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

Percentage Accurate: 95.3% → 97.9%

Time: 17.1s

Alternatives: 23

Speedup: 0.5×

• 36.8% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 95.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.9% accurate, 0.5× speedup

Math

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

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1
         (+ (+ (+ x (* z (- 1.0 y))) (* 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 + (z * (1.0 - y))) + (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 + (z * (1.0 - y))) + (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 + (z * (1.0 - y))) + (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(z * Float64(1.0 - y))) + 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 + (z * (1.0 - y))) + (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[(z * N[(1.0 - y), $MachinePrecision]), $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 62.8%

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

4. Final simplification 97.6%

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

Alternative 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 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. Step-by-step derivation

   1. +-commutative 93.7%

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

   2. fma-define 96.1%

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

   3. associate--l+ 96.1%

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

   4. sub-neg 96.1%

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

   5. metadata-eval 96.1%

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

   6. sub-neg 96.1%

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

   7. associate-+l- 96.1%

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

   8. fma-neg 96.9%

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

   9. sub-neg 96.9%

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

   10. metadata-eval 96.9%

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

   11. remove-double-neg 96.9%

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

   12. sub-neg 96.9%

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

   13. metadata-eval 96.9%

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

3. Simplified 96.9%

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

5. Final simplification 96.9%

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

Alternative 3: 37.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t - 2\right)\\ t_2 := a \cdot \left(1 - t\right)\\ \mathbf{if}\;b \leq -1.4 \cdot 10^{+171}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -5.6 \cdot 10^{+73}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;b \leq -3900:\\ \;\;\;\;x + z\\ \mathbf{elif}\;b \leq -4.6 \cdot 10^{-219}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 10^{-258}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;b \leq 1.9 \cdot 10^{-247}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 9.5 \cdot 10^{-147}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;b \leq 1.1 \cdot 10^{+50}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- t 2.0))) (t_2 (* a (- 1.0 t))))
   (if (<= b -1.4e+171)
     t_1
     (if (<= b -5.6e+73)
       (* y b)
       (if (<= b -3900.0)
         (+ x z)
         (if (<= b -4.6e-219)
           t_2
           (if (<= b 1e-258)
             (+ x z)
             (if (<= b 1.9e-247)
               t_2
               (if (<= b 9.5e-147)
                 (* y (- z))
                 (if (<= b 1.1e+50) t_2 t_1))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (t - 2.0);
	double t_2 = a * (1.0 - t);
	double tmp;
	if (b <= -1.4e+171) {
		tmp = t_1;
	} else if (b <= -5.6e+73) {
		tmp = y * b;
	} else if (b <= -3900.0) {
		tmp = x + z;
	} else if (b <= -4.6e-219) {
		tmp = t_2;
	} else if (b <= 1e-258) {
		tmp = x + z;
	} else if (b <= 1.9e-247) {
		tmp = t_2;
	} else if (b <= 9.5e-147) {
		tmp = y * -z;
	} else if (b <= 1.1e+50) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = b * (t - 2.0d0)
    t_2 = a * (1.0d0 - t)
    if (b <= (-1.4d+171)) then
        tmp = t_1
    else if (b <= (-5.6d+73)) then
        tmp = y * b
    else if (b <= (-3900.0d0)) then
        tmp = x + z
    else if (b <= (-4.6d-219)) then
        tmp = t_2
    else if (b <= 1d-258) then
        tmp = x + z
    else if (b <= 1.9d-247) then
        tmp = t_2
    else if (b <= 9.5d-147) then
        tmp = y * -z
    else if (b <= 1.1d+50) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (t - 2.0);
	double t_2 = a * (1.0 - t);
	double tmp;
	if (b <= -1.4e+171) {
		tmp = t_1;
	} else if (b <= -5.6e+73) {
		tmp = y * b;
	} else if (b <= -3900.0) {
		tmp = x + z;
	} else if (b <= -4.6e-219) {
		tmp = t_2;
	} else if (b <= 1e-258) {
		tmp = x + z;
	} else if (b <= 1.9e-247) {
		tmp = t_2;
	} else if (b <= 9.5e-147) {
		tmp = y * -z;
	} else if (b <= 1.1e+50) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * (t - 2.0)
	t_2 = a * (1.0 - t)
	tmp = 0
	if b <= -1.4e+171:
		tmp = t_1
	elif b <= -5.6e+73:
		tmp = y * b
	elif b <= -3900.0:
		tmp = x + z
	elif b <= -4.6e-219:
		tmp = t_2
	elif b <= 1e-258:
		tmp = x + z
	elif b <= 1.9e-247:
		tmp = t_2
	elif b <= 9.5e-147:
		tmp = y * -z
	elif b <= 1.1e+50:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(t - 2.0))
	t_2 = Float64(a * Float64(1.0 - t))
	tmp = 0.0
	if (b <= -1.4e+171)
		tmp = t_1;
	elseif (b <= -5.6e+73)
		tmp = Float64(y * b);
	elseif (b <= -3900.0)
		tmp = Float64(x + z);
	elseif (b <= -4.6e-219)
		tmp = t_2;
	elseif (b <= 1e-258)
		tmp = Float64(x + z);
	elseif (b <= 1.9e-247)
		tmp = t_2;
	elseif (b <= 9.5e-147)
		tmp = Float64(y * Float64(-z));
	elseif (b <= 1.1e+50)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * (t - 2.0);
	t_2 = a * (1.0 - t);
	tmp = 0.0;
	if (b <= -1.4e+171)
		tmp = t_1;
	elseif (b <= -5.6e+73)
		tmp = y * b;
	elseif (b <= -3900.0)
		tmp = x + z;
	elseif (b <= -4.6e-219)
		tmp = t_2;
	elseif (b <= 1e-258)
		tmp = x + z;
	elseif (b <= 1.9e-247)
		tmp = t_2;
	elseif (b <= 9.5e-147)
		tmp = y * -z;
	elseif (b <= 1.1e+50)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(t - 2.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.4e+171], t$95$1, If[LessEqual[b, -5.6e+73], N[(y * b), $MachinePrecision], If[LessEqual[b, -3900.0], N[(x + z), $MachinePrecision], If[LessEqual[b, -4.6e-219], t$95$2, If[LessEqual[b, 1e-258], N[(x + z), $MachinePrecision], If[LessEqual[b, 1.9e-247], t$95$2, If[LessEqual[b, 9.5e-147], N[(y * (-z)), $MachinePrecision], If[LessEqual[b, 1.1e+50], t$95$2, t$95$1]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -1.40000000000000002e171 or 1.10000000000000008e50 < b

   1. Initial program 86.2%

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

   3. Taylor expanded in b around inf 80.1%

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

   4. Taylor expanded in y around 0 59.3%

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

   if -1.40000000000000002e171 < b < -5.60000000000000016e73

   1. Initial program 86.4%

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

   3. Taylor expanded in z around 0 86.7%

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

   4. Taylor expanded in y around inf 52.7%

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

   if -5.60000000000000016e73 < b < -3900 or -4.59999999999999977e-219 < b < 9.99999999999999954e-259

   1. Initial program 97.6%

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

   3. Taylor expanded in y around 0 97.6%

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

      1. associate--l+ 97.6%

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

      2. sub-neg 97.6%

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

      3. +-commutative 97.6%

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

      4. fma-define 97.6%

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

      5. sub-neg 97.6%

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

      6. metadata-eval 97.6%

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

      7. sub-neg 97.6%

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

      8. metadata-eval 97.6%

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

      9. *-commutative 97.6%

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

      10. distribute-neg-in 97.6%

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

      11. neg-mul-1 97.6%

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

      12. remove-double-neg 97.6%

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

      13. *-commutative 97.6%

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

      14. distribute-rgt-neg-in 97.6%

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

      15. distribute-neg-in 97.6%

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

      16. metadata-eval 97.6%

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

      17. +-commutative 97.6%

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

      18. sub-neg 97.6%

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

   5. Simplified 97.6%

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

   6. Taylor expanded in t around inf 83.3%

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

      1. *-commutative 83.3%

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

   8. Simplified 83.3%

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

   9. Taylor expanded in z around inf 57.0%

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

   if -3900 < b < -4.59999999999999977e-219 or 9.99999999999999954e-259 < b < 1.89999999999999994e-247 or 9.49999999999999986e-147 < b < 1.10000000000000008e50

   1. Initial program 100.0%

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

   3. Taylor expanded in a around inf 44.0%

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

   if 1.89999999999999994e-247 < b < 9.49999999999999986e-147

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 63.0%

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

   4. Taylor expanded in b around 0 58.9%

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

      1. mul-1-neg 58.9%

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

      2. distribute-rgt-neg-out 58.9%

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

   6. Simplified 58.9%

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

4. Final simplification 52.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.4 \cdot 10^{+171}:\\ \;\;\;\;b \cdot \left(t - 2\right)\\ \mathbf{elif}\;b \leq -5.6 \cdot 10^{+73}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;b \leq -3900:\\ \;\;\;\;x + z\\ \mathbf{elif}\;b \leq -4.6 \cdot 10^{-219}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 10^{-258}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;b \leq 1.9 \cdot 10^{-247}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 9.5 \cdot 10^{-147}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;b \leq 1.1 \cdot 10^{+50}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t - 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 54.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z + \left(x + a\right)\\ t_2 := y \cdot \left(b - z\right)\\ t_3 := b \cdot \left(t - 2\right)\\ \mathbf{if}\;y \leq -1.08 \cdot 10^{+46}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -3 \cdot 10^{-84}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;y \leq -8 \cdot 10^{-309}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{-286}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{-274}:\\ \;\;\;\;x + t \cdot b\\ \mathbf{elif}\;y \leq 4.65 \cdot 10^{-228}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{-186}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{+34}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ z (+ x a))) (t_2 (* y (- b z))) (t_3 (* b (- t 2.0))))
   (if (<= y -1.08e+46)
     t_2
     (if (<= y -3e-84)
       (* t (- b a))
       (if (<= y -8e-309)
         t_1
         (if (<= y 4.5e-286)
           t_3
           (if (<= y 2.7e-274)
             (+ x (* t b))
             (if (<= y 4.65e-228)
               (* a (- 1.0 t))
               (if (<= y 8.5e-186) t_3 (if (<= y 2.4e+34) t_1 t_2))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z + (x + a);
	double t_2 = y * (b - z);
	double t_3 = b * (t - 2.0);
	double tmp;
	if (y <= -1.08e+46) {
		tmp = t_2;
	} else if (y <= -3e-84) {
		tmp = t * (b - a);
	} else if (y <= -8e-309) {
		tmp = t_1;
	} else if (y <= 4.5e-286) {
		tmp = t_3;
	} else if (y <= 2.7e-274) {
		tmp = x + (t * b);
	} else if (y <= 4.65e-228) {
		tmp = a * (1.0 - t);
	} else if (y <= 8.5e-186) {
		tmp = t_3;
	} else if (y <= 2.4e+34) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = z + (x + a)
    t_2 = y * (b - z)
    t_3 = b * (t - 2.0d0)
    if (y <= (-1.08d+46)) then
        tmp = t_2
    else if (y <= (-3d-84)) then
        tmp = t * (b - a)
    else if (y <= (-8d-309)) then
        tmp = t_1
    else if (y <= 4.5d-286) then
        tmp = t_3
    else if (y <= 2.7d-274) then
        tmp = x + (t * b)
    else if (y <= 4.65d-228) then
        tmp = a * (1.0d0 - t)
    else if (y <= 8.5d-186) then
        tmp = t_3
    else if (y <= 2.4d+34) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z + (x + a);
	double t_2 = y * (b - z);
	double t_3 = b * (t - 2.0);
	double tmp;
	if (y <= -1.08e+46) {
		tmp = t_2;
	} else if (y <= -3e-84) {
		tmp = t * (b - a);
	} else if (y <= -8e-309) {
		tmp = t_1;
	} else if (y <= 4.5e-286) {
		tmp = t_3;
	} else if (y <= 2.7e-274) {
		tmp = x + (t * b);
	} else if (y <= 4.65e-228) {
		tmp = a * (1.0 - t);
	} else if (y <= 8.5e-186) {
		tmp = t_3;
	} else if (y <= 2.4e+34) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z + (x + a)
	t_2 = y * (b - z)
	t_3 = b * (t - 2.0)
	tmp = 0
	if y <= -1.08e+46:
		tmp = t_2
	elif y <= -3e-84:
		tmp = t * (b - a)
	elif y <= -8e-309:
		tmp = t_1
	elif y <= 4.5e-286:
		tmp = t_3
	elif y <= 2.7e-274:
		tmp = x + (t * b)
	elif y <= 4.65e-228:
		tmp = a * (1.0 - t)
	elif y <= 8.5e-186:
		tmp = t_3
	elif y <= 2.4e+34:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z + Float64(x + a))
	t_2 = Float64(y * Float64(b - z))
	t_3 = Float64(b * Float64(t - 2.0))
	tmp = 0.0
	if (y <= -1.08e+46)
		tmp = t_2;
	elseif (y <= -3e-84)
		tmp = Float64(t * Float64(b - a));
	elseif (y <= -8e-309)
		tmp = t_1;
	elseif (y <= 4.5e-286)
		tmp = t_3;
	elseif (y <= 2.7e-274)
		tmp = Float64(x + Float64(t * b));
	elseif (y <= 4.65e-228)
		tmp = Float64(a * Float64(1.0 - t));
	elseif (y <= 8.5e-186)
		tmp = t_3;
	elseif (y <= 2.4e+34)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z + (x + a);
	t_2 = y * (b - z);
	t_3 = b * (t - 2.0);
	tmp = 0.0;
	if (y <= -1.08e+46)
		tmp = t_2;
	elseif (y <= -3e-84)
		tmp = t * (b - a);
	elseif (y <= -8e-309)
		tmp = t_1;
	elseif (y <= 4.5e-286)
		tmp = t_3;
	elseif (y <= 2.7e-274)
		tmp = x + (t * b);
	elseif (y <= 4.65e-228)
		tmp = a * (1.0 - t);
	elseif (y <= 8.5e-186)
		tmp = t_3;
	elseif (y <= 2.4e+34)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z + N[(x + a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(b * N[(t - 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.08e+46], t$95$2, If[LessEqual[y, -3e-84], N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -8e-309], t$95$1, If[LessEqual[y, 4.5e-286], t$95$3, If[LessEqual[y, 2.7e-274], N[(x + N[(t * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.65e-228], N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 8.5e-186], t$95$3, If[LessEqual[y, 2.4e+34], t$95$1, t$95$2]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if y < -1.07999999999999994e46 or 2.39999999999999987e34 < y

