Graphics.Rasterific.CubicBezier:cachedBezierAt from Rasterific-0.6.1

Percentage Accurate: 92.5% → 97.2%

Time: 12.5s

Alternatives: 14

Speedup: 0.5×

• 33.4% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 92.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.2% accurate, 0.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -6 \cdot 10^{+152}:\\ \;\;\;\;\mathsf{fma}\left(a, \mathsf{fma}\left(b, z, t\right), x\right)\\ \mathbf{elif}\;a \leq 2 \cdot 10^{-38}:\\ \;\;\;\;\mathsf{fma}\left(z, a \cdot b, \mathsf{fma}\left(t, a, \mathsf{fma}\left(y, z, x\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a, t + b \cdot z, \mathsf{fma}\left(y, z, x\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -6e+152)
   (fma a (fma b z t) x)
   (if (<= a 2e-38)
     (fma z (* a b) (fma t a (fma y z x)))
     (fma a (+ t (* b z)) (fma y z x)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -6e+152) {
		tmp = fma(a, fma(b, z, t), x);
	} else if (a <= 2e-38) {
		tmp = fma(z, (a * b), fma(t, a, fma(y, z, x)));
	} else {
		tmp = fma(a, (t + (b * z)), fma(y, z, x));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -6e+152)
		tmp = fma(a, fma(b, z, t), x);
	elseif (a <= 2e-38)
		tmp = fma(z, Float64(a * b), fma(t, a, fma(y, z, x)));
	else
		tmp = fma(a, Float64(t + Float64(b * z)), fma(y, z, x));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -6e+152], N[(a * N[(b * z + t), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[a, 2e-38], N[(z * N[(a * b), $MachinePrecision] + N[(t * a + N[(y * z + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(t + N[(b * z), $MachinePrecision]), $MachinePrecision] + N[(y * z + x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -5.99999999999999981e152

   1. Initial program 73.0%

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

      1. *-commutative 73.0%

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

      2. associate-*l* 66.0%

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

   3. Simplified 66.0%

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

   4. Taylor expanded in y around 0 76.9%

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

      1. distribute-lft-in 100.0%

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

      2. +-commutative 100.0%

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

      3. *-commutative 100.0%

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

      4. fma-udef 100.0%

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

      5. +-commutative 100.0%

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

      6. fma-def 100.0%

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

      7. fma-udef 100.0%

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

      8. *-commutative 100.0%

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

      9. fma-udef 100.0%

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

   6. Simplified 100.0%

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

   if -5.99999999999999981e152 < a < 1.9999999999999999e-38

   1. Initial program 97.2%

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

      1. +-commutative 97.2%

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

      2. *-commutative 97.2%

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

      3. associate-*l* 98.6%

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

      4. *-commutative 98.6%

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

      5. fma-def 99.9%

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

      6. *-commutative 99.9%

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

      7. +-commutative 99.9%

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

      8. fma-def 99.9%

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

      9. +-commutative 99.9%

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

      10. fma-def 99.9%

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

   3. Simplified 99.9%

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

   if 1.9999999999999999e-38 < a

   1. Initial program 89.1%

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

      1. associate-+l+ 89.1%

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

      2. +-commutative 89.1%

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

      3. *-commutative 89.1%

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

      4. *-commutative 89.1%

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

      5. associate-*l* 94.0%

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

      6. distribute-rgt-out 97.6%

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

      7. fma-def 98.8%

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

      8. *-commutative 98.8%

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

      9. +-commutative 98.8%

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

      10. fma-def 98.8%

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

   3. Simplified 98.8%

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

4. Final simplification 99.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6 \cdot 10^{+152}:\\ \;\;\;\;\mathsf{fma}\left(a, \mathsf{fma}\left(b, z, t\right), x\right)\\ \mathbf{elif}\;a \leq 2 \cdot 10^{-38}:\\ \;\;\;\;\mathsf{fma}\left(z, a \cdot b, \mathsf{fma}\left(t, a, \mathsf{fma}\left(y, z, x\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a, t + b \cdot z, \mathsf{fma}\left(y, z, x\right)\right)\\ \end{array} \]

