identity 75.3%

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

      10. distribute-neg-in 75.3%

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

      11. metadata-eval 75.3%

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

      12. sub-neg 75.3%

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

      13. *-commutative 75.3%

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

   6. Simplified 75.3%

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

   if -3.5000000000000001e-189 < y < 1.1e-122

   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 0 100.0%

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

   4. Taylor expanded in a around 0 85.8%

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

4. Final simplification 76.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.95 \cdot 10^{+73}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;y \leq -3.5 \cdot 10^{-189}:\\ \;\;\;\;\left(x + z\right) - a \cdot \left(t + -1\right)\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{-122}:\\ \;\;\;\;z + \left(x + b \cdot \left(t - 2\right)\right)\\ \mathbf{elif}\;y \leq 1.08 \cdot 10^{+17}:\\ \;\;\;\;\left(x + z\right) - a \cdot \left(t + -1\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 84.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{if}\;b \leq -1.9 \cdot 10^{+35}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 0.034:\\ \;\;\;\;x + \left(z \cdot \left(1 - y\right) + a \cdot \left(1 - t\right)\right)\\ \mathbf{elif}\;b \leq 1.75 \cdot 10^{+89}:\\ \;\;\;\;\left(x - \left(y + -1\right) \cdot z\right) + t \cdot \left(b - a\right)\\ \mathbf{elif}\;b \leq 9.2 \cdot 10^{+95}:\\ \;\;\;\;x + \left(a + -2 \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* b (- (+ y t) 2.0)))))
   (if (<= b -1.9e+35)
     t_1
     (if (<= b 0.034)
       (+ x (+ (* z (- 1.0 y)) (* a (- 1.0 t))))
       (if (<= b 1.75e+89)
         (+ (- x (* (+ y -1.0) z)) (* t (- b a)))
         (if (<= b 9.2e+95) (+ x (+ a (* -2.0 b))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (b * ((y + t) - 2.0));
	double tmp;
	if (b <= -1.9e+35) {
		tmp = t_1;
	} else if (b <= 0.034) {
		tmp = x + ((z * (1.0 - y)) + (a * (1.0 - t)));
	} else if (b <= 1.75e+89) {
		tmp = (x - ((y + -1.0) * z)) + (t * (b - a));
	} else if (b <= 9.2e+95) {
		tmp = x + (a + (-2.0 * b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (b * ((y + t) - 2.0d0))
    if (b <= (-1.9d+35)) then
        tmp = t_1
    else if (b <= 0.034d0) then
        tmp = x + ((z * (1.0d0 - y)) + (a * (1.0d0 - t)))
    else if (b <= 1.75d+89) then
        tmp = (x - ((y + (-1.0d0)) * z)) + (t * (b - a))
    else if (b <= 9.2d+95) then
        tmp = x + (a + ((-2.0d0) * b))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (b * ((y + t) - 2.0));
	double tmp;
	if (b <= -1.9e+35) {
		tmp = t_1;
	} else if (b <= 0.034) {
		tmp = x + ((z * (1.0 - y)) + (a * (1.0 - t)));
	} else if (b <= 1.75e+89) {
		tmp = (x - ((y + -1.0) * z)) + (t * (b - a));
	} else if (b <= 9.2e+95) {
		tmp = x + (a + (-2.0 * b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (b * ((y + t) - 2.0))
	tmp = 0
	if b <= -1.9e+35:
		tmp = t_1
	elif b <= 0.034:
		tmp = x + ((z * (1.0 - y)) + (a * (1.0 - t)))
	elif b <= 1.75e+89:
		tmp = (x - ((y + -1.0) * z)) + (t * (b - a))
	elif b <= 9.2e+95:
		tmp = x + (a + (-2.0 * b))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(b * Float64(Float64(y + t) - 2.0)))
	tmp = 0.0
	if (b <= -1.9e+35)
		tmp = t_1;
	elseif (b <= 0.034)
		tmp = Float64(x + Float64(Float64(z * Float64(1.0 - y)) + Float64(a * Float64(1.0 - t))));
	elseif (b <= 1.75e+89)
		tmp = Float64(Float64(x - Float64(Float64(y + -1.0) * z)) + Float64(t * Float64(b - a)));
	elseif (b <= 9.2e+95)
		tmp = Float64(x + Float64(a + Float64(-2.0 * b)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (b * ((y + t) - 2.0));
	tmp = 0.0;
	if (b <= -1.9e+35)
		tmp = t_1;
	elseif (b <= 0.034)
		tmp = x + ((z * (1.0 - y)) + (a * (1.0 - t)));
	elseif (b <= 1.75e+89)
		tmp = (x - ((y + -1.0) * z)) + (t * (b - a));
	elseif (b <= 9.2e+95)
		tmp = x + (a + (-2.0 * b));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.9e+35], t$95$1, If[LessEqual[b, 0.034], N[(x + N[(N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision] + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.75e+89], N[(N[(x - N[(N[(y + -1.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] + N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 9.2e+95], N[(x + N[(a + N[(-2.0 * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -1.9e35 or 9.19999999999999989e95 < b