   1. Initial program 89.3%

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

   3. Taylor expanded in y around inf 70.0%

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

   if -1.07999999999999994e46 < y < -3.0000000000000001e-84

   1. Initial program 95.8%

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

   3. Taylor expanded in t around inf 67.3%

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

   if -3.0000000000000001e-84 < y < -8.0000000000000003e-309 or 8.4999999999999994e-186 < y < 2.39999999999999987e34

   1. Initial program 97.8%

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

   3. Taylor expanded in y around 0 97.8%

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

      1. associate--l+ 97.8%

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

      2. sub-neg 97.8%

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

      3. +-commutative 97.8%

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

      4. fma-define 97.8%

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

      5. sub-neg 97.8%

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

      6. metadata-eval 97.8%

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

      7. sub-neg 97.8%

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

      8. metadata-eval 97.8%

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

      9. *-commutative 97.8%

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

      10. distribute-neg-in 97.8%

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

      11. neg-mul-1 97.8%

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

      12. remove-double-neg 97.8%

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

      13. *-commutative 97.8%

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

      14. distribute-rgt-neg-in 97.8%

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

      15. distribute-neg-in 97.8%

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

      16. metadata-eval 97.8%

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

      17. +-commutative 97.8%

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

      18. sub-neg 97.8%

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

   5. Simplified 97.8%

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

   6. Taylor expanded in t around inf 82.5%

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

      1. *-commutative 82.5%

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

   8. Simplified 82.5%

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

   9. Taylor expanded in t around 0 58.9%

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

       1. associate-+r+ 58.9%

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

       2. +-commutative 58.9%

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

   11. Simplified 58.9%

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

   if -8.0000000000000003e-309 < y < 4.50000000000000005e-286 or 4.65000000000000028e-228 < y < 8.4999999999999994e-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 66.7%

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

   4. Taylor expanded in y around 0 66.7%

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

   if 4.50000000000000005e-286 < y < 2.7e-274

   1. Initial program 66.7%

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

   3. Taylor expanded in y around 0 66.7%

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

      1. associate--l+ 66.7%

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

      2. sub-neg 66.7%

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

      3. +-commutative 66.7%

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

      4. fma-define 66.7%

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

      5. sub-neg 66.7%

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

      6. metadata-eval 66.7%

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

      7. sub-neg 66.7%

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

      8. metadata-eval 66.7%

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

      9. *-commutative 66.7%

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

      10. distribute-neg-in 66.7%

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

      11. neg-mul-1 66.7%

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

      12. remove-double-neg 66.7%

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

      13. *-commutative 66.7%

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

      14. distribute-rgt-neg-in 66.7%

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

      15. distribute-neg-in 66.7%

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

      16. metadata-eval 66.7%

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

      17. +-commutative 66.7%

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

      18. sub-neg 66.7%

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

   5. Simplified 66.7%

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

   6. Taylor expanded in a around 0 100.0%

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

      1. associate-+r+ 100.0%

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

      2. sub-neg 100.0%

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

      3. metadata-eval 100.0%

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

      4. associate-+r+ 100.0%

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

      5. +-commutative 100.0%

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

      6. fma-define 100.0%

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

   8. Simplified 100.0%

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

   9. Taylor expanded in t around inf 100.0%

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

   if 2.7e-274 < y < 4.65000000000000028e-228

   1. Initial program 100.0%

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

   3. Taylor expanded in a around inf 64.4%

      \[\leadsto \color{blue}{a \cdot \left(1 - t\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 65.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.08 \cdot 10^{+46}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;y \leq -3 \cdot 10^{-84}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;y \leq -8 \cdot 10^{-309}:\\ \;\;\;\;z + \left(x + a\right)\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{-286}:\\ \;\;\;\;b \cdot \left(t - 2\right)\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{-274}:\\ \;\;\;\;x + t \cdot b\\ \mathbf{elif}\;y \leq 4.65 \cdot 10^{-228}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{-186}:\\ \;\;\;\;b \cdot \left(t - 2\right)\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{+34}:\\ \;\;\;\;z + \left(x + a\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 54.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z + \left(x + a\right)\\ t_2 := b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{if}\;b \leq -1.3 \cdot 10^{+59}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -780:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -1.75 \cdot 10^{-66}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;b \leq 1.7 \cdot 10^{-247}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 9.8 \cdot 10^{-147}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq 2.7 \cdot 10^{+31}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1.3 \cdot 10^{+50}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ z (+ x a))) (t_2 (* b (- (+ y t) 2.0))))
   (if (<= b -1.3e+59)
     t_2
     (if (<= b -780.0)
       t_1
       (if (<= b -1.75e-66)
         (* t (- b a))
         (if (<= b 1.7e-247)
           t_1
           (if (<= b 9.8e-147)
             (* z (- 1.0 y))
             (if (<= b 2.7e+31)
               t_1
               (if (<= b 1.3e+50) (* y (- b z)) t_2)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z + (x + a);
	double t_2 = b * ((y + t) - 2.0);
	double tmp;
	if (b <= -1.3e+59) {
		tmp = t_2;
	} else if (b <= -780.0) {
		tmp = t_1;
	} else if (b <= -1.75e-66) {
		tmp = t * (b - a);
	} else if (b <= 1.7e-247) {
		tmp = t_1;
	} else if (b <= 9.8e-147) {
		tmp = z * (1.0 - y);
	} else if (b <= 2.7e+31) {
		tmp = t_1;
	} else if (b <= 1.3e+50) {
		tmp = y * (b - z);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = z + (x + a)
    t_2 = b * ((y + t) - 2.0d0)
    if (b <= (-1.3d+59)) then
        tmp = t_2
    else if (b <= (-780.0d0)) then
        tmp = t_1
    else if (b <= (-1.75d-66)) then
        tmp = t * (b - a)
    else if (b <= 1.7d-247) then
        tmp = t_1
    else if (b <= 9.8d-147) then
        tmp = z * (1.0d0 - y)
    else if (b <= 2.7d+31) then
        tmp = t_1
    else if (b <= 1.3d+50) then
        tmp = y * (b - z)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z + (x + a);
	double t_2 = b * ((y + t) - 2.0);
	double tmp;
	if (b <= -1.3e+59) {
		tmp = t_2;
	} else if (b <= -780.0) {
		tmp = t_1;
	} else if (b <= -1.75e-66) {
		tmp = t * (b - a);
	} else if (b <= 1.7e-247) {
		tmp = t_1;
	} else if (b <= 9.8e-147) {
		tmp = z * (1.0 - y);
	} else if (b <= 2.7e+31) {
		tmp = t_1;
	} else if (b <= 1.3e+50) {
		tmp = y * (b - z);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z + (x + a)
	t_2 = b * ((y + t) - 2.0)
	tmp = 0
	if b <= -1.3e+59:
		tmp = t_2
	elif b <= -780.0:
		tmp = t_1
	elif b <= -1.75e-66:
		tmp = t * (b - a)
	elif b <= 1.7e-247:
		tmp = t_1
	elif b <= 9.8e-147:
		tmp = z * (1.0 - y)
	elif b <= 2.7e+31:
		tmp = t_1
	elif b <= 1.3e+50:
		tmp = y * (b - z)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z + Float64(x + a))
	t_2 = Float64(b * Float64(Float64(y + t) - 2.0))
	tmp = 0.0
	if (b <= -1.3e+59)
		tmp = t_2;
	elseif (b <= -780.0)
		tmp = t_1;
	elseif (b <= -1.75e-66)
		tmp = Float64(t * Float64(b - a));
	elseif (b <= 1.7e-247)
		tmp = t_1;
	elseif (b <= 9.8e-147)
		tmp = Float64(z * Float64(1.0 - y));
	elseif (b <= 2.7e+31)
		tmp = t_1;
	elseif (b <= 1.3e+50)
		tmp = Float64(y * Float64(b - z));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z + (x + a);
	t_2 = b * ((y + t) - 2.0);
	tmp = 0.0;
	if (b <= -1.3e+59)
		tmp = t_2;
	elseif (b <= -780.0)
		tmp = t_1;
	elseif (b <= -1.75e-66)
		tmp = t * (b - a);
	elseif (b <= 1.7e-247)
		tmp = t_1;
	elseif (b <= 9.8e-147)
		tmp = z * (1.0 - y);
	elseif (b <= 2.7e+31)
		tmp = t_1;
	elseif (b <= 1.3e+50)
		tmp = y * (b - z);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z + N[(x + a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.3e+59], t$95$2, If[LessEqual[b, -780.0], t$95$1, If[LessEqual[b, -1.75e-66], N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.7e-247], t$95$1, If[LessEqual[b, 9.8e-147], N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.7e+31], t$95$1, If[LessEqual[b, 1.3e+50], N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -1.3e59 or 1.3000000000000001e50 < b

   1. Initial program 86.6%

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

   3. Taylor expanded in b around inf 75.4%

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

   if -1.3e59 < b < -780 or -1.75e-66 < b < 1.7000000000000001e-247 or 9.8000000000000001e-147 < b < 2.69999999999999986e31