Alternative 2: 96.6% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 98.7%

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

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

   1. Initial program 0.0%

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

      1. *-commutative 0.0%

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

      2. associate-*l* 23.5%

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

   3. Simplified 23.5%

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

   4. Taylor expanded in z around inf 82.4%

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

4. Final simplification 97.6%

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

Alternative 3: 40.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot z\right)\\ \mathbf{if}\;y \leq -7.5 \cdot 10^{+28}:\\ \;\;\;\;z \cdot y\\ \mathbf{elif}\;y \leq -2.1 \cdot 10^{-123}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -3.4 \cdot 10^{-178}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -4.4 \cdot 10^{-203}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -8.8 \cdot 10^{-251}:\\ \;\;\;\;a \cdot t\\ \mathbf{elif}\;y \leq 1.12 \cdot 10^{-110}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 4.3 \cdot 10^{+52}:\\ \;\;\;\;a \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (* a z))))
   (if (<= y -7.5e+28)
     (* z y)
     (if (<= y -2.1e-123)
       t_1
       (if (<= y -3.4e-178)
         x
         (if (<= y -4.4e-203)
           t_1
           (if (<= y -8.8e-251)
             (* a t)
             (if (<= y 1.12e-110) x (if (<= y 4.3e+52) (* a t) (* z y))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a * z);
	double tmp;
	if (y <= -7.5e+28) {
		tmp = z * y;
	} else if (y <= -2.1e-123) {
		tmp = t_1;
	} else if (y <= -3.4e-178) {
		tmp = x;
	} else if (y <= -4.4e-203) {
		tmp = t_1;
	} else if (y <= -8.8e-251) {
		tmp = a * t;
	} else if (y <= 1.12e-110) {
		tmp = x;
	} else if (y <= 4.3e+52) {
		tmp = a * t;
	} else {
		tmp = z * y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * (a * z)
    if (y <= (-7.5d+28)) then
        tmp = z * y
    else if (y <= (-2.1d-123)) then
        tmp = t_1
    else if (y <= (-3.4d-178)) then
        tmp = x
    else if (y <= (-4.4d-203)) then
        tmp = t_1
    else if (y <= (-8.8d-251)) then
        tmp = a * t
    else if (y <= 1.12d-110) then
        tmp = x
    else if (y <= 4.3d+52) then
        tmp = a * t
    else
        tmp = z * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a * z);
	double tmp;
	if (y <= -7.5e+28) {
		tmp = z * y;
	} else if (y <= -2.1e-123) {
		tmp = t_1;
	} else if (y <= -3.4e-178) {
		tmp = x;
	} else if (y <= -4.4e-203) {
		tmp = t_1;
	} else if (y <= -8.8e-251) {
		tmp = a * t;
	} else if (y <= 1.12e-110) {
		tmp = x;
	} else if (y <= 4.3e+52) {
		tmp = a * t;
	} else {
		tmp = z * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * (a * z)
	tmp = 0
	if y <= -7.5e+28:
		tmp = z * y
	elif y <= -2.1e-123:
		tmp = t_1
	elif y <= -3.4e-178:
		tmp = x
	elif y <= -4.4e-203:
		tmp = t_1
	elif y <= -8.8e-251:
		tmp = a * t
	elif y <= 1.12e-110:
		tmp = x
	elif y <= 4.3e+52:
		tmp = a * t
	else:
		tmp = z * y
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(a * z))
	tmp = 0.0
	if (y <= -7.5e+28)
		tmp = Float64(z * y);
	elseif (y <= -2.1e-123)
		tmp = t_1;
	elseif (y <= -3.4e-178)
		tmp = x;
	elseif (y <= -4.4e-203)
		tmp = t_1;
	elseif (y <= -8.8e-251)
		tmp = Float64(a * t);
	elseif (y <= 1.12e-110)
		tmp = x;
	elseif (y <= 4.3e+52)
		tmp = Float64(a * t);
	else
		tmp = Float64(z * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * (a * z);
	tmp = 0.0;
	if (y <= -7.5e+28)
		tmp = z * y;
	elseif (y <= -2.1e-123)
		tmp = t_1;
	elseif (y <= -3.4e-178)
		tmp = x;
	elseif (y <= -4.4e-203)
		tmp = t_1;
	elseif (y <= -8.8e-251)
		tmp = a * t;
	elseif (y <= 1.12e-110)
		tmp = x;
	elseif (y <= 4.3e+52)
		tmp = a * t;
	else
		tmp = z * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(a * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -7.5e+28], N[(z * y), $MachinePrecision], If[LessEqual[y, -2.1e-123], t$95$1, If[LessEqual[y, -3.4e-178], x, If[LessEqual[y, -4.4e-203], t$95$1, If[LessEqual[y, -8.8e-251], N[(a * t), $MachinePrecision], If[LessEqual[y, 1.12e-110], x, If[LessEqual[y, 4.3e+52], N[(a * t), $MachinePrecision], N[(z * y), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -7.4999999999999998e28 or 4.3e52 < y

   1. Initial program 90.3%

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

      1. *-commutative 90.3%

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

      2. associate-*l* 89.6%

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

   3. Simplified 89.6%

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

   4. Taylor expanded in y around inf 58.9%

      \[\leadsto \color{blue}{y \cdot z} \]
   5. Step-by-step derivation

      1. *-commutative 58.9%

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

   6. Simplified 58.9%

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

   if -7.4999999999999998e28 < y < -2.0999999999999999e-123 or -3.39999999999999973e-178 < y < -4.3999999999999999e-203

   1. Initial program 88.0%

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

      1. *-commutative 88.0%

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

      2. associate-*l* 88.1%

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

   3. Simplified 88.1%

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

   4. Taylor expanded in a around inf 55.5%

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

   5. Taylor expanded in t around 0 34.5%

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

      1. associate-*r* 47.6%

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

      2. *-commutative 47.6%

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

   7. Simplified 47.6%

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

   8. Taylor expanded in z around 0 34.5%

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

      1. associate-*r* 47.6%

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

      2. *-commutative 47.6%

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

      3. associate-*r* 44.5%

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

   10. Simplified 44.5%

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

   if -2.0999999999999999e-123 < y < -3.39999999999999973e-178 or -8.8e-251 < y < 1.11999999999999998e-110

   1. Initial program 98.2%

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

      1. *-commutative 98.2%

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

      2. associate-*l* 98.2%

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

   3. Simplified 98.2%

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

   4. Taylor expanded in x around inf 49.1%

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

   if -4.3999999999999999e-203 < y < -8.8e-251 or 1.11999999999999998e-110 < y < 4.3e52

   1. Initial program 93.0%

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

      1. *-commutative 93.0%

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

      2. associate-*l* 95.5%

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

   3. Simplified 95.5%

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

   4. Taylor expanded in t around inf 50.5%

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

4. Final simplification 53.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{+28}:\\ \;\;\;\;z \cdot y\\ \mathbf{elif}\;y \leq -2.1 \cdot 10^{-123}:\\ \;\;\;\;b \cdot \left(a \cdot z\right)\\ \mathbf{elif}\;y \leq -3.4 \cdot 10^{-178}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -4.4 \cdot 10^{-203}:\\ \;\;\;\;b \cdot \left(a \cdot z\right)\\ \mathbf{elif}\;y \leq -8.8 \cdot 10^{-251}:\\ \;\;\;\;a \cdot t\\ \mathbf{elif}\;y \leq 1.12 \cdot 10^{-110}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 4.3 \cdot 10^{+52}:\\ \;\;\;\;a \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot y\\ \end{array} \]

