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

Percentage Accurate: 95.3% → 97.9%

Time: 14.2s

Alternatives: 24

Speedup: 0.5×

• 35.5% 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

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

FPCore

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

C

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

Java

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

Python

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

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(x + Float64(z * Float64(1.0 - y))) + Float64(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(t * Float64(b - a));
	end
	return tmp
end

MATLAB

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

Wolfram

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

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

   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. Taylor expanded in t around inf 67.4%

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

4. Final simplification 99.2%

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

Alternative 2: 97.5% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 97.7%

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

   1. +-commutative 97.7%

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

   2. fma-def 98.4%

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

   3. associate--l+ 98.4%

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

   4. sub-neg 98.4%

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

   5. metadata-eval 98.4%

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

   6. sub-neg 98.4%

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

   7. associate-+l- 98.4%

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

   8. fma-neg 98.4%

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

   9. sub-neg 98.4%

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

   10. metadata-eval 98.4%

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

   11. remove-double-neg 98.4%

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

   12. sub-neg 98.4%

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

   13. metadata-eval 98.4%

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

3. Simplified 98.4%

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

4. Final simplification 98.4%

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

Alternative 3: 62.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(a - y \cdot z\right)\\ t_2 := x + b \cdot \left(\left(y + t\right) - 2\right)\\ t_3 := x + a \cdot \left(1 - t\right)\\ t_4 := z \cdot \left(1 - y\right)\\ \mathbf{if}\;b \leq -3.5 \cdot 10^{+49}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -4.8 \cdot 10^{-81}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -1.7 \cdot 10^{-248}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq 2.4 \cdot 10^{-299}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 2.9 \cdot 10^{-260}:\\ \;\;\;\;a + \left(x + z\right)\\ \mathbf{elif}\;b \leq 1.86 \cdot 10^{-152}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq 3.25 \cdot 10^{-115}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;b \leq 1.65 \cdot 10^{-43}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq 2.3 \cdot 10^{-9}:\\ \;\;\;\;t_4\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (- a (* y z))))
        (t_2 (+ x (* b (- (+ y t) 2.0))))
        (t_3 (+ x (* a (- 1.0 t))))
        (t_4 (* z (- 1.0 y))))
   (if (<= b -3.5e+49)
     t_2
     (if (<= b -4.8e-81)
       t_1
       (if (<= b -1.7e-248)
         t_3
         (if (<= b 2.4e-299)
           t_1
           (if (<= b 2.9e-260)
             (+ a (+ x z))
             (if (<= b 1.86e-152)
               t_3
               (if (<= b 3.25e-115)
                 t_4
                 (if (<= b 1.65e-43) t_3 (if (<= b 2.3e-9) t_4 t_2)))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (a - (y * z));
	double t_2 = x + (b * ((y + t) - 2.0));
	double t_3 = x + (a * (1.0 - t));
	double t_4 = z * (1.0 - y);
	double tmp;
	if (b <= -3.5e+49) {
		tmp = t_2;
	} else if (b <= -4.8e-81) {
		tmp = t_1;
	} else if (b <= -1.7e-248) {
		tmp = t_3;
	} else if (b <= 2.4e-299) {
		tmp = t_1;
	} else if (b <= 2.9e-260) {
		tmp = a + (x + z);
	} else if (b <= 1.86e-152) {
		tmp = t_3;
	} else if (b <= 3.25e-115) {
		tmp = t_4;
	} else if (b <= 1.65e-43) {
		tmp = t_3;
	} else if (b <= 2.3e-9) {
		tmp = t_4;
	} 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) :: t_4
    real(8) :: tmp
    t_1 = x + (a - (y * z))
    t_2 = x + (b * ((y + t) - 2.0d0))
    t_3 = x + (a * (1.0d0 - t))
    t_4 = z * (1.0d0 - y)
    if (b <= (-3.5d+49)) then
        tmp = t_2
    else if (b <= (-4.8d-81)) then
        tmp = t_1
    else if (b <= (-1.7d-248)) then
        tmp = t_3
    else if (b <= 2.4d-299) then
        tmp = t_1
    else if (b <= 2.9d-260) then
        tmp = a + (x + z)
    else if (b <= 1.86d-152) then
        tmp = t_3
    else if (b <= 3.25d-115) then
        tmp = t_4
    else if (b <= 1.65d-43) then
        tmp = t_3
    else if (b <= 2.3d-9) then
        tmp = t_4
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (a - (y * z));
	double t_2 = x + (b * ((y + t) - 2.0));
	double t_3 = x + (a * (1.0 - t));
	double t_4 = z * (1.0 - y);
	double tmp;
	if (b <= -3.5e+49) {
		tmp = t_2;
	} else if (b <= -4.8e-81) {
		tmp = t_1;
	} else if (b <= -1.7e-248) {
		tmp = t_3;
	} else if (b <= 2.4e-299) {
		tmp = t_1;
	} else if (b <= 2.9e-260) {
		tmp = a + (x + z);
	} else if (b <= 1.86e-152) {
		tmp = t_3;
	} else if (b <= 3.25e-115) {
		tmp = t_4;
	} else if (b <= 1.65e-43) {
		tmp = t_3;
	} else if (b <= 2.3e-9) {
		tmp = t_4;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (a - (y * z))
	t_2 = x + (b * ((y + t) - 2.0))
	t_3 = x + (a * (1.0 - t))
	t_4 = z * (1.0 - y)
	tmp = 0
	if b <= -3.5e+49:
		tmp = t_2
	elif b <= -4.8e-81:
		tmp = t_1
	elif b <= -1.7e-248:
		tmp = t_3
	elif b <= 2.4e-299:
		tmp = t_1
	elif b <= 2.9e-260:
		tmp = a + (x + z)
	elif b <= 1.86e-152:
		tmp = t_3
	elif b <= 3.25e-115:
		tmp = t_4
	elif b <= 1.65e-43:
		tmp = t_3
	elif b <= 2.3e-9:
		tmp = t_4
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(a - Float64(y * z)))
	t_2 = Float64(x + Float64(b * Float64(Float64(y + t) - 2.0)))
	t_3 = Float64(x + Float64(a * Float64(1.0 - t)))
	t_4 = Float64(z * Float64(1.0 - y))
	tmp = 0.0
	if (b <= -3.5e+49)
		tmp = t_2;
	elseif (b <= -4.8e-81)
		tmp = t_1;
	elseif (b <= -1.7e-248)
		tmp = t_3;
	elseif (b <= 2.4e-299)
		tmp = t_1;
	elseif (b <= 2.9e-260)
		tmp = Float64(a + Float64(x + z));
	elseif (b <= 1.86e-152)
		tmp = t_3;
	elseif (b <= 3.25e-115)
		tmp = t_4;
	elseif (b <= 1.65e-43)
		tmp = t_3;
	elseif (b <= 2.3e-9)
		tmp = t_4;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (a - (y * z));
	t_2 = x + (b * ((y + t) - 2.0));
	t_3 = x + (a * (1.0 - t));
	t_4 = z * (1.0 - y);
	tmp = 0.0;
	if (b <= -3.5e+49)
		tmp = t_2;
	elseif (b <= -4.8e-81)
		tmp = t_1;
	elseif (b <= -1.7e-248)
		tmp = t_3;
	elseif (b <= 2.4e-299)
		tmp = t_1;
	elseif (b <= 2.9e-260)
		tmp = a + (x + z);
	elseif (b <= 1.86e-152)
		tmp = t_3;
	elseif (b <= 3.25e-115)
		tmp = t_4;
	elseif (b <= 1.65e-43)
		tmp = t_3;
	elseif (b <= 2.3e-9)
		tmp = t_4;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(a - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -3.5e+49], t$95$2, If[LessEqual[b, -4.8e-81], t$95$1, If[LessEqual[b, -1.7e-248], t$95$3, If[LessEqual[b, 2.4e-299], t$95$1, If[LessEqual[b, 2.9e-260], N[(a + N[(x + z), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.86e-152], t$95$3, If[LessEqual[b, 3.25e-115], t$95$4, If[LessEqual[b, 1.65e-43], t$95$3, If[LessEqual[b, 2.3e-9], t$95$4, t$95$2]]]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -3.49999999999999975e49 or 2.2999999999999999e-9 < b

   1. Initial program 94.3%

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

   2. Taylor expanded in z around 0 88.3%

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

   3. Taylor expanded in a around 0 80.7%

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

   if -3.49999999999999975e49 < b < -4.7999999999999998e-81 or -1.6999999999999999e-248 < b < 2.40000000000000019e-299

   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. Taylor expanded in b around 0 92.6%

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

   3. Taylor expanded in t around 0 80.9%

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

      1. neg-mul-1 50.3%

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

   5. Simplified 80.9%

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

   6. Taylor expanded in y around inf 70.8%

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

      1. *-commutative 70.8%

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

   8. Simplified 70.8%

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

   if -4.7999999999999998e-81 < b < -1.6999999999999999e-248 or 2.8999999999999999e-260 < b < 1.8600000000000001e-152 or 3.25000000000000016e-115 < b < 1.65000000000000008e-43

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 75.4%

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

   3. Taylor expanded in b around 0 74.0%

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

   if 2.40000000000000019e-299 < b < 2.8999999999999999e-260

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. fma-def 100.0%

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

      3. associate--l+ 100.0%

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

      4. sub-neg 100.0%

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

      5. metadata-eval 100.0%

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

      6. sub-neg 100.0%

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

      7. associate-+l- 100.0%

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

      8. fma-neg 100.0%

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

      9. sub-neg 100.0%

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

      10. metadata-eval 100.0%

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

      11. remove-double-neg 100.0%

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

      12. sub-neg 100.0%

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

      13. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 96.7%

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

      1. +-commutative 96.7%

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

      2. sub-neg 96.7%

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

      3. metadata-eval 96.7%

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

      4. *-commutative 96.7%

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

      5. neg-mul-1 96.7%

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

      6. unsub-neg 96.7%

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

      7. *-commutative 96.7%

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

   6. Simplified 96.7%

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

   7. Taylor expanded in b around 0 96.7%

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

   8. Taylor expanded in t around 0 60.7%

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

      1. neg-mul-1 60.7%

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

   10. Simplified 60.7%

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

   if 1.8600000000000001e-152 < b < 3.25000000000000016e-115 or 1.65000000000000008e-43 < b < 2.2999999999999999e-9

   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. Taylor expanded in z around inf 76.1%

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

4. Final simplification 75.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.5 \cdot 10^{+49}:\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{elif}\;b \leq -4.8 \cdot 10^{-81}:\\ \;\;\;\;x + \left(a - y \cdot z\right)\\ \mathbf{elif}\;b \leq -1.7 \cdot 10^{-248}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 2.4 \cdot 10^{-299}:\\ \;\;\;\;x + \left(a - y \cdot z\right)\\ \mathbf{elif}\;b \leq 2.9 \cdot 10^{-260}:\\ \;\;\;\;a + \left(x + z\right)\\ \mathbf{elif}\;b \leq 1.86 \cdot 10^{-152}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 3.25 \cdot 10^{-115}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq 1.65 \cdot 10^{-43}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 2.3 \cdot 10^{-9}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \end{array} \]