   1. Initial program 99.0%

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

   3. Taylor expanded in y around 0 99.1%

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

      1. associate--l+ 99.1%

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

      2. sub-neg 99.1%

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

      3. +-commutative 99.1%

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

      4. fma-define 99.1%

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

      5. sub-neg 99.1%

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

      6. metadata-eval 99.1%

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

      7. sub-neg 99.1%

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

      8. metadata-eval 99.1%

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

      9. *-commutative 99.1%

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

      10. distribute-neg-in 99.1%

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

      11. neg-mul-1 99.1%

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

      12. remove-double-neg 99.1%

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

      13. *-commutative 99.1%

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

      14. distribute-rgt-neg-in 99.1%

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

      15. distribute-neg-in 99.1%

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

      16. metadata-eval 99.1%

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

      17. +-commutative 99.1%

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

      18. sub-neg 99.1%

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

   5. Simplified 99.1%

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

   6. Taylor expanded in t around inf 80.1%

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

      1. *-commutative 80.1%

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

   8. Simplified 80.1%

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

   9. Taylor expanded in t around 0 58.7%

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

       1. associate-+r+ 58.7%

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

       2. +-commutative 58.7%

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

   11. Simplified 58.7%

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

   if -780 < b < -1.75e-66

   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 63.7%

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

   if 1.7000000000000001e-247 < b < 9.8000000000000001e-147

   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 65.6%

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

   if 2.69999999999999986e31 < b < 1.3000000000000001e50

   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 62.7%

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

4. Final simplification 66.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.3 \cdot 10^{+59}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{elif}\;b \leq -780:\\ \;\;\;\;z + \left(x + a\right)\\ \mathbf{elif}\;b \leq -1.75 \cdot 10^{-66}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;b \leq 1.7 \cdot 10^{-247}:\\ \;\;\;\;z + \left(x + a\right)\\ \mathbf{elif}\;b \leq 9.8 \cdot 10^{-147}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq 2.7 \cdot 10^{+31}:\\ \;\;\;\;z + \left(x + a\right)\\ \mathbf{elif}\;b \leq 1.3 \cdot 10^{+50}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 36.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(1 - t\right)\\ t_2 := y \cdot \left(-z\right)\\ \mathbf{if}\;y \leq -5.7 \cdot 10^{+149}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -2.5 \cdot 10^{+82}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;y \leq -9.8 \cdot 10^{-95}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -7.5 \cdot 10^{-281}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;y \leq 4.3 \cdot 10^{-89}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{-58}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;y \leq 2.25 \cdot 10^{+35}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (- 1.0 t))) (t_2 (* y (- z))))
   (if (<= y -5.7e+149)
     t_2
     (if (<= y -2.5e+82)
       (* y b)
       (if (<= y -9.8e-95)
         t_1
         (if (<= y -7.5e-281)
           (+ x z)
           (if (<= y 4.3e-89)
             t_1
             (if (<= y 2.6e-58) (+ x z) (if (<= y 2.25e+35) t_1 t_2)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double t_2 = y * -z;
	double tmp;
	if (y <= -5.7e+149) {
		tmp = t_2;
	} else if (y <= -2.5e+82) {
		tmp = y * b;
	} else if (y <= -9.8e-95) {
		tmp = t_1;
	} else if (y <= -7.5e-281) {
		tmp = x + z;
	} else if (y <= 4.3e-89) {
		tmp = t_1;
	} else if (y <= 2.6e-58) {
		tmp = x + z;
	} else if (y <= 2.25e+35) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a * (1.0d0 - t)
    t_2 = y * -z
    if (y <= (-5.7d+149)) then
        tmp = t_2
    else if (y <= (-2.5d+82)) then
        tmp = y * b
    else if (y <= (-9.8d-95)) then
        tmp = t_1
    else if (y <= (-7.5d-281)) then
        tmp = x + z
    else if (y <= 4.3d-89) then
        tmp = t_1
    else if (y <= 2.6d-58) then
        tmp = x + z
    else if (y <= 2.25d+35) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double t_2 = y * -z;
	double tmp;
	if (y <= -5.7e+149) {
		tmp = t_2;
	} else if (y <= -2.5e+82) {
		tmp = y * b;
	} else if (y <= -9.8e-95) {
		tmp = t_1;
	} else if (y <= -7.5e-281) {
		tmp = x + z;
	} else if (y <= 4.3e-89) {
		tmp = t_1;
	} else if (y <= 2.6e-58) {
		tmp = x + z;
	} else if (y <= 2.25e+35) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (1.0 - t)
	t_2 = y * -z
	tmp = 0
	if y <= -5.7e+149:
		tmp = t_2
	elif y <= -2.5e+82:
		tmp = y * b
	elif y <= -9.8e-95:
		tmp = t_1
	elif y <= -7.5e-281:
		tmp = x + z
	elif y <= 4.3e-89:
		tmp = t_1
	elif y <= 2.6e-58:
		tmp = x + z
	elif y <= 2.25e+35:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(1.0 - t))
	t_2 = Float64(y * Float64(-z))
	tmp = 0.0
	if (y <= -5.7e+149)
		tmp = t_2;
	elseif (y <= -2.5e+82)
		tmp = Float64(y * b);
	elseif (y <= -9.8e-95)
		tmp = t_1;
	elseif (y <= -7.5e-281)
		tmp = Float64(x + z);
	elseif (y <= 4.3e-89)
		tmp = t_1;
	elseif (y <= 2.6e-58)
		tmp = Float64(x + z);
	elseif (y <= 2.25e+35)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (1.0 - t);
	t_2 = y * -z;
	tmp = 0.0;
	if (y <= -5.7e+149)
		tmp = t_2;
	elseif (y <= -2.5e+82)
		tmp = y * b;
	elseif (y <= -9.8e-95)
		tmp = t_1;
	elseif (y <= -7.5e-281)
		tmp = x + z;
	elseif (y <= 4.3e-89)
		tmp = t_1;
	elseif (y <= 2.6e-58)
		tmp = x + z;
	elseif (y <= 2.25e+35)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * (-z)), $MachinePrecision]}, If[LessEqual[y, -5.7e+149], t$95$2, If[LessEqual[y, -2.5e+82], N[(y * b), $MachinePrecision], If[LessEqual[y, -9.8e-95], t$95$1, If[LessEqual[y, -7.5e-281], N[(x + z), $MachinePrecision], If[LessEqual[y, 4.3e-89], t$95$1, If[LessEqual[y, 2.6e-58], N[(x + z), $MachinePrecision], If[LessEqual[y, 2.25e+35], t$95$1, t$95$2]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -5.69999999999999965e149 or 2.2499999999999998e35 < y

   1. Initial program 89.1%

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

   3. Taylor expanded in y around inf 73.8%

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

   4. Taylor expanded in b around 0 48.4%

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

      1. mul-1-neg 48.4%

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

      2. distribute-rgt-neg-out 48.4%

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

   6. Simplified 48.4%

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

   if -5.69999999999999965e149 < y < -2.50000000000000008e82

   1. Initial program 85.6%

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

   3. Taylor expanded in z around 0 85.6%

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

   4. Taylor expanded in y around inf 64.3%

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

   if -2.50000000000000008e82 < y < -9.8e-95 or -7.49999999999999968e-281 < y < 4.29999999999999987e-89 or 2.60000000000000007e-58 < y < 2.2499999999999998e35

   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 45.3%

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

   if -9.8e-95 < y < -7.49999999999999968e-281 or 4.29999999999999987e-89 < y < 2.60000000000000007e-58

   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 y around 0 97.7%

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

      1. associate--l+ 97.7%

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

      2. sub-neg 97.7%

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

      3. +-commutative 97.7%

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

      4. fma-define 97.7%

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

      5. sub-neg 97.7%

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

      6. metadata-eval 97.7%

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

      7. sub-neg 97.7%

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

      8. metadata-eval 97.7%

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

      9. *-commutative 97.7%

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

      10. distribute-neg-in 97.7%

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

      11. neg-mul-1 97.7%

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

      12. remove-double-neg 97.7%

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

      13. *-commutative 97.7%

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

      14. distribute-rgt-neg-in 97.7%

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

      15. distribute-neg-in 97.7%

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

      16. metadata-eval 97.7%

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

      17. +-commutative 97.7%

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

      18. sub-neg 97.7%

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

   5. Simplified 97.7%

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

   6. Taylor expanded in t around inf 80.5%

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

      1. *-commutative 80.5%

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

   8. Simplified 80.5%

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

   9. Taylor expanded in z around inf 54.8%

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

4. Final simplification 49.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.7 \cdot 10^{+149}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;y \leq -2.5 \cdot 10^{+82}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;y \leq -9.8 \cdot 10^{-95}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;y \leq -7.5 \cdot 10^{-281}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;y \leq 4.3 \cdot 10^{-89}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{-58}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;y \leq 2.25 \cdot 10^{+35}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 38.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(1 - t\right)\\ \mathbf{if}\;b \leq -1.28 \cdot 10^{+70}:\\ \;\;\;\;b \cdot \left(y - 2\right)\\ \mathbf{elif}\;b \leq -17000:\\ \;\;\;\;x + z\\ \mathbf{elif}\;b \leq -2.1 \cdot 10^{-218}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1.02 \cdot 10^{-258}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;b \leq 3 \cdot 10^{-247}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 9.5 \cdot 10^{-147}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;b \leq 4.8 \cdot 10^{+50}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t - 2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (- 1.0 t))))
   (if (<= b -1.28e+70)
     (* b (- y 2.0))
     (if (<= b -17000.0)
       (+ x z)
       (if (<= b -2.1e-218)
         t_1
         (if (<= b 1.02e-258)
           (+ x z)
           (if (<= b 3e-247)
             t_1
             (if (<= b 9.5e-147)
               (* y (- z))
               (if (<= b 4.8e+50) t_1 (* b (- t 2.0)))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double tmp;
	if (b <= -1.28e+70) {
		tmp = b * (y - 2.0);
	} else if (b <= -17000.0) {
		tmp = x + z;
	} else if (b <= -2.1e-218) {
		tmp = t_1;
	} else if (b <= 1.02e-258) {
		tmp = x + z;
	} else if (b <= 3e-247) {
		tmp = t_1;
	} else if (b <= 9.5e-147) {
		tmp = y * -z;
	} else if (b <= 4.8e+50) {
		tmp = t_1;
	} else {
		tmp = b * (t - 2.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (1.0d0 - t)
    if (b <= (-1.28d+70)) then
        tmp = b * (y - 2.0d0)
    else if (b <= (-17000.0d0)) then
        tmp = x + z
    else if (b <= (-2.1d-218)) then
        tmp = t_1
    else if (b <= 1.02d-258) then
        tmp = x + z
    else if (b <= 3d-247) then
        tmp = t_1
    else if (b <= 9.5d-147) then
        tmp = y * -z
    else if (b <= 4.8d+50) then
        tmp = t_1
    else
        tmp = b * (t - 2.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double tmp;
	if (b <= -1.28e+70) {
		tmp = b * (y - 2.0);
	} else if (b <= -17000.0) {
		tmp = x + z;
	} else if (b <= -2.1e-218) {
		tmp = t_1;
	} else if (b <= 1.02e-258) {
		tmp = x + z;
	} else if (b <= 3e-247) {
		tmp = t_1;
	} else if (b <= 9.5e-147) {
		tmp = y * -z;
	} else if (b <= 4.8e+50) {
		tmp = t_1;
	} else {
		tmp = b * (t - 2.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (1.0 - t)
	tmp = 0
	if b <= -1.28e+70:
		tmp = b * (y - 2.0)
	elif b <= -17000.0:
		tmp = x + z
	elif b <= -2.1e-218:
		tmp = t_1
	elif b <= 1.02e-258:
		tmp = x + z
	elif b <= 3e-247:
		tmp = t_1
	elif b <= 9.5e-147:
		tmp = y * -z
	elif b <= 4.8e+50:
		tmp = t_1
	else:
		tmp = b * (t - 2.0)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(1.0 - t))
	tmp = 0.0
	if (b <= -1.28e+70)
		tmp = Float64(b * Float64(y - 2.0));
	elseif (b <= -17000.0)
		tmp = Float64(x + z);
	elseif (b <= -2.1e-218)
		tmp = t_1;
	elseif (b <= 1.02e-258)
		tmp = Float64(x + z);
	elseif (b <= 3e-247)
		tmp = t_1;
	elseif (b <= 9.5e-147)
		tmp = Float64(y * Float64(-z));
	elseif (b <= 4.8e+50)
		tmp = t_1;
	else
		tmp = Float64(b * Float64(t - 2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (1.0 - t);
	tmp = 0.0;
	if (b <= -1.28e+70)
		tmp = b * (y - 2.0);
	elseif (b <= -17000.0)
		tmp = x + z;
	elseif (b <= -2.1e-218)
		tmp = t_1;
	elseif (b <= 1.02e-258)
		tmp = x + z;
	elseif (b <= 3e-247)
		tmp = t_1;
	elseif (b <= 9.5e-147)
		tmp = y * -z;
	elseif (b <= 4.8e+50)
		tmp = t_1;
	else
		tmp = b * (t - 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.28e+70], N[(b * N[(y - 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -17000.0], N[(x + z), $MachinePrecision], If[LessEqual[b, -2.1e-218], t$95$1, If[LessEqual[b, 1.02e-258], N[(x + z), $MachinePrecision], If[LessEqual[b, 3e-247], t$95$1, If[LessEqual[b, 9.5e-147], N[(y * (-z)), $MachinePrecision], If[LessEqual[b, 4.8e+50], t$95$1, N[(b * N[(t - 2.0), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -1.27999999999999994e70

   1. Initial program 87.9%

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

   3. Taylor expanded in b around inf 75.8%

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

   4. Taylor expanded in t around 0 62.8%

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

   if -1.27999999999999994e70 < b < -17000 or -2.09999999999999994e-218 < b < 1.02e-258

   1. Initial program 97.6%

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

   3. Taylor expanded in y around 0 97.6%

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

      1. associate--l+ 97.6%

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

      2. sub-neg 97.6%

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

      3. +-commutative 97.6%

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

      4. fma-define 97.6%

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

      5. sub-neg 97.6%

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

      6. metadata-eval 97.6%

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

      7. sub-neg 97.6%

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

      8. metadata-eval 97.6%

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

      9. *-commutative 97.6%

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

      10. distribute-neg-in 97.6%

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

      11. neg-mul-1 97.6%

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

      12. remove-double-neg 97.6%

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

      13. *-commutative 97.6%

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

      14. distribute-rgt-neg-in 97.6%

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

      15. distribute-neg-in 97.6%

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

      16. metadata-eval 97.6%

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

      17. +-commutative 97.6%

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

      18. sub-neg 97.6%

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

   5. Simplified 97.6%

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

   6. Taylor expanded in t around inf 83.3%

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

      1. *-commutative 83.3%

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

   8. Simplified 83.3%

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

   9. Taylor expanded in z around inf 57.0%

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

   if -17000 < b < -2.09999999999999994e-218 or 1.02e-258 < b < 2.9999999999999997e-247 or 9.49999999999999986e-147 < b < 4.8000000000000004e50