Alternative 4: 40.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{+27}:\\ \;\;\;\;z \cdot y\\ \mathbf{elif}\;y \leq -2.6 \cdot 10^{-122}:\\ \;\;\;\;z \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;y \leq -5.2 \cdot 10^{-178}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -6.5 \cdot 10^{-203}:\\ \;\;\;\;b \cdot \left(a \cdot z\right)\\ \mathbf{elif}\;y \leq -8.8 \cdot 10^{-251}:\\ \;\;\;\;a \cdot t\\ \mathbf{elif}\;y \leq 2.15 \cdot 10^{-110}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 6.6 \cdot 10^{+51}:\\ \;\;\;\;a \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -2.4e+27)
   (* z y)
   (if (<= y -2.6e-122)
     (* z (* a b))
     (if (<= y -5.2e-178)
       x
       (if (<= y -6.5e-203)
         (* b (* a z))
         (if (<= y -8.8e-251)
           (* a t)
           (if (<= y 2.15e-110) x (if (<= y 6.6e+51) (* a t) (* z y)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -2.4e+27) {
		tmp = z * y;
	} else if (y <= -2.6e-122) {
		tmp = z * (a * b);
	} else if (y <= -5.2e-178) {
		tmp = x;
	} else if (y <= -6.5e-203) {
		tmp = b * (a * z);
	} else if (y <= -8.8e-251) {
		tmp = a * t;
	} else if (y <= 2.15e-110) {
		tmp = x;
	} else if (y <= 6.6e+51) {
		tmp = a * t;
	} else {
		tmp = z * 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 (y <= (-2.4d+27)) then
        tmp = z * y
    else if (y <= (-2.6d-122)) then
        tmp = z * (a * b)
    else if (y <= (-5.2d-178)) then
        tmp = x
    else if (y <= (-6.5d-203)) then
        tmp = b * (a * z)
    else if (y <= (-8.8d-251)) then
        tmp = a * t
    else if (y <= 2.15d-110) then
        tmp = x
    else if (y <= 6.6d+51) then
        tmp = a * t
    else
        tmp = z * 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 (y <= -2.4e+27) {
		tmp = z * y;
	} else if (y <= -2.6e-122) {
		tmp = z * (a * b);
	} else if (y <= -5.2e-178) {
		tmp = x;
	} else if (y <= -6.5e-203) {
		tmp = b * (a * z);
	} else if (y <= -8.8e-251) {
		tmp = a * t;
	} else if (y <= 2.15e-110) {
		tmp = x;
	} else if (y <= 6.6e+51) {
		tmp = a * t;
	} else {
		tmp = z * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -2.4e+27:
		tmp = z * y
	elif y <= -2.6e-122:
		tmp = z * (a * b)
	elif y <= -5.2e-178:
		tmp = x
	elif y <= -6.5e-203:
		tmp = b * (a * z)
	elif y <= -8.8e-251:
		tmp = a * t
	elif y <= 2.15e-110:
		tmp = x
	elif y <= 6.6e+51:
		tmp = a * t
	else:
		tmp = z * y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -2.4e+27)
		tmp = Float64(z * y);
	elseif (y <= -2.6e-122)
		tmp = Float64(z * Float64(a * b));
	elseif (y <= -5.2e-178)
		tmp = x;
	elseif (y <= -6.5e-203)
		tmp = Float64(b * Float64(a * z));
	elseif (y <= -8.8e-251)
		tmp = Float64(a * t);
	elseif (y <= 2.15e-110)
		tmp = x;
	elseif (y <= 6.6e+51)
		tmp = Float64(a * t);
	else
		tmp = Float64(z * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -2.4e+27)
		tmp = z * y;
	elseif (y <= -2.6e-122)
		tmp = z * (a * b);
	elseif (y <= -5.2e-178)
		tmp = x;
	elseif (y <= -6.5e-203)
		tmp = b * (a * z);
	elseif (y <= -8.8e-251)
		tmp = a * t;
	elseif (y <= 2.15e-110)
		tmp = x;
	elseif (y <= 6.6e+51)
		tmp = a * t;
	else
		tmp = z * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -2.4e+27], N[(z * y), $MachinePrecision], If[LessEqual[y, -2.6e-122], N[(z * N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -5.2e-178], x, If[LessEqual[y, -6.5e-203], N[(b * N[(a * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -8.8e-251], N[(a * t), $MachinePrecision], If[LessEqual[y, 2.15e-110], x, If[LessEqual[y, 6.6e+51], N[(a * t), $MachinePrecision], N[(z * y), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -2.39999999999999998e27 or 6.5999999999999994e51 < y

   1. Initial program 90.3%

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

      1. *-commutative 90.3%

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

      2. associate-*l* 89.6%

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

   3. Simplified 89.6%

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

   4. Taylor expanded in y around inf 58.9%

      \[\leadsto \color{blue}{y \cdot z} \]
   5. Step-by-step derivation

      1. *-commutative 58.9%

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

   6. Simplified 58.9%

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

   if -2.39999999999999998e27 < y < -2.59999999999999975e-122

   1. Initial program 91.6%

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

      1. *-commutative 91.6%

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

      2. associate-*l* 94.3%

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

   3. Simplified 94.3%

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

   4. Taylor expanded in a around inf 55.9%

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

   5. Taylor expanded in t around 0 34.2%

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

      1. associate-*r* 47.0%

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

      2. *-commutative 47.0%

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

   7. Simplified 47.0%

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

   if -2.59999999999999975e-122 < y < -5.19999999999999997e-178 or -8.8e-251 < y < 2.15000000000000012e-110