Alternative 4: 86.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(1 - y\right)\\ t_2 := x + b \cdot \left(\left(y + t\right) - 2\right)\\ t_3 := a \cdot \left(1 - t\right)\\ t_4 := t_2 + t_3\\ \mathbf{if}\;b \leq -9.6 \cdot 10^{+129}:\\ \;\;\;\;\left(x + z\right) + b \cdot \left(t + \left(y + -2\right)\right)\\ \mathbf{elif}\;b \leq -4.8 \cdot 10^{+22}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;b \leq -2.5 \cdot 10^{-17}:\\ \;\;\;\;t_2 + t_1\\ \mathbf{elif}\;b \leq 5.5 \cdot 10^{-9}:\\ \;\;\;\;x + \left(t_3 + t_1\right)\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (- 1.0 y)))
        (t_2 (+ x (* b (- (+ y t) 2.0))))
        (t_3 (* a (- 1.0 t)))
        (t_4 (+ t_2 t_3)))
   (if (<= b -9.6e+129)
     (+ (+ x z) (* b (+ t (+ y -2.0))))
     (if (<= b -4.8e+22)
       t_4
       (if (<= b -2.5e-17)
         (+ t_2 t_1)
         (if (<= b 5.5e-9) (+ x (+ t_3 t_1)) t_4))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (1.0 - y);
	double t_2 = x + (b * ((y + t) - 2.0));
	double t_3 = a * (1.0 - t);
	double t_4 = t_2 + t_3;
	double tmp;
	if (b <= -9.6e+129) {
		tmp = (x + z) + (b * (t + (y + -2.0)));
	} else if (b <= -4.8e+22) {
		tmp = t_4;
	} else if (b <= -2.5e-17) {
		tmp = t_2 + t_1;
	} else if (b <= 5.5e-9) {
		tmp = x + (t_3 + t_1);
	} else {
		tmp = t_4;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = z * (1.0d0 - y)
    t_2 = x + (b * ((y + t) - 2.0d0))
    t_3 = a * (1.0d0 - t)
    t_4 = t_2 + t_3
    if (b <= (-9.6d+129)) then
        tmp = (x + z) + (b * (t + (y + (-2.0d0))))
    else if (b <= (-4.8d+22)) then
        tmp = t_4
    else if (b <= (-2.5d-17)) then
        tmp = t_2 + t_1
    else if (b <= 5.5d-9) then
        tmp = x + (t_3 + t_1)
    else
        tmp = t_4
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (1.0 - y);
	double t_2 = x + (b * ((y + t) - 2.0));
	double t_3 = a * (1.0 - t);
	double t_4 = t_2 + t_3;
	double tmp;
	if (b <= -9.6e+129) {
		tmp = (x + z) + (b * (t + (y + -2.0)));
	} else if (b <= -4.8e+22) {
		tmp = t_4;
	} else if (b <= -2.5e-17) {
		tmp = t_2 + t_1;
	} else if (b <= 5.5e-9) {
		tmp = x + (t_3 + t_1);
	} else {
		tmp = t_4;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * (1.0 - y)
	t_2 = x + (b * ((y + t) - 2.0))
	t_3 = a * (1.0 - t)
	t_4 = t_2 + t_3
	tmp = 0
	if b <= -9.6e+129:
		tmp = (x + z) + (b * (t + (y + -2.0)))
	elif b <= -4.8e+22:
		tmp = t_4
	elif b <= -2.5e-17:
		tmp = t_2 + t_1
	elif b <= 5.5e-9:
		tmp = x + (t_3 + t_1)
	else:
		tmp = t_4
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(1.0 - y))
	t_2 = Float64(x + Float64(b * Float64(Float64(y + t) - 2.0)))
	t_3 = Float64(a * Float64(1.0 - t))
	t_4 = Float64(t_2 + t_3)
	tmp = 0.0
	if (b <= -9.6e+129)
		tmp = Float64(Float64(x + z) + Float64(b * Float64(t + Float64(y + -2.0))));
	elseif (b <= -4.8e+22)
		tmp = t_4;
	elseif (b <= -2.5e-17)
		tmp = Float64(t_2 + t_1);
	elseif (b <= 5.5e-9)
		tmp = Float64(x + Float64(t_3 + t_1));
	else
		tmp = t_4;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * (1.0 - y);
	t_2 = x + (b * ((y + t) - 2.0));
	t_3 = a * (1.0 - t);
	t_4 = t_2 + t_3;
	tmp = 0.0;
	if (b <= -9.6e+129)
		tmp = (x + z) + (b * (t + (y + -2.0)));
	elseif (b <= -4.8e+22)
		tmp = t_4;
	elseif (b <= -2.5e-17)
		tmp = t_2 + t_1;
	elseif (b <= 5.5e-9)
		tmp = x + (t_3 + t_1);
	else
		tmp = t_4;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(t$95$2 + t$95$3), $MachinePrecision]}, If[LessEqual[b, -9.6e+129], N[(N[(x + z), $MachinePrecision] + N[(b * N[(t + N[(y + -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -4.8e+22], t$95$4, If[LessEqual[b, -2.5e-17], N[(t$95$2 + t$95$1), $MachinePrecision], If[LessEqual[b, 5.5e-9], N[(x + N[(t$95$3 + t$95$1), $MachinePrecision]), $MachinePrecision], t$95$4]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -9.5999999999999995e129

   1. Initial program 88.2%

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

      1. +-commutative 88.2%

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

      2. fma-def 91.2%

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

      3. associate--l+ 91.2%

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

      4. sub-neg 91.2%

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

      5. metadata-eval 91.2%

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

      6. sub-neg 91.2%

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

      7. associate-+l- 91.2%

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

      8. fma-neg 91.2%

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

      9. sub-neg 91.2%

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

      10. metadata-eval 91.2%

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

      11. remove-double-neg 91.2%

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

      12. sub-neg 91.2%

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

      13. metadata-eval 91.2%

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

   3. Simplified 91.2%

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

   4. Taylor expanded in y around 0 91.2%

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

      1. +-commutative 91.2%

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

      2. sub-neg 91.2%

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

      3. metadata-eval 91.2%

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

      4. *-commutative 91.2%

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

      5. neg-mul-1 91.2%

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

      6. unsub-neg 91.2%

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

      7. *-commutative 91.2%

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

   6. Simplified 91.2%

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

   7. Taylor expanded in a around 0 97.1%

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

      1. associate-+r+ 97.1%

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

      2. associate--l+ 97.1%

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

      3. sub-neg 97.1%

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

      4. metadata-eval 97.1%

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

   9. Simplified 97.1%

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

   if -9.5999999999999995e129 < b < -4.8e22 or 5.4999999999999996e-9 < b

   1. Initial program 97.3%

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

   2. Taylor expanded in z around 0 91.5%

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

   if -4.8e22 < b < -2.4999999999999999e-17

   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. Taylor expanded in a around 0 100.0%

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

   if -2.4999999999999999e-17 < b < 5.4999999999999996e-9

   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. Taylor expanded in b around 0 97.9%

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

4. Final simplification 96.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -9.6 \cdot 10^{+129}:\\ \;\;\;\;\left(x + z\right) + b \cdot \left(t + \left(y + -2\right)\right)\\ \mathbf{elif}\;b \leq -4.8 \cdot 10^{+22}:\\ \;\;\;\;\left(x + b \cdot \left(\left(y + t\right) - 2\right)\right) + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq -2.5 \cdot 10^{-17}:\\ \;\;\;\;\left(x + b \cdot \left(\left(y + t\right) - 2\right)\right) + z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq 5.5 \cdot 10^{-9}:\\ \;\;\;\;x + \left(a \cdot \left(1 - t\right) + z \cdot \left(1 - y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + b \cdot \left(\left(y + t\right) - 2\right)\right) + a \cdot \left(1 - t\right)\\ \end{array} \]

Alternative 5: 73.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + z\right) + a \cdot \left(1 - t\right)\\ t_2 := x + \left(a + z \cdot \left(1 - y\right)\right)\\ t_3 := \left(x + z\right) + b \cdot \left(t + \left(y + -2\right)\right)\\ \mathbf{if}\;b \leq -0.006:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq -2.1 \cdot 10^{-82}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -2.2 \cdot 10^{-249}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 9.2 \cdot 10^{-299}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 4.4 \cdot 10^{-8}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (+ x z) (* a (- 1.0 t))))
        (t_2 (+ x (+ a (* z (- 1.0 y)))))
        (t_3 (+ (+ x z) (* b (+ t (+ y -2.0))))))
   (if (<= b -0.006)
     t_3
     (if (<= b -2.1e-82)
       t_2
       (if (<= b -2.2e-249)
         t_1
         (if (<= b 9.2e-299) t_2 (if (<= b 4.4e-8) t_1 t_3)))))))

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 + (a + (z * (1.0 - y)));
	double t_3 = (x + z) + (b * (t + (y + -2.0)));
	double tmp;
	if (b <= -0.006) {
		tmp = t_3;
	} else if (b <= -2.1e-82) {
		tmp = t_2;
	} else if (b <= -2.2e-249) {
		tmp = t_1;
	} else if (b <= 9.2e-299) {
		tmp = t_2;
	} else if (b <= 4.4e-8) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (x + z) + (a * (1.0d0 - t))
    t_2 = x + (a + (z * (1.0d0 - y)))
    t_3 = (x + z) + (b * (t + (y + (-2.0d0))))
    if (b <= (-0.006d0)) then
        tmp = t_3
    else if (b <= (-2.1d-82)) then
        tmp = t_2
    else if (b <= (-2.2d-249)) then
        tmp = t_1
    else if (b <= 9.2d-299) then
        tmp = t_2
    else if (b <= 4.4d-8) then
        tmp = t_1
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + z) + (a * (1.0 - t));
	double t_2 = x + (a + (z * (1.0 - y)));
	double t_3 = (x + z) + (b * (t + (y + -2.0)));
	double tmp;
	if (b <= -0.006) {
		tmp = t_3;
	} else if (b <= -2.1e-82) {
		tmp = t_2;
	} else if (b <= -2.2e-249) {
		tmp = t_1;
	} else if (b <= 9.2e-299) {
		tmp = t_2;
	} else if (b <= 4.4e-8) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x + z) + (a * (1.0 - t))
	t_2 = x + (a + (z * (1.0 - y)))
	t_3 = (x + z) + (b * (t + (y + -2.0)))
	tmp = 0
	if b <= -0.006:
		tmp = t_3
	elif b <= -2.1e-82:
		tmp = t_2
	elif b <= -2.2e-249:
		tmp = t_1
	elif b <= 9.2e-299:
		tmp = t_2
	elif b <= 4.4e-8:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + z) + Float64(a * Float64(1.0 - t)))
	t_2 = Float64(x + Float64(a + Float64(z * Float64(1.0 - y))))
	t_3 = Float64(Float64(x + z) + Float64(b * Float64(t + Float64(y + -2.0))))
	tmp = 0.0
	if (b <= -0.006)
		tmp = t_3;
	elseif (b <= -2.1e-82)
		tmp = t_2;
	elseif (b <= -2.2e-249)
		tmp = t_1;
	elseif (b <= 9.2e-299)
		tmp = t_2;
	elseif (b <= 4.4e-8)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x + z) + (a * (1.0 - t));
	t_2 = x + (a + (z * (1.0 - y)));
	t_3 = (x + z) + (b * (t + (y + -2.0)));
	tmp = 0.0;
	if (b <= -0.006)
		tmp = t_3;
	elseif (b <= -2.1e-82)
		tmp = t_2;
	elseif (b <= -2.2e-249)
		tmp = t_1;
	elseif (b <= 9.2e-299)
		tmp = t_2;
	elseif (b <= 4.4e-8)
		tmp = t_1;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x + z), $MachinePrecision] + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(a + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x + z), $MachinePrecision] + N[(b * N[(t + N[(y + -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -0.006], t$95$3, If[LessEqual[b, -2.1e-82], t$95$2, If[LessEqual[b, -2.2e-249], t$95$1, If[LessEqual[b, 9.2e-299], t$95$2, If[LessEqual[b, 4.4e-8], t$95$1, t$95$3]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -0.0060000000000000001 or 4.3999999999999997e-8 < b

   1. Initial program 94.7%

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

      1. +-commutative 94.7%

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

      2. fma-def 96.5%

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

      3. associate--l+ 96.5%

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

      4. sub-neg 96.5%

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

      5. metadata-eval 96.5%

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

      6. sub-neg 96.5%

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

      7. associate-+l- 96.5%

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

      8. fma-neg 96.5%

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

      9. sub-neg 96.5%

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

      10. metadata-eval 96.5%

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

      11. remove-double-neg 96.5%

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

      12. sub-neg 96.5%

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

      13. metadata-eval 96.5%

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

   3. Simplified 96.5%

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

   4. Taylor expanded in y around 0 96.5%

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

      1. +-commutative 96.5%

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

      2. sub-neg 96.5%

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

      3. metadata-eval 96.5%

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

      4. *-commutative 96.5%

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

      5. neg-mul-1 96.5%

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

      6. unsub-neg 96.5%

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

      7. *-commutative 96.5%

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

   6. Simplified 96.5%

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

   7. Taylor expanded in a around 0 86.1%

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

      1. associate-+r+ 86.1%

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

      2. associate--l+ 86.1%

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

      3. sub-neg 86.1%

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

      4. metadata-eval 86.1%

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

   9. Simplified 86.1%

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

   if -0.0060000000000000001 < b < -2.1e-82 or -2.2e-249 < b < 9.2000000000000003e-299

   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. Taylor expanded in b around 0 93.6%

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

   3. Taylor expanded in t around 0 84.6%

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

      1. neg-mul-1 48.8%

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

   5. Simplified 84.6%

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

   if -2.1e-82 < b < -2.2e-249 or 9.2000000000000003e-299 < b < 4.3999999999999997e-8

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. fma-def 100.0%

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

      3. associate--l+ 100.0%

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

      4. sub-neg 100.0%

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

      5. metadata-eval 100.0%

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

      6. sub-neg 100.0%

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

      7. associate-+l- 100.0%

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

      8. fma-neg 100.0%

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

      9. sub-neg 100.0%

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

      10. metadata-eval 100.0%

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

      11. remove-double-neg 100.0%

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

      12. sub-neg 100.0%

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

      13. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 86.6%

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

      1. +-commutative 86.6%

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

      2. sub-neg 86.6%

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

      3. metadata-eval 86.6%

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

      4. *-commutative 86.6%

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

      5. neg-mul-1 86.6%

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

      6. unsub-neg 86.6%

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

      7. *-commutative 86.6%

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

   6. Simplified 86.6%

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

   7. Taylor expanded in b around 0 84.7%

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

4. Final simplification 85.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -0.006:\\ \;\;\;\;\left(x + z\right) + b \cdot \left(t + \left(y + -2\right)\right)\\ \mathbf{elif}\;b \leq -2.1 \cdot 10^{-82}:\\ \;\;\;\;x + \left(a + z \cdot \left(1 - y\right)\right)\\ \mathbf{elif}\;b \leq -2.2 \cdot 10^{-249}:\\ \;\;\;\;\left(x + z\right) + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 9.2 \cdot 10^{-299}:\\ \;\;\;\;x + \left(a + z \cdot \left(1 - y\right)\right)\\ \mathbf{elif}\;b \leq 4.4 \cdot 10^{-8}:\\ \;\;\;\;\left(x + z\right) + a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + z\right) + b \cdot \left(t + \left(y + -2\right)\right)\\ \end{array} \]