   1. Initial program 92.1%

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

   3. Taylor expanded in z around 0 90.0%

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

   4. Taylor expanded in a around 0 84.6%

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

   if -1.9e35 < b < 0.034000000000000002

   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 91.0%

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

   if 0.034000000000000002 < b < 1.75e89

   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. Step-by-step derivation

      1. associate-+l- 99.8%

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

      2. sub-neg 99.8%

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

      3. metadata-eval 99.8%

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

      4. *-commutative 99.8%

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

      5. fma-neg 99.9%

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

      6. sub-neg 99.9%

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

      7. metadata-eval 99.9%

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

      8. sub-neg 99.9%

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

      9. metadata-eval 99.9%

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

      10. associate-+r+ 99.9%

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

      11. *-commutative 99.9%

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

      12. associate-+r+ 99.9%

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

      13. +-commutative 99.9%

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

      14. associate-+l+ 99.9%

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

   4. Applied egg-rr 99.9%

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

   5. Taylor expanded in t around inf 92.3%

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

   6. Taylor expanded in t around inf 87.0%

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

   if 1.75e89 < b < 9.19999999999999989e95

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 100.0%

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

   4. Taylor expanded in t around 0 100.0%

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

      1. associate--l+ 100.0%

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

      2. sub-neg 100.0%

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

      3. metadata-eval 100.0%

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

      4. neg-mul-1 100.0%

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

   6. Simplified 100.0%

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

   7. Taylor expanded in y around 0 100.0%

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

      1. *-commutative 100.0%

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

   9. Simplified 100.0%

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

4. Final simplification 88.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.9 \cdot 10^{+35}:\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{elif}\;b \leq 0.034:\\ \;\;\;\;x + \left(z \cdot \left(1 - y\right) + a \cdot \left(1 - t\right)\right)\\ \mathbf{elif}\;b \leq 1.75 \cdot 10^{+89}:\\ \;\;\;\;\left(x - \left(y + -1\right) \cdot z\right) + t \cdot \left(b - a\right)\\ \mathbf{elif}\;b \leq 9.2 \cdot 10^{+95}:\\ \;\;\;\;x + \left(a + -2 \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 93.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y + -1\right) \cdot z\\ \mathbf{if}\;t \leq -7.5 \cdot 10^{+42} \lor \neg \left(t \leq 1.2 \cdot 10^{+78}\right):\\ \;\;\;\;\left(x - t_1\right) + t \cdot \left(b - a\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right) + \left(\left(x + a\right) - t_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (+ y -1.0) z)))
   (if (or (<= t -7.5e+42) (not (<= t 1.2e+78)))
     (+ (- x t_1) (* t (- b a)))
     (+ (* b (- (+ y t) 2.0)) (- (+ x a) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (y + -1.0) * z;
	double tmp;
	if ((t <= -7.5e+42) || !(t <= 1.2e+78)) {
		tmp = (x - t_1) + (t * (b - a));
	} else {
		tmp = (b * ((y + t) - 2.0)) + ((x + a) - t_1);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (y + (-1.0d0)) * z
    if ((t <= (-7.5d+42)) .or. (.not. (t <= 1.2d+78))) then
        tmp = (x - t_1) + (t * (b - a))
    else
        tmp = (b * ((y + t) - 2.0d0)) + ((x + a) - t_1)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (y + -1.0) * z;
	double tmp;
	if ((t <= -7.5e+42) || !(t <= 1.2e+78)) {
		tmp = (x - t_1) + (t * (b - a));
	} else {
		tmp = (b * ((y + t) - 2.0)) + ((x + a) - t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (y + -1.0) * z
	tmp = 0
	if (t <= -7.5e+42) or not (t <= 1.2e+78):
		tmp = (x - t_1) + (t * (b - a))
	else:
		tmp = (b * ((y + t) - 2.0)) + ((x + a) - t_1)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(y + -1.0) * z)
	tmp = 0.0
	if ((t <= -7.5e+42) || !(t <= 1.2e+78))
		tmp = Float64(Float64(x - t_1) + Float64(t * Float64(b - a)));
	else
		tmp = Float64(Float64(b * Float64(Float64(y + t) - 2.0)) + Float64(Float64(x + a) - t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (y + -1.0) * z;
	tmp = 0.0;
	if ((t <= -7.5e+42) || ~((t <= 1.2e+78)))
		tmp = (x - t_1) + (t * (b - a));
	else
		tmp = (b * ((y + t) - 2.0)) + ((x + a) - t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(y + -1.0), $MachinePrecision] * z), $MachinePrecision]}, If[Or[LessEqual[t, -7.5e+42], N[Not[LessEqual[t, 1.2e+78]], $MachinePrecision]], N[(N[(x - t$95$1), $MachinePrecision] + N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x + a), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < -7.50000000000000041e42 or 1.1999999999999999e78 < t