   1. Initial program 98.2%

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

      1. *-commutative 98.2%

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

      2. associate-*l* 98.2%

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

   3. Simplified 98.2%

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

   4. Taylor expanded in x around inf 49.1%

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

   if -5.19999999999999997e-178 < y < -6.50000000000000024e-203

   1. Initial program 66.4%

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

      1. *-commutative 66.4%

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

      2. associate-*l* 51.1%

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

   3. Simplified 51.1%

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

   4. Taylor expanded in a around inf 52.6%

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

   5. Taylor expanded in t around 0 36.2%

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

      1. associate-*r* 51.8%

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

      2. *-commutative 51.8%

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

   7. Simplified 51.8%

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

   8. Taylor expanded in z around 0 36.2%

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

      1. associate-*r* 51.8%

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

      2. *-commutative 51.8%

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

      3. associate-*r* 51.9%

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

   10. Simplified 51.9%

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

   if -6.50000000000000024e-203 < y < -8.8e-251 or 2.15000000000000012e-110 < y < 6.5999999999999994e51

   1. Initial program 93.0%

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

      1. *-commutative 93.0%

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

      2. associate-*l* 95.5%

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

   3. Simplified 95.5%

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

   4. Taylor expanded in t around inf 50.5%

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

4. Final simplification 53.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{+27}:\\ \;\;\;\;z \cdot y\\ \mathbf{elif}\;y \leq -2.6 \cdot 10^{-122}:\\ \;\;\;\;z \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;y \leq -5.2 \cdot 10^{-178}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -6.5 \cdot 10^{-203}:\\ \;\;\;\;b \cdot \left(a \cdot z\right)\\ \mathbf{elif}\;y \leq -8.8 \cdot 10^{-251}:\\ \;\;\;\;a \cdot t\\ \mathbf{elif}\;y \leq 2.15 \cdot 10^{-110}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 6.6 \cdot 10^{+51}:\\ \;\;\;\;a \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot y\\ \end{array} \]

Alternative 5: 90.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 2.7 \cdot 10^{-32}:\\ \;\;\;\;\left(\left(x + z \cdot y\right) + a \cdot t\right) + z \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(a \cdot b + y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z 2.7e-32)
   (+ (+ (+ x (* z y)) (* a t)) (* z (* a b)))
   (+ x (* z (+ (* a b) y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= 2.7e-32) {
		tmp = ((x + (z * y)) + (a * t)) + (z * (a * b));
	} else {
		tmp = x + (z * ((a * b) + y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= 2.7d-32) then
        tmp = ((x + (z * y)) + (a * t)) + (z * (a * b))
    else
        tmp = x + (z * ((a * b) + y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= 2.7e-32) {
		tmp = ((x + (z * y)) + (a * t)) + (z * (a * b));
	} else {
		tmp = x + (z * ((a * b) + y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= 2.7e-32:
		tmp = ((x + (z * y)) + (a * t)) + (z * (a * b))
	else:
		tmp = x + (z * ((a * b) + y))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= 2.7e-32)
		tmp = Float64(Float64(Float64(x + Float64(z * y)) + Float64(a * t)) + Float64(z * Float64(a * b)));
	else
		tmp = Float64(x + Float64(z * Float64(Float64(a * b) + y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= 2.7e-32)
		tmp = ((x + (z * y)) + (a * t)) + (z * (a * b));
	else
		tmp = x + (z * ((a * b) + y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, 2.7e-32], N[(N[(N[(x + N[(z * y), $MachinePrecision]), $MachinePrecision] + N[(a * t), $MachinePrecision]), $MachinePrecision] + N[(z * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(N[(a * b), $MachinePrecision] + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 2.69999999999999981e-32

   1. Initial program 95.8%

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

      1. *-commutative 95.8%

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

      2. associate-*l* 94.3%

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

   3. Simplified 94.3%

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

   if 2.69999999999999981e-32 < z

   1. Initial program 81.5%

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

      1. *-commutative 81.5%

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

      2. associate-*l* 86.2%

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

   3. Simplified 86.2%

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

   4. Taylor expanded in t around 0 86.3%

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

      1. +-commutative 86.3%

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

      2. +-commutative 86.3%

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

      3. associate-*r* 90.8%

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

      4. distribute-rgt-in 98.5%

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

   6. Simplified 98.5%

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

4. Final simplification 95.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 2.7 \cdot 10^{-32}:\\ \;\;\;\;\left(\left(x + z \cdot y\right) + a \cdot t\right) + z \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(a \cdot b + y\right)\\ \end{array} \]

Alternative 6: 39.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.2 \cdot 10^{-28}:\\ \;\;\;\;z \cdot y\\ \mathbf{elif}\;y \leq -1.85 \cdot 10^{-221}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -8.8 \cdot 10^{-251}:\\ \;\;\;\;a \cdot t\\ \mathbf{elif}\;y \leq 7.4 \cdot 10^{-111}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 8 \cdot 10^{-61}:\\ \;\;\;\;a \cdot t\\ \mathbf{elif}\;y \leq 1.36 \cdot 10^{+25}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -2.2e-28)
   (* z y)
   (if (<= y -1.85e-221)
     x
     (if (<= y -8.8e-251)
       (* a t)
       (if (<= y 7.4e-111)
         x
         (if (<= y 8e-61) (* a t) (if (<= y 1.36e+25) x (* z y))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -2.2e-28) {
		tmp = z * y;
	} else if (y <= -1.85e-221) {
		tmp = x;
	} else if (y <= -8.8e-251) {
		tmp = a * t;
	} else if (y <= 7.4e-111) {
		tmp = x;
	} else if (y <= 8e-61) {
		tmp = a * t;
	} else if (y <= 1.36e+25) {
		tmp = x;
	} else {
		tmp = z * 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 (y <= (-2.2d-28)) then
        tmp = z * y
    else if (y <= (-1.85d-221)) then
        tmp = x
    else if (y <= (-8.8d-251)) then
        tmp = a * t
    else if (y <= 7.4d-111) then
        tmp = x
    else if (y <= 8d-61) then
        tmp = a * t
    else if (y <= 1.36d+25) then
        tmp = x
    else
        tmp = z * 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 (y <= -2.2e-28) {
		tmp = z * y;
	} else if (y <= -1.85e-221) {
		tmp = x;
	} else if (y <= -8.8e-251) {
		tmp = a * t;
	} else if (y <= 7.4e-111) {
		tmp = x;
	} else if (y <= 8e-61) {
		tmp = a * t;
	} else if (y <= 1.36e+25) {
		tmp = x;
	} else {
		tmp = z * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -2.2e-28:
		tmp = z * y
	elif y <= -1.85e-221:
		tmp = x
	elif y <= -8.8e-251:
		tmp = a * t
	elif y <= 7.4e-111:
		tmp = x
	elif y <= 8e-61:
		tmp = a * t
	elif y <= 1.36e+25:
		tmp = x
	else:
		tmp = z * y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -2.2e-28)
		tmp = Float64(z * y);
	elseif (y <= -1.85e-221)
		tmp = x;
	elseif (y <= -8.8e-251)
		tmp = Float64(a * t);
	elseif (y <= 7.4e-111)
		tmp = x;
	elseif (y <= 8e-61)
		tmp = Float64(a * t);
	elseif (y <= 1.36e+25)
		tmp = x;
	else
		tmp = Float64(z * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -2.2e-28)
		tmp = z * y;
	elseif (y <= -1.85e-221)
		tmp = x;
	elseif (y <= -8.8e-251)
		tmp = a * t;
	elseif (y <= 7.4e-111)
		tmp = x;
	elseif (y <= 8e-61)
		tmp = a * t;
	elseif (y <= 1.36e+25)
		tmp = x;
	else
		tmp = z * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -2.2e-28], N[(z * y), $MachinePrecision], If[LessEqual[y, -1.85e-221], x, If[LessEqual[y, -8.8e-251], N[(a * t), $MachinePrecision], If[LessEqual[y, 7.4e-111], x, If[LessEqual[y, 8e-61], N[(a * t), $MachinePrecision], If[LessEqual[y, 1.36e+25], x, N[(z * y), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.19999999999999996e-28 or 1.36e25 < y