Alternative 6: 70.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + z\right) + a \cdot \left(1 - t\right)\\ t_2 := x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{if}\;b \leq -3.3 \cdot 10^{+53}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -0.0061:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -0.006:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;b \leq -6.6 \cdot 10^{-81}:\\ \;\;\;\;x + \left(a - y \cdot z\right)\\ \mathbf{elif}\;b \leq 1.15 \cdot 10^{+116}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (+ x z) (* a (- 1.0 t)))) (t_2 (+ x (* b (- (+ y t) 2.0)))))
   (if (<= b -3.3e+53)
     t_2
     (if (<= b -0.0061)
       t_1
       (if (<= b -0.006)
         (* y b)
         (if (<= b -6.6e-81)
           (+ x (- a (* y z)))
           (if (<= b 1.15e+116) t_1 t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + z) + (a * (1.0 - t));
	double t_2 = x + (b * ((y + t) - 2.0));
	double tmp;
	if (b <= -3.3e+53) {
		tmp = t_2;
	} else if (b <= -0.0061) {
		tmp = t_1;
	} else if (b <= -0.006) {
		tmp = y * b;
	} else if (b <= -6.6e-81) {
		tmp = x + (a - (y * z));
	} else if (b <= 1.15e+116) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x + z) + (a * (1.0d0 - t))
    t_2 = x + (b * ((y + t) - 2.0d0))
    if (b <= (-3.3d+53)) then
        tmp = t_2
    else if (b <= (-0.0061d0)) then
        tmp = t_1
    else if (b <= (-0.006d0)) then
        tmp = y * b
    else if (b <= (-6.6d-81)) then
        tmp = x + (a - (y * z))
    else if (b <= 1.15d+116) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + z) + (a * (1.0 - t));
	double t_2 = x + (b * ((y + t) - 2.0));
	double tmp;
	if (b <= -3.3e+53) {
		tmp = t_2;
	} else if (b <= -0.0061) {
		tmp = t_1;
	} else if (b <= -0.006) {
		tmp = y * b;
	} else if (b <= -6.6e-81) {
		tmp = x + (a - (y * z));
	} else if (b <= 1.15e+116) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x + z) + (a * (1.0 - t))
	t_2 = x + (b * ((y + t) - 2.0))
	tmp = 0
	if b <= -3.3e+53:
		tmp = t_2
	elif b <= -0.0061:
		tmp = t_1
	elif b <= -0.006:
		tmp = y * b
	elif b <= -6.6e-81:
		tmp = x + (a - (y * z))
	elif b <= 1.15e+116:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + z) + Float64(a * Float64(1.0 - t)))
	t_2 = Float64(x + Float64(b * Float64(Float64(y + t) - 2.0)))
	tmp = 0.0
	if (b <= -3.3e+53)
		tmp = t_2;
	elseif (b <= -0.0061)
		tmp = t_1;
	elseif (b <= -0.006)
		tmp = Float64(y * b);
	elseif (b <= -6.6e-81)
		tmp = Float64(x + Float64(a - Float64(y * z)));
	elseif (b <= 1.15e+116)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x + z) + (a * (1.0 - t));
	t_2 = x + (b * ((y + t) - 2.0));
	tmp = 0.0;
	if (b <= -3.3e+53)
		tmp = t_2;
	elseif (b <= -0.0061)
		tmp = t_1;
	elseif (b <= -0.006)
		tmp = y * b;
	elseif (b <= -6.6e-81)
		tmp = x + (a - (y * z));
	elseif (b <= 1.15e+116)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x + z), $MachinePrecision] + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -3.3e+53], t$95$2, If[LessEqual[b, -0.0061], t$95$1, If[LessEqual[b, -0.006], N[(y * b), $MachinePrecision], If[LessEqual[b, -6.6e-81], N[(x + N[(a - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.15e+116], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -3.3000000000000002e53 or 1.14999999999999997e116 < b

   1. Initial program 93.9%

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

   2. Taylor expanded in z around 0 90.8%

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

   3. Taylor expanded in a around 0 88.1%

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

   if -3.3000000000000002e53 < b < -0.00610000000000000039 or -6.59999999999999975e-81 < b < 1.14999999999999997e116

   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. Step-by-step derivation

      1. +-commutative 99.3%

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

      2. fma-def 100.0%

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

      3. associate--l+ 100.0%

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

      4. sub-neg 100.0%

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

      5. metadata-eval 100.0%

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

      6. sub-neg 100.0%

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

      7. associate-+l- 100.0%

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

      8. fma-neg 100.0%

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

      9. sub-neg 100.0%

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

      10. metadata-eval 100.0%

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

      11. remove-double-neg 100.0%

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

      12. sub-neg 100.0%

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

      13. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 86.5%

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

      1. +-commutative 86.5%

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

      2. sub-neg 86.5%

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

      3. metadata-eval 86.5%

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

      4. *-commutative 86.5%

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

      5. neg-mul-1 86.5%

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

      6. unsub-neg 86.5%

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

      7. *-commutative 86.5%

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

   6. Simplified 86.5%

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

   7. Taylor expanded in b around 0 79.7%

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

   if -0.00610000000000000039 < b < -0.0060000000000000001

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. fma-def 100.0%

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

      3. associate--l+ 100.0%

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

      4. sub-neg 100.0%

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

      5. metadata-eval 100.0%

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

      6. sub-neg 100.0%

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

      7. associate-+l- 100.0%

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

      8. fma-neg 100.0%

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

      9. sub-neg 100.0%

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

      10. metadata-eval 100.0%

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

      11. remove-double-neg 100.0%

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

      12. sub-neg 100.0%

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

      13. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 100.0%

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

      1. +-commutative 100.0%

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

      2. sub-neg 100.0%

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

      3. metadata-eval 100.0%

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

      4. *-commutative 100.0%

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

      5. neg-mul-1 100.0%

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

      6. unsub-neg 100.0%

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

      7. *-commutative 100.0%

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

   6. Simplified 100.0%

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

   7. Taylor expanded in y around inf 100.0%

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

   if -0.0060000000000000001 < b < -6.59999999999999975e-81

   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. Taylor expanded in b around 0 87.2%

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

   3. Taylor expanded in t around 0 82.7%

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

      1. neg-mul-1 43.0%

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

   5. Simplified 82.7%

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

   6. Taylor expanded in y around inf 67.9%

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

      1. *-commutative 67.9%

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

   8. Simplified 67.9%

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

4. Final simplification 81.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.3 \cdot 10^{+53}:\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{elif}\;b \leq -0.0061:\\ \;\;\;\;\left(x + z\right) + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq -0.006:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;b \leq -6.6 \cdot 10^{-81}:\\ \;\;\;\;x + \left(a - y \cdot z\right)\\ \mathbf{elif}\;b \leq 1.15 \cdot 10^{+116}:\\ \;\;\;\;\left(x + z\right) + a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \end{array} \]

Alternative 7: 71.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(a + z \cdot \left(1 - y\right)\right)\\ t_2 := x + b \cdot \left(\left(y + t\right) - 2\right)\\ t_3 := \left(x + z\right) + a \cdot \left(1 - t\right)\\ \mathbf{if}\;b \leq -4 \cdot 10^{+53}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -1.55 \cdot 10^{-81}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -2.05 \cdot 10^{-249}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq 3.1 \cdot 10^{-299}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 1.15 \cdot 10^{+116}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (+ a (* z (- 1.0 y)))))
        (t_2 (+ x (* b (- (+ y t) 2.0))))
        (t_3 (+ (+ x z) (* a (- 1.0 t)))))
   (if (<= b -4e+53)
     t_2
     (if (<= b -1.55e-81)
       t_1
       (if (<= b -2.05e-249)
         t_3
         (if (<= b 3.1e-299) t_1 (if (<= b 1.15e+116) t_3 t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (a + (z * (1.0 - y)));
	double t_2 = x + (b * ((y + t) - 2.0));
	double t_3 = (x + z) + (a * (1.0 - t));
	double tmp;
	if (b <= -4e+53) {
		tmp = t_2;
	} else if (b <= -1.55e-81) {
		tmp = t_1;
	} else if (b <= -2.05e-249) {
		tmp = t_3;
	} else if (b <= 3.1e-299) {
		tmp = t_1;
	} else if (b <= 1.15e+116) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = x + (a + (z * (1.0d0 - y)))
    t_2 = x + (b * ((y + t) - 2.0d0))
    t_3 = (x + z) + (a * (1.0d0 - t))
    if (b <= (-4d+53)) then
        tmp = t_2
    else if (b <= (-1.55d-81)) then
        tmp = t_1
    else if (b <= (-2.05d-249)) then
        tmp = t_3
    else if (b <= 3.1d-299) then
        tmp = t_1
    else if (b <= 1.15d+116) then
        tmp = t_3
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (a + (z * (1.0 - y)));
	double t_2 = x + (b * ((y + t) - 2.0));
	double t_3 = (x + z) + (a * (1.0 - t));
	double tmp;
	if (b <= -4e+53) {
		tmp = t_2;
	} else if (b <= -1.55e-81) {
		tmp = t_1;
	} else if (b <= -2.05e-249) {
		tmp = t_3;
	} else if (b <= 3.1e-299) {
		tmp = t_1;
	} else if (b <= 1.15e+116) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (a + (z * (1.0 - y)))
	t_2 = x + (b * ((y + t) - 2.0))
	t_3 = (x + z) + (a * (1.0 - t))
	tmp = 0
	if b <= -4e+53:
		tmp = t_2
	elif b <= -1.55e-81:
		tmp = t_1
	elif b <= -2.05e-249:
		tmp = t_3
	elif b <= 3.1e-299:
		tmp = t_1
	elif b <= 1.15e+116:
		tmp = t_3
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(a + Float64(z * Float64(1.0 - y))))
	t_2 = Float64(x + Float64(b * Float64(Float64(y + t) - 2.0)))
	t_3 = Float64(Float64(x + z) + Float64(a * Float64(1.0 - t)))
	tmp = 0.0
	if (b <= -4e+53)
		tmp = t_2;
	elseif (b <= -1.55e-81)
		tmp = t_1;
	elseif (b <= -2.05e-249)
		tmp = t_3;
	elseif (b <= 3.1e-299)
		tmp = t_1;
	elseif (b <= 1.15e+116)
		tmp = t_3;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (a + (z * (1.0 - y)));
	t_2 = x + (b * ((y + t) - 2.0));
	t_3 = (x + z) + (a * (1.0 - t));
	tmp = 0.0;
	if (b <= -4e+53)
		tmp = t_2;
	elseif (b <= -1.55e-81)
		tmp = t_1;
	elseif (b <= -2.05e-249)
		tmp = t_3;
	elseif (b <= 3.1e-299)
		tmp = t_1;
	elseif (b <= 1.15e+116)
		tmp = t_3;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(a + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x + z), $MachinePrecision] + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -4e+53], t$95$2, If[LessEqual[b, -1.55e-81], t$95$1, If[LessEqual[b, -2.05e-249], t$95$3, If[LessEqual[b, 3.1e-299], t$95$1, If[LessEqual[b, 1.15e+116], t$95$3, t$95$2]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -4e53 or 1.14999999999999997e116 < b

   1. Initial program 93.9%

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

   2. Taylor expanded in z around 0 90.8%

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

   3. Taylor expanded in a around 0 88.1%

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

   if -4e53 < b < -1.54999999999999994e-81 or -2.05000000000000002e-249 < b < 3.1e-299

   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. Taylor expanded in b around 0 92.9%

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

   3. Taylor expanded in t around 0 81.7%

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

      1. neg-mul-1 51.6%

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

   5. Simplified 81.7%

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

   if -1.54999999999999994e-81 < b < -2.05000000000000002e-249 or 3.1e-299 < b < 1.14999999999999997e116