   1. Initial program 100.0%

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

   3. Taylor expanded in a around inf 44.0%

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

   if 2.9999999999999997e-247 < b < 9.49999999999999986e-147

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 63.0%

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

   4. Taylor expanded in b around 0 58.9%

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

      1. mul-1-neg 58.9%

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

      2. distribute-rgt-neg-out 58.9%

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

   6. Simplified 58.9%

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

   if 4.8000000000000004e50 < b

   1. Initial program 84.3%

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

   3. Taylor expanded in b around inf 77.5%

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

   4. Taylor expanded in y around 0 55.5%

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

4. Final simplification 53.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.28 \cdot 10^{+70}:\\ \;\;\;\;b \cdot \left(y - 2\right)\\ \mathbf{elif}\;b \leq -17000:\\ \;\;\;\;x + z\\ \mathbf{elif}\;b \leq -2.1 \cdot 10^{-218}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 1.02 \cdot 10^{-258}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;b \leq 3 \cdot 10^{-247}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 9.5 \cdot 10^{-147}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;b \leq 4.8 \cdot 10^{+50}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t - 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 66.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - b \cdot \left(2 - \left(y + t\right)\right)\\ t_2 := y \cdot \left(b - z\right)\\ \mathbf{if}\;y \leq -7.6 \cdot 10^{+169}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -1.9 \cdot 10^{+63}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -9.5 \cdot 10^{+45}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -0.00029:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;y \leq 8.3 \cdot 10^{-10}:\\ \;\;\;\;x + \left(z + \left(t + -2\right) \cdot b\right)\\ \mathbf{elif}\;y \leq 1.75 \cdot 10^{+141}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- x (* b (- 2.0 (+ y t))))) (t_2 (* y (- b z))))
   (if (<= y -7.6e+169)
     t_2
     (if (<= y -1.9e+63)
       t_1
       (if (<= y -9.5e+45)
         t_2
         (if (<= y -0.00029)
           (* t (- b a))
           (if (<= y 8.3e-10)
             (+ x (+ z (* (+ t -2.0) b)))
             (if (<= y 1.75e+141) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x - (b * (2.0 - (y + t)));
	double t_2 = y * (b - z);
	double tmp;
	if (y <= -7.6e+169) {
		tmp = t_2;
	} else if (y <= -1.9e+63) {
		tmp = t_1;
	} else if (y <= -9.5e+45) {
		tmp = t_2;
	} else if (y <= -0.00029) {
		tmp = t * (b - a);
	} else if (y <= 8.3e-10) {
		tmp = x + (z + ((t + -2.0) * b));
	} else if (y <= 1.75e+141) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x - (b * (2.0d0 - (y + t)))
    t_2 = y * (b - z)
    if (y <= (-7.6d+169)) then
        tmp = t_2
    else if (y <= (-1.9d+63)) then
        tmp = t_1
    else if (y <= (-9.5d+45)) then
        tmp = t_2
    else if (y <= (-0.00029d0)) then
        tmp = t * (b - a)
    else if (y <= 8.3d-10) then
        tmp = x + (z + ((t + (-2.0d0)) * b))
    else if (y <= 1.75d+141) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x - (b * (2.0 - (y + t)));
	double t_2 = y * (b - z);
	double tmp;
	if (y <= -7.6e+169) {
		tmp = t_2;
	} else if (y <= -1.9e+63) {
		tmp = t_1;
	} else if (y <= -9.5e+45) {
		tmp = t_2;
	} else if (y <= -0.00029) {
		tmp = t * (b - a);
	} else if (y <= 8.3e-10) {
		tmp = x + (z + ((t + -2.0) * b));
	} else if (y <= 1.75e+141) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x - (b * (2.0 - (y + t)))
	t_2 = y * (b - z)
	tmp = 0
	if y <= -7.6e+169:
		tmp = t_2
	elif y <= -1.9e+63:
		tmp = t_1
	elif y <= -9.5e+45:
		tmp = t_2
	elif y <= -0.00029:
		tmp = t * (b - a)
	elif y <= 8.3e-10:
		tmp = x + (z + ((t + -2.0) * b))
	elif y <= 1.75e+141:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x - Float64(b * Float64(2.0 - Float64(y + t))))
	t_2 = Float64(y * Float64(b - z))
	tmp = 0.0
	if (y <= -7.6e+169)
		tmp = t_2;
	elseif (y <= -1.9e+63)
		tmp = t_1;
	elseif (y <= -9.5e+45)
		tmp = t_2;
	elseif (y <= -0.00029)
		tmp = Float64(t * Float64(b - a));
	elseif (y <= 8.3e-10)
		tmp = Float64(x + Float64(z + Float64(Float64(t + -2.0) * b)));
	elseif (y <= 1.75e+141)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x - (b * (2.0 - (y + t)));
	t_2 = y * (b - z);
	tmp = 0.0;
	if (y <= -7.6e+169)
		tmp = t_2;
	elseif (y <= -1.9e+63)
		tmp = t_1;
	elseif (y <= -9.5e+45)
		tmp = t_2;
	elseif (y <= -0.00029)
		tmp = t * (b - a);
	elseif (y <= 8.3e-10)
		tmp = x + (z + ((t + -2.0) * b));
	elseif (y <= 1.75e+141)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x - N[(b * N[(2.0 - N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -7.6e+169], t$95$2, If[LessEqual[y, -1.9e+63], t$95$1, If[LessEqual[y, -9.5e+45], t$95$2, If[LessEqual[y, -0.00029], N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 8.3e-10], N[(x + N[(z + N[(N[(t + -2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.75e+141], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -7.59999999999999983e169 or -1.9000000000000001e63 < y < -9.4999999999999998e45 or 1.75e141 < y

   1. Initial program 86.1%

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

   3. Taylor expanded in y around inf 83.5%

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

   if -7.59999999999999983e169 < y < -1.9000000000000001e63 or 8.3000000000000003e-10 < y < 1.75e141

   1. Initial program 94.1%

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

   3. Taylor expanded in y around 0 84.3%

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

      1. associate--l+ 84.3%

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

      2. sub-neg 84.3%

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

      3. +-commutative 84.3%

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

      4. fma-define 94.1%

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

      5. sub-neg 94.1%

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

      6. metadata-eval 94.1%

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

      7. sub-neg 94.1%

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

      8. metadata-eval 94.1%

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

      9. *-commutative 94.1%

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

      10. distribute-neg-in 94.1%

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

      11. neg-mul-1 94.1%

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

      12. remove-double-neg 94.1%

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

      13. *-commutative 94.1%

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

      14. distribute-rgt-neg-in 94.1%

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

      15. distribute-neg-in 94.1%

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

      16. metadata-eval 94.1%

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

      17. +-commutative 94.1%

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

      18. sub-neg 94.1%

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

   5. Simplified 94.1%

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

   6. Taylor expanded in b around inf 69.3%

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

   if -9.4999999999999998e45 < y < -2.9e-4

   1. Initial program 92.3%

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

   3. Taylor expanded in t around inf 77.1%

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

   if -2.9e-4 < y < 8.3000000000000003e-10

   1. Initial program 97.6%

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

   3. Taylor expanded in y around 0 97.6%

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

      1. associate--l+ 97.6%

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

      2. sub-neg 97.6%

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

      3. +-commutative 97.6%

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

      4. fma-define 97.6%

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

      5. sub-neg 97.6%

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

      6. metadata-eval 97.6%

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

      7. sub-neg 97.6%

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

      8. metadata-eval 97.6%

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

      9. *-commutative 97.6%

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

      10. distribute-neg-in 97.6%

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

      11. neg-mul-1 97.6%

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

      12. remove-double-neg 97.6%

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

      13. *-commutative 97.6%

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

      14. distribute-rgt-neg-in 97.6%

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

      15. distribute-neg-in 97.6%

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

      16. metadata-eval 97.6%

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

      17. +-commutative 97.6%

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

      18. sub-neg 97.6%

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

   5. Simplified 97.6%

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

   6. Taylor expanded in a around 0 67.6%

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

      1. associate-+r+ 67.6%

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

      2. sub-neg 67.6%

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

      3. metadata-eval 67.6%

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

      4. associate-+r+ 67.6%

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

      5. +-commutative 67.6%

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

      6. fma-define 67.6%

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

   8. Simplified 67.6%

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

   9. Taylor expanded in y around 0 67.4%

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

       1. +-commutative 67.4%

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

       2. sub-neg 67.4%

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

       3. metadata-eval 67.4%

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

   11. Simplified 67.4%

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

4. Final simplification 72.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.6 \cdot 10^{+169}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;y \leq -1.9 \cdot 10^{+63}:\\ \;\;\;\;x - b \cdot \left(2 - \left(y + t\right)\right)\\ \mathbf{elif}\;y \leq -9.5 \cdot 10^{+45}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;y \leq -0.00029:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;y \leq 8.3 \cdot 10^{-10}:\\ \;\;\;\;x + \left(z + \left(t + -2\right) \cdot b\right)\\ \mathbf{elif}\;y \leq 1.75 \cdot 10^{+141}:\\ \;\;\;\;x - b \cdot \left(2 - \left(y + t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 73.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(\left(z + a\right) + t \cdot \left(b - a\right)\right)\\ t_2 := x - b \cdot \left(2 - \left(y + t\right)\right)\\ \mathbf{if}\;b \leq -3.4 \cdot 10^{+74}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 2.65 \cdot 10^{-247}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1.2 \cdot 10^{-146}:\\ \;\;\;\;x + z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq 1.1 \cdot 10^{+82}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (+ (+ z a) (* t (- b a)))))
        (t_2 (- x (* b (- 2.0 (+ y t))))))
   (if (<= b -3.4e+74)
     t_2
     (if (<= b 2.65e-247)
       t_1
       (if (<= b 1.2e-146)
         (+ x (* z (- 1.0 y)))
         (if (<= b 1.1e+82) 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 * (b - a)));
	double t_2 = x - (b * (2.0 - (y + t)));
	double tmp;
	if (b <= -3.4e+74) {
		tmp = t_2;
	} else if (b <= 2.65e-247) {
		tmp = t_1;
	} else if (b <= 1.2e-146) {
		tmp = x + (z * (1.0 - y));
	} else if (b <= 1.1e+82) {
		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 * (b - a)))
    t_2 = x - (b * (2.0d0 - (y + t)))
    if (b <= (-3.4d+74)) then
        tmp = t_2
    else if (b <= 2.65d-247) then
        tmp = t_1
    else if (b <= 1.2d-146) then
        tmp = x + (z * (1.0d0 - y))
    else if (b <= 1.1d+82) 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 * (b - a)));
	double t_2 = x - (b * (2.0 - (y + t)));
	double tmp;
	if (b <= -3.4e+74) {
		tmp = t_2;
	} else if (b <= 2.65e-247) {
		tmp = t_1;
	} else if (b <= 1.2e-146) {
		tmp = x + (z * (1.0 - y));
	} else if (b <= 1.1e+82) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + ((z + a) + (t * (b - a)))
	t_2 = x - (b * (2.0 - (y + t)))
	tmp = 0
	if b <= -3.4e+74:
		tmp = t_2
	elif b <= 2.65e-247:
		tmp = t_1
	elif b <= 1.2e-146:
		tmp = x + (z * (1.0 - y))
	elif b <= 1.1e+82:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(Float64(z + a) + Float64(t * Float64(b - a))))
	t_2 = Float64(x - Float64(b * Float64(2.0 - Float64(y + t))))
	tmp = 0.0
	if (b <= -3.4e+74)
		tmp = t_2;
	elseif (b <= 2.65e-247)
		tmp = t_1;
	elseif (b <= 1.2e-146)
		tmp = Float64(x + Float64(z * Float64(1.0 - y)));
	elseif (b <= 1.1e+82)
		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 * (b - a)));
	t_2 = x - (b * (2.0 - (y + t)));
	tmp = 0.0;
	if (b <= -3.4e+74)
		tmp = t_2;
	elseif (b <= 2.65e-247)
		tmp = t_1;
	elseif (b <= 1.2e-146)
		tmp = x + (z * (1.0 - y));
	elseif (b <= 1.1e+82)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(N[(z + a), $MachinePrecision] + N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x - N[(b * N[(2.0 - N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -3.4e+74], t$95$2, If[LessEqual[b, 2.65e-247], t$95$1, If[LessEqual[b, 1.2e-146], N[(x + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.1e+82], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -3.3999999999999999e74 or 1.1000000000000001e82 < b

   1. Initial program 85.9%

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

   3. Taylor expanded in y around 0 83.8%

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

      1. associate--l+ 83.8%

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

      2. sub-neg 83.8%

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

      3. +-commutative 83.8%

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

      4. fma-define 89.9%

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

      5. sub-neg 89.9%

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

      6. metadata-eval 89.9%

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

      7. sub-neg 89.9%

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

      8. metadata-eval 89.9%

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

      9. *-commutative 89.9%

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

      10. distribute-neg-in 89.9%

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

      11. neg-mul-1 89.9%

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

      12. remove-double-neg 89.9%

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

      13. *-commutative 89.9%

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

      14. distribute-rgt-neg-in 89.9%

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

      15. distribute-neg-in 89.9%

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

      16. metadata-eval 89.9%

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

      17. +-commutative 89.9%

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

      18. sub-neg 89.9%

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

   5. Simplified 89.9%

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

   6. Taylor expanded in b around inf 84.5%

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

   if -3.3999999999999999e74 < b < 2.6499999999999999e-247 or 1.2000000000000001e-146 < b < 1.1000000000000001e82