   1. Initial program 90.9%

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

      1. *-commutative 90.9%

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

      2. associate-*l* 90.3%

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

   3. Simplified 90.3%

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

   4. Taylor expanded in y around inf 54.2%

      \[\leadsto \color{blue}{y \cdot z} \]
   5. Step-by-step derivation

      1. *-commutative 54.2%

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

   6. Simplified 54.2%

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

   if -2.19999999999999996e-28 < y < -1.84999999999999993e-221 or -8.8e-251 < y < 7.4000000000000003e-111 or 8.0000000000000003e-61 < y < 1.36e25

   1. Initial program 93.4%

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

      1. *-commutative 93.4%

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

      2. associate-*l* 93.5%

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

   3. Simplified 93.5%

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

   4. Taylor expanded in x around inf 42.8%

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

   if -1.84999999999999993e-221 < y < -8.8e-251 or 7.4000000000000003e-111 < y < 8.0000000000000003e-61

   1. Initial program 93.9%

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

      1. *-commutative 93.9%

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

      2. associate-*l* 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in t around inf 77.9%

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

4. Final simplification 51.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.2 \cdot 10^{-28}:\\ \;\;\;\;z \cdot y\\ \mathbf{elif}\;y \leq -1.85 \cdot 10^{-221}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -8.8 \cdot 10^{-251}:\\ \;\;\;\;a \cdot t\\ \mathbf{elif}\;y \leq 7.4 \cdot 10^{-111}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 8 \cdot 10^{-61}:\\ \;\;\;\;a \cdot t\\ \mathbf{elif}\;y \leq 1.36 \cdot 10^{+25}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot y\\ \end{array} \]

Alternative 7: 82.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -6.2 \cdot 10^{+152} \lor \neg \left(a \leq 1.56 \cdot 10^{+199}\right):\\ \;\;\;\;a \cdot \left(t + b \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(a \cdot t + z \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -6.2e+152) (not (<= a 1.56e+199)))
   (* a (+ t (* b z)))
   (+ x (+ (* a t) (* z y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -6.2e+152) || !(a <= 1.56e+199)) {
		tmp = a * (t + (b * z));
	} else {
		tmp = x + ((a * t) + (z * 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 ((a <= (-6.2d+152)) .or. (.not. (a <= 1.56d+199))) then
        tmp = a * (t + (b * z))
    else
        tmp = x + ((a * t) + (z * 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 ((a <= -6.2e+152) || !(a <= 1.56e+199)) {
		tmp = a * (t + (b * z));
	} else {
		tmp = x + ((a * t) + (z * y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (a <= -6.2e+152) or not (a <= 1.56e+199):
		tmp = a * (t + (b * z))
	else:
		tmp = x + ((a * t) + (z * y))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((a <= -6.2e+152) || !(a <= 1.56e+199))
		tmp = Float64(a * Float64(t + Float64(b * z)));
	else
		tmp = Float64(x + Float64(Float64(a * t) + Float64(z * y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((a <= -6.2e+152) || ~((a <= 1.56e+199)))
		tmp = a * (t + (b * z));
	else
		tmp = x + ((a * t) + (z * y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[a, -6.2e+152], N[Not[LessEqual[a, 1.56e+199]], $MachinePrecision]], N[(a * N[(t + N[(b * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(a * t), $MachinePrecision] + N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -6.2e152 or 1.56e199 < a

   1. Initial program 77.1%

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

      1. *-commutative 77.1%

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

      2. associate-*l* 73.4%

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

   3. Simplified 73.4%

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

   4. Taylor expanded in a around inf 97.9%

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

   if -6.2e152 < a < 1.56e199

   1. Initial program 95.6%

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

      1. *-commutative 95.6%

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

      2. associate-*l* 96.6%

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

   3. Simplified 96.6%

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

   4. Taylor expanded in b around 0 85.1%

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

4. Final simplification 87.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6.2 \cdot 10^{+152} \lor \neg \left(a \leq 1.56 \cdot 10^{+199}\right):\\ \;\;\;\;a \cdot \left(t + b \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(a \cdot t + z \cdot y\right)\\ \end{array} \]