   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. Step-by-step derivation

      1. +-commutative 99.2%

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

      2. fma-def 100.0%

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

      3. associate--l+ 100.0%

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

      4. sub-neg 100.0%

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

      5. metadata-eval 100.0%

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

      6. sub-neg 100.0%

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

      7. associate-+l- 100.0%

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

      8. fma-neg 100.0%

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

      9. sub-neg 100.0%

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

      10. metadata-eval 100.0%

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

      11. remove-double-neg 100.0%

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

      12. sub-neg 100.0%

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

      13. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 89.0%

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

      1. +-commutative 89.0%

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

      2. sub-neg 89.0%

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

      3. metadata-eval 89.0%

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

      4. *-commutative 89.0%

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

      5. neg-mul-1 89.0%

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

      6. unsub-neg 89.0%

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

      7. *-commutative 89.0%

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

   6. Simplified 89.0%

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

   7. Taylor expanded in b around 0 80.5%

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

4. Final simplification 83.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4 \cdot 10^{+53}:\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{elif}\;b \leq -1.55 \cdot 10^{-81}:\\ \;\;\;\;x + \left(a + z \cdot \left(1 - y\right)\right)\\ \mathbf{elif}\;b \leq -2.05 \cdot 10^{-249}:\\ \;\;\;\;\left(x + z\right) + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 3.1 \cdot 10^{-299}:\\ \;\;\;\;x + \left(a + z \cdot \left(1 - y\right)\right)\\ \mathbf{elif}\;b \leq 1.15 \cdot 10^{+116}:\\ \;\;\;\;\left(x + z\right) + a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \end{array} \]

Alternative 8: 85.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(1 - t\right)\\ t_2 := z \cdot \left(1 - y\right)\\ \mathbf{if}\;t \leq -1.55 \cdot 10^{+44}:\\ \;\;\;\;\left(x + b \cdot \left(\left(y + t\right) - 2\right)\right) + t_1\\ \mathbf{elif}\;t \leq 6 \cdot 10^{+25}:\\ \;\;\;\;\left(x + b \cdot \left(y - 2\right)\right) + \left(a + t_2\right)\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{+239}:\\ \;\;\;\;x + \left(t_1 + t_2\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (- 1.0 t))) (t_2 (* z (- 1.0 y))))
   (if (<= t -1.55e+44)
     (+ (+ x (* b (- (+ y t) 2.0))) t_1)
     (if (<= t 6e+25)
       (+ (+ x (* b (- y 2.0))) (+ a t_2))
       (if (<= t 4.6e+239) (+ x (+ t_1 t_2)) (* t (- b a)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double t_2 = z * (1.0 - y);
	double tmp;
	if (t <= -1.55e+44) {
		tmp = (x + (b * ((y + t) - 2.0))) + t_1;
	} else if (t <= 6e+25) {
		tmp = (x + (b * (y - 2.0))) + (a + t_2);
	} else if (t <= 4.6e+239) {
		tmp = x + (t_1 + t_2);
	} else {
		tmp = t * (b - a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a * (1.0d0 - t)
    t_2 = z * (1.0d0 - y)
    if (t <= (-1.55d+44)) then
        tmp = (x + (b * ((y + t) - 2.0d0))) + t_1
    else if (t <= 6d+25) then
        tmp = (x + (b * (y - 2.0d0))) + (a + t_2)
    else if (t <= 4.6d+239) then
        tmp = x + (t_1 + t_2)
    else
        tmp = t * (b - a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double t_2 = z * (1.0 - y);
	double tmp;
	if (t <= -1.55e+44) {
		tmp = (x + (b * ((y + t) - 2.0))) + t_1;
	} else if (t <= 6e+25) {
		tmp = (x + (b * (y - 2.0))) + (a + t_2);
	} else if (t <= 4.6e+239) {
		tmp = x + (t_1 + t_2);
	} else {
		tmp = t * (b - a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (1.0 - t)
	t_2 = z * (1.0 - y)
	tmp = 0
	if t <= -1.55e+44:
		tmp = (x + (b * ((y + t) - 2.0))) + t_1
	elif t <= 6e+25:
		tmp = (x + (b * (y - 2.0))) + (a + t_2)
	elif t <= 4.6e+239:
		tmp = x + (t_1 + t_2)
	else:
		tmp = t * (b - a)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(1.0 - t))
	t_2 = Float64(z * Float64(1.0 - y))
	tmp = 0.0
	if (t <= -1.55e+44)
		tmp = Float64(Float64(x + Float64(b * Float64(Float64(y + t) - 2.0))) + t_1);
	elseif (t <= 6e+25)
		tmp = Float64(Float64(x + Float64(b * Float64(y - 2.0))) + Float64(a + t_2));
	elseif (t <= 4.6e+239)
		tmp = Float64(x + Float64(t_1 + t_2));
	else
		tmp = Float64(t * Float64(b - a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (1.0 - t);
	t_2 = z * (1.0 - y);
	tmp = 0.0;
	if (t <= -1.55e+44)
		tmp = (x + (b * ((y + t) - 2.0))) + t_1;
	elseif (t <= 6e+25)
		tmp = (x + (b * (y - 2.0))) + (a + t_2);
	elseif (t <= 4.6e+239)
		tmp = x + (t_1 + t_2);
	else
		tmp = t * (b - a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.55e+44], N[(N[(x + N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[t, 6e+25], N[(N[(x + N[(b * N[(y - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a + t$95$2), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.6e+239], N[(x + N[(t$95$1 + t$95$2), $MachinePrecision]), $MachinePrecision], N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.54999999999999998e44

   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. Taylor expanded in z around 0 91.6%

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

   if -1.54999999999999998e44 < t < 6.00000000000000011e25

   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. Taylor expanded in t around 0 98.8%

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

   if 6.00000000000000011e25 < t < 4.6000000000000004e239

   1. Initial program 98.0%

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

   2. Taylor expanded in b around 0 84.3%

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

   if 4.6000000000000004e239 < t

   1. Initial program 85.7%

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

   2. Taylor expanded in t around inf 100.0%

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

4. Final simplification 94.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.55 \cdot 10^{+44}:\\ \;\;\;\;\left(x + b \cdot \left(\left(y + t\right) - 2\right)\right) + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;t \leq 6 \cdot 10^{+25}:\\ \;\;\;\;\left(x + b \cdot \left(y - 2\right)\right) + \left(a + z \cdot \left(1 - y\right)\right)\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{+239}:\\ \;\;\;\;x + \left(a \cdot \left(1 - t\right) + z \cdot \left(1 - y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \]

Alternative 9: 86.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(1 - t\right)\\ \mathbf{if}\;b \leq -2.4 \cdot 10^{+53}:\\ \;\;\;\;\left(x + z\right) + b \cdot \left(t + \left(y + -2\right)\right)\\ \mathbf{elif}\;b \leq 4.6 \cdot 10^{-9}:\\ \;\;\;\;x + \left(t_1 + z \cdot \left(1 - y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + b \cdot \left(\left(y + t\right) - 2\right)\right) + t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (- 1.0 t))))
   (if (<= b -2.4e+53)
     (+ (+ x z) (* b (+ t (+ y -2.0))))
     (if (<= b 4.6e-9)
       (+ x (+ t_1 (* z (- 1.0 y))))
       (+ (+ x (* b (- (+ y t) 2.0))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double tmp;
	if (b <= -2.4e+53) {
		tmp = (x + z) + (b * (t + (y + -2.0)));
	} else if (b <= 4.6e-9) {
		tmp = x + (t_1 + (z * (1.0 - y)));
	} else {
		tmp = (x + (b * ((y + t) - 2.0))) + t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (1.0d0 - t)
    if (b <= (-2.4d+53)) then
        tmp = (x + z) + (b * (t + (y + (-2.0d0))))
    else if (b <= 4.6d-9) then
        tmp = x + (t_1 + (z * (1.0d0 - y)))
    else
        tmp = (x + (b * ((y + t) - 2.0d0))) + t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double tmp;
	if (b <= -2.4e+53) {
		tmp = (x + z) + (b * (t + (y + -2.0)));
	} else if (b <= 4.6e-9) {
		tmp = x + (t_1 + (z * (1.0 - y)));
	} else {
		tmp = (x + (b * ((y + t) - 2.0))) + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (1.0 - t)
	tmp = 0
	if b <= -2.4e+53:
		tmp = (x + z) + (b * (t + (y + -2.0)))
	elif b <= 4.6e-9:
		tmp = x + (t_1 + (z * (1.0 - y)))
	else:
		tmp = (x + (b * ((y + t) - 2.0))) + t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(1.0 - t))
	tmp = 0.0
	if (b <= -2.4e+53)
		tmp = Float64(Float64(x + z) + Float64(b * Float64(t + Float64(y + -2.0))));
	elseif (b <= 4.6e-9)
		tmp = Float64(x + Float64(t_1 + Float64(z * Float64(1.0 - y))));
	else
		tmp = Float64(Float64(x + Float64(b * Float64(Float64(y + t) - 2.0))) + t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (1.0 - t);
	tmp = 0.0;
	if (b <= -2.4e+53)
		tmp = (x + z) + (b * (t + (y + -2.0)));
	elseif (b <= 4.6e-9)
		tmp = x + (t_1 + (z * (1.0 - y)));
	else
		tmp = (x + (b * ((y + t) - 2.0))) + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2.4e+53], N[(N[(x + z), $MachinePrecision] + N[(b * N[(t + N[(y + -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 4.6e-9], N[(x + N[(t$95$1 + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if b < -2.4e53

   1. Initial program 91.5%

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

      1. +-commutative 91.5%

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

      2. fma-def 93.6%

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

      3. associate--l+ 93.6%

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

      4. sub-neg 93.6%

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

      5. metadata-eval 93.6%

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

      6. sub-neg 93.6%

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

      7. associate-+l- 93.6%

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

      8. fma-neg 93.6%

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

      9. sub-neg 93.6%

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

      10. metadata-eval 93.6%

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

      11. remove-double-neg 93.6%

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

      12. sub-neg 93.6%

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

      13. metadata-eval 93.6%

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

   3. Simplified 93.6%

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

   4. Taylor expanded in y around 0 93.6%

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

      1. +-commutative 93.6%

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

      2. sub-neg 93.6%

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

      3. metadata-eval 93.6%

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

      4. *-commutative 93.6%

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

      5. neg-mul-1 93.6%

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

      6. unsub-neg 93.6%

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

      7. *-commutative 93.6%

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

   6. Simplified 93.6%

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

   7. Taylor expanded in a around 0 91.7%

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

      1. associate-+r+ 91.7%

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

      2. associate--l+ 91.7%

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

      3. sub-neg 91.7%

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

      4. metadata-eval 91.7%

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

   9. Simplified 91.7%

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

   if -2.4e53 < b < 4.5999999999999998e-9

   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. Taylor expanded in b around 0 96.3%

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

   if 4.5999999999999998e-9 < b

   1. Initial program 96.5%

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

   2. Taylor expanded in z around 0 90.4%

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

4. Final simplification 94.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.4 \cdot 10^{+53}:\\ \;\;\;\;\left(x + z\right) + b \cdot \left(t + \left(y + -2\right)\right)\\ \mathbf{elif}\;b \leq 4.6 \cdot 10^{-9}:\\ \;\;\;\;x + \left(a \cdot \left(1 - t\right) + z \cdot \left(1 - y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + b \cdot \left(\left(y + t\right) - 2\right)\right) + a \cdot \left(1 - t\right)\\ \end{array} \]

Alternative 10: 65.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a + \left(x + b \cdot \left(y + -2\right)\right)\\ t_2 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -7.2 \cdot 10^{+50}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{-196}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{-179}:\\ \;\;\;\;a + \left(x + z\right)\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{+29}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{+79}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ a (+ x (* b (+ y -2.0))))) (t_2 (* t (- b a))))
   (if (<= t -7.2e+50)
     t_2
     (if (<= t 2.3e-196)
       t_1
       (if (<= t 2.1e-179)
         (+ a (+ x z))
         (if (<= t 1.6e+29) t_1 (if (<= t 2.3e+79) (* 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 + (x + (b * (y + -2.0)));
	double t_2 = t * (b - a);
	double tmp;
	if (t <= -7.2e+50) {
		tmp = t_2;
	} else if (t <= 2.3e-196) {
		tmp = t_1;
	} else if (t <= 2.1e-179) {
		tmp = a + (x + z);
	} else if (t <= 1.6e+29) {
		tmp = t_1;
	} else if (t <= 2.3e+79) {
		tmp = 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 + (x + (b * (y + (-2.0d0))))
    t_2 = t * (b - a)
    if (t <= (-7.2d+50)) then
        tmp = t_2
    else if (t <= 2.3d-196) then
        tmp = t_1
    else if (t <= 2.1d-179) then
        tmp = a + (x + z)
    else if (t <= 1.6d+29) then
        tmp = t_1
    else if (t <= 2.3d+79) then
        tmp = 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 + (x + (b * (y + -2.0)));
	double t_2 = t * (b - a);
	double tmp;
	if (t <= -7.2e+50) {
		tmp = t_2;
	} else if (t <= 2.3e-196) {
		tmp = t_1;
	} else if (t <= 2.1e-179) {
		tmp = a + (x + z);
	} else if (t <= 1.6e+29) {
		tmp = t_1;
	} else if (t <= 2.3e+79) {
		tmp = z * (1.0 - y);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a + (x + (b * (y + -2.0)))
	t_2 = t * (b - a)
	tmp = 0
	if t <= -7.2e+50:
		tmp = t_2
	elif t <= 2.3e-196:
		tmp = t_1
	elif t <= 2.1e-179:
		tmp = a + (x + z)
	elif t <= 1.6e+29:
		tmp = t_1
	elif t <= 2.3e+79:
		tmp = z * (1.0 - y)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a + Float64(x + Float64(b * Float64(y + -2.0))))
	t_2 = Float64(t * Float64(b - a))
	tmp = 0.0
	if (t <= -7.2e+50)
		tmp = t_2;
	elseif (t <= 2.3e-196)
		tmp = t_1;
	elseif (t <= 2.1e-179)
		tmp = Float64(a + Float64(x + z));
	elseif (t <= 1.6e+29)
		tmp = t_1;
	elseif (t <= 2.3e+79)
		tmp = 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 + (x + (b * (y + -2.0)));
	t_2 = t * (b - a);
	tmp = 0.0;
	if (t <= -7.2e+50)
		tmp = t_2;
	elseif (t <= 2.3e-196)
		tmp = t_1;
	elseif (t <= 2.1e-179)
		tmp = a + (x + z);
	elseif (t <= 1.6e+29)
		tmp = t_1;
	elseif (t <= 2.3e+79)
		tmp = 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[(x + N[(b * N[(y + -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -7.2e+50], t$95$2, If[LessEqual[t, 2.3e-196], t$95$1, If[LessEqual[t, 2.1e-179], N[(a + N[(x + z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.6e+29], t$95$1, If[LessEqual[t, 2.3e+79], N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -7.19999999999999972e50 or 2.3e79 < t