   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 y around 0 98.6%

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

      1. associate--l+ 98.6%

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

      2. sub-neg 98.6%

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

      3. +-commutative 98.6%

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

      4. fma-define 98.6%

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

      5. sub-neg 98.6%

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

      6. metadata-eval 98.6%

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

      7. sub-neg 98.6%

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

      8. metadata-eval 98.6%

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

      9. *-commutative 98.6%

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

      10. distribute-neg-in 98.6%

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

      11. neg-mul-1 98.6%

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

      12. remove-double-neg 98.6%

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

      13. *-commutative 98.6%

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

      14. distribute-rgt-neg-in 98.6%

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

      15. distribute-neg-in 98.6%

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

      16. metadata-eval 98.6%

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

      17. +-commutative 98.6%

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

      18. sub-neg 98.6%

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

   5. Simplified 98.6%

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

   6. Taylor expanded in t around inf 77.5%

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

      1. *-commutative 77.5%

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

   8. Simplified 77.5%

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

   9. Taylor expanded in t around 0 78.2%

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

       1. associate-+r+ 78.2%

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

       2. +-commutative 78.2%

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

       3. mul-1-neg 78.2%

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

   11. Simplified 78.2%

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

   if 2.6499999999999999e-247 < b < 1.2000000000000001e-146

   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 b around 0 95.9%

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

   4. Taylor expanded in a around 0 71.3%

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

4. Final simplification 80.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.4 \cdot 10^{+74}:\\ \;\;\;\;x - b \cdot \left(2 - \left(y + t\right)\right)\\ \mathbf{elif}\;b \leq 2.65 \cdot 10^{-247}:\\ \;\;\;\;x + \left(\left(z + a\right) + t \cdot \left(b - a\right)\right)\\ \mathbf{elif}\;b \leq 1.2 \cdot 10^{-146}:\\ \;\;\;\;x + z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq 1.1 \cdot 10^{+82}:\\ \;\;\;\;x + \left(\left(z + a\right) + t \cdot \left(b - a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x - b \cdot \left(2 - \left(y + t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 47.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(y - 2\right)\\ t_2 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -23000000000000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -1.42 \cdot 10^{-117}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -9 \cdot 10^{-247}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;t \leq 2.05 \cdot 10^{-109}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 8 \cdot 10^{+61}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- y 2.0))) (t_2 (* t (- b a))))
   (if (<= t -23000000000000.0)
     t_2
     (if (<= t -1.42e-117)
       t_1
       (if (<= t -9e-247)
         (+ x z)
         (if (<= t 2.05e-109) t_1 (if (<= t 8e+61) (+ x z) t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (y - 2.0);
	double t_2 = t * (b - a);
	double tmp;
	if (t <= -23000000000000.0) {
		tmp = t_2;
	} else if (t <= -1.42e-117) {
		tmp = t_1;
	} else if (t <= -9e-247) {
		tmp = x + z;
	} else if (t <= 2.05e-109) {
		tmp = t_1;
	} else if (t <= 8e+61) {
		tmp = x + z;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = b * (y - 2.0d0)
    t_2 = t * (b - a)
    if (t <= (-23000000000000.0d0)) then
        tmp = t_2
    else if (t <= (-1.42d-117)) then
        tmp = t_1
    else if (t <= (-9d-247)) then
        tmp = x + z
    else if (t <= 2.05d-109) then
        tmp = t_1
    else if (t <= 8d+61) then
        tmp = x + z
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (y - 2.0);
	double t_2 = t * (b - a);
	double tmp;
	if (t <= -23000000000000.0) {
		tmp = t_2;
	} else if (t <= -1.42e-117) {
		tmp = t_1;
	} else if (t <= -9e-247) {
		tmp = x + z;
	} else if (t <= 2.05e-109) {
		tmp = t_1;
	} else if (t <= 8e+61) {
		tmp = x + z;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * (y - 2.0)
	t_2 = t * (b - a)
	tmp = 0
	if t <= -23000000000000.0:
		tmp = t_2
	elif t <= -1.42e-117:
		tmp = t_1
	elif t <= -9e-247:
		tmp = x + z
	elif t <= 2.05e-109:
		tmp = t_1
	elif t <= 8e+61:
		tmp = x + z
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(y - 2.0))
	t_2 = Float64(t * Float64(b - a))
	tmp = 0.0
	if (t <= -23000000000000.0)
		tmp = t_2;
	elseif (t <= -1.42e-117)
		tmp = t_1;
	elseif (t <= -9e-247)
		tmp = Float64(x + z);
	elseif (t <= 2.05e-109)
		tmp = t_1;
	elseif (t <= 8e+61)
		tmp = Float64(x + z);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * (y - 2.0);
	t_2 = t * (b - a);
	tmp = 0.0;
	if (t <= -23000000000000.0)
		tmp = t_2;
	elseif (t <= -1.42e-117)
		tmp = t_1;
	elseif (t <= -9e-247)
		tmp = x + z;
	elseif (t <= 2.05e-109)
		tmp = t_1;
	elseif (t <= 8e+61)
		tmp = x + z;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(y - 2.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -23000000000000.0], t$95$2, If[LessEqual[t, -1.42e-117], t$95$1, If[LessEqual[t, -9e-247], N[(x + z), $MachinePrecision], If[LessEqual[t, 2.05e-109], t$95$1, If[LessEqual[t, 8e+61], N[(x + z), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.3e13 or 7.9999999999999996e61 < t

   1. Initial program 89.3%

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

   3. Taylor expanded in t around inf 68.3%

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

   if -2.3e13 < t < -1.42000000000000001e-117 or -9.0000000000000005e-247 < t < 2.0500000000000001e-109

   1. Initial program 96.7%

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

   3. Taylor expanded in b around inf 45.0%

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

   4. Taylor expanded in t around 0 44.3%

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

   if -1.42000000000000001e-117 < t < -9.0000000000000005e-247 or 2.0500000000000001e-109 < t < 7.9999999999999996e61

   1. Initial program 96.8%

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

   3. Taylor expanded in y around 0 98.4%

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

      1. associate--l+ 98.4%

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

      2. sub-neg 98.4%

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

      3. +-commutative 98.4%

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

      4. fma-define 98.4%

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

      5. sub-neg 98.4%

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

      6. metadata-eval 98.4%

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

      7. sub-neg 98.4%

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

      8. metadata-eval 98.4%

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

      9. *-commutative 98.4%

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

      10. distribute-neg-in 98.4%

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

      11. neg-mul-1 98.4%

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

      12. remove-double-neg 98.4%

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

      13. *-commutative 98.4%

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

      14. distribute-rgt-neg-in 98.4%

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

      15. distribute-neg-in 98.4%

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

      16. metadata-eval 98.4%

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

      17. +-commutative 98.4%

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

      18. sub-neg 98.4%

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

   5. Simplified 98.4%

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

   6. Taylor expanded in t around inf 66.0%

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

      1. *-commutative 66.0%

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

   8. Simplified 66.0%

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

   9. Taylor expanded in z around inf 45.5%

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

4. Final simplification 54.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -23000000000000:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq -1.42 \cdot 10^{-117}:\\ \;\;\;\;b \cdot \left(y - 2\right)\\ \mathbf{elif}\;t \leq -9 \cdot 10^{-247}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;t \leq 2.05 \cdot 10^{-109}:\\ \;\;\;\;b \cdot \left(y - 2\right)\\ \mathbf{elif}\;t \leq 8 \cdot 10^{+61}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 49.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(b - z\right)\\ \mathbf{if}\;y \leq -8.8 \cdot 10^{+44}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.8 \cdot 10^{-79}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;y \leq -6.8 \cdot 10^{-296}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{-130}:\\ \;\;\;\;b \cdot \left(t - 2\right)\\ \mathbf{elif}\;y \leq 4.1 \cdot 10^{+34}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (- b z))))
   (if (<= y -8.8e+44)
     t_1
     (if (<= y -1.8e-79)
       (* t (- b a))
       (if (<= y -6.8e-296)
         (+ x z)
         (if (<= y 2.3e-130)
           (* b (- t 2.0))
           (if (<= y 4.1e+34) (* 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 <= -8.8e+44) {
		tmp = t_1;
	} else if (y <= -1.8e-79) {
		tmp = t * (b - a);
	} else if (y <= -6.8e-296) {
		tmp = x + z;
	} else if (y <= 2.3e-130) {
		tmp = b * (t - 2.0);
	} else if (y <= 4.1e+34) {
		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 <= (-8.8d+44)) then
        tmp = t_1
    else if (y <= (-1.8d-79)) then
        tmp = t * (b - a)
    else if (y <= (-6.8d-296)) then
        tmp = x + z
    else if (y <= 2.3d-130) then
        tmp = b * (t - 2.0d0)
    else if (y <= 4.1d+34) 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 <= -8.8e+44) {
		tmp = t_1;
	} else if (y <= -1.8e-79) {
		tmp = t * (b - a);
	} else if (y <= -6.8e-296) {
		tmp = x + z;
	} else if (y <= 2.3e-130) {
		tmp = b * (t - 2.0);
	} else if (y <= 4.1e+34) {
		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 <= -8.8e+44:
		tmp = t_1
	elif y <= -1.8e-79:
		tmp = t * (b - a)
	elif y <= -6.8e-296:
		tmp = x + z
	elif y <= 2.3e-130:
		tmp = b * (t - 2.0)
	elif y <= 4.1e+34:
		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 <= -8.8e+44)
		tmp = t_1;
	elseif (y <= -1.8e-79)
		tmp = Float64(t * Float64(b - a));
	elseif (y <= -6.8e-296)
		tmp = Float64(x + z);
	elseif (y <= 2.3e-130)
		tmp = Float64(b * Float64(t - 2.0));
	elseif (y <= 4.1e+34)
		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 <= -8.8e+44)
		tmp = t_1;
	elseif (y <= -1.8e-79)
		tmp = t * (b - a);
	elseif (y <= -6.8e-296)
		tmp = x + z;
	elseif (y <= 2.3e-130)
		tmp = b * (t - 2.0);
	elseif (y <= 4.1e+34)
		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, -8.8e+44], t$95$1, If[LessEqual[y, -1.8e-79], N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -6.8e-296], N[(x + z), $MachinePrecision], If[LessEqual[y, 2.3e-130], N[(b * N[(t - 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.1e+34], N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -8.79999999999999983e44 or 4.0999999999999998e34 < y