Alternative 8: 87.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -175000000 \lor \neg \left(z \leq 2.7 \cdot 10^{-32}\right):\\ \;\;\;\;x + z \cdot \left(a \cdot b + y\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(a \cdot t + z \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -175000000.0) (not (<= z 2.7e-32)))
   (+ x (* z (+ (* a b) y)))
   (+ x (+ (* a t) (* z y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -175000000.0) || !(z <= 2.7e-32)) {
		tmp = x + (z * ((a * b) + y));
	} else {
		tmp = x + ((a * t) + (z * 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 ((z <= (-175000000.0d0)) .or. (.not. (z <= 2.7d-32))) then
        tmp = x + (z * ((a * b) + y))
    else
        tmp = x + ((a * t) + (z * 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 ((z <= -175000000.0) || !(z <= 2.7e-32)) {
		tmp = x + (z * ((a * b) + y));
	} else {
		tmp = x + ((a * t) + (z * y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -175000000.0) or not (z <= 2.7e-32):
		tmp = x + (z * ((a * b) + y))
	else:
		tmp = x + ((a * t) + (z * y))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -175000000.0) || !(z <= 2.7e-32))
		tmp = Float64(x + Float64(z * Float64(Float64(a * b) + y)));
	else
		tmp = Float64(x + Float64(Float64(a * t) + Float64(z * y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -175000000.0) || ~((z <= 2.7e-32)))
		tmp = x + (z * ((a * b) + y));
	else
		tmp = x + ((a * t) + (z * y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -175000000.0], N[Not[LessEqual[z, 2.7e-32]], $MachinePrecision]], N[(x + N[(z * N[(N[(a * b), $MachinePrecision] + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(a * t), $MachinePrecision] + N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.75e8 or 2.69999999999999981e-32 < z

   1. Initial program 86.5%

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

      1. *-commutative 86.5%

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

      2. associate-*l* 91.3%

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

   3. Simplified 91.3%

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

   4. Taylor expanded in t around 0 82.5%

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

      1. +-commutative 82.5%

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

      2. +-commutative 82.5%

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

      3. associate-*r* 91.5%

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

      4. distribute-rgt-in 95.4%

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

   6. Simplified 95.4%

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

   if -1.75e8 < z < 2.69999999999999981e-32

   1. Initial program 97.7%

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

      1. *-commutative 97.7%

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

      2. associate-*l* 93.2%

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

   3. Simplified 93.2%

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

   4. Taylor expanded in b around 0 91.8%

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

4. Final simplification 93.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -175000000 \lor \neg \left(z \leq 2.7 \cdot 10^{-32}\right):\\ \;\;\;\;x + z \cdot \left(a \cdot b + y\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(a \cdot t + z \cdot y\right)\\ \end{array} \]

Alternative 9: 73.3% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.95 \cdot 10^{+78} \lor \neg \left(a \leq 3.3 \cdot 10^{+96}\right):\\ \;\;\;\;a \cdot \left(t + b \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -1.95e+78) (not (<= a 3.3e+96)))
   (* a (+ t (* b z)))
   (+ x (* z y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -1.95e+78) || !(a <= 3.3e+96)) {
		tmp = a * (t + (b * z));
	} else {
		tmp = x + (z * 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 ((a <= (-1.95d+78)) .or. (.not. (a <= 3.3d+96))) then
        tmp = a * (t + (b * z))
    else
        tmp = x + (z * 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 ((a <= -1.95e+78) || !(a <= 3.3e+96)) {
		tmp = a * (t + (b * z));
	} else {
		tmp = x + (z * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (a <= -1.95e+78) or not (a <= 3.3e+96):
		tmp = a * (t + (b * z))
	else:
		tmp = x + (z * y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((a <= -1.95e+78) || !(a <= 3.3e+96))
		tmp = Float64(a * Float64(t + Float64(b * z)));
	else
		tmp = Float64(x + Float64(z * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((a <= -1.95e+78) || ~((a <= 3.3e+96)))
		tmp = a * (t + (b * z));
	else
		tmp = x + (z * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[a, -1.95e+78], N[Not[LessEqual[a, 3.3e+96]], $MachinePrecision]], N[(a * N[(t + N[(b * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.9500000000000002e78 or 3.29999999999999984e96 < a

   1. Initial program 81.9%

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

      1. *-commutative 81.9%

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

      2. associate-*l* 79.9%

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

   3. Simplified 79.9%

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

   4. Taylor expanded in a around inf 81.2%

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

   if -1.9500000000000002e78 < a < 3.29999999999999984e96

   1. Initial program 97.1%

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

      1. *-commutative 97.1%

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

      2. associate-*l* 98.2%

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

   3. Simplified 98.2%

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

   4. Taylor expanded in a around 0 74.5%

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

4. Final simplification 76.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.95 \cdot 10^{+78} \lor \neg \left(a \leq 3.3 \cdot 10^{+96}\right):\\ \;\;\;\;a \cdot \left(t + b \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot y\\ \end{array} \]

Alternative 10: 74.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.195 \lor \neg \left(z \leq 1.15 \cdot 10^{-61}\right):\\ \;\;\;\;z \cdot \left(a \cdot b + y\right)\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -0.195) (not (<= z 1.15e-61)))
   (* z (+ (* a b) y))
   (+ x (* a t))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -0.195) || !(z <= 1.15e-61)) {
		tmp = z * ((a * b) + y);
	} else {
		tmp = x + (a * t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-0.195d0)) .or. (.not. (z <= 1.15d-61))) then
        tmp = z * ((a * b) + y)
    else
        tmp = x + (a * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -0.195) || !(z <= 1.15e-61)) {
		tmp = z * ((a * b) + y);
	} else {
		tmp = x + (a * t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -0.195) or not (z <= 1.15e-61):
		tmp = z * ((a * b) + y)
	else:
		tmp = x + (a * t)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -0.195) || !(z <= 1.15e-61))
		tmp = Float64(z * Float64(Float64(a * b) + y));
	else
		tmp = Float64(x + Float64(a * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -0.195) || ~((z <= 1.15e-61)))
		tmp = z * ((a * b) + y);
	else
		tmp = x + (a * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -0.195], N[Not[LessEqual[z, 1.15e-61]], $MachinePrecision]], N[(z * N[(N[(a * b), $MachinePrecision] + y), $MachinePrecision]), $MachinePrecision], N[(x + N[(a * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -0.19500000000000001 or 1.14999999999999996e-61 < z