   1. Initial program 95.4%

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

      1. associate-+l- 95.4%

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

      2. sub-neg 95.4%

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

      3. metadata-eval 95.4%

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

      4. *-commutative 95.4%

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

      5. fma-neg 95.4%

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

      6. sub-neg 95.4%

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

      7. metadata-eval 95.4%

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

      8. sub-neg 95.4%

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

      9. metadata-eval 95.4%

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

      10. associate-+r+ 95.4%

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

      11. *-commutative 95.4%

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

      12. associate-+r+ 95.4%

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

      13. +-commutative 95.4%

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

      14. associate-+l+ 95.4%

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

   4. Applied egg-rr 95.4%

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

   5. Taylor expanded in t around inf 90.9%

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

   6. Taylor expanded in t around inf 93.1%

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

   if -7.50000000000000041e42 < t < 1.1999999999999999e78

   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 t around 0 96.0%

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

      1. associate--r+ 96.0%

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

      2. sub-neg 96.0%

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

      3. metadata-eval 96.0%

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

      4. sub-neg 96.0%

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

      5. cancel-sign-sub-inv 96.0%

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

      6. metadata-eval 96.0%

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

      7. *-lft-identity 96.0%

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

      8. distribute-rgt-in 96.0%

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

      9. +-commutative 96.0%

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

      10. distribute-neg-in 96.0%

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

      11. distribute-lft-neg-in 96.0%

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

      12. metadata-eval 96.0%

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

      13. mul-1-neg 96.0%

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

      14. associate-*r* 96.0%

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

      15. *-commutative 96.0%

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

      16. distribute-rgt-in 96.0%

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

      17. *-commutative 96.0%

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

      18. neg-mul-1 96.0%

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

      19. sub-neg 96.0%

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

   5. Simplified 96.0%

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

4. Final simplification 95.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.5 \cdot 10^{+42} \lor \neg \left(t \leq 1.2 \cdot 10^{+78}\right):\\ \;\;\;\;\left(x - \left(y + -1\right) \cdot z\right) + t \cdot \left(b - a\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right) + \left(\left(x + a\right) - \left(y + -1\right) \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 55.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(b - z\right)\\ \mathbf{if}\;y \leq -2.25 \cdot 10^{+72}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -3.4 \cdot 10^{-265}:\\ \;\;\;\;x - a \cdot \left(t + -1\right)\\ \mathbf{elif}\;y \leq 2.55 \cdot 10^{-186}:\\ \;\;\;\;b \cdot \left(t - 2\right)\\ \mathbf{elif}\;y \leq 108000000:\\ \;\;\;\;x + \left(z + a\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (- b z))))
   (if (<= y -2.25e+72)
     t_1
     (if (<= y -3.4e-265)
       (- x (* a (+ t -1.0)))
       (if (<= y 2.55e-186)
         (* b (- t 2.0))
         (if (<= y 108000000.0) (+ x (+ z a)) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (b - z);
	double tmp;
	if (y <= -2.25e+72) {
		tmp = t_1;
	} else if (y <= -3.4e-265) {
		tmp = x - (a * (t + -1.0));
	} else if (y <= 2.55e-186) {
		tmp = b * (t - 2.0);
	} else if (y <= 108000000.0) {
		tmp = x + (z + a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (b - z)
    if (y <= (-2.25d+72)) then
        tmp = t_1
    else if (y <= (-3.4d-265)) then
        tmp = x - (a * (t + (-1.0d0)))
    else if (y <= 2.55d-186) then
        tmp = b * (t - 2.0d0)
    else if (y <= 108000000.0d0) then
        tmp = x + (z + a)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (b - z);
	double tmp;
	if (y <= -2.25e+72) {
		tmp = t_1;
	} else if (y <= -3.4e-265) {
		tmp = x - (a * (t + -1.0));
	} else if (y <= 2.55e-186) {
		tmp = b * (t - 2.0);
	} else if (y <= 108000000.0) {
		tmp = x + (z + a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y * (b - z)
	tmp = 0
	if y <= -2.25e+72:
		tmp = t_1
	elif y <= -3.4e-265:
		tmp = x - (a * (t + -1.0))
	elif y <= 2.55e-186:
		tmp = b * (t - 2.0)
	elif y <= 108000000.0:
		tmp = x + (z + a)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y * Float64(b - z))
	tmp = 0.0
	if (y <= -2.25e+72)
		tmp = t_1;
	elseif (y <= -3.4e-265)
		tmp = Float64(x - Float64(a * Float64(t + -1.0)));
	elseif (y <= 2.55e-186)
		tmp = Float64(b * Float64(t - 2.0));
	elseif (y <= 108000000.0)
		tmp = Float64(x + Float64(z + a));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y * (b - z);
	tmp = 0.0;
	if (y <= -2.25e+72)
		tmp = t_1;
	elseif (y <= -3.4e-265)
		tmp = x - (a * (t + -1.0));
	elseif (y <= 2.55e-186)
		tmp = b * (t - 2.0);
	elseif (y <= 108000000.0)
		tmp = x + (z + a);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.25e+72], t$95$1, If[LessEqual[y, -3.4e-265], N[(x - N[(a * N[(t + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.55e-186], N[(b * N[(t - 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 108000000.0], N[(x + N[(z + a), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -2.2499999999999999e72 or 1.08e8 < y

   1. Initial program 94.5%

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

   3. Taylor expanded in y around inf 71.2%

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

   if -2.2499999999999999e72 < y < -3.4000000000000001e-265

   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 z around 0 87.2%

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

   4. Taylor expanded in b around 0 61.0%

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

   if -3.4000000000000001e-265 < y < 2.5500000000000002e-186

   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 inf 72.7%

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

   4. Taylor expanded in y around 0 72.7%

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

   if 2.5500000000000002e-186 < y < 1.08e8

   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. Step-by-step derivation

      1. +-commutative 99.9%

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

      2. fma-def 99.9%

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

      3. associate--l+ 99.9%

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

      4. sub-neg 99.9%

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

      5. metadata-eval 99.9%

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

      6. sub-neg 99.9%

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

      7. associate-+l- 99.9%

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

      8. fma-neg 99.9%

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

      9. sub-neg 99.9%

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

      10. metadata-eval 99.9%

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

      11. remove-double-neg 99.9%

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

      12. sub-neg 99.9%

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

      13. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in t around 0 91.9%

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

   6. Taylor expanded in b around 0 75.0%

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

      1. associate--r+ 75.0%

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

      2. sub-neg 75.0%

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

      3. mul-1-neg 75.0%

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

      4. remove-double-neg 75.0%

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

      5. sub-neg 75.0%

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

      6. metadata-eval 75.0%

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

      7. +-commutative 75.0%

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

   8. Simplified 75.0%

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

   9. Taylor expanded in y around 0 71.3%

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

       1. cancel-sign-sub-inv 71.3%

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

       2. metadata-eval 71.3%

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

       3. *-lft-identity 71.3%

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

       4. +-commutative 71.3%

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

       5. associate-+l+ 71.3%

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

   11. Simplified 71.3%

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

4. Final simplification 68.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.25 \cdot 10^{+72}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;y \leq -3.4 \cdot 10^{-265}:\\ \;\;\;\;x - a \cdot \left(t + -1\right)\\ \mathbf{elif}\;y \leq 2.55 \cdot 10^{-186}:\\ \;\;\;\;b \cdot \left(t - 2\right)\\ \mathbf{elif}\;y \leq 108000000:\\ \;\;\;\;x + \left(z + a\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 57.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(b - z\right)\\ \mathbf{if}\;y \leq -7 \cdot 10^{+71}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.36 \cdot 10^{-163}:\\ \;\;\;\;x - a \cdot \left(t + -1\right)\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{-186}:\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{elif}\;y \leq 1500000000:\\ \;\;\;\;x + \left(z + a\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (- b z))))
   (if (<= y -7e+71)
     t_1
     (if (<= y -1.36e-163)
       (- x (* a (+ t -1.0)))
       (if (<= y 2.8e-186)
         (+ x (* b (- (+ y t) 2.0)))
         (if (<= y 1500000000.0) (+ x (+ z a)) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (b - z);
	double tmp;
	if (y <= -7e+71) {
		tmp = t_1;
	} else if (y <= -1.36e-163) {
		tmp = x - (a * (t + -1.0));
	} else if (y <= 2.8e-186) {
		tmp = x + (b * ((y + t) - 2.0));
	} else if (y <= 1500000000.0) {
		tmp = x + (z + a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (b - z)
    if (y <= (-7d+71)) then
        tmp = t_1
    else if (y <= (-1.36d-163)) then
        tmp = x - (a * (t + (-1.0d0)))
    else if (y <= 2.8d-186) then
        tmp = x + (b * ((y + t) - 2.0d0))
    else if (y <= 1500000000.0d0) then
        tmp = x + (z + a)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (b - z);
	double tmp;
	if (y <= -7e+71) {
		tmp = t_1;
	} else if (y <= -1.36e-163) {
		tmp = x - (a * (t + -1.0));
	} else if (y <= 2.8e-186) {
		tmp = x + (b * ((y + t) - 2.0));
	} else if (y <= 1500000000.0) {
		tmp = x + (z + a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y * (b - z)
	tmp = 0
	if y <= -7e+71:
		tmp = t_1
	elif y <= -1.36e-163:
		tmp = x - (a * (t + -1.0))
	elif y <= 2.8e-186:
		tmp = x + (b * ((y + t) - 2.0))
	elif y <= 1500000000.0:
		tmp = x + (z + a)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y * Float64(b - z))
	tmp = 0.0
	if (y <= -7e+71)
		tmp = t_1;
	elseif (y <= -1.36e-163)
		tmp = Float64(x - Float64(a * Float64(t + -1.0)));
	elseif (y <= 2.8e-186)
		tmp = Float64(x + Float64(b * Float64(Float64(y + t) - 2.0)));
	elseif (y <= 1500000000.0)
		tmp = Float64(x + Float64(z + a));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y * (b - z);
	tmp = 0.0;
	if (y <= -7e+71)
		tmp = t_1;
	elseif (y <= -1.36e-163)
		tmp = x - (a * (t + -1.0));
	elseif (y <= 2.8e-186)
		tmp = x + (b * ((y + t) - 2.0));
	elseif (y <= 1500000000.0)
		tmp = x + (z + a);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -7e+71], t$95$1, If[LessEqual[y, -1.36e-163], N[(x - N[(a * N[(t + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.8e-186], N[(x + N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1500000000.0], N[(x + N[(z + a), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -6.9999999999999998e71 or 1.5e9 < y