   1. Initial program 94.9%

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

   2. Taylor expanded in t around inf 78.1%

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

   if -7.19999999999999972e50 < t < 2.3000000000000002e-196 or 2.0999999999999999e-179 < t < 1.59999999999999993e29

   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. Taylor expanded in z around 0 72.6%

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

   3. Taylor expanded in t around 0 70.7%

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

      1. neg-mul-1 70.7%

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

      2. sub-neg 70.7%

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

      3. sub-neg 70.7%

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

      4. metadata-eval 70.7%

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

      5. remove-double-neg 70.7%

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

   5. Simplified 70.7%

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

   if 2.3000000000000002e-196 < t < 2.0999999999999999e-179

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. fma-def 100.0%

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

      3. associate--l+ 100.0%

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

      4. sub-neg 100.0%

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

      5. metadata-eval 100.0%

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

      6. sub-neg 100.0%

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

      7. associate-+l- 100.0%

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

      8. fma-neg 100.0%

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

      9. sub-neg 100.0%

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

      10. metadata-eval 100.0%

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

      11. remove-double-neg 100.0%

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

      12. sub-neg 100.0%

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

      13. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 90.1%

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

      1. +-commutative 90.1%

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

      2. sub-neg 90.1%

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

      3. metadata-eval 90.1%

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

      4. *-commutative 90.1%

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

      5. neg-mul-1 90.1%

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

      6. unsub-neg 90.1%

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

      7. *-commutative 90.1%

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

   6. Simplified 90.1%

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

   7. Taylor expanded in b around 0 90.1%

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

   8. Taylor expanded in t around 0 90.1%

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

      1. neg-mul-1 90.1%

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

   10. Simplified 90.1%

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

   if 1.59999999999999993e29 < t < 2.3e79

   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. Taylor expanded in z around inf 68.1%

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

4. Final simplification 74.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.2 \cdot 10^{+50}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{-196}:\\ \;\;\;\;a + \left(x + b \cdot \left(y + -2\right)\right)\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{-179}:\\ \;\;\;\;a + \left(x + z\right)\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{+29}:\\ \;\;\;\;a + \left(x + b \cdot \left(y + -2\right)\right)\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{+79}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \]

Alternative 11: 74.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -8.2 \cdot 10^{+52}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 5 \cdot 10^{-9}:\\ \;\;\;\;a + \left(\left(x + z\right) + b \cdot \left(y + -2\right)\right)\\ \mathbf{elif}\;t \leq 2.02 \cdot 10^{+239}:\\ \;\;\;\;x + \left(z \cdot \left(1 - y\right) - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (- b a))))
   (if (<= t -8.2e+52)
     t_1
     (if (<= t 5e-9)
       (+ a (+ (+ x z) (* b (+ y -2.0))))
       (if (<= t 2.02e+239) (+ x (- (* z (- 1.0 y)) (* t a))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (b - a);
	double tmp;
	if (t <= -8.2e+52) {
		tmp = t_1;
	} else if (t <= 5e-9) {
		tmp = a + ((x + z) + (b * (y + -2.0)));
	} else if (t <= 2.02e+239) {
		tmp = x + ((z * (1.0 - y)) - (t * a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (b - a)
    if (t <= (-8.2d+52)) then
        tmp = t_1
    else if (t <= 5d-9) then
        tmp = a + ((x + z) + (b * (y + (-2.0d0))))
    else if (t <= 2.02d+239) then
        tmp = x + ((z * (1.0d0 - y)) - (t * a))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (b - a);
	double tmp;
	if (t <= -8.2e+52) {
		tmp = t_1;
	} else if (t <= 5e-9) {
		tmp = a + ((x + z) + (b * (y + -2.0)));
	} else if (t <= 2.02e+239) {
		tmp = x + ((z * (1.0 - y)) - (t * a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t * (b - a)
	tmp = 0
	if t <= -8.2e+52:
		tmp = t_1
	elif t <= 5e-9:
		tmp = a + ((x + z) + (b * (y + -2.0)))
	elif t <= 2.02e+239:
		tmp = x + ((z * (1.0 - y)) - (t * a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t * Float64(b - a))
	tmp = 0.0
	if (t <= -8.2e+52)
		tmp = t_1;
	elseif (t <= 5e-9)
		tmp = Float64(a + Float64(Float64(x + z) + Float64(b * Float64(y + -2.0))));
	elseif (t <= 2.02e+239)
		tmp = Float64(x + Float64(Float64(z * Float64(1.0 - y)) - Float64(t * a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t * (b - a);
	tmp = 0.0;
	if (t <= -8.2e+52)
		tmp = t_1;
	elseif (t <= 5e-9)
		tmp = a + ((x + z) + (b * (y + -2.0)));
	elseif (t <= 2.02e+239)
		tmp = x + ((z * (1.0 - y)) - (t * a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -8.2e+52], t$95$1, If[LessEqual[t, 5e-9], N[(a + N[(N[(x + z), $MachinePrecision] + N[(b * N[(y + -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.02e+239], N[(x + N[(N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -8.1999999999999999e52 or 2.01999999999999992e239 < t

   1. Initial program 93.5%

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

   2. Taylor expanded in t around inf 89.1%

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

   if -8.1999999999999999e52 < t < 5.0000000000000001e-9

   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. Step-by-step derivation

      1. +-commutative 99.3%

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

      2. fma-def 99.3%

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

      3. associate--l+ 99.3%

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

      4. sub-neg 99.3%

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

      5. metadata-eval 99.3%

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

      6. sub-neg 99.3%

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

      7. associate-+l- 99.3%

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

      8. fma-neg 99.3%

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

      9. sub-neg 99.3%

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

      10. metadata-eval 99.3%

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

      11. remove-double-neg 99.3%

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

      12. sub-neg 99.3%

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

      13. metadata-eval 99.3%

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

   3. Simplified 99.3%

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

   4. Taylor expanded in y around 0 89.6%

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

      1. +-commutative 89.6%

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

      2. sub-neg 89.6%

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

      3. metadata-eval 89.6%

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

      4. *-commutative 89.6%

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

      5. neg-mul-1 89.6%

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

      6. unsub-neg 89.6%

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

      7. *-commutative 89.6%

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

   6. Simplified 89.6%

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

   7. Taylor expanded in t around 0 87.7%

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

      1. neg-mul-1 87.7%

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

      2. sub-neg 87.7%

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

      3. remove-double-neg 87.7%

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

      4. associate-+r+ 87.7%

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

      5. sub-neg 87.7%

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

      6. metadata-eval 87.7%

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

   9. Simplified 87.7%

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

   if 5.0000000000000001e-9 < t < 2.01999999999999992e239

   1. Initial program 98.2%

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

   2. Taylor expanded in b around 0 84.0%

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

   3. Taylor expanded in t around inf 84.0%

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

4. Final simplification 87.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.2 \cdot 10^{+52}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq 5 \cdot 10^{-9}:\\ \;\;\;\;a + \left(\left(x + z\right) + b \cdot \left(y + -2\right)\right)\\ \mathbf{elif}\;t \leq 2.02 \cdot 10^{+239}:\\ \;\;\;\;x + \left(z \cdot \left(1 - y\right) - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \]

Alternative 12: 84.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -3.5 \cdot 10^{+53} \lor \neg \left(b \leq 1.35 \cdot 10^{-7}\right):\\ \;\;\;\;\left(x + z\right) + b \cdot \left(t + \left(y + -2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(a \cdot \left(1 - t\right) + z \cdot \left(1 - y\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -3.5e+53) (not (<= b 1.35e-7)))
   (+ (+ x z) (* b (+ t (+ y -2.0))))
   (+ 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 <= -3.5e+53) || !(b <= 1.35e-7)) {
		tmp = (x + z) + (b * (t + (y + -2.0)));
	} 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 <= (-3.5d+53)) .or. (.not. (b <= 1.35d-7))) then
        tmp = (x + z) + (b * (t + (y + (-2.0d0))))
    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 <= -3.5e+53) || !(b <= 1.35e-7)) {
		tmp = (x + z) + (b * (t + (y + -2.0)));
	} 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 <= -3.5e+53) or not (b <= 1.35e-7):
		tmp = (x + z) + (b * (t + (y + -2.0)))
	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 <= -3.5e+53) || !(b <= 1.35e-7))
		tmp = Float64(Float64(x + z) + Float64(b * Float64(t + Float64(y + -2.0))));
	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 <= -3.5e+53) || ~((b <= 1.35e-7)))
		tmp = (x + z) + (b * (t + (y + -2.0)));
	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, -3.5e+53], N[Not[LessEqual[b, 1.35e-7]], $MachinePrecision]], N[(N[(x + z), $MachinePrecision] + N[(b * N[(t + N[(y + -2.0), $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 < -3.50000000000000019e53 or 1.35000000000000004e-7 < b

   1. Initial program 94.2%

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

      1. +-commutative 94.2%

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

      2. fma-def 96.2%

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

      3. associate--l+ 96.2%

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

      4. sub-neg 96.2%

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

      5. metadata-eval 96.2%

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

      6. sub-neg 96.2%

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

      7. associate-+l- 96.2%

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

      8. fma-neg 96.2%

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

      9. sub-neg 96.2%

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

      10. metadata-eval 96.2%

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

      11. remove-double-neg 96.2%

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

      12. sub-neg 96.2%

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

      13. metadata-eval 96.2%

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

   3. Simplified 96.2%

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

   4. Taylor expanded in y around 0 96.2%

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

      1. +-commutative 96.2%

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

      2. sub-neg 96.2%

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

      3. metadata-eval 96.2%

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

      4. *-commutative 96.2%

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

      5. neg-mul-1 96.2%

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

      6. unsub-neg 96.2%

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

      7. *-commutative 96.2%

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

   6. Simplified 96.2%

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

   7. Taylor expanded in a around 0 87.8%

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

      1. associate-+r+ 87.8%

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

      2. associate--l+ 87.8%

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

      3. sub-neg 87.8%

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

      4. metadata-eval 87.8%

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

   9. Simplified 87.8%

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

   if -3.50000000000000019e53 < b < 1.35000000000000004e-7

   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. Taylor expanded in b around 0 96.3%

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

4. Final simplification 92.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.5 \cdot 10^{+53} \lor \neg \left(b \leq 1.35 \cdot 10^{-7}\right):\\ \;\;\;\;\left(x + z\right) + b \cdot \left(t + \left(y + -2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(a \cdot \left(1 - t\right) + z \cdot \left(1 - y\right)\right)\\ \end{array} \]