   1. Initial program 87.2%

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

      1. *-commutative 87.2%

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

      2. associate-*l* 91.7%

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

   3. Simplified 91.7%

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

   4. Taylor expanded in z around inf 79.1%

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

   if -0.19500000000000001 < z < 1.14999999999999996e-61

   1. Initial program 97.5%

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

      1. *-commutative 97.5%

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

      2. associate-*l* 92.8%

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

   3. Simplified 92.8%

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

   4. Taylor expanded in z around 0 79.4%

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

      1. +-commutative 79.4%

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

   6. Simplified 79.4%

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

4. Final simplification 79.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.195 \lor \neg \left(z \leq 1.15 \cdot 10^{-61}\right):\\ \;\;\;\;z \cdot \left(a \cdot b + y\right)\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot t\\ \end{array} \]

Alternative 11: 63.3% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.3 \cdot 10^{+85} \lor \neg \left(a \leq 6.8 \cdot 10^{+69}\right):\\ \;\;\;\;x + a \cdot t\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -2.3e+85) (not (<= a 6.8e+69))) (+ x (* a t)) (+ x (* z y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -2.3e+85) || !(a <= 6.8e+69)) {
		tmp = x + (a * t);
	} else {
		tmp = x + (z * 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 ((a <= (-2.3d+85)) .or. (.not. (a <= 6.8d+69))) then
        tmp = x + (a * t)
    else
        tmp = x + (z * 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 ((a <= -2.3e+85) || !(a <= 6.8e+69)) {
		tmp = x + (a * t);
	} else {
		tmp = x + (z * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (a <= -2.3e+85) or not (a <= 6.8e+69):
		tmp = x + (a * t)
	else:
		tmp = x + (z * y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((a <= -2.3e+85) || !(a <= 6.8e+69))
		tmp = Float64(x + Float64(a * t));
	else
		tmp = Float64(x + Float64(z * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((a <= -2.3e+85) || ~((a <= 6.8e+69)))
		tmp = x + (a * t);
	else
		tmp = x + (z * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[a, -2.3e+85], N[Not[LessEqual[a, 6.8e+69]], $MachinePrecision]], N[(x + N[(a * t), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -2.2999999999999999e85 or 6.79999999999999973e69 < a

   1. Initial program 80.6%

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

      1. *-commutative 80.6%

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

      2. associate-*l* 79.9%

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

   3. Simplified 79.9%

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

   4. Taylor expanded in z around 0 64.5%

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

      1. +-commutative 64.5%

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

   6. Simplified 64.5%

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

   if -2.2999999999999999e85 < a < 6.79999999999999973e69

   1. Initial program 98.2%

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

      1. *-commutative 98.2%

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

      2. associate-*l* 98.8%

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

   3. Simplified 98.8%

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

   4. Taylor expanded in a around 0 74.7%

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

4. Final simplification 71.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.3 \cdot 10^{+85} \lor \neg \left(a \leq 6.8 \cdot 10^{+69}\right):\\ \;\;\;\;x + a \cdot t\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot y\\ \end{array} \]

Alternative 12: 58.9% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.9 \cdot 10^{+100}:\\ \;\;\;\;a \cdot t\\ \mathbf{elif}\;a \leq 3.3 \cdot 10^{+179}:\\ \;\;\;\;x + z \cdot y\\ \mathbf{else}:\\ \;\;\;\;a \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -1.9e+100) (* a t) (if (<= a 3.3e+179) (+ x (* z y)) (* a t))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -1.9e+100) {
		tmp = a * t;
	} else if (a <= 3.3e+179) {
		tmp = x + (z * y);
	} else {
		tmp = a * t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (a <= (-1.9d+100)) then
        tmp = a * t
    else if (a <= 3.3d+179) then
        tmp = x + (z * y)
    else
        tmp = a * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -1.9e+100) {
		tmp = a * t;
	} else if (a <= 3.3e+179) {
		tmp = x + (z * y);
	} else {
		tmp = a * t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -1.9e+100:
		tmp = a * t
	elif a <= 3.3e+179:
		tmp = x + (z * y)
	else:
		tmp = a * t
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -1.9e+100)
		tmp = Float64(a * t);
	elseif (a <= 3.3e+179)
		tmp = Float64(x + Float64(z * y));
	else
		tmp = Float64(a * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= -1.9e+100)
		tmp = a * t;
	elseif (a <= 3.3e+179)
		tmp = x + (z * y);
	else
		tmp = a * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -1.9e+100], N[(a * t), $MachinePrecision], If[LessEqual[a, 3.3e+179], N[(x + N[(z * y), $MachinePrecision]), $MachinePrecision], N[(a * t), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if a < -1.89999999999999982e100 or 3.29999999999999978e179 < a

   1. Initial program 78.9%

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

      1. *-commutative 78.9%

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

      2. associate-*l* 77.6%

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

   3. Simplified 77.6%

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

   4. Taylor expanded in t around inf 62.0%

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

   if -1.89999999999999982e100 < a < 3.29999999999999978e179

   1. Initial program 95.9%

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

      1. *-commutative 95.9%

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

      2. associate-*l* 96.5%

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

   3. Simplified 96.5%

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

   4. Taylor expanded in a around 0 71.0%

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

4. Final simplification 69.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.9 \cdot 10^{+100}:\\ \;\;\;\;a \cdot t\\ \mathbf{elif}\;a \leq 3.3 \cdot 10^{+179}:\\ \;\;\;\;x + z \cdot y\\ \mathbf{else}:\\ \;\;\;\;a \cdot t\\ \end{array} \]