   1. Initial program 94.5%

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

   3. Taylor expanded in y around inf 71.2%

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

   if -6.9999999999999998e71 < y < -1.36e-163

   1. Initial program 98.0%

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

   3. Taylor expanded in z around 0 88.7%

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

   4. Taylor expanded in b around 0 66.1%

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

   if -1.36e-163 < y < 2.79999999999999983e-186

   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 85.9%

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

   4. Taylor expanded in a around 0 70.6%

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

   if 2.79999999999999983e-186 < y < 1.5e9

   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. Step-by-step derivation

      1. +-commutative 99.9%

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

      2. fma-def 99.9%

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

      3. associate--l+ 99.9%

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

      4. sub-neg 99.9%

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

      5. metadata-eval 99.9%

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

      6. sub-neg 99.9%

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

      7. associate-+l- 99.9%

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

      8. fma-neg 99.9%

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

      9. sub-neg 99.9%

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

      10. metadata-eval 99.9%

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

      11. remove-double-neg 99.9%

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

      12. sub-neg 99.9%

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

      13. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in t around 0 91.9%

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

   6. Taylor expanded in b around 0 75.0%

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

      1. associate--r+ 75.0%

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

      2. sub-neg 75.0%

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

      3. mul-1-neg 75.0%

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

      4. remove-double-neg 75.0%

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

      5. sub-neg 75.0%

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

      6. metadata-eval 75.0%

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

      7. +-commutative 75.0%

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

   8. Simplified 75.0%

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

   9. Taylor expanded in y around 0 71.3%

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

       1. cancel-sign-sub-inv 71.3%

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

       2. metadata-eval 71.3%

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

       3. *-lft-identity 71.3%

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

       4. +-commutative 71.3%

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

       5. associate-+l+ 71.3%

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

   11. Simplified 71.3%

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

4. Final simplification 70.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7 \cdot 10^{+71}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;y \leq -1.36 \cdot 10^{-163}:\\ \;\;\;\;x - a \cdot \left(t + -1\right)\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{-186}:\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{elif}\;y \leq 1500000000:\\ \;\;\;\;x + \left(z + a\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 86.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -33000000000000 \lor \neg \left(z \leq 1200000000\right):\\ \;\;\;\;\left(x - \left(y + -1\right) \cdot z\right) + t \cdot \left(b - a\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + b \cdot \left(\left(y + t\right) - 2\right)\right) + a \cdot \left(1 - t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -33000000000000.0) (not (<= z 1200000000.0)))
   (+ (- x (* (+ y -1.0) z)) (* t (- b a)))
   (+ (+ x (* b (- (+ y t) 2.0))) (* a (- 1.0 t)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -33000000000000.0) || !(z <= 1200000000.0)) {
		tmp = (x - ((y + -1.0) * z)) + (t * (b - a));
	} else {
		tmp = (x + (b * ((y + t) - 2.0))) + (a * (1.0 - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-33000000000000.0d0)) .or. (.not. (z <= 1200000000.0d0))) then
        tmp = (x - ((y + (-1.0d0)) * z)) + (t * (b - a))
    else
        tmp = (x + (b * ((y + t) - 2.0d0))) + (a * (1.0d0 - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -33000000000000.0) || !(z <= 1200000000.0)) {
		tmp = (x - ((y + -1.0) * z)) + (t * (b - a));
	} else {
		tmp = (x + (b * ((y + t) - 2.0))) + (a * (1.0 - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -33000000000000.0) or not (z <= 1200000000.0):
		tmp = (x - ((y + -1.0) * z)) + (t * (b - a))
	else:
		tmp = (x + (b * ((y + t) - 2.0))) + (a * (1.0 - t))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -33000000000000.0) || !(z <= 1200000000.0))
		tmp = Float64(Float64(x - Float64(Float64(y + -1.0) * z)) + Float64(t * Float64(b - a)));
	else
		tmp = Float64(Float64(x + Float64(b * Float64(Float64(y + t) - 2.0))) + Float64(a * Float64(1.0 - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -33000000000000.0) || ~((z <= 1200000000.0)))
		tmp = (x - ((y + -1.0) * z)) + (t * (b - a));
	else
		tmp = (x + (b * ((y + t) - 2.0))) + (a * (1.0 - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -33000000000000.0], N[Not[LessEqual[z, 1200000000.0]], $MachinePrecision]], N[(N[(x - N[(N[(y + -1.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] + N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.3e13 or 1.2e9 < z