   1. Initial program 89.3%

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

   3. Taylor expanded in y around inf 70.0%

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

   if -8.79999999999999983e44 < y < -1.8000000000000001e-79

   1. Initial program 95.8%

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

   3. Taylor expanded in t around inf 67.3%

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

   if -1.8000000000000001e-79 < y < -6.79999999999999993e-296

   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 y around 0 97.5%

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

      1. associate--l+ 97.5%

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

      2. sub-neg 97.5%

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

      3. +-commutative 97.5%

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

      4. fma-define 97.5%

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

      5. sub-neg 97.5%

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

      6. metadata-eval 97.5%

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

      7. sub-neg 97.5%

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

      8. metadata-eval 97.5%

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

      9. *-commutative 97.5%

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

      10. distribute-neg-in 97.5%

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

      11. neg-mul-1 97.5%

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

      12. remove-double-neg 97.5%

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

      13. *-commutative 97.5%

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

      14. distribute-rgt-neg-in 97.5%

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

      15. distribute-neg-in 97.5%

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

      16. metadata-eval 97.5%

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

      17. +-commutative 97.5%

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

      18. sub-neg 97.5%

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

   5. Simplified 97.5%

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

   6. Taylor expanded in t around inf 80.8%

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

      1. *-commutative 80.8%

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

   8. Simplified 80.8%

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

   9. Taylor expanded in z around inf 48.5%

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

   if -6.79999999999999993e-296 < y < 2.3000000000000001e-130

   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 48.5%

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

   4. Taylor expanded in y around 0 48.5%

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

   if 2.3000000000000001e-130 < y < 4.0999999999999998e34

   1. Initial program 97.4%

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

   3. Taylor expanded in a around inf 47.5%

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

4. Final simplification 59.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.8 \cdot 10^{+44}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;y \leq -1.8 \cdot 10^{-79}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;y \leq -6.8 \cdot 10^{-296}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{-130}:\\ \;\;\;\;b \cdot \left(t - 2\right)\\ \mathbf{elif}\;y \leq 4.1 \cdot 10^{+34}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 63.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - b \cdot \left(2 - \left(y + t\right)\right)\\ \mathbf{if}\;b \leq -1.15 \cdot 10^{+59}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -720:\\ \;\;\;\;z + \left(x + a\right)\\ \mathbf{elif}\;b \leq -2.05 \cdot 10^{-58}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;b \leq 4.25 \cdot 10^{+49}:\\ \;\;\;\;x + z \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- x (* b (- 2.0 (+ y t))))))
   (if (<= b -1.15e+59)
     t_1
     (if (<= b -720.0)
       (+ z (+ x a))
       (if (<= b -2.05e-58)
         (* t (- b a))
         (if (<= b 4.25e+49) (+ x (* z (- 1.0 y))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x - (b * (2.0 - (y + t)));
	double tmp;
	if (b <= -1.15e+59) {
		tmp = t_1;
	} else if (b <= -720.0) {
		tmp = z + (x + a);
	} else if (b <= -2.05e-58) {
		tmp = t * (b - a);
	} else if (b <= 4.25e+49) {
		tmp = x + (z * (1.0 - y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x - (b * (2.0d0 - (y + t)))
    if (b <= (-1.15d+59)) then
        tmp = t_1
    else if (b <= (-720.0d0)) then
        tmp = z + (x + a)
    else if (b <= (-2.05d-58)) then
        tmp = t * (b - a)
    else if (b <= 4.25d+49) then
        tmp = x + (z * (1.0d0 - y))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x - (b * (2.0 - (y + t)));
	double tmp;
	if (b <= -1.15e+59) {
		tmp = t_1;
	} else if (b <= -720.0) {
		tmp = z + (x + a);
	} else if (b <= -2.05e-58) {
		tmp = t * (b - a);
	} else if (b <= 4.25e+49) {
		tmp = x + (z * (1.0 - y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x - (b * (2.0 - (y + t)))
	tmp = 0
	if b <= -1.15e+59:
		tmp = t_1
	elif b <= -720.0:
		tmp = z + (x + a)
	elif b <= -2.05e-58:
		tmp = t * (b - a)
	elif b <= 4.25e+49:
		tmp = x + (z * (1.0 - y))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x - Float64(b * Float64(2.0 - Float64(y + t))))
	tmp = 0.0
	if (b <= -1.15e+59)
		tmp = t_1;
	elseif (b <= -720.0)
		tmp = Float64(z + Float64(x + a));
	elseif (b <= -2.05e-58)
		tmp = Float64(t * Float64(b - a));
	elseif (b <= 4.25e+49)
		tmp = Float64(x + Float64(z * Float64(1.0 - y)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x - (b * (2.0 - (y + t)));
	tmp = 0.0;
	if (b <= -1.15e+59)
		tmp = t_1;
	elseif (b <= -720.0)
		tmp = z + (x + a);
	elseif (b <= -2.05e-58)
		tmp = t * (b - a);
	elseif (b <= 4.25e+49)
		tmp = x + (z * (1.0 - y));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x - N[(b * N[(2.0 - N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.15e+59], t$95$1, If[LessEqual[b, -720.0], N[(z + N[(x + a), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -2.05e-58], N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 4.25e+49], N[(x + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -1.15000000000000004e59 or 4.2499999999999998e49 < b

   1. Initial program 86.6%

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

   3. Taylor expanded in y around 0 84.8%

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

      1. associate--l+ 84.8%

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

      2. sub-neg 84.8%

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

      3. +-commutative 84.8%

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

      4. fma-define 90.2%

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

      5. sub-neg 90.2%

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

      6. metadata-eval 90.2%

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

      7. sub-neg 90.2%

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

      8. metadata-eval 90.2%

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

      9. *-commutative 90.2%

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

      10. distribute-neg-in 90.2%

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

      11. neg-mul-1 90.2%

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

      12. remove-double-neg 90.2%

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

      13. *-commutative 90.2%

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

      14. distribute-rgt-neg-in 90.2%

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

      15. distribute-neg-in 90.2%

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

      16. metadata-eval 90.2%

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

      17. +-commutative 90.2%

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

      18. sub-neg 90.2%

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

   5. Simplified 90.2%

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

   6. Taylor expanded in b around inf 80.1%

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

   if -1.15000000000000004e59 < b < -720

   1. Initial program 92.9%

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

   3. Taylor expanded in y around 0 92.9%

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

      1. associate--l+ 92.9%

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

      2. sub-neg 92.9%

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

      3. +-commutative 92.9%

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

      4. fma-define 92.9%

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

      5. sub-neg 92.9%

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

      6. metadata-eval 92.9%

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

      7. sub-neg 92.9%

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

      8. metadata-eval 92.9%

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

      9. *-commutative 92.9%

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

      10. distribute-neg-in 92.9%

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

      11. neg-mul-1 92.9%

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

      12. remove-double-neg 92.9%

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

      13. *-commutative 92.9%

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

      14. distribute-rgt-neg-in 92.9%

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

      15. distribute-neg-in 92.9%

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

      16. metadata-eval 92.9%

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

      17. +-commutative 92.9%

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

      18. sub-neg 92.9%

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

   5. Simplified 92.9%

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

   6. Taylor expanded in t around inf 85.7%

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

      1. *-commutative 85.7%

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

   8. Simplified 85.7%

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

   9. Taylor expanded in t around 0 79.0%

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

       1. associate-+r+ 79.0%

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

       2. +-commutative 79.0%

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

   11. Simplified 79.0%

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

   if -720 < b < -2.05000000000000014e-58

   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 73.3%

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

   if -2.05000000000000014e-58 < b < 4.2499999999999998e49

   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 91.6%

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

   4. Taylor expanded in a around 0 55.7%

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

4. Final simplification 68.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.15 \cdot 10^{+59}:\\ \;\;\;\;x - b \cdot \left(2 - \left(y + t\right)\right)\\ \mathbf{elif}\;b \leq -720:\\ \;\;\;\;z + \left(x + a\right)\\ \mathbf{elif}\;b \leq -2.05 \cdot 10^{-58}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;b \leq 4.25 \cdot 10^{+49}:\\ \;\;\;\;x + z \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;x - b \cdot \left(2 - \left(y + t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 70.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(z + a \cdot \left(1 - t\right)\right)\\ t_2 := x - b \cdot \left(2 - \left(y + t\right)\right)\\ \mathbf{if}\;b \leq -7.8 \cdot 10^{+71}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 1.7 \cdot 10^{-247}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1.05 \cdot 10^{-146}:\\ \;\;\;\;x + z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq 3 \cdot 10^{+50}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (+ z (* a (- 1.0 t))))) (t_2 (- x (* b (- 2.0 (+ y t))))))
   (if (<= b -7.8e+71)
     t_2
     (if (<= b 1.7e-247)
       t_1
       (if (<= b 1.05e-146)
         (+ x (* z (- 1.0 y)))
         (if (<= b 3e+50) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (z + (a * (1.0 - t)));
	double t_2 = x - (b * (2.0 - (y + t)));
	double tmp;
	if (b <= -7.8e+71) {
		tmp = t_2;
	} else if (b <= 1.7e-247) {
		tmp = t_1;
	} else if (b <= 1.05e-146) {
		tmp = x + (z * (1.0 - y));
	} else if (b <= 3e+50) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + (z + (a * (1.0d0 - t)))
    t_2 = x - (b * (2.0d0 - (y + t)))
    if (b <= (-7.8d+71)) then
        tmp = t_2
    else if (b <= 1.7d-247) then
        tmp = t_1
    else if (b <= 1.05d-146) then
        tmp = x + (z * (1.0d0 - y))
    else if (b <= 3d+50) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (z + (a * (1.0 - t)));
	double t_2 = x - (b * (2.0 - (y + t)));
	double tmp;
	if (b <= -7.8e+71) {
		tmp = t_2;
	} else if (b <= 1.7e-247) {
		tmp = t_1;
	} else if (b <= 1.05e-146) {
		tmp = x + (z * (1.0 - y));
	} else if (b <= 3e+50) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (z + (a * (1.0 - t)))
	t_2 = x - (b * (2.0 - (y + t)))
	tmp = 0
	if b <= -7.8e+71:
		tmp = t_2
	elif b <= 1.7e-247:
		tmp = t_1
	elif b <= 1.05e-146:
		tmp = x + (z * (1.0 - y))
	elif b <= 3e+50:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(z + Float64(a * Float64(1.0 - t))))
	t_2 = Float64(x - Float64(b * Float64(2.0 - Float64(y + t))))
	tmp = 0.0
	if (b <= -7.8e+71)
		tmp = t_2;
	elseif (b <= 1.7e-247)
		tmp = t_1;
	elseif (b <= 1.05e-146)
		tmp = Float64(x + Float64(z * Float64(1.0 - y)));
	elseif (b <= 3e+50)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (z + (a * (1.0 - t)));
	t_2 = x - (b * (2.0 - (y + t)));
	tmp = 0.0;
	if (b <= -7.8e+71)
		tmp = t_2;
	elseif (b <= 1.7e-247)
		tmp = t_1;
	elseif (b <= 1.05e-146)
		tmp = x + (z * (1.0 - y));
	elseif (b <= 3e+50)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(z + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x - N[(b * N[(2.0 - N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -7.8e+71], t$95$2, If[LessEqual[b, 1.7e-247], t$95$1, If[LessEqual[b, 1.05e-146], N[(x + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3e+50], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -7.8000000000000002e71 or 2.9999999999999998e50 < b

   1. Initial program 86.2%

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

   3. Taylor expanded in y around 0 84.4%

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

      1. associate--l+ 84.4%

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

      2. sub-neg 84.4%

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

      3. +-commutative 84.4%

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

      4. fma-define 89.9%

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

      5. sub-neg 89.9%

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

      6. metadata-eval 89.9%

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

      7. sub-neg 89.9%

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

      8. metadata-eval 89.9%

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

      9. *-commutative 89.9%

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

      10. distribute-neg-in 89.9%

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

      11. neg-mul-1 89.9%

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

      12. remove-double-neg 89.9%

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

      13. *-commutative 89.9%

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

      14. distribute-rgt-neg-in 89.9%

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

      15. distribute-neg-in 89.9%

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

      16. metadata-eval 89.9%

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

      17. +-commutative 89.9%

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

      18. sub-neg 89.9%

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

   5. Simplified 89.9%

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

   6. Taylor expanded in b around inf 81.4%

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

   if -7.8000000000000002e71 < b < 1.7000000000000001e-247 or 1.05e-146 < b < 2.9999999999999998e50

   1. Initial program 99.2%

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

   3. Taylor expanded in b around 0 88.7%

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

   4. Taylor expanded in y around 0 72.0%

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

      1. neg-mul-1 72.0%

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

      2. +-commutative 72.0%

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

      3. sub-neg 72.0%

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

      4. metadata-eval 72.0%

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

      5. unsub-neg 72.0%

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

   6. Simplified 72.0%

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

   if 1.7000000000000001e-247 < b < 1.05e-146

   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 b around 0 95.9%

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

   4. Taylor expanded in a around 0 71.3%

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

4. Final simplification 76.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -7.8 \cdot 10^{+71}:\\ \;\;\;\;x - b \cdot \left(2 - \left(y + t\right)\right)\\ \mathbf{elif}\;b \leq 1.7 \cdot 10^{-247}:\\ \;\;\;\;x + \left(z + a \cdot \left(1 - t\right)\right)\\ \mathbf{elif}\;b \leq 1.05 \cdot 10^{-146}:\\ \;\;\;\;x + z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq 3 \cdot 10^{+50}:\\ \;\;\;\;x + \left(z + a \cdot \left(1 - t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x - b \cdot \left(2 - \left(y + t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 60.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{if}\;b \leq -1.45 \cdot 10^{+59}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -960:\\ \;\;\;\;z + \left(x + a\right)\\ \mathbf{elif}\;b \leq -2.8 \cdot 10^{-58}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;b \leq 3.9 \cdot 10^{+49}:\\ \;\;\;\;x + z \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- (+ y t) 2.0))))
   (if (<= b -1.45e+59)
     t_1
     (if (<= b -960.0)
       (+ z (+ x a))
       (if (<= b -2.8e-58)
         (* t (- b a))
         (if (<= b 3.9e+49) (+ x (* z (- 1.0 y))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * ((y + t) - 2.0);
	double tmp;
	if (b <= -1.45e+59) {
		tmp = t_1;
	} else if (b <= -960.0) {
		tmp = z + (x + a);
	} else if (b <= -2.8e-58) {
		tmp = t * (b - a);
	} else if (b <= 3.9e+49) {
		tmp = x + (z * (1.0 - y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * ((y + t) - 2.0d0)
    if (b <= (-1.45d+59)) then
        tmp = t_1
    else if (b <= (-960.0d0)) then
        tmp = z + (x + a)
    else if (b <= (-2.8d-58)) then
        tmp = t * (b - a)
    else if (b <= 3.9d+49) then
        tmp = x + (z * (1.0d0 - y))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * ((y + t) - 2.0);
	double tmp;
	if (b <= -1.45e+59) {
		tmp = t_1;
	} else if (b <= -960.0) {
		tmp = z + (x + a);
	} else if (b <= -2.8e-58) {
		tmp = t * (b - a);
	} else if (b <= 3.9e+49) {
		tmp = x + (z * (1.0 - y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * ((y + t) - 2.0)
	tmp = 0
	if b <= -1.45e+59:
		tmp = t_1
	elif b <= -960.0:
		tmp = z + (x + a)
	elif b <= -2.8e-58:
		tmp = t * (b - a)
	elif b <= 3.9e+49:
		tmp = x + (z * (1.0 - y))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(Float64(y + t) - 2.0))
	tmp = 0.0
	if (b <= -1.45e+59)
		tmp = t_1;
	elseif (b <= -960.0)
		tmp = Float64(z + Float64(x + a));
	elseif (b <= -2.8e-58)
		tmp = Float64(t * Float64(b - a));
	elseif (b <= 3.9e+49)
		tmp = Float64(x + Float64(z * Float64(1.0 - y)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * ((y + t) - 2.0);
	tmp = 0.0;
	if (b <= -1.45e+59)
		tmp = t_1;
	elseif (b <= -960.0)
		tmp = z + (x + a);
	elseif (b <= -2.8e-58)
		tmp = t * (b - a);
	elseif (b <= 3.9e+49)
		tmp = x + (z * (1.0 - y));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.45e+59], t$95$1, If[LessEqual[b, -960.0], N[(z + N[(x + a), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -2.8e-58], N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.9e+49], N[(x + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -1.44999999999999995e59 or 3.9000000000000001e49 < b