Alternative 13: 39.3% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.36 \cdot 10^{+73}:\\ \;\;\;\;a \cdot t\\ \mathbf{elif}\;a \leq 3.3 \cdot 10^{-21}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;a \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -1.36e+73) (* a t) (if (<= a 3.3e-21) x (* a t))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -1.36e+73) {
		tmp = a * t;
	} else if (a <= 3.3e-21) {
		tmp = x;
	} else {
		tmp = a * t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (a <= (-1.36d+73)) then
        tmp = a * t
    else if (a <= 3.3d-21) then
        tmp = x
    else
        tmp = a * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -1.36e+73) {
		tmp = a * t;
	} else if (a <= 3.3e-21) {
		tmp = x;
	} else {
		tmp = a * t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -1.36e+73:
		tmp = a * t
	elif a <= 3.3e-21:
		tmp = x
	else:
		tmp = a * t
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -1.36e+73)
		tmp = Float64(a * t);
	elseif (a <= 3.3e-21)
		tmp = x;
	else
		tmp = Float64(a * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= -1.36e+73)
		tmp = a * t;
	elseif (a <= 3.3e-21)
		tmp = x;
	else
		tmp = a * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -1.36e+73], N[(a * t), $MachinePrecision], If[LessEqual[a, 3.3e-21], x, N[(a * t), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if a < -1.3599999999999999e73 or 3.30000000000000009e-21 < a

   1. Initial program 84.0%

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

      1. *-commutative 84.0%

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

      2. associate-*l* 83.4%

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

   3. Simplified 83.4%

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

   4. Taylor expanded in t around inf 47.2%

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

   if -1.3599999999999999e73 < a < 3.30000000000000009e-21

   1. Initial program 98.6%

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

      1. *-commutative 98.6%

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

      2. associate-*l* 99.2%

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

   3. Simplified 99.2%

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

   4. Taylor expanded in x around inf 37.1%

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

4. Final simplification 41.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.36 \cdot 10^{+73}:\\ \;\;\;\;a \cdot t\\ \mathbf{elif}\;a \leq 3.3 \cdot 10^{-21}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;a \cdot t\\ \end{array} \]

Alternative 14: 25.8% accurate, 15.0× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = x
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_] := x

Derivation

1. Initial program 92.2%

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

   1. *-commutative 92.2%

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

   2. associate-*l* 92.3%

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

3. Simplified 92.3%

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

4. Taylor expanded in x around inf 27.4%

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

5. Final simplification 27.4%

   \[\leadsto x \]

Developer target: 97.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(b \cdot a + y\right) + \left(x + t \cdot a\right)\\ \mathbf{if}\;z < -11820553527347888000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z < 4.7589743188364287 \cdot 10^{-122}:\\ \;\;\;\;\left(b \cdot z + t\right) \cdot a + \left(z \cdot y + x\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (* z (+ (* b a) y)) (+ x (* t a)))))
   (if (< z -11820553527347888000.0)
     t_1
     (if (< z 4.7589743188364287e-122)
       (+ (* (+ (* b z) t) a) (+ (* z y) x))
       t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z * ((b * a) + y)) + (x + (t * a));
	double tmp;
	if (z < -11820553527347888000.0) {
		tmp = t_1;
	} else if (z < 4.7589743188364287e-122) {
		tmp = (((b * z) + t) * a) + ((z * y) + x);
	} 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 = (z * ((b * a) + y)) + (x + (t * a))
    if (z < (-11820553527347888000.0d0)) then
        tmp = t_1
    else if (z < 4.7589743188364287d-122) then
        tmp = (((b * z) + t) * a) + ((z * y) + x)
    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 = (z * ((b * a) + y)) + (x + (t * a));
	double tmp;
	if (z < -11820553527347888000.0) {
		tmp = t_1;
	} else if (z < 4.7589743188364287e-122) {
		tmp = (((b * z) + t) * a) + ((z * y) + x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z * ((b * a) + y)) + (x + (t * a))
	tmp = 0
	if z < -11820553527347888000.0:
		tmp = t_1
	elif z < 4.7589743188364287e-122:
		tmp = (((b * z) + t) * a) + ((z * y) + x)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z * Float64(Float64(b * a) + y)) + Float64(x + Float64(t * a)))
	tmp = 0.0
	if (z < -11820553527347888000.0)
		tmp = t_1;
	elseif (z < 4.7589743188364287e-122)
		tmp = Float64(Float64(Float64(Float64(b * z) + t) * a) + Float64(Float64(z * y) + x));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z * ((b * a) + y)) + (x + (t * a));
	tmp = 0.0;
	if (z < -11820553527347888000.0)
		tmp = t_1;
	elseif (z < 4.7589743188364287e-122)
		tmp = (((b * z) + t) * a) + ((z * y) + x);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z * N[(N[(b * a), $MachinePrecision] + y), $MachinePrecision]), $MachinePrecision] + N[(x + N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[z, -11820553527347888000.0], t$95$1, If[Less[z, 4.7589743188364287e-122], N[(N[(N[(N[(b * z), $MachinePrecision] + t), $MachinePrecision] * a), $MachinePrecision] + N[(N[(z * y), $MachinePrecision] + x), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Reproduce

herbie shell --seed 2023275 
(FPCore (x y z t a b)
  :name "Graphics.Rasterific.CubicBezier:cachedBezierAt from Rasterific-0.6.1"
  :precision binary64

  :herbie-target
  (if (< z -11820553527347888000.0) (+ (* z (+ (* b a) y)) (+ x (* t a))) (if (< z 4.7589743188364287e-122) (+ (* (+ (* b z) t) a) (+ (* z y) x)) (+ (* z (+ (* b a) y)) (+ x (* t a)))))

  (+ (+ (+ x (* y z)) (* t a)) (* (* a z) b)))