   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. Step-by-step derivation

      1. associate-+l- 95.2%

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

      2. sub-neg 95.2%

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

      3. metadata-eval 95.2%

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

      4. *-commutative 95.2%

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

      5. fma-neg 95.2%

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

      6. sub-neg 95.2%

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

      7. metadata-eval 95.2%

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

      8. sub-neg 95.2%

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

      9. metadata-eval 95.2%

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

      10. associate-+r+ 95.2%

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

      11. *-commutative 95.2%

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

      12. associate-+r+ 95.2%

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

      13. +-commutative 95.2%

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

      14. associate-+l+ 95.2%

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

   4. Applied egg-rr 95.2%

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

   5. Taylor expanded in t around inf 89.8%

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

   6. Taylor expanded in t around inf 85.1%

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

   if -3.3e13 < z < 1.2e9

   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 z around 0 94.7%

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

4. Final simplification 90.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -33000000000000 \lor \neg \left(z \leq 1200000000\right):\\ \;\;\;\;\left(x - \left(y + -1\right) \cdot z\right) + t \cdot \left(b - a\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + b \cdot \left(\left(y + t\right) - 2\right)\right) + a \cdot \left(1 - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 87.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(1 - y\right)\\ t_2 := x + b \cdot \left(\left(y + t\right) - 2\right)\\ t_3 := a \cdot \left(1 - t\right)\\ \mathbf{if}\;b \leq -2.5 \cdot 10^{+24}:\\ \;\;\;\;t_2 + t_1\\ \mathbf{elif}\;b \leq 225000000000:\\ \;\;\;\;x + \left(t_1 + t_3\right)\\ \mathbf{else}:\\ \;\;\;\;t_2 + t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (- 1.0 y)))
        (t_2 (+ x (* b (- (+ y t) 2.0))))
        (t_3 (* a (- 1.0 t))))
   (if (<= b -2.5e+24)
     (+ t_2 t_1)
     (if (<= b 225000000000.0) (+ x (+ t_1 t_3)) (+ t_2 t_3)))))

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 = x + (b * ((y + t) - 2.0));
	double t_3 = a * (1.0 - t);
	double tmp;
	if (b <= -2.5e+24) {
		tmp = t_2 + t_1;
	} else if (b <= 225000000000.0) {
		tmp = x + (t_1 + t_3);
	} else {
		tmp = t_2 + 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 = z * (1.0d0 - y)
    t_2 = x + (b * ((y + t) - 2.0d0))
    t_3 = a * (1.0d0 - t)
    if (b <= (-2.5d+24)) then
        tmp = t_2 + t_1
    else if (b <= 225000000000.0d0) then
        tmp = x + (t_1 + t_3)
    else
        tmp = t_2 + 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 = z * (1.0 - y);
	double t_2 = x + (b * ((y + t) - 2.0));
	double t_3 = a * (1.0 - t);
	double tmp;
	if (b <= -2.5e+24) {
		tmp = t_2 + t_1;
	} else if (b <= 225000000000.0) {
		tmp = x + (t_1 + t_3);
	} else {
		tmp = t_2 + t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * (1.0 - y)
	t_2 = x + (b * ((y + t) - 2.0))
	t_3 = a * (1.0 - t)
	tmp = 0
	if b <= -2.5e+24:
		tmp = t_2 + t_1
	elif b <= 225000000000.0:
		tmp = x + (t_1 + t_3)
	else:
		tmp = t_2 + t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(1.0 - y))
	t_2 = Float64(x + Float64(b * Float64(Float64(y + t) - 2.0)))
	t_3 = Float64(a * Float64(1.0 - t))
	tmp = 0.0
	if (b <= -2.5e+24)
		tmp = Float64(t_2 + t_1);
	elseif (b <= 225000000000.0)
		tmp = Float64(x + Float64(t_1 + t_3));
	else
		tmp = Float64(t_2 + t_3);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * (1.0 - y);
	t_2 = x + (b * ((y + t) - 2.0));
	t_3 = a * (1.0 - t);
	tmp = 0.0;
	if (b <= -2.5e+24)
		tmp = t_2 + t_1;
	elseif (b <= 225000000000.0)
		tmp = x + (t_1 + t_3);
	else
		tmp = t_2 + t_3;
	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[(x + N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2.5e+24], N[(t$95$2 + t$95$1), $MachinePrecision], If[LessEqual[b, 225000000000.0], N[(x + N[(t$95$1 + t$95$3), $MachinePrecision]), $MachinePrecision], N[(t$95$2 + t$95$3), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -2.50000000000000023e24

   1. Initial program 92.5%

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

   3. Taylor expanded in a around 0 87.2%

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

   if -2.50000000000000023e24 < b < 2.25e11

   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 91.1%

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

   if 2.25e11 < b

   1. Initial program 94.5%

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

   3. Taylor expanded in z around 0 94.4%

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

4. Final simplification 91.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.5 \cdot 10^{+24}:\\ \;\;\;\;\left(x + b \cdot \left(\left(y + t\right) - 2\right)\right) + z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq 225000000000:\\ \;\;\;\;x + \left(z \cdot \left(1 - y\right) + a \cdot \left(1 - t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + b \cdot \left(\left(y + t\right) - 2\right)\right) + a \cdot \left(1 - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 25.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{+157}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;y \leq -4 \cdot 10^{-146}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{-186}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;y \leq 45:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -1.05e+157)
   (* y b)
   (if (<= y -4e-146)
     x
     (if (<= y 7.2e-186) (* t b) (if (<= y 45.0) z (* y b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1.05e+157) {
		tmp = y * b;
	} else if (y <= -4e-146) {
		tmp = x;
	} else if (y <= 7.2e-186) {
		tmp = t * b;
	} else if (y <= 45.0) {
		tmp = z;
	} 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 <= (-1.05d+157)) then
        tmp = y * b
    else if (y <= (-4d-146)) then
        tmp = x
    else if (y <= 7.2d-186) then
        tmp = t * b
    else if (y <= 45.0d0) then
        tmp = z
    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 <= -1.05e+157) {
		tmp = y * b;
	} else if (y <= -4e-146) {
		tmp = x;
	} else if (y <= 7.2e-186) {
		tmp = t * b;
	} else if (y <= 45.0) {
		tmp = z;
	} else {
		tmp = y * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -1.05e+157:
		tmp = y * b
	elif y <= -4e-146:
		tmp = x
	elif y <= 7.2e-186:
		tmp = t * b
	elif y <= 45.0:
		tmp = z
	else:
		tmp = y * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -1.05e+157)
		tmp = Float64(y * b);
	elseif (y <= -4e-146)
		tmp = x;
	elseif (y <= 7.2e-186)
		tmp = Float64(t * b);
	elseif (y <= 45.0)
		tmp = z;
	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 <= -1.05e+157)
		tmp = y * b;
	elseif (y <= -4e-146)
		tmp = x;
	elseif (y <= 7.2e-186)
		tmp = t * b;
	elseif (y <= 45.0)
		tmp = z;
	else
		tmp = y * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -1.05e+157], N[(y * b), $MachinePrecision], If[LessEqual[y, -4e-146], x, If[LessEqual[y, 7.2e-186], N[(t * b), $MachinePrecision], If[LessEqual[y, 45.0], z, N[(y * b), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.05e157 or 45 < y