Alternative 13: 25.5% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.25 \cdot 10^{+41}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;t \leq -3.5 \cdot 10^{-206}:\\ \;\;\;\;z\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{-198}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq 3.9 \cdot 10^{-149}:\\ \;\;\;\;z\\ \mathbf{elif}\;t \leq 1.02 \cdot 10^{-100}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{+58}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -2.25e+41)
   (* t b)
   (if (<= t -3.5e-206)
     z
     (if (<= t 2.9e-198)
       a
       (if (<= t 3.9e-149)
         z
         (if (<= t 1.02e-100) a (if (<= t 1.9e+58) x (* t b))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -2.25e+41) {
		tmp = t * b;
	} else if (t <= -3.5e-206) {
		tmp = z;
	} else if (t <= 2.9e-198) {
		tmp = a;
	} else if (t <= 3.9e-149) {
		tmp = z;
	} else if (t <= 1.02e-100) {
		tmp = a;
	} else if (t <= 1.9e+58) {
		tmp = x;
	} else {
		tmp = t * b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-2.25d+41)) then
        tmp = t * b
    else if (t <= (-3.5d-206)) then
        tmp = z
    else if (t <= 2.9d-198) then
        tmp = a
    else if (t <= 3.9d-149) then
        tmp = z
    else if (t <= 1.02d-100) then
        tmp = a
    else if (t <= 1.9d+58) then
        tmp = x
    else
        tmp = t * b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -2.25e+41) {
		tmp = t * b;
	} else if (t <= -3.5e-206) {
		tmp = z;
	} else if (t <= 2.9e-198) {
		tmp = a;
	} else if (t <= 3.9e-149) {
		tmp = z;
	} else if (t <= 1.02e-100) {
		tmp = a;
	} else if (t <= 1.9e+58) {
		tmp = x;
	} else {
		tmp = t * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -2.25e+41:
		tmp = t * b
	elif t <= -3.5e-206:
		tmp = z
	elif t <= 2.9e-198:
		tmp = a
	elif t <= 3.9e-149:
		tmp = z
	elif t <= 1.02e-100:
		tmp = a
	elif t <= 1.9e+58:
		tmp = x
	else:
		tmp = t * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -2.25e+41)
		tmp = Float64(t * b);
	elseif (t <= -3.5e-206)
		tmp = z;
	elseif (t <= 2.9e-198)
		tmp = a;
	elseif (t <= 3.9e-149)
		tmp = z;
	elseif (t <= 1.02e-100)
		tmp = a;
	elseif (t <= 1.9e+58)
		tmp = x;
	else
		tmp = Float64(t * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -2.25e+41)
		tmp = t * b;
	elseif (t <= -3.5e-206)
		tmp = z;
	elseif (t <= 2.9e-198)
		tmp = a;
	elseif (t <= 3.9e-149)
		tmp = z;
	elseif (t <= 1.02e-100)
		tmp = a;
	elseif (t <= 1.9e+58)
		tmp = x;
	else
		tmp = t * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -2.25e+41], N[(t * b), $MachinePrecision], If[LessEqual[t, -3.5e-206], z, If[LessEqual[t, 2.9e-198], a, If[LessEqual[t, 3.9e-149], z, If[LessEqual[t, 1.02e-100], a, If[LessEqual[t, 1.9e+58], x, N[(t * b), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -2.2500000000000001e41 or 1.8999999999999999e58 < t

   1. Initial program 95.4%

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

   2. Taylor expanded in b around inf 42.1%

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

   3. Taylor expanded in t around inf 36.7%

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

   if -2.2500000000000001e41 < t < -3.49999999999999989e-206 or 2.90000000000000001e-198 < t < 3.9000000000000002e-149

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. fma-def 100.0%

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

      3. associate--l+ 100.0%

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

      4. sub-neg 100.0%

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

      5. metadata-eval 100.0%

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

      6. sub-neg 100.0%

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

      7. associate-+l- 100.0%

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

      8. fma-neg 100.0%

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

      9. sub-neg 100.0%

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

      10. metadata-eval 100.0%

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

      11. remove-double-neg 100.0%

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

      12. sub-neg 100.0%

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

      13. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 84.6%

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

      1. +-commutative 84.6%

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

      2. sub-neg 84.6%

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

      3. metadata-eval 84.6%

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

      4. *-commutative 84.6%

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

      5. neg-mul-1 84.6%

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

      6. unsub-neg 84.6%

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

      7. *-commutative 84.6%

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

   6. Simplified 84.6%

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

   7. Taylor expanded in z around inf 31.4%

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

   if -3.49999999999999989e-206 < t < 2.90000000000000001e-198 or 3.9000000000000002e-149 < t < 1.02e-100

   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. Taylor expanded in a around inf 35.7%

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

   3. Taylor expanded in t around 0 35.7%

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

   if 1.02e-100 < t < 1.8999999999999999e58

   1. Initial program 97.1%

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

   2. Taylor expanded in x around inf 29.8%

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

4. Final simplification 34.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.25 \cdot 10^{+41}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;t \leq -3.5 \cdot 10^{-206}:\\ \;\;\;\;z\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{-198}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq 3.9 \cdot 10^{-149}:\\ \;\;\;\;z\\ \mathbf{elif}\;t \leq 1.02 \cdot 10^{-100}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{+58}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \]

Alternative 14: 35.9% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(-t\right)\\ \mathbf{if}\;t \leq -2.6 \cdot 10^{+42}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -0.62:\\ \;\;\;\;z\\ \mathbf{elif}\;t \leq -3.3 \cdot 10^{-32}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;t \leq 2.05 \cdot 10^{+37}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{+262}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (- t))))
   (if (<= t -2.6e+42)
     t_1
     (if (<= t -0.62)
       z
       (if (<= t -3.3e-32)
         (* y b)
         (if (<= t 2.05e+37) (+ x a) (if (<= t 2.9e+262) t_1 (* t b))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * -t;
	double tmp;
	if (t <= -2.6e+42) {
		tmp = t_1;
	} else if (t <= -0.62) {
		tmp = z;
	} else if (t <= -3.3e-32) {
		tmp = y * b;
	} else if (t <= 2.05e+37) {
		tmp = x + a;
	} else if (t <= 2.9e+262) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = a * -t
    if (t <= (-2.6d+42)) then
        tmp = t_1
    else if (t <= (-0.62d0)) then
        tmp = z
    else if (t <= (-3.3d-32)) then
        tmp = y * b
    else if (t <= 2.05d+37) then
        tmp = x + a
    else if (t <= 2.9d+262) then
        tmp = t_1
    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 t_1 = a * -t;
	double tmp;
	if (t <= -2.6e+42) {
		tmp = t_1;
	} else if (t <= -0.62) {
		tmp = z;
	} else if (t <= -3.3e-32) {
		tmp = y * b;
	} else if (t <= 2.05e+37) {
		tmp = x + a;
	} else if (t <= 2.9e+262) {
		tmp = t_1;
	} else {
		tmp = t * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * -t
	tmp = 0
	if t <= -2.6e+42:
		tmp = t_1
	elif t <= -0.62:
		tmp = z
	elif t <= -3.3e-32:
		tmp = y * b
	elif t <= 2.05e+37:
		tmp = x + a
	elif t <= 2.9e+262:
		tmp = t_1
	else:
		tmp = t * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(-t))
	tmp = 0.0
	if (t <= -2.6e+42)
		tmp = t_1;
	elseif (t <= -0.62)
		tmp = z;
	elseif (t <= -3.3e-32)
		tmp = Float64(y * b);
	elseif (t <= 2.05e+37)
		tmp = Float64(x + a);
	elseif (t <= 2.9e+262)
		tmp = t_1;
	else
		tmp = Float64(t * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * -t;
	tmp = 0.0;
	if (t <= -2.6e+42)
		tmp = t_1;
	elseif (t <= -0.62)
		tmp = z;
	elseif (t <= -3.3e-32)
		tmp = y * b;
	elseif (t <= 2.05e+37)
		tmp = x + a;
	elseif (t <= 2.9e+262)
		tmp = t_1;
	else
		tmp = t * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * (-t)), $MachinePrecision]}, If[LessEqual[t, -2.6e+42], t$95$1, If[LessEqual[t, -0.62], z, If[LessEqual[t, -3.3e-32], N[(y * b), $MachinePrecision], If[LessEqual[t, 2.05e+37], N[(x + a), $MachinePrecision], If[LessEqual[t, 2.9e+262], t$95$1, N[(t * b), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -2.5999999999999999e42 or 2.0499999999999999e37 < t < 2.8999999999999998e262

   1. Initial program 98.0%

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

   2. Taylor expanded in a around inf 45.6%

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

   3. Taylor expanded in t around inf 45.6%

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

      1. associate-*r* 45.6%

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

      2. neg-mul-1 45.6%

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

   5. Simplified 45.6%

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

   if -2.5999999999999999e42 < t < -0.619999999999999996

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. fma-def 100.0%

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

      3. associate--l+ 100.0%

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

      4. sub-neg 100.0%

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

      5. metadata-eval 100.0%

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

      6. sub-neg 100.0%

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

      7. associate-+l- 100.0%

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

      8. fma-neg 100.0%

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

      9. sub-neg 100.0%

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

      10. metadata-eval 100.0%

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

      11. remove-double-neg 100.0%

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

      12. sub-neg 100.0%

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

      13. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 78.5%

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

      1. +-commutative 78.5%

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

      2. sub-neg 78.5%

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

      3. metadata-eval 78.5%

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

      4. *-commutative 78.5%

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

      5. neg-mul-1 78.5%

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

      6. unsub-neg 78.5%

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

      7. *-commutative 78.5%

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

   6. Simplified 78.5%

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

   7. Taylor expanded in z around inf 56.6%

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

   if -0.619999999999999996 < t < -3.30000000000000025e-32

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. fma-def 100.0%

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

      3. associate--l+ 100.0%

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

      4. sub-neg 100.0%

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

      5. metadata-eval 100.0%

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

      6. sub-neg 100.0%

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

      7. associate-+l- 100.0%

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

      8. fma-neg 100.0%

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

      9. sub-neg 100.0%

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

      10. metadata-eval 100.0%

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

      11. remove-double-neg 100.0%

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

      12. sub-neg 100.0%

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

      13. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 100.0%

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

      1. +-commutative 100.0%

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

      2. sub-neg 100.0%

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

      3. metadata-eval 100.0%

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

      4. *-commutative 100.0%

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

      5. neg-mul-1 100.0%

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

      6. unsub-neg 100.0%

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

      7. *-commutative 100.0%

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

   6. Simplified 100.0%

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

   7. Taylor expanded in y around inf 75.1%

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

   if -3.30000000000000025e-32 < t < 2.0499999999999999e37

   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. Taylor expanded in z around 0 70.2%

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

   3. Taylor expanded in b around 0 43.6%

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

   4. Taylor expanded in t around 0 43.4%

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

      1. cancel-sign-sub-inv 43.4%

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

      2. metadata-eval 43.4%

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

      3. *-lft-identity 43.4%

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

      4. +-commutative 43.4%

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

   6. Simplified 43.4%

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

   if 2.8999999999999998e262 < t

   1. Initial program 78.6%

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

   2. Taylor expanded in b around inf 78.6%

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

   3. Taylor expanded in t around inf 78.6%

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

4. Final simplification 47.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.6 \cdot 10^{+42}:\\ \;\;\;\;a \cdot \left(-t\right)\\ \mathbf{elif}\;t \leq -0.62:\\ \;\;\;\;z\\ \mathbf{elif}\;t \leq -3.3 \cdot 10^{-32}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;t \leq 2.05 \cdot 10^{+37}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{+262}:\\ \;\;\;\;a \cdot \left(-t\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \]

Alternative 15: 50.4% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(b - z\right)\\ t_2 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -6.8 \cdot 10^{+40}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -2.5 \cdot 10^{-186}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{-8}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq 4.4 \cdot 10^{+77}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (- b z))) (t_2 (* t (- b a))))
   (if (<= t -6.8e+40)
     t_2
     (if (<= t -2.5e-186)
       t_1
       (if (<= t 1.25e-8) (+ x a) (if (<= t 4.4e+77) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (b - z);
	double t_2 = t * (b - a);
	double tmp;
	if (t <= -6.8e+40) {
		tmp = t_2;
	} else if (t <= -2.5e-186) {
		tmp = t_1;
	} else if (t <= 1.25e-8) {
		tmp = x + a;
	} else if (t <= 4.4e+77) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y * (b - z)
    t_2 = t * (b - a)
    if (t <= (-6.8d+40)) then
        tmp = t_2
    else if (t <= (-2.5d-186)) then
        tmp = t_1
    else if (t <= 1.25d-8) then
        tmp = x + a
    else if (t <= 4.4d+77) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (b - z);
	double t_2 = t * (b - a);
	double tmp;
	if (t <= -6.8e+40) {
		tmp = t_2;
	} else if (t <= -2.5e-186) {
		tmp = t_1;
	} else if (t <= 1.25e-8) {
		tmp = x + a;
	} else if (t <= 4.4e+77) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y * (b - z)
	t_2 = t * (b - a)
	tmp = 0
	if t <= -6.8e+40:
		tmp = t_2
	elif t <= -2.5e-186:
		tmp = t_1
	elif t <= 1.25e-8:
		tmp = x + a
	elif t <= 4.4e+77:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y * Float64(b - z))
	t_2 = Float64(t * Float64(b - a))
	tmp = 0.0
	if (t <= -6.8e+40)
		tmp = t_2;
	elseif (t <= -2.5e-186)
		tmp = t_1;
	elseif (t <= 1.25e-8)
		tmp = Float64(x + a);
	elseif (t <= 4.4e+77)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y * (b - z);
	t_2 = t * (b - a);
	tmp = 0.0;
	if (t <= -6.8e+40)
		tmp = t_2;
	elseif (t <= -2.5e-186)
		tmp = t_1;
	elseif (t <= 1.25e-8)
		tmp = x + a;
	elseif (t <= 4.4e+77)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -6.8e+40], t$95$2, If[LessEqual[t, -2.5e-186], t$95$1, If[LessEqual[t, 1.25e-8], N[(x + a), $MachinePrecision], If[LessEqual[t, 4.4e+77], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -6.79999999999999977e40 or 4.4000000000000001e77 < t