   1. Initial program 86.6%

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

   3. Taylor expanded in b around inf 75.4%

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

   if -1.44999999999999995e59 < b < -960

   1. Initial program 92.9%

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

   3. Taylor expanded in y around 0 92.9%

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

      1. associate--l+ 92.9%

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

      2. sub-neg 92.9%

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

      3. +-commutative 92.9%

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

      4. fma-define 92.9%

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

      5. sub-neg 92.9%

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

      6. metadata-eval 92.9%

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

      7. sub-neg 92.9%

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

      8. metadata-eval 92.9%

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

      9. *-commutative 92.9%

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

      10. distribute-neg-in 92.9%

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

      11. neg-mul-1 92.9%

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

      12. remove-double-neg 92.9%

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

      13. *-commutative 92.9%

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

      14. distribute-rgt-neg-in 92.9%

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

      15. distribute-neg-in 92.9%

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

      16. metadata-eval 92.9%

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

      17. +-commutative 92.9%

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

      18. sub-neg 92.9%

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

   5. Simplified 92.9%

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

   6. Taylor expanded in t around inf 85.7%

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

      1. *-commutative 85.7%

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

   8. Simplified 85.7%

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

   9. Taylor expanded in t around 0 79.0%

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

       1. associate-+r+ 79.0%

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

       2. +-commutative 79.0%

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

   11. Simplified 79.0%

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

   if -960 < b < -2.8000000000000001e-58

   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 73.3%

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

   if -2.8000000000000001e-58 < b < 3.9000000000000001e49

   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 91.6%

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

   4. Taylor expanded in a around 0 55.7%

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

4. Final simplification 66.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.45 \cdot 10^{+59}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{elif}\;b \leq -960:\\ \;\;\;\;z + \left(x + a\right)\\ \mathbf{elif}\;b \leq -2.8 \cdot 10^{-58}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;b \leq 3.9 \cdot 10^{+49}:\\ \;\;\;\;x + z \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 86.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(1 - t\right)\\ t_2 := x - b \cdot \left(2 - \left(y + t\right)\right)\\ t_3 := z \cdot \left(1 - y\right)\\ \mathbf{if}\;b \leq -9 \cdot 10^{+70}:\\ \;\;\;\;t\_2 + t\_1\\ \mathbf{elif}\;b \leq 2.75 \cdot 10^{-51}:\\ \;\;\;\;x + \left(t\_1 + t\_3\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2 + t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (- 1.0 t)))
        (t_2 (- x (* b (- 2.0 (+ y t)))))
        (t_3 (* z (- 1.0 y))))
   (if (<= b -9e+70)
     (+ t_2 t_1)
     (if (<= b 2.75e-51) (+ 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 = a * (1.0 - t);
	double t_2 = x - (b * (2.0 - (y + t)));
	double t_3 = z * (1.0 - y);
	double tmp;
	if (b <= -9e+70) {
		tmp = t_2 + t_1;
	} else if (b <= 2.75e-51) {
		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 = a * (1.0d0 - t)
    t_2 = x - (b * (2.0d0 - (y + t)))
    t_3 = z * (1.0d0 - y)
    if (b <= (-9d+70)) then
        tmp = t_2 + t_1
    else if (b <= 2.75d-51) 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 = a * (1.0 - t);
	double t_2 = x - (b * (2.0 - (y + t)));
	double t_3 = z * (1.0 - y);
	double tmp;
	if (b <= -9e+70) {
		tmp = t_2 + t_1;
	} else if (b <= 2.75e-51) {
		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 = a * (1.0 - t)
	t_2 = x - (b * (2.0 - (y + t)))
	t_3 = z * (1.0 - y)
	tmp = 0
	if b <= -9e+70:
		tmp = t_2 + t_1
	elif b <= 2.75e-51:
		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(a * Float64(1.0 - t))
	t_2 = Float64(x - Float64(b * Float64(2.0 - Float64(y + t))))
	t_3 = Float64(z * Float64(1.0 - y))
	tmp = 0.0
	if (b <= -9e+70)
		tmp = Float64(t_2 + t_1);
	elseif (b <= 2.75e-51)
		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 = a * (1.0 - t);
	t_2 = x - (b * (2.0 - (y + t)));
	t_3 = z * (1.0 - y);
	tmp = 0.0;
	if (b <= -9e+70)
		tmp = t_2 + t_1;
	elseif (b <= 2.75e-51)
		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[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x - N[(b * N[(2.0 - N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -9e+70], N[(t$95$2 + t$95$1), $MachinePrecision], If[LessEqual[b, 2.75e-51], 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 < -8.9999999999999999e70

   1. Initial program 87.9%

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

   3. Taylor expanded in z around 0 86.5%

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

   if -8.9999999999999999e70 < b < 2.7499999999999999e-51

   1. Initial program 99.2%

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

   3. Taylor expanded in b around 0 92.7%

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

   if 2.7499999999999999e-51 < b

   1. Initial program 88.8%

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

   3. Taylor expanded in a around 0 82.2%

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

4. Final simplification 88.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -9 \cdot 10^{+70}:\\ \;\;\;\;\left(x - b \cdot \left(2 - \left(y + t\right)\right)\right) + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 2.75 \cdot 10^{-51}:\\ \;\;\;\;x + \left(a \cdot \left(1 - t\right) + z \cdot \left(1 - y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x - b \cdot \left(2 - \left(y + t\right)\right)\right) + z \cdot \left(1 - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 35.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(-z\right)\\ \mathbf{if}\;y \leq -1.6 \cdot 10^{+150}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.5 \cdot 10^{+45}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;y \leq -2 \cdot 10^{-47}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;y \leq 0.175:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (- z))))
   (if (<= y -1.6e+150)
     t_1
     (if (<= y -1.5e+45)
       (* y b)
       (if (<= y -2e-47) (* t b) (if (<= y 0.175) (+ x z) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * -z;
	double tmp;
	if (y <= -1.6e+150) {
		tmp = t_1;
	} else if (y <= -1.5e+45) {
		tmp = y * b;
	} else if (y <= -2e-47) {
		tmp = t * b;
	} else if (y <= 0.175) {
		tmp = x + z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * -z
    if (y <= (-1.6d+150)) then
        tmp = t_1
    else if (y <= (-1.5d+45)) then
        tmp = y * b
    else if (y <= (-2d-47)) then
        tmp = t * b
    else if (y <= 0.175d0) then
        tmp = x + z
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * -z;
	double tmp;
	if (y <= -1.6e+150) {
		tmp = t_1;
	} else if (y <= -1.5e+45) {
		tmp = y * b;
	} else if (y <= -2e-47) {
		tmp = t * b;
	} else if (y <= 0.175) {
		tmp = x + z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y * -z
	tmp = 0
	if y <= -1.6e+150:
		tmp = t_1
	elif y <= -1.5e+45:
		tmp = y * b
	elif y <= -2e-47:
		tmp = t * b
	elif y <= 0.175:
		tmp = x + z
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y * Float64(-z))
	tmp = 0.0
	if (y <= -1.6e+150)
		tmp = t_1;
	elseif (y <= -1.5e+45)
		tmp = Float64(y * b);
	elseif (y <= -2e-47)
		tmp = Float64(t * b);
	elseif (y <= 0.175)
		tmp = Float64(x + z);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y * -z;
	tmp = 0.0;
	if (y <= -1.6e+150)
		tmp = t_1;
	elseif (y <= -1.5e+45)
		tmp = y * b;
	elseif (y <= -2e-47)
		tmp = t * b;
	elseif (y <= 0.175)
		tmp = x + z;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y * (-z)), $MachinePrecision]}, If[LessEqual[y, -1.6e+150], t$95$1, If[LessEqual[y, -1.5e+45], N[(y * b), $MachinePrecision], If[LessEqual[y, -2e-47], N[(t * b), $MachinePrecision], If[LessEqual[y, 0.175], N[(x + z), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.60000000000000008e150 or 0.17499999999999999 < y

   1. Initial program 89.3%

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

   3. Taylor expanded in y around inf 72.3%

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

   4. Taylor expanded in b around 0 47.5%

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

      1. mul-1-neg 47.5%

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

      2. distribute-rgt-neg-out 47.5%

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

   6. Simplified 47.5%

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

   if -1.60000000000000008e150 < y < -1.50000000000000005e45

   1. Initial program 90.4%

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

   3. Taylor expanded in z around 0 86.1%

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

   4. Taylor expanded in y around inf 48.6%

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

   if -1.50000000000000005e45 < y < -1.9999999999999999e-47

   1. Initial program 94.1%

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

   3. Taylor expanded in b around inf 49.9%

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

   4. Taylor expanded in t around inf 48.0%

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

   if -1.9999999999999999e-47 < y < 0.17499999999999999

   1. Initial program 97.6%

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

   3. Taylor expanded in y around 0 97.6%

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

      1. associate--l+ 97.6%

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

      2. sub-neg 97.6%

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

      3. +-commutative 97.6%

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

      4. fma-define 97.6%

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

      5. sub-neg 97.6%

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

      6. metadata-eval 97.6%

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

      7. sub-neg 97.6%

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

      8. metadata-eval 97.6%

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

      9. *-commutative 97.6%

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

      10. distribute-neg-in 97.6%

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

      11. neg-mul-1 97.6%

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

      12. remove-double-neg 97.6%

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

      13. *-commutative 97.6%

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

      14. distribute-rgt-neg-in 97.6%

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

      15. distribute-neg-in 97.6%

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

      16. metadata-eval 97.6%

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

      17. +-commutative 97.6%

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

      18. sub-neg 97.6%

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

   5. Simplified 97.6%

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

   6. Taylor expanded in t around inf 77.9%

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

      1. *-commutative 77.9%

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

   8. Simplified 77.9%

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

   9. Taylor expanded in z around inf 34.8%

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

4. Final simplification 41.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{+150}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;y \leq -1.5 \cdot 10^{+45}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;y \leq -2 \cdot 10^{-47}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;y \leq 0.175:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 84.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -6.3 \cdot 10^{+72} \lor \neg \left(b \leq 5 \cdot 10^{+71}\right):\\ \;\;\;\;x - b \cdot \left(2 - \left(y + t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(a \cdot \left(1 - t\right) + z \cdot \left(1 - y\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -6.3e+72) (not (<= b 5e+71)))
   (- x (* b (- 2.0 (+ y t))))
   (+ x (+ (* a (- 1.0 t)) (* z (- 1.0 y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -6.3e+72) || !(b <= 5e+71)) {
		tmp = x - (b * (2.0 - (y + t)));
	} else {
		tmp = x + ((a * (1.0 - t)) + (z * (1.0 - y)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-6.3d+72)) .or. (.not. (b <= 5d+71))) then
        tmp = x - (b * (2.0d0 - (y + t)))
    else
        tmp = x + ((a * (1.0d0 - t)) + (z * (1.0d0 - y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -6.3e+72) || !(b <= 5e+71)) {
		tmp = x - (b * (2.0 - (y + t)));
	} else {
		tmp = x + ((a * (1.0 - t)) + (z * (1.0 - y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -6.3e+72) or not (b <= 5e+71):
		tmp = x - (b * (2.0 - (y + t)))
	else:
		tmp = x + ((a * (1.0 - t)) + (z * (1.0 - y)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -6.3e+72) || !(b <= 5e+71))
		tmp = Float64(x - Float64(b * Float64(2.0 - Float64(y + t))));
	else
		tmp = Float64(x + Float64(Float64(a * Float64(1.0 - t)) + Float64(z * Float64(1.0 - y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -6.3e+72) || ~((b <= 5e+71)))
		tmp = x - (b * (2.0 - (y + t)));
	else
		tmp = x + ((a * (1.0 - t)) + (z * (1.0 - y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -6.3e+72], N[Not[LessEqual[b, 5e+71]], $MachinePrecision]], N[(x - N[(b * N[(2.0 - N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision] + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -6.29999999999999963e72 or 4.99999999999999972e71 < b