   1. Initial program 93.9%

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

   3. Taylor expanded in b around inf 44.0%

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

   4. Taylor expanded in y around inf 39.0%

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

   if -1.05e157 < y < -4.0000000000000001e-146

   1. Initial program 98.3%

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

   3. Taylor expanded in x around inf 28.1%

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

   if -4.0000000000000001e-146 < y < 7.1999999999999997e-186

   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-def 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

   5. Taylor expanded in t around 0 86.6%

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

   6. Taylor expanded in t around inf 36.1%

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

   if 7.1999999999999997e-186 < y < 45

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 36.5%

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

   4. Taylor expanded in y around 0 34.6%

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

4. Final simplification 35.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{+157}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;y \leq -4 \cdot 10^{-146}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{-186}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;y \leq 45:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 31.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{+158}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;y \leq -8.6 \cdot 10^{-265}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{-186}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{+119}:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -4.5e+158)
   (* y b)
   (if (<= y -8.6e-265)
     (+ x a)
     (if (<= y 1.1e-186) (* t b) (if (<= y 4.4e+119) (+ x a) (* y b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -4.5e+158) {
		tmp = y * b;
	} else if (y <= -8.6e-265) {
		tmp = x + a;
	} else if (y <= 1.1e-186) {
		tmp = t * b;
	} else if (y <= 4.4e+119) {
		tmp = x + a;
	} 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 <= (-4.5d+158)) then
        tmp = y * b
    else if (y <= (-8.6d-265)) then
        tmp = x + a
    else if (y <= 1.1d-186) then
        tmp = t * b
    else if (y <= 4.4d+119) then
        tmp = x + a
    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 <= -4.5e+158) {
		tmp = y * b;
	} else if (y <= -8.6e-265) {
		tmp = x + a;
	} else if (y <= 1.1e-186) {
		tmp = t * b;
	} else if (y <= 4.4e+119) {
		tmp = x + a;
	} else {
		tmp = y * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -4.5e+158:
		tmp = y * b
	elif y <= -8.6e-265:
		tmp = x + a
	elif y <= 1.1e-186:
		tmp = t * b
	elif y <= 4.4e+119:
		tmp = x + a
	else:
		tmp = y * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -4.5e+158)
		tmp = Float64(y * b);
	elseif (y <= -8.6e-265)
		tmp = Float64(x + a);
	elseif (y <= 1.1e-186)
		tmp = Float64(t * b);
	elseif (y <= 4.4e+119)
		tmp = Float64(x + a);
	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 <= -4.5e+158)
		tmp = y * b;
	elseif (y <= -8.6e-265)
		tmp = x + a;
	elseif (y <= 1.1e-186)
		tmp = t * b;
	elseif (y <= 4.4e+119)
		tmp = x + a;
	else
		tmp = y * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -4.5e+158], N[(y * b), $MachinePrecision], If[LessEqual[y, -8.6e-265], N[(x + a), $MachinePrecision], If[LessEqual[y, 1.1e-186], N[(t * b), $MachinePrecision], If[LessEqual[y, 4.4e+119], N[(x + a), $MachinePrecision], N[(y * b), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.50000000000000046e158 or 4.4000000000000003e119 < y

   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 b around inf 51.9%

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

   4. Taylor expanded in y around inf 47.3%

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

   if -4.50000000000000046e158 < y < -8.6000000000000003e-265 or 1.10000000000000007e-186 < y < 4.4000000000000003e119

   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 z around 0 71.8%

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

   4. Taylor expanded in b around 0 52.6%

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

   5. Taylor expanded in t around 0 34.1%

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

      1. cancel-sign-sub-inv 34.1%

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

      2. metadata-eval 34.1%

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

      3. *-lft-identity 34.1%

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

      4. +-commutative 34.1%

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

   7. Simplified 34.1%

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

   if -8.6000000000000003e-265 < y < 1.10000000000000007e-186

   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-def 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

   5. Taylor expanded in t around 0 90.8%

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

   6. Taylor expanded in t around inf 42.6%

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

4. Final simplification 39.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{+158}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;y \leq -8.6 \cdot 10^{-265}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{-186}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{+119}:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 83.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.9 \cdot 10^{+35} \lor \neg \left(b \leq 2.85 \cdot 10^{+49}\right):\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(z \cdot \left(1 - y\right) + a \cdot \left(1 - t\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -1.9e+35) (not (<= b 2.85e+49)))
   (+ x (* b (- (+ y t) 2.0)))
   (+ x (+ (* z (- 1.0 y)) (* a (- 1.0 t))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -1.9e+35) || !(b <= 2.85e+49)) {
		tmp = x + (b * ((y + t) - 2.0));
	} else {
		tmp = x + ((z * (1.0 - y)) + (a * (1.0 - t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-1.9d+35)) .or. (.not. (b <= 2.85d+49))) then
        tmp = x + (b * ((y + t) - 2.0d0))
    else
        tmp = x + ((z * (1.0d0 - y)) + (a * (1.0d0 - t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -1.9e+35) || !(b <= 2.85e+49)) {
		tmp = x + (b * ((y + t) - 2.0));
	} else {
		tmp = x + ((z * (1.0 - y)) + (a * (1.0 - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -1.9e+35) or not (b <= 2.85e+49):
		tmp = x + (b * ((y + t) - 2.0))
	else:
		tmp = x + ((z * (1.0 - y)) + (a * (1.0 - t)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -1.9e+35) || !(b <= 2.85e+49))
		tmp = Float64(x + Float64(b * Float64(Float64(y + t) - 2.0)));
	else
		tmp = Float64(x + Float64(Float64(z * Float64(1.0 - y)) + Float64(a * Float64(1.0 - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -1.9e+35) || ~((b <= 2.85e+49)))
		tmp = x + (b * ((y + t) - 2.0));
	else
		tmp = x + ((z * (1.0 - y)) + (a * (1.0 - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -1.9e+35], N[Not[LessEqual[b, 2.85e+49]], $MachinePrecision]], N[(x + N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision] + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.9e35 or 2.8499999999999999e49 < b