   1. Initial program 95.3%

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

   2. Taylor expanded in t around inf 75.0%

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

   if -6.79999999999999977e40 < t < -2.5e-186 or 1.2499999999999999e-8 < t < 4.4000000000000001e77

   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. Taylor expanded in y around inf 51.4%

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

   if -2.5e-186 < t < 1.2499999999999999e-8

   1. Initial program 98.8%

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

   2. Taylor expanded in z around 0 76.7%

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

   3. Taylor expanded in b around 0 50.3%

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

   4. Taylor expanded in t around 0 49.9%

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

      1. cancel-sign-sub-inv 49.9%

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

      2. metadata-eval 49.9%

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

      3. *-lft-identity 49.9%

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

      4. +-commutative 49.9%

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

   6. Simplified 49.9%

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

4. Final simplification 60.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.8 \cdot 10^{+40}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq -2.5 \cdot 10^{-186}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{-8}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq 4.4 \cdot 10^{+77}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \]

Alternative 16: 50.0% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -3.4 \cdot 10^{+39}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.55 \cdot 10^{-176}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{-8}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{+77}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (- b a))))
   (if (<= t -3.4e+39)
     t_1
     (if (<= t -1.55e-176)
       (* y (- b z))
       (if (<= t 1.4e-8) (+ x a) (if (<= t 2.8e+77) (* z (- 1.0 y)) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (b - a);
	double tmp;
	if (t <= -3.4e+39) {
		tmp = t_1;
	} else if (t <= -1.55e-176) {
		tmp = y * (b - z);
	} else if (t <= 1.4e-8) {
		tmp = x + a;
	} else if (t <= 2.8e+77) {
		tmp = z * (1.0 - y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (b - a)
    if (t <= (-3.4d+39)) then
        tmp = t_1
    else if (t <= (-1.55d-176)) then
        tmp = y * (b - z)
    else if (t <= 1.4d-8) then
        tmp = x + a
    else if (t <= 2.8d+77) then
        tmp = z * (1.0d0 - y)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (b - a);
	double tmp;
	if (t <= -3.4e+39) {
		tmp = t_1;
	} else if (t <= -1.55e-176) {
		tmp = y * (b - z);
	} else if (t <= 1.4e-8) {
		tmp = x + a;
	} else if (t <= 2.8e+77) {
		tmp = z * (1.0 - y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t * (b - a)
	tmp = 0
	if t <= -3.4e+39:
		tmp = t_1
	elif t <= -1.55e-176:
		tmp = y * (b - z)
	elif t <= 1.4e-8:
		tmp = x + a
	elif t <= 2.8e+77:
		tmp = z * (1.0 - y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t * Float64(b - a))
	tmp = 0.0
	if (t <= -3.4e+39)
		tmp = t_1;
	elseif (t <= -1.55e-176)
		tmp = Float64(y * Float64(b - z));
	elseif (t <= 1.4e-8)
		tmp = Float64(x + a);
	elseif (t <= 2.8e+77)
		tmp = Float64(z * Float64(1.0 - y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t * (b - a);
	tmp = 0.0;
	if (t <= -3.4e+39)
		tmp = t_1;
	elseif (t <= -1.55e-176)
		tmp = y * (b - z);
	elseif (t <= 1.4e-8)
		tmp = x + a;
	elseif (t <= 2.8e+77)
		tmp = z * (1.0 - y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.4e+39], t$95$1, If[LessEqual[t, -1.55e-176], N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.4e-8], N[(x + a), $MachinePrecision], If[LessEqual[t, 2.8e+77], N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -3.3999999999999999e39 or 2.8e77 < t

   1. Initial program 95.3%

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

   2. Taylor expanded in t around inf 75.0%

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

   if -3.3999999999999999e39 < t < -1.54999999999999996e-176

   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. Taylor expanded in y around inf 50.6%

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

   if -1.54999999999999996e-176 < t < 1.4e-8

   1. Initial program 98.8%

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

   2. Taylor expanded in z around 0 76.7%

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

   3. Taylor expanded in b around 0 50.3%

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

   4. Taylor expanded in t around 0 49.9%

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

      1. cancel-sign-sub-inv 49.9%

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

      2. metadata-eval 49.9%

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

      3. *-lft-identity 49.9%

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

      4. +-commutative 49.9%

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

   6. Simplified 49.9%

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

   if 1.4e-8 < t < 2.8e77

   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. Taylor expanded in z around inf 61.0%

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

4. Final simplification 61.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.4 \cdot 10^{+39}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq -1.55 \cdot 10^{-176}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{-8}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{+77}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \]

Alternative 17: 55.9% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -7.2 \cdot 10^{+39}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.76 \cdot 10^{-68}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{+29}:\\ \;\;\;\;a + \left(x + z\right)\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{+81}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (- b a))))
   (if (<= t -7.2e+39)
     t_1
     (if (<= t -1.76e-68)
       (* y (- b z))
       (if (<= t 1.4e+29)
         (+ a (+ x z))
         (if (<= t 2.3e+81) (* z (- 1.0 y)) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (b - a);
	double tmp;
	if (t <= -7.2e+39) {
		tmp = t_1;
	} else if (t <= -1.76e-68) {
		tmp = y * (b - z);
	} else if (t <= 1.4e+29) {
		tmp = a + (x + z);
	} else if (t <= 2.3e+81) {
		tmp = z * (1.0 - y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (b - a)
    if (t <= (-7.2d+39)) then
        tmp = t_1
    else if (t <= (-1.76d-68)) then
        tmp = y * (b - z)
    else if (t <= 1.4d+29) then
        tmp = a + (x + z)
    else if (t <= 2.3d+81) then
        tmp = z * (1.0d0 - y)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (b - a);
	double tmp;
	if (t <= -7.2e+39) {
		tmp = t_1;
	} else if (t <= -1.76e-68) {
		tmp = y * (b - z);
	} else if (t <= 1.4e+29) {
		tmp = a + (x + z);
	} else if (t <= 2.3e+81) {
		tmp = z * (1.0 - y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t * (b - a)
	tmp = 0
	if t <= -7.2e+39:
		tmp = t_1
	elif t <= -1.76e-68:
		tmp = y * (b - z)
	elif t <= 1.4e+29:
		tmp = a + (x + z)
	elif t <= 2.3e+81:
		tmp = z * (1.0 - y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t * Float64(b - a))
	tmp = 0.0
	if (t <= -7.2e+39)
		tmp = t_1;
	elseif (t <= -1.76e-68)
		tmp = Float64(y * Float64(b - z));
	elseif (t <= 1.4e+29)
		tmp = Float64(a + Float64(x + z));
	elseif (t <= 2.3e+81)
		tmp = Float64(z * Float64(1.0 - y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t * (b - a);
	tmp = 0.0;
	if (t <= -7.2e+39)
		tmp = t_1;
	elseif (t <= -1.76e-68)
		tmp = y * (b - z);
	elseif (t <= 1.4e+29)
		tmp = a + (x + z);
	elseif (t <= 2.3e+81)
		tmp = z * (1.0 - y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -7.2e+39], t$95$1, If[LessEqual[t, -1.76e-68], N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.4e+29], N[(a + N[(x + z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.3e+81], N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -7.19999999999999969e39 or 2.2999999999999999e81 < t

   1. Initial program 95.3%

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

   2. Taylor expanded in t around inf 75.0%

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

   if -7.19999999999999969e39 < t < -1.76e-68

   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. Taylor expanded in y around inf 66.4%

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

   if -1.76e-68 < t < 1.4e29

   1. Initial program 99.1%

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

      1. +-commutative 99.1%

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

      2. fma-def 99.1%

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

      3. associate--l+ 99.1%

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

      4. sub-neg 99.1%

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

      5. metadata-eval 99.1%

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

      6. sub-neg 99.1%

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

      7. associate-+l- 99.1%

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

      8. fma-neg 99.1%

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

      9. sub-neg 99.1%

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

      10. metadata-eval 99.1%

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

      11. remove-double-neg 99.1%

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

      12. sub-neg 99.1%

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

      13. metadata-eval 99.1%

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

   3. Simplified 99.1%

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

   4. Taylor expanded in y around 0 90.8%

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

      1. +-commutative 90.8%

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

      2. sub-neg 90.8%

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

      3. metadata-eval 90.8%

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

      4. *-commutative 90.8%

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

      5. neg-mul-1 90.8%

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

      6. unsub-neg 90.8%

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

      7. *-commutative 90.8%

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

   6. Simplified 90.8%

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

   7. Taylor expanded in b around 0 64.8%

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

   8. Taylor expanded in t around 0 64.6%

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

      1. neg-mul-1 64.6%

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

   10. Simplified 64.6%

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

   if 1.4e29 < t < 2.2999999999999999e81

   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. Taylor expanded in z around inf 68.1%

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

4. Final simplification 69.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.2 \cdot 10^{+39}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq -1.76 \cdot 10^{-68}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{+29}:\\ \;\;\;\;a + \left(x + z\right)\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{+81}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \]

Alternative 18: 48.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -2.1 \cdot 10^{+41}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -2.2 \cdot 10^{-68}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;t \leq 1.45 \cdot 10^{+37}:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (- b a))))
   (if (<= t -2.1e+41)
     t_1
     (if (<= t -2.2e-68) (* y b) (if (<= t 1.45e+37) (+ x a) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (b - a);
	double tmp;
	if (t <= -2.1e+41) {
		tmp = t_1;
	} else if (t <= -2.2e-68) {
		tmp = y * b;
	} else if (t <= 1.45e+37) {
		tmp = x + a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (b - a)
    if (t <= (-2.1d+41)) then
        tmp = t_1
    else if (t <= (-2.2d-68)) then
        tmp = y * b
    else if (t <= 1.45d+37) then
        tmp = x + a
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (b - a);
	double tmp;
	if (t <= -2.1e+41) {
		tmp = t_1;
	} else if (t <= -2.2e-68) {
		tmp = y * b;
	} else if (t <= 1.45e+37) {
		tmp = x + a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t * (b - a)
	tmp = 0
	if t <= -2.1e+41:
		tmp = t_1
	elif t <= -2.2e-68:
		tmp = y * b
	elif t <= 1.45e+37:
		tmp = x + a
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t * Float64(b - a))
	tmp = 0.0
	if (t <= -2.1e+41)
		tmp = t_1;
	elseif (t <= -2.2e-68)
		tmp = Float64(y * b);
	elseif (t <= 1.45e+37)
		tmp = Float64(x + a);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t * (b - a);
	tmp = 0.0;
	if (t <= -2.1e+41)
		tmp = t_1;
	elseif (t <= -2.2e-68)
		tmp = y * b;
	elseif (t <= 1.45e+37)
		tmp = x + a;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.1e+41], t$95$1, If[LessEqual[t, -2.2e-68], N[(y * b), $MachinePrecision], If[LessEqual[t, 1.45e+37], N[(x + a), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.1e41 or 1.44999999999999989e37 < t

   1. Initial program 95.6%

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

   2. Taylor expanded in t around inf 71.0%

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

   if -2.1e41 < t < -2.20000000000000002e-68

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. fma-def 100.0%

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

      3. associate--l+ 100.0%

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

      4. sub-neg 100.0%

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

      5. metadata-eval 100.0%

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

      6. sub-neg 100.0%

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

      7. associate-+l- 100.0%

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

      8. fma-neg 100.0%

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

      9. sub-neg 100.0%

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

      10. metadata-eval 100.0%

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

      11. remove-double-neg 100.0%

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

      12. sub-neg 100.0%

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

      13. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 80.1%

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

      1. +-commutative 80.1%

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

      2. sub-neg 80.1%

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

      3. metadata-eval 80.1%

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

      4. *-commutative 80.1%

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

      5. neg-mul-1 80.1%

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

      6. unsub-neg 80.1%

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

      7. *-commutative 80.1%

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

   6. Simplified 80.1%

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

   7. Taylor expanded in y around inf 43.3%

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

   if -2.20000000000000002e-68 < t < 1.44999999999999989e37

   1. Initial program 99.1%

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

   2. Taylor expanded in z around 0 69.9%

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

   3. Taylor expanded in b around 0 44.9%

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

   4. Taylor expanded in t around 0 44.7%

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

      1. cancel-sign-sub-inv 44.7%

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

      2. metadata-eval 44.7%

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

      3. *-lft-identity 44.7%

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

      4. +-commutative 44.7%

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

   6. Simplified 44.7%

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

4. Final simplification 56.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.1 \cdot 10^{+41}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq -2.2 \cdot 10^{-68}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;t \leq 1.45 \cdot 10^{+37}:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \]