   1. Initial program 86.1%

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

   3. Taylor expanded in y around 0 84.1%

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

      1. associate--l+ 84.1%

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

      2. sub-neg 84.1%

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

      3. +-commutative 84.1%

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

      4. fma-define 90.1%

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

      5. sub-neg 90.1%

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

      6. metadata-eval 90.1%

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

      7. sub-neg 90.1%

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

      8. metadata-eval 90.1%

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

      9. *-commutative 90.1%

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

      10. distribute-neg-in 90.1%

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

      11. neg-mul-1 90.1%

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

      12. remove-double-neg 90.1%

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

      13. *-commutative 90.1%

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

      14. distribute-rgt-neg-in 90.1%

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

      15. distribute-neg-in 90.1%

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

      16. metadata-eval 90.1%

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

      17. +-commutative 90.1%

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

      18. sub-neg 90.1%

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

   5. Simplified 90.1%

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

   6. Taylor expanded in b around inf 83.9%

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

   if -6.29999999999999963e72 < b < 4.99999999999999972e71

   1. Initial program 98.7%

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

   3. Taylor expanded in b around 0 87.5%

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

4. Final simplification 86.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -6.3 \cdot 10^{+72} \lor \neg \left(b \leq 5 \cdot 10^{+71}\right):\\ \;\;\;\;x - b \cdot \left(2 - \left(y + t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(a \cdot \left(1 - t\right) + z \cdot \left(1 - y\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 84.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(1 - t\right)\\ t_2 := x - b \cdot \left(2 - \left(y + t\right)\right)\\ \mathbf{if}\;b \leq -7.2 \cdot 10^{+69}:\\ \;\;\;\;t\_2 + t\_1\\ \mathbf{elif}\;b \leq 5.6 \cdot 10^{+71}:\\ \;\;\;\;x + \left(t\_1 + z \cdot \left(1 - y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (- 1.0 t))) (t_2 (- x (* b (- 2.0 (+ y t))))))
   (if (<= b -7.2e+69)
     (+ t_2 t_1)
     (if (<= b 5.6e+71) (+ x (+ t_1 (* z (- 1.0 y)))) t_2))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double t_2 = x - (b * (2.0 - (y + t)));
	double tmp;
	if (b <= -7.2e+69) {
		tmp = t_2 + t_1;
	} else if (b <= 5.6e+71) {
		tmp = x + (t_1 + (z * (1.0 - y)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a * (1.0d0 - t)
    t_2 = x - (b * (2.0d0 - (y + t)))
    if (b <= (-7.2d+69)) then
        tmp = t_2 + t_1
    else if (b <= 5.6d+71) then
        tmp = x + (t_1 + (z * (1.0d0 - y)))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double t_2 = x - (b * (2.0 - (y + t)));
	double tmp;
	if (b <= -7.2e+69) {
		tmp = t_2 + t_1;
	} else if (b <= 5.6e+71) {
		tmp = x + (t_1 + (z * (1.0 - y)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (1.0 - t)
	t_2 = x - (b * (2.0 - (y + t)))
	tmp = 0
	if b <= -7.2e+69:
		tmp = t_2 + t_1
	elif b <= 5.6e+71:
		tmp = x + (t_1 + (z * (1.0 - y)))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(1.0 - t))
	t_2 = Float64(x - Float64(b * Float64(2.0 - Float64(y + t))))
	tmp = 0.0
	if (b <= -7.2e+69)
		tmp = Float64(t_2 + t_1);
	elseif (b <= 5.6e+71)
		tmp = Float64(x + Float64(t_1 + Float64(z * Float64(1.0 - y))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (1.0 - t);
	t_2 = x - (b * (2.0 - (y + t)));
	tmp = 0.0;
	if (b <= -7.2e+69)
		tmp = t_2 + t_1;
	elseif (b <= 5.6e+71)
		tmp = x + (t_1 + (z * (1.0 - y)));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x - N[(b * N[(2.0 - N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -7.2e+69], N[(t$95$2 + t$95$1), $MachinePrecision], If[LessEqual[b, 5.6e+71], N[(x + N[(t$95$1 + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 3 regimes

2. if b < -7.2000000000000005e69

   1. Initial program 87.9%

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

   3. Taylor expanded in z around 0 86.5%

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

   if -7.2000000000000005e69 < b < 5.60000000000000004e71

   1. Initial program 98.7%

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

   3. Taylor expanded in b around 0 87.5%

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

   if 5.60000000000000004e71 < b

   1. Initial program 83.7%

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

   3. Taylor expanded in y around 0 81.4%

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

      1. associate--l+ 81.4%

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

      2. sub-neg 81.4%

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

      3. +-commutative 81.4%

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

      4. fma-define 86.0%

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

      5. sub-neg 86.0%

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

      6. metadata-eval 86.0%

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

      7. sub-neg 86.0%

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

      8. metadata-eval 86.0%

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

      9. *-commutative 86.0%

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

      10. distribute-neg-in 86.0%

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

      11. neg-mul-1 86.0%

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

      12. remove-double-neg 86.0%

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

      13. *-commutative 86.0%

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

      14. distribute-rgt-neg-in 86.0%

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

      15. distribute-neg-in 86.0%

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

      16. metadata-eval 86.0%

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

      17. +-commutative 86.0%

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

      18. sub-neg 86.0%

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

   5. Simplified 86.0%

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

   6. Taylor expanded in b around inf 88.8%

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

4. Final simplification 87.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -7.2 \cdot 10^{+69}:\\ \;\;\;\;\left(x - b \cdot \left(2 - \left(y + t\right)\right)\right) + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 5.6 \cdot 10^{+71}:\\ \;\;\;\;x + \left(a \cdot \left(1 - t\right) + z \cdot \left(1 - y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x - b \cdot \left(2 - \left(y + t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 26.7% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.7 \cdot 10^{+38} \lor \neg \left(t \leq 4 \cdot 10^{+37}\right):\\ \;\;\;\;t \cdot b\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -2.7e+38) (not (<= t 4e+37))) (* t b) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -2.7e+38) || !(t <= 4e+37)) {
		tmp = t * b;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-2.7d+38)) .or. (.not. (t <= 4d+37))) then
        tmp = t * b
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -2.7e+38) || !(t <= 4e+37)) {
		tmp = t * b;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -2.7e+38) or not (t <= 4e+37):
		tmp = t * b
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -2.7e+38) || !(t <= 4e+37))
		tmp = Float64(t * b);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -2.7e+38) || ~((t <= 4e+37)))
		tmp = t * b;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -2.7e+38], N[Not[LessEqual[t, 4e+37]], $MachinePrecision]], N[(t * b), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if t < -2.69999999999999996e38 or 3.99999999999999982e37 < t

   1. Initial program 89.0%

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

   3. Taylor expanded in b around inf 44.5%

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

   4. Taylor expanded in t around inf 37.3%

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

   if -2.69999999999999996e38 < t < 3.99999999999999982e37

   1. Initial program 97.2%

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

   3. Taylor expanded in x around inf 17.8%

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

4. Final simplification 26.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.7 \cdot 10^{+38} \lor \neg \left(t \leq 4 \cdot 10^{+37}\right):\\ \;\;\;\;t \cdot b\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 26.2% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -3.8 \cdot 10^{+71}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;b \leq 2.4 \cdot 10^{+33}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -3.8e+71) (* y b) (if (<= b 2.4e+33) x (* t b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -3.8e+71) {
		tmp = y * b;
	} else if (b <= 2.4e+33) {
		tmp = x;
	} else {
		tmp = t * b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-3.8d+71)) then
        tmp = y * b
    else if (b <= 2.4d+33) then
        tmp = x
    else
        tmp = t * b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -3.8e+71) {
		tmp = y * b;
	} else if (b <= 2.4e+33) {
		tmp = x;
	} else {
		tmp = t * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -3.8e+71:
		tmp = y * b
	elif b <= 2.4e+33:
		tmp = x
	else:
		tmp = t * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -3.8e+71)
		tmp = Float64(y * b);
	elseif (b <= 2.4e+33)
		tmp = x;
	else
		tmp = Float64(t * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -3.8e+71)
		tmp = y * b;
	elseif (b <= 2.4e+33)
		tmp = x;
	else
		tmp = t * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -3.8e+71], N[(y * b), $MachinePrecision], If[LessEqual[b, 2.4e+33], x, N[(t * b), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -3.8000000000000001e71

   1. Initial program 87.9%

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

   3. Taylor expanded in z around 0 86.5%

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

   4. Taylor expanded in y around inf 39.9%

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

   if -3.8000000000000001e71 < b < 2.4e33

   1. Initial program 99.3%

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

   3. Taylor expanded in x around inf 20.4%

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

   if 2.4e33 < b

   1. Initial program 85.4%

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

   3. Taylor expanded in b around inf 72.2%

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

   4. Taylor expanded in t around inf 35.9%

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

4. Final simplification 28.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.8 \cdot 10^{+71}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;b \leq 2.4 \cdot 10^{+33}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 33.4% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.15 \cdot 10^{+75}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;b \leq 1.02 \cdot 10^{+34}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1.15e+75) (* y b) (if (<= b 1.02e+34) (+ x z) (* t b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.15e+75) {
		tmp = y * b;
	} else if (b <= 1.02e+34) {
		tmp = x + 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 <= (-1.15d+75)) then
        tmp = y * b
    else if (b <= 1.02d+34) then
        tmp = x + 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 <= -1.15e+75) {
		tmp = y * b;
	} else if (b <= 1.02e+34) {
		tmp = x + z;
	} else {
		tmp = t * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -1.15e+75:
		tmp = y * b
	elif b <= 1.02e+34:
		tmp = x + z
	else:
		tmp = t * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1.15e+75)
		tmp = Float64(y * b);
	elseif (b <= 1.02e+34)
		tmp = Float64(x + 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 <= -1.15e+75)
		tmp = y * b;
	elseif (b <= 1.02e+34)
		tmp = x + z;
	else
		tmp = t * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1.15e+75], N[(y * b), $MachinePrecision], If[LessEqual[b, 1.02e+34], N[(x + z), $MachinePrecision], N[(t * b), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.1499999999999999e75

   1. Initial program 87.9%

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

   3. Taylor expanded in z around 0 86.5%

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

   4. Taylor expanded in y around inf 39.9%

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

   if -1.1499999999999999e75 < b < 1.02e34

   1. Initial program 99.3%

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

   3. Taylor expanded in y around 0 99.3%

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

      1. associate--l+ 99.3%

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

      2. sub-neg 99.3%

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

      3. +-commutative 99.3%

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

      4. fma-define 99.3%

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

      5. sub-neg 99.3%

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

      6. metadata-eval 99.3%

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

      7. sub-neg 99.3%

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

      8. metadata-eval 99.3%

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

      9. *-commutative 99.3%

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

      10. distribute-neg-in 99.3%

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

      11. neg-mul-1 99.3%

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

      12. remove-double-neg 99.3%

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

      13. *-commutative 99.3%

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

      14. distribute-rgt-neg-in 99.3%

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

      15. distribute-neg-in 99.3%

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

      16. metadata-eval 99.3%

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

      17. +-commutative 99.3%

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

      18. sub-neg 99.3%

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

   5. Simplified 99.3%

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

   6. Taylor expanded in t around inf 74.7%

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

      1. *-commutative 74.7%

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

   8. Simplified 74.7%

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

   9. Taylor expanded in z around inf 33.2%

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

   if 1.02e34 < b

   1. Initial program 85.4%

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

   3. Taylor expanded in b around inf 72.2%

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

   4. Taylor expanded in t around inf 35.9%

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

4. Final simplification 35.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.15 \cdot 10^{+75}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;b \leq 1.02 \cdot 10^{+34}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 20.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.1 \cdot 10^{+78}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{+62}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -2.1e+78) x (if (<= x 9.5e+62) z x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -2.1e+78) {
		tmp = x;
	} else if (x <= 9.5e+62) {
		tmp = z;
	} 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 <= (-2.1d+78)) then
        tmp = x
    else if (x <= 9.5d+62) then
        tmp = z
    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 <= -2.1e+78) {
		tmp = x;
	} else if (x <= 9.5e+62) {
		tmp = z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -2.1e+78:
		tmp = x
	elif x <= 9.5e+62:
		tmp = z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -2.1e+78)
		tmp = x;
	elseif (x <= 9.5e+62)
		tmp = z;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -2.1e+78)
		tmp = x;
	elseif (x <= 9.5e+62)
		tmp = z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -2.1e+78], x, If[LessEqual[x, 9.5e+62], z, x]]

Derivation

1. Split input into 2 regimes

2. if x < -2.1000000000000001e78 or 9.5000000000000003e62 < x

   1. Initial program 92.6%

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

   3. Taylor expanded in x around inf 33.2%

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

   if -2.1000000000000001e78 < x < 9.5000000000000003e62

   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 z around inf 34.0%

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

   4. Taylor expanded in y around 0 13.6%

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

4. Final simplification 20.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.1 \cdot 10^{+78}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{+62}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 15.6% accurate, 21.0× speedup

Math

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

FPCore

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

C

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

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
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 93.7%

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

3. Taylor expanded in x around inf 13.9%

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

4. Final simplification 13.9%

   \[\leadsto x \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024039 
(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)))