   1. Initial program 93.0%

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

   3. Taylor expanded in z around 0 90.1%

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

   4. Taylor expanded in a around 0 82.3%

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

   if -1.9e35 < b < 2.8499999999999999e49

   1. Initial program 100.0%

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

   3. Taylor expanded in b around 0 90.0%

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

4. Final simplification 87.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.9 \cdot 10^{+35} \lor \neg \left(b \leq 2.85 \cdot 10^{+49}\right):\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(z \cdot \left(1 - y\right) + a \cdot \left(1 - t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 48.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -200000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -4.5 \cdot 10^{-182}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq 118:\\ \;\;\;\;b \cdot \left(y - 2\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (- b a))))
   (if (<= t -200000000.0)
     t_1
     (if (<= t -4.5e-182) (+ x a) (if (<= t 118.0) (* b (- y 2.0)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (b - a);
	double tmp;
	if (t <= -200000000.0) {
		tmp = t_1;
	} else if (t <= -4.5e-182) {
		tmp = x + a;
	} else if (t <= 118.0) {
		tmp = b * (y - 2.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (b - a)
    if (t <= (-200000000.0d0)) then
        tmp = t_1
    else if (t <= (-4.5d-182)) then
        tmp = x + a
    else if (t <= 118.0d0) then
        tmp = b * (y - 2.0d0)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (b - a);
	double tmp;
	if (t <= -200000000.0) {
		tmp = t_1;
	} else if (t <= -4.5e-182) {
		tmp = x + a;
	} else if (t <= 118.0) {
		tmp = b * (y - 2.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t * (b - a)
	tmp = 0
	if t <= -200000000.0:
		tmp = t_1
	elif t <= -4.5e-182:
		tmp = x + a
	elif t <= 118.0:
		tmp = b * (y - 2.0)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t * Float64(b - a))
	tmp = 0.0
	if (t <= -200000000.0)
		tmp = t_1;
	elseif (t <= -4.5e-182)
		tmp = Float64(x + a);
	elseif (t <= 118.0)
		tmp = Float64(b * Float64(y - 2.0));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t * (b - a);
	tmp = 0.0;
	if (t <= -200000000.0)
		tmp = t_1;
	elseif (t <= -4.5e-182)
		tmp = x + a;
	elseif (t <= 118.0)
		tmp = b * (y - 2.0);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -200000000.0], t$95$1, If[LessEqual[t, -4.5e-182], N[(x + a), $MachinePrecision], If[LessEqual[t, 118.0], N[(b * N[(y - 2.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2e8 or 118 < t

   1. Initial program 95.5%

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

   3. Taylor expanded in t around inf 66.4%

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

   if -2e8 < t < -4.4999999999999999e-182

   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 77.9%

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

   4. Taylor expanded in b around 0 64.1%

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

   5. Taylor expanded in t around 0 63.2%

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

      1. cancel-sign-sub-inv 63.2%

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

      2. metadata-eval 63.2%

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

      3. *-lft-identity 63.2%

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

      4. +-commutative 63.2%

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

   7. Simplified 63.2%

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

   if -4.4999999999999999e-182 < t < 118

   1. Initial program 98.1%

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

   3. Taylor expanded in b around inf 36.3%

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

   4. Taylor expanded in t around 0 36.3%

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

4. Final simplification 53.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -200000000:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq -4.5 \cdot 10^{-182}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq 118:\\ \;\;\;\;b \cdot \left(y - 2\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 25.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -7.6 \cdot 10^{+35}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;b \leq 9 \cdot 10^{-104}:\\ \;\;\;\;x\\ \mathbf{elif}\;b \leq 3.3 \cdot 10^{+47}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -7.6e+35)
   (* t b)
   (if (<= b 9e-104) x (if (<= b 3.3e+47) z (* t b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -7.6e+35) {
		tmp = t * b;
	} else if (b <= 9e-104) {
		tmp = x;
	} else if (b <= 3.3e+47) {
		tmp = 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 (b <= (-7.6d+35)) then
        tmp = t * b
    else if (b <= 9d-104) then
        tmp = x
    else if (b <= 3.3d+47) then
        tmp = 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 (b <= -7.6e+35) {
		tmp = t * b;
	} else if (b <= 9e-104) {
		tmp = x;
	} else if (b <= 3.3e+47) {
		tmp = z;
	} else {
		tmp = t * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -7.6e+35:
		tmp = t * b
	elif b <= 9e-104:
		tmp = x
	elif b <= 3.3e+47:
		tmp = z
	else:
		tmp = t * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -7.6e+35)
		tmp = Float64(t * b);
	elseif (b <= 9e-104)
		tmp = x;
	elseif (b <= 3.3e+47)
		tmp = 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 (b <= -7.6e+35)
		tmp = t * b;
	elseif (b <= 9e-104)
		tmp = x;
	elseif (b <= 3.3e+47)
		tmp = z;
	else
		tmp = t * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -7.6e+35], N[(t * b), $MachinePrecision], If[LessEqual[b, 9e-104], x, If[LessEqual[b, 3.3e+47], z, N[(t * b), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if b < -7.5999999999999999e35 or 3.2999999999999999e47 < b