Alternative 19: 35.8% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5.8 \cdot 10^{+51}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;t \leq 1.45 \cdot 10^{+29}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{+128}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -5.8e+51)
   (* t b)
   (if (<= t 1.45e+29) (+ x a) (if (<= t 1.05e+128) (* y (- z)) (* t b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -5.8e+51) {
		tmp = t * b;
	} else if (t <= 1.45e+29) {
		tmp = x + a;
	} else if (t <= 1.05e+128) {
		tmp = y * -z;
	} else {
		tmp = t * b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-5.8d+51)) then
        tmp = t * b
    else if (t <= 1.45d+29) then
        tmp = x + a
    else if (t <= 1.05d+128) then
        tmp = y * -z
    else
        tmp = t * b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -5.8e+51) {
		tmp = t * b;
	} else if (t <= 1.45e+29) {
		tmp = x + a;
	} else if (t <= 1.05e+128) {
		tmp = y * -z;
	} else {
		tmp = t * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -5.8e+51:
		tmp = t * b
	elif t <= 1.45e+29:
		tmp = x + a
	elif t <= 1.05e+128:
		tmp = y * -z
	else:
		tmp = t * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -5.8e+51)
		tmp = Float64(t * b);
	elseif (t <= 1.45e+29)
		tmp = Float64(x + a);
	elseif (t <= 1.05e+128)
		tmp = Float64(y * Float64(-z));
	else
		tmp = Float64(t * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -5.8e+51)
		tmp = t * b;
	elseif (t <= 1.45e+29)
		tmp = x + a;
	elseif (t <= 1.05e+128)
		tmp = y * -z;
	else
		tmp = t * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -5.8e+51], N[(t * b), $MachinePrecision], If[LessEqual[t, 1.45e+29], N[(x + a), $MachinePrecision], If[LessEqual[t, 1.05e+128], N[(y * (-z)), $MachinePrecision], N[(t * b), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -5.7999999999999997e51 or 1.05e128 < t

   1. Initial program 95.0%

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

   2. Taylor expanded in b around inf 49.2%

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

   3. Taylor expanded in t around inf 44.4%

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

   if -5.7999999999999997e51 < t < 1.45e29

   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. Taylor expanded in z around 0 70.4%

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

   3. Taylor expanded in b around 0 42.3%

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

   4. Taylor expanded in t around 0 41.3%

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

      1. cancel-sign-sub-inv 41.3%

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

      2. metadata-eval 41.3%

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

      3. *-lft-identity 41.3%

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

      4. +-commutative 41.3%

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

   6. Simplified 41.3%

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

   if 1.45e29 < t < 1.05e128

   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. Taylor expanded in y around inf 49.6%

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

   3. Taylor expanded in b around 0 39.8%

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

      1. mul-1-neg 39.8%

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

      2. *-commutative 39.8%

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

      3. distribute-rgt-neg-in 39.8%

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

   5. Simplified 39.8%

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

4. Final simplification 42.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.8 \cdot 10^{+51}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;t \leq 1.45 \cdot 10^{+29}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{+128}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \]

Alternative 20: 26.1% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{+62}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{-278}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 7.4 \cdot 10^{+22}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -1.9e+62)
   (* y b)
   (if (<= y 8.5e-278) x (if (<= y 7.4e+22) z (* y b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1.9e+62) {
		tmp = y * b;
	} else if (y <= 8.5e-278) {
		tmp = x;
	} else if (y <= 7.4e+22) {
		tmp = z;
	} else {
		tmp = y * b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-1.9d+62)) then
        tmp = y * b
    else if (y <= 8.5d-278) then
        tmp = x
    else if (y <= 7.4d+22) then
        tmp = z
    else
        tmp = y * b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1.9e+62) {
		tmp = y * b;
	} else if (y <= 8.5e-278) {
		tmp = x;
	} else if (y <= 7.4e+22) {
		tmp = z;
	} else {
		tmp = y * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -1.9e+62:
		tmp = y * b
	elif y <= 8.5e-278:
		tmp = x
	elif y <= 7.4e+22:
		tmp = z
	else:
		tmp = y * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -1.9e+62)
		tmp = Float64(y * b);
	elseif (y <= 8.5e-278)
		tmp = x;
	elseif (y <= 7.4e+22)
		tmp = z;
	else
		tmp = Float64(y * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -1.9e+62)
		tmp = y * b;
	elseif (y <= 8.5e-278)
		tmp = x;
	elseif (y <= 7.4e+22)
		tmp = z;
	else
		tmp = y * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -1.9e+62], N[(y * b), $MachinePrecision], If[LessEqual[y, 8.5e-278], x, If[LessEqual[y, 7.4e+22], z, N[(y * b), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.89999999999999992e62 or 7.3999999999999996e22 < y

   1. Initial program 95.5%

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

      1. +-commutative 95.5%

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

      2. fma-def 97.3%

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

      3. associate--l+ 97.3%

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

      4. sub-neg 97.3%

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

      5. metadata-eval 97.3%

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

      6. sub-neg 97.3%

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

      7. associate-+l- 97.3%

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

      8. fma-neg 97.3%

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

      9. sub-neg 97.3%

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

      10. metadata-eval 97.3%

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

      11. remove-double-neg 97.3%

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

      12. sub-neg 97.3%

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

      13. metadata-eval 97.3%

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

   3. Simplified 97.3%

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

   4. Taylor expanded in y around 0 75.8%

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

      1. +-commutative 75.8%

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

      2. sub-neg 75.8%

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

      3. metadata-eval 75.8%

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

      4. *-commutative 75.8%

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

      5. neg-mul-1 75.8%

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

      6. unsub-neg 75.8%

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

      7. *-commutative 75.8%

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

   6. Simplified 75.8%

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

   7. Taylor expanded in y around inf 42.0%

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

   if -1.89999999999999992e62 < y < 8.49999999999999955e-278

   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. Taylor expanded in x around inf 28.7%

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

   if 8.49999999999999955e-278 < y < 7.3999999999999996e22

   1. Initial program 98.0%

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

      1. +-commutative 98.0%

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

      2. fma-def 98.0%

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

      3. associate--l+ 98.0%

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

      4. sub-neg 98.0%

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

      5. metadata-eval 98.0%

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

      6. sub-neg 98.0%

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

      7. associate-+l- 98.0%

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

      8. fma-neg 98.0%

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

      9. sub-neg 98.0%

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

      10. metadata-eval 98.0%

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

      11. remove-double-neg 98.0%

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

      12. sub-neg 98.0%

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

      13. metadata-eval 98.0%

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

   3. Simplified 98.0%

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

   4. Taylor expanded in y around 0 95.6%

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

      1. +-commutative 95.6%

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

      2. sub-neg 95.6%

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

      3. metadata-eval 95.6%

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

      4. *-commutative 95.6%

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

      5. neg-mul-1 95.6%

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

      6. unsub-neg 95.6%

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

      7. *-commutative 95.6%

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

   6. Simplified 95.6%

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

   7. Taylor expanded in z around inf 31.9%

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

4. Final simplification 35.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{+62}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{-278}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 7.4 \cdot 10^{+22}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \]

Alternative 21: 36.1% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5.5 \cdot 10^{+50} \lor \neg \left(t \leq 4.6 \cdot 10^{+77}\right):\\ \;\;\;\;t \cdot b\\ \mathbf{else}:\\ \;\;\;\;x + a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -5.5e+50) (not (<= t 4.6e+77))) (* t b) (+ x a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -5.5e+50) || !(t <= 4.6e+77)) {
		tmp = t * b;
	} else {
		tmp = x + a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-5.5d+50)) .or. (.not. (t <= 4.6d+77))) then
        tmp = t * b
    else
        tmp = x + a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -5.5e+50) || !(t <= 4.6e+77)) {
		tmp = t * b;
	} else {
		tmp = x + a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -5.5e+50) or not (t <= 4.6e+77):
		tmp = t * b
	else:
		tmp = x + a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -5.5e+50) || !(t <= 4.6e+77))
		tmp = Float64(t * b);
	else
		tmp = Float64(x + a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -5.5e+50) || ~((t <= 4.6e+77)))
		tmp = t * b;
	else
		tmp = x + a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -5.5e+50], N[Not[LessEqual[t, 4.6e+77]], $MachinePrecision]], N[(t * b), $MachinePrecision], N[(x + a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -5.4999999999999998e50 or 4.5999999999999999e77 < t

   1. Initial program 94.9%

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

   2. Taylor expanded in b around inf 43.8%

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

   3. Taylor expanded in t around inf 38.8%

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

   if -5.4999999999999998e50 < t < 4.5999999999999999e77

   1. Initial program 99.4%

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

   2. Taylor expanded in z around 0 68.3%

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

   3. Taylor expanded in b around 0 41.1%

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

   4. Taylor expanded in t around 0 38.7%

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

      1. cancel-sign-sub-inv 38.7%

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

      2. metadata-eval 38.7%

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

      3. *-lft-identity 38.7%

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

      4. +-commutative 38.7%

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

   6. Simplified 38.7%

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

4. Final simplification 38.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.5 \cdot 10^{+50} \lor \neg \left(t \leq 4.6 \cdot 10^{+77}\right):\\ \;\;\;\;t \cdot b\\ \mathbf{else}:\\ \;\;\;\;x + a\\ \end{array} \]

Alternative 22: 21.4% accurate, 4.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -4 \cdot 10^{+89}:\\ \;\;\;\;a\\ \mathbf{elif}\;a \leq 1.55 \cdot 10^{+99}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -4e+89) a (if (<= a 1.55e+99) x a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -4e+89) {
		tmp = a;
	} else if (a <= 1.55e+99) {
		tmp = x;
	} else {
		tmp = a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (a <= (-4d+89)) then
        tmp = a
    else if (a <= 1.55d+99) then
        tmp = x
    else
        tmp = a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -4e+89) {
		tmp = a;
	} else if (a <= 1.55e+99) {
		tmp = x;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -4e+89:
		tmp = a
	elif a <= 1.55e+99:
		tmp = x
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -4e+89)
		tmp = a;
	elseif (a <= 1.55e+99)
		tmp = x;
	else
		tmp = a;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= -4e+89)
		tmp = a;
	elseif (a <= 1.55e+99)
		tmp = x;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -4e+89], a, If[LessEqual[a, 1.55e+99], x, a]]

Derivation

1. Split input into 2 regimes

2. if a < -3.99999999999999998e89 or 1.55e99 < a

   1. Initial program 96.6%

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

   2. Taylor expanded in a around inf 67.3%

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

   3. Taylor expanded in t around 0 28.7%

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

   if -3.99999999999999998e89 < a < 1.55e99

   1. Initial program 98.2%

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

   2. Taylor expanded in x around inf 20.8%

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

4. Final simplification 23.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4 \cdot 10^{+89}:\\ \;\;\;\;a\\ \mathbf{elif}\;a \leq 1.55 \cdot 10^{+99}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]

Alternative 23: 21.5% accurate, 4.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{+85}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{+35}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -2.9e+85) z (if (<= z 4.2e+35) x z)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -2.9e+85) {
		tmp = z;
	} else if (z <= 4.2e+35) {
		tmp = x;
	} else {
		tmp = z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-2.9d+85)) then
        tmp = z
    else if (z <= 4.2d+35) then
        tmp = x
    else
        tmp = z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -2.9e+85) {
		tmp = z;
	} else if (z <= 4.2e+35) {
		tmp = x;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -2.9e+85:
		tmp = z
	elif z <= 4.2e+35:
		tmp = x
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -2.9e+85)
		tmp = z;
	elseif (z <= 4.2e+35)
		tmp = x;
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -2.9e+85)
		tmp = z;
	elseif (z <= 4.2e+35)
		tmp = x;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -2.9e+85], z, If[LessEqual[z, 4.2e+35], x, z]]

Derivation

1. Split input into 2 regimes

2. if z < -2.89999999999999997e85 or 4.1999999999999998e35 < z

   1. Initial program 97.1%

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

      1. +-commutative 97.1%

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

      2. fma-def 99.0%

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

      3. associate--l+ 99.0%

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

      4. sub-neg 99.0%

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

      5. metadata-eval 99.0%

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

      6. sub-neg 99.0%

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

      7. associate-+l- 99.0%

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

      8. fma-neg 99.0%

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

      9. sub-neg 99.0%

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

      10. metadata-eval 99.0%

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

      11. remove-double-neg 99.0%

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

      12. sub-neg 99.0%

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

      13. metadata-eval 99.0%

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

   3. Simplified 99.0%

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

   4. Taylor expanded in y around 0 79.4%

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

      1. +-commutative 79.4%

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

      2. sub-neg 79.4%

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

      3. metadata-eval 79.4%

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

      4. *-commutative 79.4%

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

      5. neg-mul-1 79.4%

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

      6. unsub-neg 79.4%

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

      7. *-commutative 79.4%

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

   6. Simplified 79.4%

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

   7. Taylor expanded in z around inf 31.5%

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

   if -2.89999999999999997e85 < z < 4.1999999999999998e35

   1. Initial program 98.0%

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

   2. Taylor expanded in x around inf 22.4%

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

4. Final simplification 26.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{+85}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{+35}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]

Alternative 24: 11.3% accurate, 21.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.7%

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

2. Taylor expanded in a around inf 30.9%

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

3. Taylor expanded in t around 0 11.9%

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

4. Final simplification 11.9%

   \[\leadsto a \]

Reproduce

herbie shell --seed 2023322 
(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)))