   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. Step-by-step derivation

      1. +-commutative 92.9%

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

      2. fma-def 95.9%

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

      3. associate--l+ 95.9%

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

      4. sub-neg 95.9%

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

      5. metadata-eval 95.9%

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

      6. sub-neg 95.9%

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

      7. associate-+l- 95.9%

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

      8. fma-neg 97.0%

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

      9. sub-neg 97.0%

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

      10. metadata-eval 97.0%

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

      11. remove-double-neg 97.0%

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

      12. sub-neg 97.0%

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

      13. metadata-eval 97.0%

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

   3. Simplified 97.0%

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

   5. Taylor expanded in t around 0 93.6%

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

   6. Taylor expanded in t around inf 35.8%

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

   if -7.5999999999999999e35 < b < 8.9999999999999995e-104

   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 24.7%

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

   if 8.9999999999999995e-104 < b < 3.2999999999999999e47

   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 z around inf 48.5%

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

   4. Taylor expanded in y around 0 22.8%

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

4. Final simplification 28.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -7.6 \cdot 10^{+35}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;b \leq 9 \cdot 10^{-104}:\\ \;\;\;\;x\\ \mathbf{elif}\;b \leq 3.3 \cdot 10^{+47}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 13.6% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7 \cdot 10^{-265}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{-182}:\\ \;\;\;\;-2 \cdot b\\ \mathbf{elif}\;y \leq 0.00032:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -7e-265) x (if (<= y 2.4e-182) (* -2.0 b) (if (<= y 0.00032) z a))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -7e-265) {
		tmp = x;
	} else if (y <= 2.4e-182) {
		tmp = -2.0 * b;
	} else if (y <= 0.00032) {
		tmp = z;
	} 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 (y <= (-7d-265)) then
        tmp = x
    else if (y <= 2.4d-182) then
        tmp = (-2.0d0) * b
    else if (y <= 0.00032d0) then
        tmp = z
    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 (y <= -7e-265) {
		tmp = x;
	} else if (y <= 2.4e-182) {
		tmp = -2.0 * b;
	} else if (y <= 0.00032) {
		tmp = z;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -7e-265:
		tmp = x
	elif y <= 2.4e-182:
		tmp = -2.0 * b
	elif y <= 0.00032:
		tmp = z
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -7e-265)
		tmp = x;
	elseif (y <= 2.4e-182)
		tmp = Float64(-2.0 * b);
	elseif (y <= 0.00032)
		tmp = z;
	else
		tmp = a;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -7e-265)
		tmp = x;
	elseif (y <= 2.4e-182)
		tmp = -2.0 * b;
	elseif (y <= 0.00032)
		tmp = z;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -7e-265], x, If[LessEqual[y, 2.4e-182], N[(-2.0 * b), $MachinePrecision], If[LessEqual[y, 0.00032], z, a]]]

Derivation

1. Split input into 4 regimes

2. if y < -7.00000000000000031e-265

   1. Initial program 95.6%

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

   3. Taylor expanded in x around inf 19.7%

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

   if -7.00000000000000031e-265 < y < 2.3999999999999998e-182

   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 inf 68.8%

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

   4. Taylor expanded in t around 0 29.2%

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

   5. Taylor expanded in y around 0 29.2%

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

      1. *-commutative 29.2%

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

   7. Simplified 29.2%

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

   if 2.3999999999999998e-182 < y < 3.20000000000000026e-4

   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 40.6%

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

   4. Taylor expanded in y around 0 38.4%

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

   if 3.20000000000000026e-4 < y

   1. Initial program 96.9%

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

   3. Taylor expanded in a around inf 26.5%

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

   4. Taylor expanded in t around 0 14.1%

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

4. Final simplification 22.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7 \cdot 10^{-265}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{-182}:\\ \;\;\;\;-2 \cdot b\\ \mathbf{elif}\;y \leq 0.00032:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]
5. Add Preprocessing

Alternative 25: 20.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7.5 \cdot 10^{-45}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.55 \cdot 10^{+84}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -7.5e-45) x (if (<= x 1.55e+84) a x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -7.5e-45) {
		tmp = x;
	} else if (x <= 1.55e+84) {
		tmp = a;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= (-7.5d-45)) then
        tmp = x
    else if (x <= 1.55d+84) then
        tmp = a
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -7.5e-45) {
		tmp = x;
	} else if (x <= 1.55e+84) {
		tmp = a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -7.5e-45:
		tmp = x
	elif x <= 1.55e+84:
		tmp = a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -7.5e-45)
		tmp = x;
	elseif (x <= 1.55e+84)
		tmp = a;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -7.5e-45)
		tmp = x;
	elseif (x <= 1.55e+84)
		tmp = a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -7.5e-45], x, If[LessEqual[x, 1.55e+84], a, x]]

Derivation

1. Split input into 2 regimes

2. if x < -7.5000000000000006e-45 or 1.55000000000000001e84 < x

   1. Initial program 97.3%

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

   3. Taylor expanded in x around inf 28.0%

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

   if -7.5000000000000006e-45 < x < 1.55000000000000001e84

   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 a around inf 31.1%

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

   4. Taylor expanded in t around 0 14.5%

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

4. Final simplification 20.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.5 \cdot 10^{-45}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.55 \cdot 10^{+84}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 26: 14.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.8 \cdot 10^{-265}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 0.0026:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -8.8e-265) x (if (<= y 0.0026) z a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -8.8e-265) {
		tmp = x;
	} else if (y <= 0.0026) {
		tmp = z;
	} 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 (y <= (-8.8d-265)) then
        tmp = x
    else if (y <= 0.0026d0) then
        tmp = z
    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 (y <= -8.8e-265) {
		tmp = x;
	} else if (y <= 0.0026) {
		tmp = z;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -8.8e-265:
		tmp = x
	elif y <= 0.0026:
		tmp = z
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -8.8e-265)
		tmp = x;
	elseif (y <= 0.0026)
		tmp = z;
	else
		tmp = a;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -8.8e-265)
		tmp = x;
	elseif (y <= 0.0026)
		tmp = z;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -8.8e-265], x, If[LessEqual[y, 0.0026], z, a]]

Derivation

1. Split input into 3 regimes

2. if y < -8.80000000000000042e-265

   1. Initial program 95.6%

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

   3. Taylor expanded in x around inf 19.7%

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

   if -8.80000000000000042e-265 < y < 0.0025999999999999999

   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 28.5%

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

   4. Taylor expanded in y around 0 27.3%

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

   if 0.0025999999999999999 < y

   1. Initial program 96.9%

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

   3. Taylor expanded in a around inf 26.5%

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

   4. Taylor expanded in t around 0 14.1%

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

4. Final simplification 20.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.8 \cdot 10^{-265}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 0.0026:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]
5. Add Preprocessing

Alternative 27: 11.5% 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 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 a around inf 27.1%

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

4. Taylor expanded in t around 0 11.9%

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

5. Final simplification 11.9%

   \[\leadsto a \]
6. Add Preprocessing

Reproduce

herbie shell --seed 2024020 
(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)))